PhysRevLett[1].104.035002 Picosecond Short-Range Disordering in Isochorically Heated Aluminum at Sol

July 20092003-2009 Cadence Design Systems, Inc. All rights reserved.Portions © Concept Engineering GmbH. Used by permission.Printed in the United States of America.Cadence Design Systems, Inc. (Cadence), 2655 Seely Ave., San Jose, CA 95134, USA.Product Encounter™ RTL Compiler contains technology licensed from, and copyrighted by: Concept Engineering GmbH, and is 1998-2006, Concept Engineering GmbH. All rights reserved.Open SystemC,Open SystemC Initiative,OSCI,SystemC,and SystemC Initiative are trademarks or registered trademarks of Open SystemC Initiative, Inc. in the United States and other countries and are used with permission.Trademarks:Trademarks and service marks of Cadence Design Systems,Inc.contained in this document are attributed to Cadence with the appropriate symbol. For queries regarding Cadence’s trademarks, contact the corporate legal department at the address shown above or call 800.862.4522. All other trademarks are the property of their respective holders.Restricted Permission:This publication is protected by copyright law and international treaties and contains trade secrets and proprietary information owned by Cadence.Unauthorized reproduction or distribution of this publication,or any portion of it,may result in civil and criminal penalties.Except as specified in this permission statement,this publication may not be copied,reproduced,modified,published,uploaded,posted,transmitted, or distributed in any way, without prior written permission from Cadence. Unless otherwise agreed to by Cadence in writing, this statement grants Cadence customers permission to print one (1) hard copy of this publication subject to the following conditions:1.The publication may be used only in accordance with a written agreement between Cadence and itscustomer.2.The publication may not be modified in any way.3.Any authorized copy of the publication or portion thereof must include all original copyright, trademark,and other proprietary notices and this permission statement.4.The information contained in this document cannot be used in the development of like products orsoftware, whether for internal or external use, and shall not be used for the benefit of any other party, whether or not for consideration.Patents:Cadence Product Encounter™RTL Compiler described in this document,is protected by U.S.Patents [5,892,687]; [6,470,486]; 6,772,398]; [6,772,399]; [6,807,651]; [6,832,357]; and [7,007,247]Disclaimer:Information in this publication is subject to change without notice and does not represent a commitment on the part of Cadence. Except as may be explicitly set forth in such agreement, Cadence does not make, and expressly disclaims, any representations or warranties as to the completeness, accuracy or usefulness of the information contained in this document. Cadence does not warrant that use of such information will not infringe any third party rights,nor does Cadence assume any liability for damages or costs of any kind that may result from use of such information.Restricted Rights:Use,duplication,or disclosure by the Government is subject to restrictions as set forth in FAR52.227-14 and DFAR252.227-7013 et seq. or its successorContentsAlphabetical List of Commands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 About This Manual. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 Additional References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 How to Use the Documentation Set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 Reporting Problems or Errors in Manuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Customer Support. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Cadence Online Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Other Support Offerings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 Man Pages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 Command-Line Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 Getting the Syntax for a Command . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 Getting the Syntax for an Attribute. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 Searching for Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 Searching For Commands When Y ou Are Unsure of the Name . . . . . . . . . . . . . . . .29 Documentation Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 T ext Command Syntax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .301Navigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 basename. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32 cd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 dirname . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 dirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36filter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..37find . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 inout_mate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44 ll . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45ls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 popd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 pushd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 pwd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 vdir_lsearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 what_is. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .542General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 alias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..58 all_inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 all_outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 apropos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 clear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..62 date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 enable_transparent_latches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 exec_embedded_script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 exit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..67 get_attribute. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68 get_liberty_attribute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 get_read_files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72 help. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..73 include . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 lcd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76 license checkin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 license checkout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78 license list. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79 lls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80 lpopd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81 lpushd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82 lpwd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 man . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84 more. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85quit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 rc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 redirect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 reset_attribute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94 resume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96 sdc_shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97 set_attribute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98 shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101 suppress_messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102 suspend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103 unsuppress_messages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1043GUI Text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105 General GUI T ext Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106 gui_hide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 gui_info. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 gui_raise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 gui_reset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 .gui_selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 gui_show . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 gui_status. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 gui_update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 HDL Viewer GUI Text Commands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 gui_hv_clear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110 gui_hv_get_file. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110 gui_hv_load_file. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110 gui_hv_set_indicators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111 Schematic Viewer GUI T ext Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112 gui_sv_clear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 gui_sv_get_instance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 gui_sv_grey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 gui_sv_highlight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114 gui_sv_load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115 Physical Viewer GUI T ext Commands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116gui_pv_airline_add. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 gui_pv_airline_delete. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118 gui_pv_airline_display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118 gui_pv_airline_raw_add. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119 gui_pv_clear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119 gui_pv_highlight. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120 gui_pv_highlight_update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122 gui_pv_label. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122 gui_pv_redraw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123 gui_pv_selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123 gui_pv_snapshot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123 gui_pv_zoom_fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125 gui_pv_zoom_in. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125 gui_pv_zoom_out. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125 gui_pv_zoom_to. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1254Chipware Developer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127 cwd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128 cwd check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129 cwd create_check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133 cwd report_check. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135 hdl_create. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137 hdl_create binding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138 hdl_create component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140 hdl_create implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 hdl_create library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144 hdl_create operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145 hdl_create package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 hdl_create parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 hdl_create pin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1505Input and Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153 decrypt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155encrypt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156 export_critical_endpoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159 read_config_file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161 read_cpf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162 read_def. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 read_dfm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164 read_dft_abstract_model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166 read_encounter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .167 read_hdl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168 read_io_speclist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172 read_netlist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173 read_saif. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175 read_sdc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 read_spef. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178 read_tcf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179 read_vcd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180 restore_design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181 write_atpg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .183 write_bsdl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .184 write_compression_macro. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .185 write_config_template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .186 write_def. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .187 write_design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188 write_dft_abstract_model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .189 write_do_ccd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190 write_do_ccd compare_sdc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191 write_do_ccd generate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .192 write_do_ccd propagate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .193 write_do_ccd validate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .195 write_do_clp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .196 write_do_lec. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .198 write_do_verify cdc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200 write_encounter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .202 write_et_atpg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205 write_et_bsv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .206 write_et_mbist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .207write_et_rrfa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208 write_ets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .209 write_ett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .210 write_forward_saif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .211 write_hdl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .212 write_io_speclist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215 write_saif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .216 write_scandef. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217 write_script. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .218 write_sdc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .221 write_sdf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224 write_set_load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227 write_spef. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .228 write_tcf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .229 write_template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2306Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .233 clock_uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .234 create_mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .237 define_clock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .240 define_cost_group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .245 derive_environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246 external_delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .248 generate_constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .252 multi_cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .254 path_adjust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .259 path_delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263 path_disable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .266 path_group. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .269 propagate_constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .272 specify_paths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .274 validate_constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2807Elaboration and Synthesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .283 elaborate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284 remove_assigns_without_optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .286 remove_inserted_sync_enable_logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .288 retime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .289 set_remove_assign_options. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .291 synthesize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2948Analysis and Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .301 all_connected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .304 all des. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .305 all des inps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .306 all des insts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307 all des outs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308 all des seqs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309 all lib. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .311 all lib bufs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312 all lib ties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .313 analyze_library_corners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .314 check_design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .316 clock_ports. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .321 compare_sdc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .322 fanin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .323 fanout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .326 report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .328 report area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .332 report boundary_opto. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .334 report buskeepers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .335 report cdn_loop_breaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .336 report cell_delay_calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .338 report checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .339 report clock_gating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342。

vgreduce --removemissing详解vgreduce removemissing 是LVM （Logical Volume Manager，逻辑卷管理器）命令中的一种，用于删除一个失踪的PV （Physical Volume，物理卷）。

在某些情况下，物理卷可能会从卷组中消失（如磁盘故障、操作失误等），而此时仍会保留在卷组的元数据中。

在这种情况下，使用vgreduce 命令可以将失踪的卷从卷组中移除，以保持整个系统的稳定性和安全性。

使用vgreduce removemissing 命令的前提条件是需要查看当前的卷组。

可以使用vgs 命令查看当前系统中的卷组及其状态，如下所示：# vgsVG #PV #LV #SN Attr VSize VFreevg01 1 2 0 wzn- 100.00g 50.00g查看命令的输出可以看到系统中只有一个卷组"vg01" ，有一块物理卷，“#PV”为1。

其中，“#LV”表示卷组所包含的逻辑卷数，“#SN”表示卷组所包含的快照数，“Attr”列代表卷组的属性，“VSize”代表卷组的实际大小，“VFree”代表卷组的可用空间。

如果系统中的物理卷在某些情况下消失了，那么使用"vgs" 命令仍然可以看到该物理卷，但在属性中显示为"missing" ，如下所示：# vgsVG #PV #LV #SN Attr VSize VFreevg01 2 2 0 wzn- 200.00g 100.00gvg01_pv01 0 0 0 wzn- 0 0vg01_pv02 1 2 0 wzn- 100.00g 50.00gvg01_pv03 1 0 0 wzn- 100.00g 50.00g [missing]查看上面的命令输出可以发现，“vg01”卷组中原本有三块物理卷，但是之前已经损坏的一块卷已经被从卷组中删除，现在只有两块物理卷了。

基于扫描电化学显微镜技术研究细胞实时释放ROS樊孝银;鲁理平;康天放【摘要】本研究利用扫描电化学显微镜(SECM)技术考察了十四烷酰佛波醇乙酸酯(PMA)刺激肺癌细胞(A549)活性氧物种(ROS)的实时变化.以过氧化氢(H2O2)为目标检测物,获得了细胞氧化应激的电化学响应图像.以氯化六氨基合钌(Ru(NH3)6Cl3)为体系介质,利用电流负反馈技术获得细胞形貌的清晰图像,同时优化获得探针与基底之间的最佳检测距离.将探针电位设定为过氧化氢的还原电位(-0.65 V)时,通过电流成像图可观察到ROS实时释放,实现了A549细胞被PMA即时刺激时ROS 释放的实时检测.扩大扫描区域,获得了不同个体细胞ROS释放的SECM图像,实现了SECM对ROS信号的实时捕捉及再现性.结果显示:PMA可破坏细胞含氧物种的动态平衡,诱发细胞产生氧化应激响应.将探针放置在细胞ROS释放位点,检测其电流随时间变化,可观察到电流随时间呈现波动状态,推测ROS的胞外释放是一个动态的脉动过程.【期刊名称】《分析测试学报》【年(卷),期】2019(038)004【总页数】6页(P379-384)【关键词】扫描电化学显微镜(SECM);活性氧物种(ROS);H2O2;细胞【作者】樊孝银;鲁理平;康天放【作者单位】北京工业大学环境与能源工程学院,北京 100124;北京工业大学环境与能源工程学院,北京 100124;北京工业大学环境与能源工程学院,北京 100124【正文语种】中文【中图分类】O657.1;TQ460.72活性氧物种(Reactive oxygen species,ROS)是需氧细胞在代谢过程中产生的一系列活性氧簇，包括：O2·-，HOO·，OH·，H2O2等[1-2]，在正常生理条件下，细胞内ROS的产生处于动态平衡状态[3]。

然而，当动态平衡被打破时会造成氧化应激，导致大量ROS产生[4-5]，而且ROS的强氧化性可以引起细胞广泛的氧化损伤，从而导致细胞凋亡[6]。

在探讨胰腺癌代谢重编程与肿瘤微环境相互作用这一主题时，我们首先需要了解胰腺癌的基本情况。

胰腺癌是一种非常严重的癌症，通常在晚期才被发现，且治疗效果不佳。

与许多其他类型的癌症一样，胰腺癌也存在异常的代谢重编程，以及与周围肿瘤微环境的复杂相互作用。

1. 胰腺癌代谢重编程我们将着重讨论胰腺癌的代谢重编程。

代谢重编程是指癌细胞改变其代谢方式，以适应增长和扩散的需要。

在胰腺癌中，这种代谢重编程通常表现为对葡萄糖和谷氨酸的异常利用，以及对脂质和蛋白质合成途径的增强。

这些变化使得癌细胞能够更有效地获取生长所需的能量和物质，并且在一定程度上逃避免疼痛和治疗的影响。

2. 肿瘤微环境相互作用接下来，我们将探讨肿瘤微环境对胰腺癌代谢重编程的影响。

肿瘤微环境是指癌细胞周围的细胞、血管、免疫细胞等组成的环境。

它们与癌细胞之间存在着复杂的相互作用，相互影响。

在胰腺癌中，肿瘤微环境会影响代谢重编程，通过改变供应营养物质和释放信号分子等方式影响癌细胞的代谢状态。

3. 主题文字反复出现在以上内容中，我们可以看到胰腺癌代谢重编程和肿瘤微环境相互作用这一主题文字多次出现。

这是为了强调这一主题的重要性和深度，以及我们对它的高度关注。

总结回顾胰腺癌代谢重编程与肿瘤微环境相互作用是一个非常复杂且值得深入研究的主题。

了解和探索这一主题对于更好地理解胰腺癌的发生、发展和治疗至关重要。

未来的研究应该继续深入探讨代谢重编程和肿瘤微环境之间的关系，以寻找更有效的治疗策略。

个人观点和理解在个人观点和理解方面，我认为对于胰腺癌代谢重编程和肿瘤微环境相互作用的研究是十分重要的。

只有通过深入了解这些复杂的生物学过程，我们才能找到更有效的治疗方法，并最终提高胰腺癌患者的生存率和生活质量。

在文章中，我们简要讨论了胰腺癌的代谢重编程和肿瘤微环境相互作用，重点突出了这一主题。

我们希望这篇文章能够帮助您更好地理解胰腺癌的疾病特点以及相关研究的重要性，从而促进更深入的探讨和研究。

vmd包络解调谱轴承故障诊断python一、概述针对机械设备中轴承常见的故障问题，如断裂、磨损和松动等，传统的故障诊断方法主要是依靠振动信号分析和特征提取。

而在这些方法中，vmd包络解调谱（vmd-envelope demodulation spectrum）技术作为一种新型的信号处理方法，正在逐渐受到人们的重视。

结合Python编程语言，可以更好地应用vmd包络解调谱技术来实现轴承故障的诊断。

二、vmd包络解调谱技术1. 理论原理vmd包络解调谱技术是一种基于变分模态分解（VMD）和包络解调分析的信号处理方法。

VMD是一种自适应信号分解技术，通过将信号分解为多个自适应模态函数（AMFs），可以提取出不同频率和能量的振动分量。

而包络解调分析则是一种针对振动信号中包络线的调制谐波进行分析的方法，主要用于提取信号的低频部分表示系统的振动特征。

2. 算法步骤vmd包络解调谱技术主要包括以下几个步骤：（1）VMD分解：将原始振动信号分解为多个自适应模态函数。

（2）包络提取：对每个模态函数进行包络提取，得到各个模态函数的包络线。

（3）谱分析：对包络信号进行频谱分析，得到系统的振动频谱特征。

（4）故障诊断：通过对振动频谱特征进行分析，可以识别出轴承的故障类型和程度。

三、Python编程实现1. 数据采集首先需要通过传感器或振动采集设备获取到轴承的振动信号数据，这些数据可以是时间域的原始振动信号或频域的频谱数据。

2. VMD分解利用Python编程语言的信号处理库，可以实现VMD算法对原始振动信号进行分解。

将振动信号分解为多个自适应模态函数，每个模态函数代表了不同频率和能量分量的振动模态。

3. 包络提取针对每个模态函数，利用Python编程语言的包络分析方法提取其包络线，得到各个模态函数的包络信号。

4. 谱分析对各个模态函数的包络信号进行频谱分析，得到系统的振动频谱特征。

利用Python编程语言的谱分析库，可以实现对频谱数据的处理和分析。

Eur.Phys.J.D58,1–22(2010) DOI:10.1140/epjd/e2010-00103-y Colloquium T HE E UROPEANP HYSICAL J OURNAL DQuantum memoriesA review based on the European integrated project“Qubit Applications(QAP)”C.Simon1,2,a,M.Afzelius1,J.Appel3,A.Boyer de la Giroday4,S.J.Dewhurst4,N.Gisin1,C.Y.Hu5,F.Jelezko6,S.Kr¨o ll7,J.H.M¨u ller3,J.Nunn8,E.S.Polzik3,J.G.Rarity5,H.De Riedmatten1,W.Rosenfeld9,10,A.J.Shields4,N.Sk¨o ld4,R.M.Stevenson4,R.Thew1,I.A.Walmsley8,M.C.Weber9,10,H.Weinfurter9,10,J.Wrachtrup6,and R.J.Young41Group of Applied Physics,University of Geneva,1211Geneva,Switzerland2Institute for Quantum Information Science and Department of Physics and Astronomy,University of Calgary,Calgary T2N1N4,Canada3Niels Bohr Institute,Copenhagen University,Blegdamsvej17,2100KøbenhavnØ,Denmark4Toshiba Research Europe Limited,208Cambridge Science Park,Cambridge CB40GZ,UK5Electrical and Electronic Engineering,University of Bristol,Bristol BS81UB,UK6Physikalisches Institut,Universit¨a t Stuttgart,Stuttgart,Germany7Department of Physics,Lund University,Box118,22100Lund,Sweden8Clarendon Laboratory,University of Oxford,Oxford OX13PU,UK9Ludwig-Maximilians-Universit¨a t M¨u nchen,80799M¨u nchen,Germany10Max-Planck-Institut f¨u r Quantenoptik,85748Garching,GermanyReceived4March2010Published online20April2010–c EDP Sciences,Societ`a Italiana di Fisica,Springer-Verlag2010Abstract.We perform a review of various approaches to the implementation of quantum memories,with an emphasis on activities within the quantum memory sub-project of the EU integrated project“Qubit Applications”.We begin with a brief overview over different applications for quantum memories and different types of quantum memories.We discuss the most important criteria for assessing quantum memory performance and the most important physical requirements.Then we review the different approaches represented in“Qubit Applications”in some detail.They include solid-state atomic ensembles,NV centers, quantum dots,single atoms,atomic gases and optical phonons in diamond.We compare the different approaches using the discussed criteria.1IntroductionQuantum memories are important elements for quantum information processing applications such as quantum net-works[1],quantum repeaters[2,3]and linear optics quan-tum computing[4,5].Thefield of quantum memories has recently been very active.Recent reviews include refer-ence[6],which gives a compact overview over different memory protocols with atomic ensembles,reference[7], which deals with ensemble-based memories with a detailed focus on atomic gases,and reference[8],which deals with photon-echo based quantum memories,in particular in solid-state atomic ensembles,as well as reference[9],which is focused on quantum memories based on electromagnet-ically induced transparency.Quantum memories were also discussed in the Strategic Report on quantum information processing and communication in Europe[10].The high activity of thefield was also reflected in the European in-tegrated project“Qubit Applications(QAP)”,which had a e-mail:christoph.simon@ a sub-project involving seven research groups devoted to the development of quantum memories.As members of this sub-project we made a sustained effort over the course of the project to compare our various approaches.This in-cluded the definition of appropriate criteria for such com-parisons.The present paper has grown out of this effort. We hope that it will be useful for a wider audience.The approaches to quantum memories represented in the project are quite diverse,including solid-state atomic ensembles in rare-earth doped crystals,NV centers in diamond,semiconductor quantum dots,single trapped atoms,room-temperature and cold atomic gases,and opti-cal phonons in bulk diamond.It was therefore an interest-ing challenge to develop a common language,in order to be able to perform a meaningful comparison.We will begin this review by discussing different applications for quan-tum memories in Section2,followed by a brief overview of the different meanings that the term“quantum memory”can have in Section3.We will then review the most im-portant criteria for assessing the performance of quantum2The European Physical Journal Dmemories in Section4.Section5discusses two physical requirements that are important for good quantum mem-ory performance in a range of different approaches,namely good light-matter coupling and good coherence.Section6, which is divided in seven sub-sections,is devoted to an overview of the different physical approaches that were represented in“Qubit Applications”.In Section7we sum-marize ourfindings.This section includes a comparative table that positions the different approaches with respect to a number of relevant criteria.2Applications of quantum memoriesQuantum memories are important in a number of con-texts,including the implementation of single-photon sources,quantum repeaters,loophole-free Bell inequality tests,communication complexity protocols and precision measurements.2.1Deterministic single photon sourcesOne simple,but potentially very important application of a quantum memory is the implementation of a single-photon source.Given a non-deterministic source of photon pairs such as parametric down-conversion,one can realize a deterministic source of single photons by detecting one photon of a pair(when it is emitted),while storing the other one in a memory.Detection of thefirst photon sig-nals that the memory has been“charged”and can now be used as a single-photon source.In order to implement a close to ideal single-photon source the memory has to be highly efficient.Deterministic single photon sources are important ingredients for linear optics quantum comput-ing[4,5].They are also useful for certain quantum repeater protocols[3,11].2.2Quantum repeatersAnother area where quantum memories are absolutely es-sential is for the implementation of long-distance quan-tum communication via quantum repeaters.The direct distribution of quantum states is limited by unavoidable transmission losses in combination with the no-cloning theorem.The quantum repeater approach[2]overcomes this difficulty by combining quantum teleportation and quantum state storage.The idea is to divide a given long distance into shorter elementary links,create and store entanglement independently for each link,then extend it to the whole distance via entanglement swapping(i.e. quantum teleportation of entanglement).This approach is possible only if quantum memories are available.Require-ments for quantum memories in this context include long coherence times,efficient interfacing with photons(which serve as long-distance carriers of quantum information) and the possibility of performing entanglement swapping operations[3].However,it is not absolutely necessary for the memories to be able to both absorb and emit pho-tons as we assumed in our previous example for realizing a single-photon source.There are different possible ap-proaches,cf.the next section.2.3Loophole-free Bell testA more fundamental application for quantum memories is the realization of a loophole-free test of Bell’s inequal-ity.A loophole-free test requires both creating entangle-ment over a long distance in order to enforce the locality condition and detecting the entangled systems with high efficiency in order to close the efficiency loophole.One at-tractive approach towards achieving this goal is to create entanglement between distant atoms or ions via the detec-tion of photons[12,13].These atoms or ions can be seen as quantum memories.Their interest in the present context lies in the fact that they can be detected with high(essen-tially unit)efficiency.At the same time such a setup can also be seen as an elementary link of a quantum repeater.2.4Communication complexity and protocols requiring local operations and classical communication(LOCC) Communication complexity,i.e.the number of qubits needed for achieving a certain communication task,has recently been shown to be tightly linked to the violation of Bell-type inequalities[14].It may be useful to store quantum states transmitted by light in memories in order to achieve loophole free violations of this mu-nication protocols which require LOCC use memories to perform local operations and store the results while clas-sical communication is going on.Examples of such proto-cols for continuous variables include iterative continuous variable entanglement distillation[15],continuous vari-able cluster state quantum computation[16],communica-tion/cryptography protocols involving several rounds[17], and quantum illumination[18].2.5Precision measurementsA good quantum memory is capable of storing long-lived entanglement.As such,it can be used as a resource for entanglement enhanced sensing and precision metrology applications.A standard technique to enhance the weak coupling between light and matter is to use ensembles of many atoms.This approach does not only promise effi-cient quantum memories[19–21],but it can also increase the precision when detecting external disturbances on the state of such a system with quantum mechanically lim-ited resolution.By preparing a collective entangled state of the atomic ensemble(e.g.by storing a squeezed state of light in the memory[22,23]or by squeezing a collective atomic observable via a quantum-non-demolition(QND) measurement[24]),the projection noise can be reduced. Due to the non-classical correlations between the atoms aC.Simon et al.:Quantum memories.A review based on the QAP project3measurement precision beyond the classical limit is pos-sible.Already,spin squeezing on the cesium clock tran-sition has been demonstrated,which potentially can im-prove the precision of optical lattice clocks[25].Also,an ultra-sensitive RF-magnetometer employing entanglement in a room-temperature Cs vapour cell has been success-fully developed[26].In NMR systems NOON states of 10entangled spins have been employed to improve upon magneticfield sensing almost tenfold compared to stan-dard measuring strategies[27].3Different types of quantum memoriesIt is useful to distinguish different ways of using quantum memories and of characterizing their performance.This includes the use of quantum memories for storing single photons,for general states of light,and memories that are charged through the emission of photons.3.1Memories for single photonsFor applications such as the implementation of a single photon source,or quantum repeaters,one often knows that the desired output state of the memory is a single-photon state.For example,a quantum repeater protocol might involve memories that are designed to absorb and reemit photons that are emitted by other sources[11,28] (e.g.photon-pair sources based on parametric down-conversion,or more ideal single-photon or photon-pair sources based on single atoms or quantum dots).In such a situation,it is natural to verify the performance of the memory using photon counting.The memory can then fail in two distinct ways:it can fail to re-emit a photon at all, or it can re-emit a photon whose quantum state has im-perfect overlap with the photon that was to be stored. This motivates the distinction between efficiency(proba-bility to emit a photon)andfidelity(overlap of the emit-ted photon with the original one).The latter is sometimes more precisely denoted conditionalfidelity,since it is con-ditional on a photon having been emitted by the memory. For quantum repeater applications,for example,both ef-ficiency andfidelity should typically be high[3],however the requirements on the efficiency tend to be somewhat less demanding than those on thefidelity.It is interesting to note that for certain ensemble-based implementations of quantum memories decoherence can affect only the ef-ficiency without degrading thefidelity[29].The memory performance can also be characterized by quantum tomog-raphy of the state of the emitted photon.The tomography performed via a homodyne measurement is a deterministic process which produces a full characterization of the mem-ory,from which efficiency andfidelity can be extracted.3.2Memories for general states of lightOne may also have the goal of storing general states of light independently produced by a third party.Possible applications range from linear optics quantum comput-ing to complex quantum communication protocols.Fol-lowing the storage of the state,the memory can either be measured in some basis,or for other applications re-trieved onto another light pulse.Various types of states can be useful here,such as coherent states,squeezed states,Schr¨o dinger cat states,single photon,or Fock states.The characterization of the memory performance can then be done either by quantum tomography of the atomic state or by quantum tomography of the retrieved state of light[31].Here again homodyne measurements on light are used and thus one important concept is the (unconditional)fidelity[30].3.3Memories that emit photons and whose statecan be measured directlyA different approach to quantum repeaters,but also to the implementation of a loophole-free Bell test,cf. previous section,involves memories(for example,single trapped atoms)that emit photons which are entangled with the memory,and where the atomic state is detected directly[32–35].The atomic state detection is typically a deterministic process,so the distinction between efficiency andfidelity does not apply in this case,the appropriate concept is(unconditional)fidelity.3.4Memories that emit photonsand that are measured via retrievalEven though they were not represented in QAP,we would like to mention ensemble-based memories of the DLCZ (Duan-Lukin-Cirac-Zoller)type[21]where memory exci-tations are created through the emission of a photon,but where thefinal readout of the memory is done via con-version of the memory excitation into a single photon. Memory performance can then be characterized in anal-ogy with Section3.1[3,7].4Criteria for assessing quantum memory performanceWe now discuss a number of evaluation criteria(figures of merit)and their relevance for different applications and implementations.4.1FidelityIn general terms,fidelity is related to the overlap between the quantum state that is written into the memory and the state that is read out.It should be noted that the definition offidelity that is typically used in the context of quantum memories is different from thefidelity used in quantum information theory,e.g.in the context of unam-biguous state discrimination,Uhlmann’s theorem etc.[36].4The European Physical Journal DFor two pure states,the latter corresponds to the modulus of their overlap,whereas the former is the square of that modulus.The precise operational meaning of thefidelity de-pends on the specific approach.For memories that store and re-emit single photons,thefidelity is defined as the overlap between the single-photon wave packet that was sent in and the one that is recovered from the memory. This is also denoted conditionalfidelity,because it is con-ditional on the re-emission a photon.The probability to actually recover a photon is denoted efficiency,cf.the next subsection.For memories that are meant to store general states of light,the conditionalfidelity is not an appropriate concept,and one has to consider unconditionalfidelities.Note that for some applications,the purity of the out-put state(for a pure input)can be a better criterion than thefidelity.If the output state is related to the input state by a unitary transformation,this may do no harm.For example,a Bell measurement involving two photon wave packets[37]that have both been stored in quantum mem-ories can be performed with high accuracy if both wave packets have been subject to the same unitary transfor-mation(distortion).However,it seems that impurity of the output state would be a problem for most conceiv-able applications in quantum information.Such impurity could have different forms,depending on the implementa-tion(e.g.timing jitter,depolarization).It is clearly important to study which processes will limit thefidelity(purity)of a given implementation.It is also interesting to study which encodings of quantum information are the most advantageous in a given physical system(are there“decoherence-free subspaces”?[38]). 4.2EfficiencyWe already introduced the concept of memory efficiency in the previous section.It is most clearly defined for the case of memories that are meant to store and emit single pho-tons,where it is the probability to re-emit a photon that has been stored.In atomic ensembles the efficiency can in principle be close to one thanks to collective interference effects.For single atomic systems(including quantum dots and NV centers),the efficiency with which a single emit-ted photon can be recovered is typically small,but it can be enhanced through the use of optical cavities.Efficiency is not a well-defined concept for memories that are meant to store general states of light,the use of(unconditional)fidelity is usually more appropriate.It is interesting to note that,while high recall effi-ciency is clearly desirable,it is not always necessary to be very close to100%for the memory to be useful,for ex-ample for proof-of-principle demonstrations of quantum repeaters.However,some applications,such as teleporta-tion of an unknown state,require that the storage of a light state in the memory has unconditional highfidelity. In other words,the combinedfidelity times efficiency must be higher than the classical limit.It is important to study the efficiency required for different applications,see e.g. reference[3]for quantum repeater requirements.4.3Storage timeThis is clearly very important for long-distance quan-tum communication applications,where the communica-tion time between distant nodes imposes a lower bound on the required storage time.Storage times have to be at least as long as the average entanglement creation times, which are at least in the second range for realistic repeater protocols and relevant distances[3].A quantitative study of the effect of storage time limitations was recently per-formed in reference[39].Long storage times are less impor-tant for other applications such as single-photon sources or loophole-free Bell tests.4.4BandwidthThis will influence the practical usefulness of a given memory for most applications,because it determines the achievable repetition rates,and also the multiplexing po-tential,cf.below.Bandwidth considerations can also be important for matching sources(e.g.parametric down-conversion)and memories.Of course the required numer-ical value will depend on the desired application.4.5Capacity to store multiple photonsand dimensionalityThe capacity to store several modes is a natural capability for certain ensemble implementations,which can allow a multiplication of the repetition rate,e.g.in quantum com-munication[28,40].It is then of interest to quantify the maximum number of photons(modes)that can be stored. The criterion does not apply to single-atom approaches in the same way.The ability to store multiple spatial modes, i.e.to generate quantum holograms,which is inherent to atomic ensembles is one exciting perspective[41].For a single-mode memory,it can be interesting to quantify its dimensionality,i.e.how many excitations(photons)can be stored.4.6WavelengthAs mentioned above,for long-distance quantum communi-cation applications it is important that the wavelength of the photons that propagate over long distances is within the region of small absorption in opticalfibers(unless one considers free-space transmission,e.g.to satellites).De-pending on the protocol under consideration,this may constrain the operating wavelength of the respective quan-tum memory.5Physical requirementsIn this section we want to focus on the physical require-ments for implementing good memories,where“good”is defined with respect to thefigures of merit discussed inC.Simon et al.:Quantum memories.A review based on the QAP project5the previous section.We will focus onfigures of merit that seem particularly important,and that are relevant for all approaches,namely efficiency and/orfidelity,and storage time.The described criteria are generally not in-dependent.For example,the longer the desired storage time,the harder it may become to achieve high efficiency and/or highfidelity.We suggest that for any memory protocol there are at least two requirements in order to achieve high effi-ciency/fidelity and significant storage time,namely good coupling between traveling and stationary excitations,and good coherence.5.1Light-matter couplingThe notion of light-matter coupling is most easily defined for memories that operate by absorbing and re-emitting states of light(cases2.1and2.2above).In this case,the notion of coupling is directly related to the probability of absorbing the light.In the case of atomic ensembles (whether in gaseous form or in solids),good coupling is achieved by having high optical depth.If such a memory is realized by a single quantum system inside a high-finesse cavity,for example,then thefinesse of the cavity will play a role that is analogous to the optical depth.For memories where the memory excitation is created via the emission of a photon(cases2.3and2.4),a critical point is the probability to emit this photon into a well-defined mode.It is at this point that the notion of good coupling intervenes in such systems.For case2.4,it is also important in the readout process.Optical depths that are sufficient for excellent mem-ory performance have already been achieved in atomic gas cells(both hot and cold),and are in the process of being achieved for rare-earth doped crystals,using multi-pass configurations and/or particularly strongly absorb-ing materials.High unconditionalfidelity furthermore re-quires good coherence and high detection efficiency(for the homodyne detection),which have both been achieved in experiments in Copenhagen(see Sect.6.5).For individ-ual systems such as trapped atoms and NV centers effi-cient collection of the emitted photons could be achieved with high-Q cavities.It is also worth noting that the pos-sibility of storing multiple modes(temporal,spatial,di-rectional)is being investigated in several ensemble-based approaches.These points will be discussed in detail in Sec-tion6.5.2CoherenceWe also discuss decoherence.Its effects can be different for different approaches.For example,for memory protocols based on collective effects,such as controlled reversible in-homogeneous broadening(CRIB),decoherence affects the efficiency,but not the conditionalfidelity.On the other hand,for single atoms decoherence primarily affects the fidelity,but not the readout or recall efficiency.Neverthe-less,decoherence is an important consideration for all im-plementations.In most systems the coherence is limited byfluctuating magneticfields.These can be externally appliedfields(for trapped atoms)orfields generated by the solid-state environment,in particular nuclear spins in the host material(NV centers,quantum dots,rare-earth ion ensembles).Coherence properties can then be greatly improved by optimizing the choice of host material(e.g. isotopically purified crystals that have very low concen-tration of nuclear spins).The following section develops the described topics in more detail for the different exper-imental approaches within QAP.6Implementations6.1Rare-earth ions in solids(Lund/Geneva)We now discuss the possible realizations of quantum mem-ories using ensembles of rare-earth ions in solids.The op-tical4f-4f transitions in rare-earth ions are known for their long optical coherence times(100μs−1ms)[42,43]at cryogenic temperatures and it is also possible tofind spin transitions with extremely long coherence time(>1s)[44–46].This make them very suitable for transferring pho-tonic quantum states onto collective atomic coherences, which can be optical as well as spin.Doped into solids the optical transitions have inhomogeneous broadening[47] much larger than the homogeneous broadening given by the optical coherence time.This causes inhomogeneous de-phasing of the induced optical coherence that needs to be compensated for.We mention already that the inhomoge-neous broadening offers the possibility of a large-bandwith light-matter interface.In order to control the inhomogeneous dephasing the considered storage protocols are based on absorption and re-emission of photons using photon-echo effects.It has been shown,however,that traditional two-pulse pho-ton echoes are not suitable for the storage of quantum light[48,49].This is due to intrinsic spontaneous-emission noise induced by the strongπ-pulse used for rephasing of dipole moments.We are going to describe two modified photon echo protocols that can in principle store single photons with efficiency andfidelity up to unity.Thefirst protocol is based on the controlled and reversible inhomo-geneous broadening(CRIB)[50–58]of a single absorption line(for a recent review see[8]).The second protocol is based on the reversible absorption by a periodic structure of narrow absorption peaks,a so called atomic frequency comb(AFC)[59–63].Potential areas of application for this type of quantum memories are for long-distance quantum communication(quantum repeaters)and the realization of quasi-deterministic single-photon sources.6.1.1Controlled reversible inhomogeneous broadeningWe now describe thefirst scheme,controlled reversible in-homogeneous broadening(CRIB)[8].This involves broad-ening an initially narrow absorption line using the linear Stark effect and an applied external electricfield gradi-ent[51,52,54,57].The width of the broadened line should6The European Physical Journal D match the spectral width of the light that is to be ab-sorbed.Re-emission of the light is triggered by changingthe sign of thefield,which inverts the atomic transitionfrequencies around the central frequency.The rephasingmechanism can be understood by the following argument.Atoms at detuningΔwith respect to the carrier frequencyof the light accumulates a phase exp(−iΔτ)between ab-sorption(t=0)and the polarity inversion of the electricfield(t=τ).By inverting the polarity,the atoms inverttheir detuningsΔ→−Δ.After a time t=2τthe atomswill have accumulated an opposite phase factor exp(iΔτ)which results in a rephasing of all atomic dipoles.The following formula can be derived for the memoryefficiencyηCRIB[54,64]:ηCRIB(t)=1−e−˜d2sinc2(γ0t),(1)where˜d=dγ0/γ.Hereγ0is the width of the initial narrow line,γis the width of the broadened line,d is the opti-cal depth of the initial line,and t is the storage time in the excited state.Note that the initial absorption depth is decreased by the broadening factorγ/γ0.Thus the more broadening that is added,the less efficient the storage effi-ciency becomes.The storage of a single pulse(one mode) can be chosen to be essentially equal to the pulse dura-tion(and thus inversely proportional toγ).Once the pulse has been absorbed,the created atomic excitation can be transferred to a lower-lying state[51,52],e.g.a state that lies in the same hyperfine multiplet as the ground state. The storage time in such a hyperfine state is limited only by(hyperfine)decoherence,cf.below.One can see that the total efficiency is the product of two factors.Thefirst one is related to the absorption of the light.In fact,it is precisely the square of the absorption probability in the broadened ensemble,since is the op-tical depth of the broadened line.The square intervenes because in the CRIB protocol,the re-emission process is the exact time reversal of the absorption,so the proba-bility is the same for both processes.The second factor (the squared sinc function)describes the dephasing which is due to the fact that the initial narrow line has afinite widthγ0.The exact form of the last factor depend on the shape of initial line(which we here assume to be a square function),it being related to its Fourier transform.In reference[28]an analysis of the performance of CRIB was performed,particularly in terms of multimode storage.It was found that an optical depth of about30 is required to achieve an efficiency of0.9for the storage of a single pulse(one mode).If larger optical depths are available,one can store multiple temporal modes(trains of pulses),which can be very attractive for certain ap-plications,e.g.quantum repeaters.The number of modes that can be stored with a certainfixed efficiency grows linearly with the optical depth[28,65].6.1.2Atomic frequency combsIn order to fully exploit temporal multiplexing in quantum repeater architectures,the memory should be able to storeAtomicdensity(a)00s(b)Fig.1.The AFC quantum memory scheme.Figure from ref-erence[59].many temporal modes with high efficiency[28].For EIT based quantum memories,this requires extremely high and currently unrealistic value of optical depth[59,65]. The scaling is better for CRIB based quantum memories but the required optical depth are still very high(e.g.3000 for100modes with90%efficiency)[28,65].Recently,a new scheme was proposed[59]for inhomogeneously broadened materials,where the number of stored modes does not de-pend on the initial optical depth d.The scheme is based on atomic frequency combs(AFC).The idea of AFC is to tailor the absorption profile of an inhomogeneously broadened solid state atomic medium with a series of periodic and narrow absorbing peaks of widthγ0,height d and separated byΔ(see Fig.1).The single photon to be stored is then collectively absorbed by all the atoms in the comb,and the state of the light is transferred to collective atomic excitations at the op-tical transition.After absorption,the atoms at different frequencies will dephase,but thanks to the periodic struc-ture of the absorption profile,a rephasing occurs after a time2π/Δwhich depends on the comb spacing.When the atoms are all in phase again,the light is re-emitted in the forward direction as a result of a collective interference between all the emitters.In order to achieve longer storage times and on-demand retrieval of the stored photons,the optical collec-tive excitation can be transferred to a long lived ground state before the re-emission of the light.This transfer freezes the evolution of the atomic dipoles,and the excita-tion is stored as a collective spin wave for a programmable time.The read out is achieved by transferring back the excitation to the excited state where the rephasing of the atomic dipoles takes place.If the two controlfields are applied in a counterpropagating way,the photon is re-emitted backward.In that case,it has been shown that the re-absorption of the light can be suppressed thanks to a。

Autler-T ownes Splitting in the Multiphoton Resonance Ionization Spectrum of MoleculesProduced by Ultrashort Laser PulsesZhigang Sun and Nanquan LouState Key Laboratory of Molecular Reaction Dynamics,Dalian Institute of Chemical Physics,Chinese Academy of Sciences,Dalian116023,People’s Republic of China(Received30December2002;published10July2003)W e report for thefirst time the proper conditions to observe Autler-Townes splitting(ac-Starksplitting)from vibrationally coherent states belonging to the different electronic terms of a diatomicmolecule.W ave packet dynamics simulations demonstrate that such a process is feasible by multiphotonresonance ionization of the molecule Na2with a single ultrashort intense laser pulse.With the ultrahightime resolution of a femtosecond laser pulse,one can directly measure the absolute value of thetransition dipole moment between any kinds of molecular states by this kind of Autler-Townes splitting,which is a function of the internuclear distance R.DOI:10.1103/PhysRevLett.91.023002P ACS numbers:33.80.–b,42.50.–pAtomic Autler-Townes(AT)splitting has been ob-served on a radio-frequency transition for a long time [1],but AT splitting in a gas-phase molecule has only recently been investigated[2–6].Quesada et al.[2]re-ported the transition dipole moment of H2by measuring the ratio of AT splitting to the electricfield strength. Qi et al.demonstrated that the transition dipole moment of the lithium dimer could be measured by AT splitting using cw triple resonance spectroscopy[5,6].AT splitting on the Na atom[7]and a semiconductor[8]with an ultrashort intense pulse have also been explored recently [8].But,perhaps,because of the relatively small size of the typical molecular transition dipole moment,few papers reported any result about molecular AT splitting on vibrationally coherent states with an ultrashort laser pulse.In this Letter,with multiphoton ionization wave packet dynamics simulations,we demonstrate that one can ob-serve AT splitting in the photoelectron spectrum with a proper single laser pulse and a prototype dimer Na2. Because of the direct relation of AT splitting with the local transition dipole moment and the intensity of the electricfield,AT splitting can be used to precisely mea-sure,in principle,the peak intensity of the laser pulse if the transition dipole moment is known,which is not easy to accurately determine.On the other hand,one can also measure the internuclear-distance R-dependent local transition dipole moment by AT splitting with a properly localized wave packet if the intensity of the ultrashort laser pulse is known.Along with the development of the ultrashort laser pulse,real-time molecular dynamics has been directly observed and many new phenomena have been investi-gated[9–13]and will be discovered.In explanation and foreseeing the experimental results,quantum wave packet dynamics simulations play the central role[14–18].In order to entail the excitation of a local coherent wave packet with the common available femtosecond laser system,one must choose the target molecule character-ized by small vibrational energy.From this point of view, the sodium dimer is an excellent prototype molecule [12,16–18],also for its detailed information of potential energy curves and that of its single cation[19,20]. Therefore we employed a model of the sodium dimer with three electronic states in this Letter to establish the picture of AT splitting of coherent molecular states: the ground state j X i 11 g ,the double minimum state j S i(21 u),and the ionic ground state j I i(12 g)[16].W e ignore the rotational degree of freedom in our study.The relevant potential energy curves are shown in Fig.1,as is the laser interaction process.The laser is centered at 340nm in this work.W e note here that the objective of this exploratory study is to show us the concept of the novel molecular AT splitting which is out from coherent wave packets,and the possible participation of electronic states other than the selected ones here is neglected.In actual experiments,one mayfind other systems more suitable for observing this novel physical phenomenon. The time-dependent Schro¨dinger equation is numeri-cally solved for the vibrational wave functions X, S, and I in the three electronic states which are coupled by a laserfield with the split-operator fast-Fourier transform technique.The ionization continuum is traditionally dis-cretized into a band of quasicontinuum levels in terms of the electron eigenstates j E i containing the core and free electron.The states are labeled according to the kinetic energy of the ejected electron:j I R;t iX N1I R;E n;t j E n i;(1)where E1and E N are the smallest and largest energies which can be transferred to the electron,respectively, and R is the internuclear distance. I R;E n;t are the vibrational wave functions of Na 2,corresponding to the emission of an electron with kinetic energy E n.This leadsto a Hamiltonian matrix of N 2 N 2 ,including the two neutral states and the ionization quasicontinuum N levels.N is typically set to 40in this work.It is time consuming to treat the ionization continuum with this model for diagonalizing the Hamiltonian matrix,but easy and accurate [15,21–23].The laser field of frequency !is described by F t E 0cos !t ,with F t being the pulse shape which is chosen to be a exp ÿ4ln2 t 2=T 2 Gaussian function and E 0being the peak intensity.The time-dependentSchro¨dinger equation is solved with the condition that the molecule is initially in its electronic and vibrational ground state of energy "0.The time-dependent population of the first excited state is obtained from the numerical calculationP S ZdR j S R;t j 2(2)and the electron spectra,defined asP I E n lim t !1ZdR j I R ;E n ;t j 2:The transition dipole moment XS between the neutral states is given its ab initio value from Ref.[24].Employing the Condon approximation, XS is set to the value at the equilibrium position in the ground state.The transition dipole moment SI between j S i and j I i states is set to 1=20of XS [21].Consistent with the model ex-panding the ionization continuum in a set of orthogonal polynomials,varying SI by a factor of 10essentially does not affect the construction of the final electron spectra [25].W e furthermore assumed the dipole moment being independent of the electron energy E ,and we do not apply the rotating wave approximation.Figure 2displays the electron spectra calculated within the quantum wave packet model detailed above using the three potential curves of Fig.1and a T 20fs pulse (FWHM)with intensities of 1:0I 0,2:5I 0,and 5:0I 0(I 0 1:0 1011W cm ÿ2).Also,the time evolution of the population in the j S i state of the molecule is shown.The dash-dotted line is the shape function F t of the pulse.For an intensity of 1:0I 0the electron distribution is a smooth function of energy peaked around 2.286e V ,which is simply "0 2 h!ÿV I R 0 , h!being the photon en-ergy and V I R 0 the potential of the j I i state at the equilibrium distance of the ground neutral state.The one-peak appearance of the spectrum splits into two symmetric humps progressively with increasing strength of the electric field.Figure 3shows the different evolutions of the photoelectron spectra with the laser intensities of 1:0I 0and 5:0I 0,corresponding to the top and bottom plots displayed in Fig.2.W e will show that,neglecting the vibrational motion,the pattern in the electronic spectrum can be regarded as another kind of Autler-Townes splitting which comes from two strongly coupled vibrational coherent states evolving along their own molecular electronic potentialcurves.FIG.2.Left panels:j S i -state population (full line)obtained with three pulse intensities as indicated (I 0 1:0 1011W cm ÿ2).The dot-dashed lines display the temporal variation of the envelope function of the laser pulse of width 20fs.Right panels:Corresponding photoelectron spectroscopy simulated within the quantum multiphoton ionization wave packetdescription.FIG.1.Potential energy curves of the electronic states in-volved in the direct two-photon resonant photoionization of the sodium dimer.The arrows are the excitation energy of the laser pulse,centered at 340nm.It is known that an ultrashort laser pulse of 20fscreates wave packets in the j S i electronic state which are coherent superpositions of the vibrational eigenstates.During field-molecule interaction on this time scale,the j S i -state wave packet has no time to move away from the initial region where they are resonantly coupled by the laser field.The resonant region R is located around the equilibrium position R 0in the electronic ground state where h!equals the energy difference between the potentials of the two electronic states.Therefore the process of the field-molecule interaction can be regarded as that of a two-level laser-atom inter-action,and the corresponding levels are of energies V X R 0 and V S R 0 ,respectively.In terms of the tradi-tional explanation of ac-Stark splitting in the dressed-state picture,the doublet structure arises whenever there is a sufficient Rabi oscillation between a pair of inter-mediate resonant states during the ionization process [7,26].Therefore we can expect that the energy difference between these two peaks displayed in Fig.2equals the Rabi frequency XS E 0.In the spectra calcu-lated with the laser field strength of 5:0I 0,the splitting is 0.276eV ,and the corresponding Rabi frequency is 0.385eV for XS is 3.76a.u.Considering the time-dependent shape of the laser field,the energy splitting agrees well with the Rabi frequency.With a stronger strength of the electric field,we can expect the energy splitting to be nearer to the Rabi frequency.If an intense 20fs rectanglelike pulse with steep leading and tailing edges is applied,the am-plitude of the ac-Stark split is expected to agree exactly with the Rabi frequency.The numerical spectra shown in Fig.4verify our prediction.The electric field strength of the rectanglelike pulse is 6:5I 0,i.e.,4:3 10ÿ3a :u :,there-fore the Rabi frequency is 0.44eV .The numerical result displays the energy splitting as exactly 0.44e V .The vibrationally coherent AT splitting shares many features of the traditional one.It also has its special characteristics because of the ultrashort excitation.Such as,first,it is obvious that it comes from dressed eigen-states of vibrational wave packets,and second,the split-ting of the spectrum is not sensitive to the photon energy of the laser field,for the large bandwidth of the laser pulse is capable of exciting many vibrational levels at the same time and so on.This novel phenomenon is worth investigating further both with theory and experiment.If there are three resonant states involved in the multi-photon ionization,we expect that the photoelectron spec-tra generated by a short and intense enough laser pulse are characterized by three peaks,according to our devel-oped concept for the traditional concept of ac-Stark splitting [27].In fact,the experiments on multiphoton three-state resonance ionization with an ultrashort in-tense laser pulse have been carried out by several groups on the alkali dimer [10,25,28].Therefore it is surprising that no reports have appeared until now on AT splitting of vibrational coherent states.One possible reason is that the FWHM of the commonly available electric field pulse is typically 80fs.With this much longer pulse of 80fs,the vibrational motion of the wave packets cannot be ne-glected.The excited wave packet moves away from the resonance region during laser-molecule interaction and the ‘‘perfect’’Rabi oscillation does not arise any more.Figure 5displays the spectrum and the time-dependent population of the j S i state obtained with a Gaussian pulse of 80fs and 0:8I 0.The spectrum is similar to that of the nonresonance case of the traditional ac-Stark splitting:the spectrum no longer consists of two symmetricpeaks,FIG.4.Same as Fig.2but for an intensity of 6:5I 0(I 0 1:0 1011W cm ÿ2)and a rectanglelike pulse with steep edges.The energy between doublets agrees exactly to the value,0.44e V ,of the Rabifrequency.FIG.5.Same as Fig.2but for an intensity of 0:8I 0(I 0 1:0 1011W cm ÿ2)and a pulse width of 80fs.The Rabi oscillations are not complete,like that of the nonresonant two-level system,and the spectrum arises with a predominant narrow peak at 2.26e V and a small one at 2.4e V.FIG.3.The comparison of the temporal evolutions of the photoelectron spectra obtained with different electric field strengths (the conditions are the same as those of the corre-sponding ones of Fig.2).After more than two perfect Rabi floppings arise,the spectrum splits into two completely sepa-rate peaks—AT splitting appears.but one predominant and another vanishing.W e might ignore the much weaker peaks in our analysis of the experimental results.Another reason might be the spatial inhomogeneity of the laserfield in practice.The inhomo-geneity smears out the trough between the peaks and only a much broadened spectrum is observed[10].In this sense,it should be more practical to observe this new molecular AT splitting with two pulses[4].In Ref.[25]the same kind of complex ionization spec-trum on the sodium dimer was theoretically reported,but was not profoundly investigated and regarded as the result of a certain interference.This might be another reason as to why no experimental results have been reported on this new kind of AT splitting.Even if the rotational motion of the molecule has been ignored in our numerical simulation,the effect of experi-mental inhomogeneity of the rotational distribution of the molecules on the coherent vibrational AT splitting cannot be neglected in practice.This also accounts for the fact that this kind of 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面向3维片上网络的轻量级细粒度容错机制周君;李华伟;王天成;李晓维【摘要】片上网络(networks-on-chip,NoC)是3维集成电路的主要通信技术之一.其中,路由器是3维片上网络的重要组成部件.现有的面向3维片上网络中路由器的容错技术,通常采取路由器整体冗余技术或者直接舍弃失效路由器的方法,这导致网络资源损失较为严重.提出一种面向3维片上网络的轻量级细粒度容错机制,充分利用故障路由器中仍能正常运行的有效资源,保障系统通信.提出的容错机制包括一种高可靠性路由器微体系结构设计和一种与之匹配的容错路由机制.通过实验对比和分析,相比较于已有的3维片上网络容错机制,提出的细粒度容错机制具备较高的通信性能和可靠性,同时面积和功耗开销较小.【期刊名称】《计算机研究与发展》【年(卷),期】2016(053)002【总页数】13页(P341-353)【关键词】片上网络;3维mesh;细粒度;容错;路由机制【作者】周君;李华伟;王天成;李晓维【作者单位】计算机体系结构国家重点实验室(中国科学院计算技术研究所) 北京100190;中国科学院大学北京100049;计算机体系结构国家重点实验室(中国科学院计算技术研究所) 北京 100190;计算机体系结构国家重点实验室(中国科学院计算技术研究所) 北京 100190;中国科学院大学北京100049;计算机体系结构国家重点实验室(中国科学院计算技术研究所) 北京 100190【正文语种】中文【中图分类】TP302A Lightweight Fine－Grained Fault－Tolerant Scheme for 3DNetworks－on －Chip片上网络（network－on－chip，NoC）是一种主流的3维集成电路［1－2］通信技术．网络中的每一个处理单元（processing element，PE）皆通过网络接口（network interface，NI）及路由器节点（简称“节点”，下文同）与网络中的其他处理单元通信．不同的节点（node）是通过水平或者垂直链接（link）与周围的其他节点通信的．图1所示的是一个典型的4× 2×3的3维mesh网络．图1中每个节点表示一个路由器，是网络通信的基本单元部件．随着集成电路复杂度和集成度的提高，片上网络通信也受到了较为严重的影响，部件故障发生概率不断提高．为了保证集成电路的正常通信，需要引入高效的容错机制．一般而言，片上网络的故障分为瞬时性故障和永久性故障．这些故障可能发生在处理单元、链接、或者是路由器中．在本文中，我们主要关注的是3维片上网络中的永久性故障．这类故障不可修复，对于片上网络的正常功能有较为严重的影响．本文的主要研究目的，是针对资源有限且存在永久性故障的3维片上网络，提出并实现一种低成本、高可靠性，且通信性能适度降级（相比较于无故障网络，下文同）的容错机制．国内外面向传统2维片上网络路由器容错机制的研究已经有较丰富的研究成果，但是面向3维片上网络的相关研究进展较少．通常，针对片上网络路由器永久性故障的容错机制主要有以下4类［3－4］：1）将故障的路由器内部模块由对应的冗余模块整体替换；2）通过在路由器中故障部分添加一些外围逻辑电路使数据包绕过故障区；3）设计细粒度的高可靠性路由器微体系结构，利用路由器剩余有效资源执行网络任务；4）使用容错路由机制，直接绕过故障路由器．通常，路由器包含控制通路和数据通路2部分．控制通路包括路由计算单元（routing computation unit，RCU）和仲裁器（arbiter）；数据通路包括流水线寄存器（pipeline register，PR）、端口缓存（port buffer）、内部链接和交叉开关（crossbar，CR）．图2表示的是一个典型的路由器内部模块面积分布，我们可以从中发现数据通路整体占据了较大的面积［4］．由于冗余机制和设计外围电路的方法会产生一定的面积和功耗需求，电路规模越大该需求越明显．因此，在低成本的设计前提下，这2项容错技术对于面积较大的路由器数据通路并不适用．另一方面，控制通路占据的面积相对于数据通路小很多，则可以考虑使用冗余机制或设计外围电路的方法进行容错，对系统整体开销的影响不大．由于数据通路占据了路由器中的较大面积，这使得数据通路的故障发生概率比控制通路高出很多，因此这里我们主要关注的是数据通路上的功能模块故障．考虑到系统开销，成本较低的细粒度高可靠性路由器微体系结构设计和容错路由机制将是合适的选择，特别适合于某些资源受限的多处理器芯片．同时，我们注意到，3维片上网络中路由器的功能模块一般比2维片上网络的对应功能模块的结构要更加复杂．因此，3维片上网络路由器的功能模块故障对网络通信会产生更加严重的影响．这也为引入细粒度的路由器容错控制提供了可能性，从而获得较高的通信可靠性．因此，路由器中数据通路上的模块功能需要细化来提高路由器的容错能力．在本文中，我们提出一种面向3维片上网络的轻量级细粒度容错机制，包括：1）一种新的高可靠性路由器微体系结构．在该结构中，我们细化了交叉开关的功能，使得故障路由器中的有效资源可以继续工作．2）一种与提出的路由器微体系结构匹配的低成本容错路由机制．在该机制中，我们给出了一种基于逻辑的3维容错路由算法．同时，本文还提出一种用于引导该路由算法的3维转向模型，用于避免网络通信的死锁现象，并且保证3维mesh网络中较高的转向公平度和流量平衡．已有的面向片上网络的细粒度容错机制主要面向的是传统的2维片上网络．在文献［5］中，一个传统的2维片上网络路由器中的交叉开关被分为2个独立的子模块．东向和西向的通信由行交叉开关子模块管理．类似地，北向和南向的通信由列交叉开关子模块控制．这种结构可以缓解路由器中东－西向和南－北向2个维度上可能出现的通信竞争，并且在其中一个交叉开关子模块出现故障时保证路由器的部分功能依然可以正常执行．在文献［6］中，2维片上网络的路由器故障被分为静态故障与动态故障2类．该文提出了动态缓存交换机制（dynamic buffer swapping，DBS）和动态多路选择器交换机制（dynamic MUX swapping，DMS），分别用于发生故障的路由器输入缓存和交叉开关，用有效的模块“交换”失效的资源．与前二者不同，文献［4］关注的是路由器中的“切片级（slicelevel）”故障，作者采用时分复用（time division multiplexer）技术，利用数据通路上功能模块的有效切片维持路由器的正常操作．以上的容错机制主要关注的是路由器微体系结构的可靠性设计．此外，也有一些容错机制不仅设计了不同的路由器结构，同时还提出了相应的防死锁路由机制．在文献［7］中，作者通过在线的诊断，获得路由器中永久性故障的细节信息；同时，结合网络中的通信冲突区域信息，提出了一种基于代价矩阵的自适应路由机制．其中，代价矩阵用于判断路由器合法输出端口的优先级．缓存重用技术是文献［8］中提出的另一种容错技术．通过在路由器同一端口的输入缓存和输出缓存之间添加一种自通信通道（selfcommunication channel，SCC），经由有效内部链接绕过2个端口之间的故障链接．此外，该文还使用经典的奇偶转向模型（Odd－Even turn model）［9］确保网络无死锁．但是，针对片上网络，尤其是3维片上网络，现有方案中很少提出与路由器可靠性设计相匹配的容错路由机制，从而缺少一个整体的、可以获得较高通信可靠性和适度性能降级特性的片上网络容错机制．路由器微体系结构和路由机制之间的关联在之前的工作中没有得到较好的重视和体现．在本文中，我们提出的轻量级细粒度容错机制是面向3维mesh片上网络的一个整体的容错解决机制．具体而言，我们设计出一种新的针对路由器数据通路的可靠性微体系结构及其故障模型．此外，我们还提出一种与该高可靠性路由器微体系结构匹配的、基于逻辑的低成本容错路由机制，其中还包括用于引导该路由机制的公平3维转向模型和用于驱使数据包避开通信冲突区域的端口选择机制．路由器可靠性设计、路由算法的执行方式和网络防死锁方法是本文方法的核心组成部分，本节将提供针对这些方面的一些背景技术．2．1 路由器微体系结构在传统2维片上网络中，每个路由器有5个端口．每个端口对应一个方向：东（east，E），南（south，S），西（west，W），北（north，N）和本地（local，L）．在3维网络中，随着垂直链接的引入，又添加了上（up，U）和下（down，D）2个方向的端口．如图3（a）所示，标准的7×7路由器在3维片上网络中应用广泛［10］．在文献［11］中，Lafi等人提出一种层次化路由器，其示意图如图3（b）所示．该路由器由一个5×5的水平子路由器和一个4×4的垂直子路由器组成．在这个结构中，路由器的整体功能并没有改变，同时可以有效缓解不同内部子路由器之间的通信竞争．与标准的路由器相比，层次化路由器可以获得较高的系统通信性能和容错能力．但是，层次化路由器内部2个子路由器以及本地端口间的密切联系是彼此的功能独立性的一大阻碍．例如，垂直子路由器的故障不仅影响到本地数据的接收与发送，还会影响到来自或待发送至水平子路由器的数据包通信．因此，我们提出一种新的高可靠性路由器微体系结构来更好地解决这一问题．2．2 基于逻辑的分布式路由一般而言，路由算法有2种实现方式：一种是基于逻辑，另一种是基于路由表．基于逻辑的路由算法，比如XYZ路由，具备时间和空间的有效性，不足是这种方法的灵活性较差．而基于路由表的实现方式比较灵活，不过可能引入较大的面积和时延开销．Flich等人在文献［12］中提出一种基于逻辑的分布式路由算法（logic－based distributed routing，LBDR）．该算法是一种最短路径路由算法，通过4个连接位（CE，CS，CW，CN）和8个路由位（REN，RES，RSE，RSW，RWN，RWS，RNE，RNW）由转向模型引导执行．其中，连接位表明相应的邻居节点是否可连接，路由位表明邻居节点是否能够接收需要发生该路由位下标所示转向的数据包．例如，CE＝1和RES＝1表明当前节点的东边邻居节点是可连通的，同时能够接收东南方向的数据包（允许ES转向）．此外，作者在文献［12］中还将LBDR拓展至任意方向（即东、南、西、北4个方向）的前2跳场景，并命名为LBDRe（extended LBDR）方法．考虑到LBDR及LBDRe的低成本特性和较好的灵活性，本文在3维场景下对其进行了融入容错特性的拓展，详见3．3节的介绍．2．3 3维转向模型通常，转向模型和虚通道技术是2种最常见的用于解决片上网络死锁问题的方法［13－15］．由于虚通道会引入额外的缓存面积和复杂的控制逻辑，因此转向模型对于开销敏感的电路更加适用．在3维mesh网络中，若干转向模型也被相继提出．Glass等人在文献［16］中提出了3种转向模型，分别是West－South－First，North－Up－Last和Negative－First．这些模型是基于2维场景中的West－First，North－Last和Negative－First模型［16］拓展而来．在文献［17］中，Pasricha等人提出另一种3维转向模型4NP－First．这个模型可以分为2个子模型：4N－First和4P －First．虞潇等人在文献［18］中将3维空间划分为8个区域，共禁止12个转向．基于此模型，作者提出了一种名为TFRA的高度自适应路由算法．Chiu在文献［9］中，给出了一种基于奇偶转向模型拓展的经典3维转向模型OE－3D．在文献［19］中，Dahir等人同样也是在奇偶转向模型的基础上设计了名为Balanced－OE的3维转向模型．在该模型中，奇偶转向模型和一种修改后的奇偶转向模型分别被应用于3维集成电路的奇数器件层和偶数器件层，使得网络流量相对于OE－3D变得更加平衡．由于文献［17－18］中在全网络范围中存在不同的转向模型，需要使用虚通道支持，因此，这2种方法并不适用于低开销容错机制的设计．Balanced－OE作为OE－3D的改进型版本，是目前最新提出的3维转向模型．在3．4节中，我们将对Balanced－OE的转向公平度和网络通信流量平衡作进一步的改进．本文目的是提升路由器微体系结构的可靠性，同时利用LBDR和LBDRe的特点使我们的容错机制轻量级化．3．1 可靠性路由微体系结构针对文献［11］中的层次化路由器，一旦数据包需要在水平和垂直方向之间交叉路由，同时某一个子路由器出现故障，则会使整个层次化路由器的功能失效．此外，当数据包到达目的节点，如果垂直子路由器存在故障，则对应的处理单元将无法获得该数据包．在本文中，我们提出一种新的高可靠性路由微体系结构Re－MA（reliable micro －architecture），来进一步提高3维片上网络的通信可靠性．如图4所示，本文提出的路由器微体系结构主要针对数据通路上的重要模块交叉开关进行优化，而并不像层次路由器那样将路由器划分为若干子路由器．图4中，交叉开关划分为水平交叉开关子模块和垂直交叉开关子模块2部分．为了获得较好的容错能力，我们选用文献［5］中的2维交叉开关结构设计水平交叉开关子模块，通过设置行交叉开关和列交叉开关（即图4所示的行通信模块和列通信模块），分离水平2维空间中的东－西向和南－北向通信，缓解通信竞争，提高子模块容错能力．和层次化路由器中的子路由器类似，Re－MA中的每个交叉开关子模块都是控制不同方向维度上的通信．但与之不同的是，Re－MA中每个交叉开关子模块的功能相对独立，之间关联较少．在数据包被路由分流模块分流之后，数据包可以根据自己的目的端口选择对应的交叉开关子模块进行输出操作．在这样的架构下，即使其中一个交叉开关子模块出现故障无法正常使用，也不影响所有输入路由器的数据包通过另一个交叉开关子模块输出．并且，本地输出端口独立于其他输出端口，这样本地的输出操作就不会受到路由器水平、垂直通信的影响．应注意到，Re－MA是2级流水架构．第1级流水由路由分流模块负责执行，其中包括路由计算（routing computing，RC）和开关分配（switch allocating，SA）；第2级流水负责交叉开关传输（crossbar traversal，CT）．路由分流模块其实可以视作一个虚拟模块，因此在图4中也是用虚线框表示．该模块是由路由计算单元、仲裁器和一些额外的分流判断逻辑构成，主要功能是根据路由计算的结果将由本地处理单元注入网络或者经过当前路由器的数据包分流至对应的交叉开关子模块或者是本地端口．此处的分流判断逻辑可以通过一个简单的1∶2的DEMUX实现．相对于路由器整体面积而言，其所占比重很小．因此，与控制通路类似，这一部分电路的容错机制可以通过冗余技术来实现．3．2 故障模型和故障诊断故障模型对于一个失效模块的分析至关重要．故障模型设置的不同会极大影响容错机制的设计复杂度和执行效率．在引言部分我们已经提到，本文主要关注的是路由器数据通路上的故障模块．作为数据通路上重要的组成部分，输入端口缓存和交叉开关占据了数据通路较大的面积比例．例如，在文献［20］中的示例路由器中，FIFO缓存和交叉开关分别占据了67．68%和11．14%的比例．因此，大部分的故障可能发生在这2个部件上［6，20］．在本文中，我们基于此提出相应的故障模型．这里，我们引入故障矩阵来记录检测到的故障信息．图5所示是2个故障矩阵的示例．其中，“Input”表示路由器输入端口，“Output”表示输出端口．矩阵中的“1”表示相应2个端口之间的通信正常，“0”则表示无法通信的情形．为了避免死锁，片上网络中禁止180°的路由转向，因此相应的矩阵元素值置为“－”．显然，在图5（a）中，该故障矩阵对应的路由器的水平交叉开关子模块中的行通信模块出现故障，因此目的输出端口在东－西向的数据包无法正常通过路由器输出．同理，在图5（b）中，除了水平交叉开关子模块中的列通信模块，路由器的东向（E）端口的输入缓存也同样失效．电路的故障诊断技术主要是用来定位故障的位置，同时确定故障的类型和其他相关信息．由于本文主要关注的是永久性故障，因此适宜采用离线式的诊断技术．离线式故障诊断可以通过生产测试（production test）和内建自检（built－in self－test，BIST）等技术执行．在本文的容错机制设计中，负责诊断执行的检测模块设置于网络的各处理单元中，这样可以缓解路由器的设计成本压力．在系统通电后，特定的故障检测数据包由处理单元中的检测模块经由网络接口发送至本地路由器．通过分析获得的反馈可以掌握路由器中的故障情况，并建立相应的故障矩阵．同时，故障矩阵也需要在检测模块中进行维护．随后，生成的故障矩阵再次通过网络端口传回路由器中的指定寄存器保存，并通过路由器各端口发送至临近的相关路由器节点（具体操作详见3．3节）．故障矩阵通过使用路由器中设计的独立串行线路进行传输．所以，存在故障的输入端口缓存不会给故障矩阵的接收带来影响．需要注意的是，以上的相关操作需要在片上网络的初始化阶段内完成．所以，故障的诊断可以与网络的正常通信相互隔离开来．由于瞬时性故障并不是本文关注的重点，我们设定在网络常规通信时不进行内建自检操作．同时，因为只涉及小范围、小规模（例如，单个故障矩阵的信息量仅30b）的故障信息传输，网络初始化阶段不会占用太多的时间．另一方面，在路由器中只需要很少的面积开销来用于传输和存储故障矩阵．因此，这一部分额外的电路依然可以通过冗余技术来进行低成本的容错操作．3．3 轻量级路由算法考虑到LBDR和LBDRe的低成本和高效率特性，我们在设计的新容错机制中也采用这些方法来降低系统开销．需要注意的是，在3维片上网络中，一些失效的节点可能会成为“死胡同”节点．一旦成为这种节点，数据包在该节点将无法继续路由至目的节点．这主要是由于该节点的故障模块及其他的操作限制导致的．由于LBDR和LBDRe这2个方法都是面向无故障的2维片上网络设计的，并且获取的路由信息有限，因此无法直接将其拓展至3维场景来避免可能的“死胡同”节点．这里，为了消除可能的通信“死胡同”现象，当前节点需要获得更多的路由信息来加以判断输出端口的选择．在本节中，考虑到较低系统开销的设计需求，我们设定路由信息的来源范围为距离当前节点2跳距离以内的任意节点，来有效避免数据包路由至“死胡同”节点．例如，如果西向（W）端口是可选择的输出端口之一，则不仅是当前节点西边的距离在2跳范围内的节点的故障矩阵，其余任意可经由W端口到达并且在2跳范围之内的节点的故障矩阵也应发送至当前节点．这一点和LBDRe方法不同，后者只接收在某一个方向上的且距离在2跳范围之内的节点路由信息．因此，我们将与本文需求较为接近的LBDRe方法拓展至3维场景，并记为LBDRem（modified LBDRe）方法．该方法将容错能力和“死胡同”现象纳入考虑范畴．在3维mesh片上网络中，除本地端口外，一个节点最多有6个端口．对于6个距离为1跳的邻居节点而言，LBDRem的连接位的个数增至6b （CE，CS，CW，CN，CU，CD），同时路由位个数增至30b（REN，RES，REU，RED，REE，RSE，RSW，RSU，RSD，RSS，RWN，RWS，RWU，RWD，RWW，RNE，RNW，RNU，RND，RNN，RUN，RUE，RUS，RUW，RUU，RDN，RDE，RDS，RDW，RDD）．这些路由信息所表明的含义与LBDRe中的相同．类似地，根据3维空间中方向和维度上的推导，对于距离当前节点为2跳的节点，需要另外的30b连接位和126b路由位作为当前节点的“辅助路由信息”．例如，CES表明当前节点的东边邻居节点（记为A）是否与节点A的南边邻居节点可连接；再比如，RSE?EU表明当前节点的东南方向的、与其距离为2跳的节点（记为B）是否可以允许从节点B西向（W）端口输入的数据包发生EU转向．由于原理类似，我们这里不再逐一列举所有相应的连接位与路由位．作为“辅助路由信息”，距离当前节点2跳距离的节点路由信息主要是用于辅助距离当前节点为1跳范围的路由信息的取值判断，从而有效避开可能的“死胡同”节点．这是因为当前节点的下一跳节点选择，最终还是要根据上面枚举的6b连接位和30b路由位的取值进行操作．由于本文不考虑路由器节点之间的链接故障，因此LBDRem方法中的所有连接位取值始终为“1”．LBDRem方法的执行步骤为2步：1）比较当前节点和目的节点的网络坐标．比较的结果将得出可选数据包的继续行进方向，从而使数据包与目的节点的距离更近一步．2）当前节点检查掌握的所有路由信息，并决定选择的合法输出端口．需要说明的是，这里的路由信息是由在网络初始化阶段获得的周边邻居节点的故障矩阵转化而来．例如，假设图5（b）中的故障矩阵来自于当前节点的北边邻居节点，则RNU和RND的取值为“0”，而CN，RNE，RNW，RNN的取值则为“1”．3．4 用于引导路由算法的转向模型作为一种最短路径路由算法，LBDRem可以为3维片上网络的通信提供足够的灵活性．但是，若不加入一些其他限制，网络死锁现象依然无法避免．作为一种有效且开销较低的方法，转向模型对于我们的轻量级容错机制很适用．与具有统一限制的转向模型（即每个节点的转向限制相同）相比，基于区域的转向模型，例如2．3节提到的OE－3D和Balanced－OE模型，通常具备更好的路由自适应度和转向公平性．在网络的不同区域的节点，需要执行的转向限制也不相同，这与“完全不同的多个转向模型”的概念是有区别的，后者需要高成本的虚通道加以支持．以经典的奇偶转向模型为例，如图6所示．在2维mesh网络中的奇数列和偶数列（奇、偶数列取决于列上节点的X坐标的奇偶性）．在奇数列上的所有节点禁止NW和SW转向，而在偶数列上的节点禁止EN和ES转向．这里，我们提出一种相比较于最新的Balanced－OE模型转向更加公平且流量更加平衡的转向模型，命名为Full－OE（即完全OE模型）．Full－OE模型相比较于Balanced－OE模型的不同之处在于，二者的水平器件层内部的转向限制不同．在垂直转向（即层间转向）方面，Full－OE模型采用和Balanced－OE模型相同的转向限制．图7是Balanced－OE模型的水平器件层的转向限制示意图．传统的奇偶转向模型和修改后的奇偶转向模型分别应用于3维集成电路的奇数器件层和偶数器件层．图7（a）中虚线左边是奇数列的禁止转向NW和SW，右边是偶数列的禁止。