Anomalous pinning behavior in an incommensurate two-chain model of friction
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tpo32三篇托福阅读TOEFL原文译文题目答案译文背景知识阅读-1 (2)原文 (2)译文 (5)题目 (7)答案 (16)背景知识 (16)阅读-2 (25)原文 (25)译文 (28)题目 (31)答案 (40)背景知识 (41)阅读-3 (49)原文 (49)译文 (53)题目 (55)答案 (63)背景知识 (64)阅读-1原文Plant Colonization①Colonization is one way in which plants can change the ecology of a site.Colonization is a process with two components:invasion and survival.The rate at which a site is colonized by plants depends on both the rate at which individual organisms(seeds,spores,immature or mature individuals)arrive at the site and their success at becoming established and surviving.Success in colonization depends to a great extent on there being a site available for colonization–a safe site where disturbance by fire or by cutting down of trees has either removed competing species or reduced levels of competition and other negative interactions to a level at which the invading species can become established.For a given rate of invasion,colonization of a moist,fertile site is likely to be much more rapid than that of a dry, infertile site because of poor survival on the latter.A fertile,plowed field is rapidly invaded by a large variety of weeds,whereas a neighboring construction site from which the soil has been compacted or removed to expose a coarse,infertile parent material may remain virtually free of vegetation for many months or even years despite receiving the same input of seeds as the plowed field.②Both the rate of invasion and the rate of extinction vary greatly among different plant species.Pioneer species-those that occur only in the earliest stages of colonization-tend to have high rates of invasion because they produce very large numbers of reproductive propagules(seeds,spores,and so on)and because they have an efficient means of dispersal(normally,wind).③If colonizers produce short-lived reproductive propagules,they must produce very large numbers unless they have an efficient means of dispersal to suitable new habitats.Many plants depend on wind for dispersal and produce abundant quantities of small,relatively short-lived seeds to compensate for the fact that wind is not always a reliable means If reaching the appropriate type of habitat.Alternative strategies have evolved in some plants,such as those that produce fewer but larger seeds that are dispersed to suitable sites by birds or small mammals or those that produce long-lived seeds.Many forest plants seem to exhibit the latter adaptation,and viable seeds of pioneer species can be found in large numbers on some forest floors. For example,as many as1,125viable seeds per square meter were found in a100-year-old Douglas fir/western hemlock forest in coastal British Columbia.Nearly all the seeds that had germinated from this seed bank were from pioneer species.The rapid colonization of such sites after disturbance is undoubtedly in part a reflection of the largeseed band on the forest floor.④An adaptation that is well developed in colonizing species is a high degree of variation in germination(the beginning of a seed’s growth). Seeds of a given species exhibit a wide range of germination dates, increasing the probability that at least some of the seeds will germinate during a period of favorable environmental conditions.This is particularly important for species that colonize an environment where there is no existing vegetation to ameliorate climatic extremes and in which there may be great climatic diversity.⑤Species succession in plant communities,i.e.,the temporal sequence of appearance and disappearance of species is dependent on events occurring at different stages in the life history of a species. Variation in rates of invasion and growth plays an important role in determining patterns of succession,especially secondary succession. The species that are first to colonize a site are those that produce abundant seed that is distributed successfully to new sites.Such species generally grow rapidly and quickly dominate new sites, excluding other species with lower invasion and growth rates.The first community that occupies a disturbed area therefore may be composed of specie with the highest rate of invasion,whereas the community of the subsequent stage may consist of plants with similar survival ratesbut lower invasion rates.译文植物定居①定居是植物改变一个地点生态环境的一种方式。
详细解析新GRE阅读出题点今天三立在线老师带同学们通过几个具体例子来感性体会GRE阅读所谓隐蔽和出题点的概念。
先从一道No题中的难题开始。
在一篇关于有氧代谢和无氧糖酵解的生命科学文章中,第三段有这样一个长达数行的难句子:With the conclusion of a burst of activity, the lactic acid level is high in the body fluids, leaving the large animal vulnerable to attack until the acid is reconverted, via oxidative metabolism, by the liver into glucose, which is then sent (in part) back to the muscles for glycogen resynthesis.面对这样一个充斥着烦难专业名词的难句,很多同学读完之后几乎当场晕倒。
这里重点强调的不是句子本身的结构和各因素相互之间的制约联系。
而是因为这句难句对应了一道非常有代表性的罗马数字类型题。
It can be inferred from the passage that the time required to replenish muscle glycogen following anaerobicglycolysis is determined by which of the following factors?I. Rate of oxidative metabolismII. Quantity of lactic acid in the body fluidsIII. Percentage of glucose that is returned to the muscles(A) I only(B) III only(C) I and II only(D) I and III only(E) I, II, and III题目问及无氧糖酵解过程转化糖原时间和哪些因素有关?有氧代谢率和乳酸本身含量是比较明显的因素。
小学上册英语第3单元真题英语试题一、综合题(本题有100小题,每小题1分,共100分.每小题不选、错误,均不给分)1.What do you call a person who studies the Earth?A. GeographerB. GeologistC. MeteorologistD. BiologistA2.The witch has a ___ (black) cat.3. A __________ is a large landform that stretches across a region.4. A _______ (小刺猬) curls up when it feels threatened.5.The chemical symbol for nihonium is ______.6.The capital of the Netherlands is _______.7.What is 2 x 3?A. 5B. 6C. 7D. 8B8. A __________ can tell us about the Earth's temperature.9.What do you call a person who fixes cars?A. MechanicB. PlumberC. ElectricianD. CarpenterA10.The _____ (小鸟) finds food among the trees.11.The __________ is a large area of grassy plains.12.The __________ (生态研究) informs public policy.13.The __________ is a famous area known for its underwater attractions.14.What is 5 + 3?A. 6B. 8C. 9D. 10B15.The capital of Vanuatu is ________ (瓦努阿图的首都是________).16.The _______ (The Roman Republic) preceded the Roman Empire.17.My family goes ________ every summer.18.Acids can change the color of indicators to ______.19.What is the name of the famous volcano in Italy?A. Mount EtnaB. Mount VesuviusC. Mount St. HelensD. Mount Fuji20.I have a _____ (玩具火车) that makes sounds while it moves. 我有一辆会发出声音的玩具火车。
北京市西城区2023-2024学年高一下学期期末考试英语试题15小题;每小题1.5分,共22.5分)阅读下面短文,掌握其大意,从每题所给的A、B、C、D四个选项中,选出可以填入空白处的最佳选项。
It's a gift more than 50 years in the making.In 1972, Barbara Rieco 1. a heartfelt children's book. It was based on a true story—a little boy she had met while she was a teenager living in Appalachia briefly. It was Barbara's first encounter with poverty (贫困). She came from a middle-class family. She got to see another side of life that she'd heard of, but never seen. It 2.her and had a lasting influence on her life.3.her best efforts, the manuscript (手稿) faced repeated refusal from publishers, leading her to eventually 4.her dreams of becoming a published author.Little did she know that, many years later, her grandson would turn those dreams into reality. Chad Cooper, a design and production professional based in New York City, decided to give his grandmother the perfect Christmas gift—the 5.of her treasured book. Visiting her for the holidays, he 6.took her original manuscript, along with the illustrations she had an artist draw years ago, and turned them into a beautifully printed book.On Christmas morning, as Barbara 7.the carefully wrapped gift, she was overcome with emotion. The moment, 8.by Chad, quickly became popular with viewers, and the video went viral online."This is probably the nicest thing anyone's ever done for me in my entire life," Barbara says in the video.Chad's 9.act didn't just end with the surprise. He also included a(n) 10.to the book on Amazon, making it accessible to the public. The 11.was nothing short of a miracle (奇迹)—within days, Barbara's 12.book skyrocketed to the top of the bestseller list.As the world 13.this unexpected Christmas miracle, Barbara Rieco's book, now 14.by a new generation of readers, continues to spread joy and inspiration, proving that sometimes the most extraordinary 15.are the ones we never knew we needed.1.A.edited B.adapted C.penned D.translated 2.A.worried B.touched C.supported D.challenged 3.A.Despite B.Through C.Without D.For4.A.take on B.live up toC.hold on to D.set aside5.A.promotion B.revisionC.publication D.recommendation6.A.curiously B.secretly C.calmly D.shyly 7.A.bought B.held C.opened D.showed 8.A.photographed B.filmed C.written D.described 9.A.respectful B.faithful C.thankful D.thoughtful 10.A.link B.introduction C.approach D.guide 11.A.comment B.impression C.response D.prediction 12.A.once-forgotten B.badly-neededC.well-known D.fully-prepared13.A.accepts B.presents C.ignores D.celebrates 14.A.sold B.donated C.rated D.loved 15.A.videos B.gifts C.belongings D.materials阅读下面短文,从每题所给的A、B、C、D四个选项中选出最佳选项。
中考英语阅读理解推理判断题单选题30题1. The man in the story always smiles at people. We can infer that he is _____.A. friendlyB. shyC. angryD. sad答案:A。
本题考查对人物性格的推理判断。
文中提到这个人总是对人微笑,微笑通常表示友好,A 选项friendly 意为友好的,符合语境。
B 选项shy 意为害羞的,总是微笑的人不太可能是害羞的。
C 选项angry 意为生气的,与总是微笑不符。
D 选项sad 意为悲伤的,也与总是微笑相矛盾。
2. The woman in the passage helps an old man cross the street. We can guess she is _____.A. selfishB. kindC. cruelD. lazy答案:B。
根据文中女人帮助老人过马路的行为,可以推断她是善良的。
B 选项kind 意为善良的,符合推理。
A 选项selfish 意为自私的,与帮助他人的行为相反。
C 选项cruel 意为残忍的,与帮助行为不符。
D 选项lazy 意为懒惰的,与帮助行为无关。
3. The boy in the story studies hard every day. We can think he wants to _____.A. play gamesB. get good gradesC. sleep moreD. watch TV答案:B。
男孩每天努力学习,通常是为了取得好成绩。
B 选项get good grades 意为取得好成绩,符合逻辑。
A 选项play games 意为玩游戏,与努力学习的行为相悖。
C 选项sleep more 意为睡更多觉,不是努力学习的目的。
D 选项watch TV 意为看电视,也不是努力学习的目的。
4. The girl in the text gives her food to a hungry dog. We can assume she is _____.A. meanB. kind-heartedC. coldD. proud答案:B。
2019年春四川省棠湖中学高二第一学月考试英语试题第I卷选择题(100分)第一部分听力第一节(共5小题;每小题1.5分,满分7.5分)请听下面5段对话,选出最佳选项。
1. Why does the man come here?A. To relax.B. To study.C. To borrow books.2. What happens to the speakers?A. They are lost.B. Their car is broken.C. They are running out of gas.3. What sport did the woman watch?A. Football.B. Tennis.C. Swimming.4. When will the woman leave for the airport tomorrow?A. At 5:30.B. At 6:30.C. At 7:30.5. What does the professor suggest the woman do?A. Hand in the final paper.B. Write another paper.C. Revise her paper.第二节(共15小题;每小题1.5分,满分22.5分)请听下面5段对话或独白,选出最佳选项。
请听第6段材料,回答第6、7题。
6. How does the man probably feel now?A. Impatient.B. Regretful.C. Confused.7. What is the man doing?A. Complaining.B. Comforting.C. Encouraging.请听第7段材料,回答第8、9题。
8. When does the conversation take place?A. In the morning.B. At noon.C. In the evening.9. What did the man attend?A. A party.B. A discussion.C. The opening ceremony. 听第8段材料,回答第10至12题。
a r X i v :c o n d -m a t /9511007v 1 2 N o v 1995Anomalous diffusion in the presence of external forces:exacttime-dependent solutions and entropyConstantino TsallisDepartment of Chemistry,Baker Laboratory,and Materials Science CenterCornell University,Ithaca,NY 14853-1301and Centro Brasileiro de Pesquisas F´ısicas Rua Xavier Sigaud 150,22290-180–Rio de Janeiro –RJ,Brazil ∗Dirk Jan Bukman Department of Chemistry,Baker Laboratory,Cornell University,Ithaca,NY 14853-1301(February 1,2008)Abstract The optimization of the usual entropy S 1[p ]=− du p (u )ln p (u )un-der appropriate constraints is closely related to the Gaussian form of the exact time-dependent solution of the Fokker-Planck equation describing animportant class of normal diffusions.We show here that the optimizationof the generalized entropic form S q [p ]={1− du [p (u )]q }/(q −1)(withq =1+µ−ν∈R )is closely related to the calculation of the exact time-dependent solutions of a generalized,nonlinear,Fokker Planck equation,namely ∂∂x [F (x )p µ]+D ∂2∗Permanent address (tsallis@cat.cbpf.br)a great variety of physical situations become unified in a single picture.05.20.-y;05.40.+j;05.60.+w;66.10.CbTypeset using REVT E XAnomalous diffusion is intensively studied nowadays,both theoretically and experimen-tally.It is observed,for instance,in CTAB micelles dissolved in salted water[1],the analysis of heartbeat histograms in a healthy individual[2],chaotic transport in laminarfluidflow of a water-glycerol mixture in a rapidly rotating annulus[3],subrecoil laser cooling[4],particle chaotic dynamics along the stochastic web associated with a d=3Hamiltonianflow with hexagonal symmetry in a plane[5],conservative motion in a d=2periodic potential[6], transport offluid in porous media(see[7]and references therein),surface growth[7],and many other interesting physical systems.Its thermostatistical foundation(as it is known for normal diffusion)is naturally highly desirable and has,since long,been looked for(see, for instance,[8]and references therein).This goal was recently achieved by Alemany and Zanette[9](see also[10])for L´e vy-like anomalous diffusion,in the context of a generalized, not necessarily extensive(additive),thermostatistics that has been recently proposed[11,12]. This thermostatistics(already applied to a considerable variety of physical systems[13]and optimization techniques[14])is based upon the entropic formS q[p]≡1− du[p(u)]q∂t [p(x,t)]µ=−∂∂x2[p(x,t)]ν(3)where(µ,ν)∈R2,D>0is a(dimensionless)diffusion constant,F(x)≡−dV(x)/dx is a(dimensionless)external force(drift)associated with the potential V(x),and(x,t)is a (dimensionless)1+1space-time.Let us mention that,in variance with the correlated type we are focusing on here,the L´e vy-like anomalous diffusion is associated with a linear equation, though in fractional derivatives[5].We intend to consider here a specific(but very common)drift,namely characterized by F(x)=k1−k2x(k1∈R and k2≥0;k2=0corresponds to the important case of constant external force,and k1=0corresponds to the so called Uhlenbeck-Ornstein process[15]). The particular caseµ=ν=1corresponds to the standard Fokker-Planck equation,i.e.,to normal diffusion.The particular case F(x)=0(no drift)has been considered by Spohn[7] forµ=1and arbitraryν(for instance,ν=3satisfactorily describes a standard solid-on-solid model for surface growth),and has been extended by Duxbury[16]for arbitraryµand ν.The case(µ,k1)=(1,0)has been considered by Plastino and Plastino[17].Our present discussion recovers all of these as particular instances.First,let us illustrate the procedure we intend to follow,by briefly reviewing normal diffusion(µ=ν=1).We wish to optimize S1(given by Eq.(2))with the constraintsdu p(u)=1,(4)u−u M 1≡ du(u−u M)p(u)=0(5) and(u−u M)2 1≡ du(u−u M)2p(u)=σ2,(6) u M andσbeingfixedfinite real quantities.The optimization straightforwardly yields the solutione−β(u−u M)2p1(u)=e−β(t)[x−x M(t)]2p1(x,t)== Z1(0)β(0)= Z1(0)[1−2Dβ(0)k2(11)β(0)anddx M(t)+ x M(0)−k1k2essential)fact that by doing so we preserve[12]the Legendre structure of Thermodynamics and(through the nonnegativity of C q/q[18],where C q denotes the specific heat)guarantee thermodynamic stability.Let us consistently stress that the constraint(14)is equivalent to u q= u M q,but not to u q=u M(since,unless q=1, u M q=u M).All these peculiarities are of course originated by the essential nonextensivity that the index q introduces in the theory.For example,if we have two independent systems A and B(i.e.,p A∗B(u A,u B)= p A(u A)p B(u B)),we immediately verify that S q(A∗B)=S q(A)+S q(B)+(1−q)S q(A)S q(B).It is straightforward to see that the above described optimization of S q yieldsp q(u)=[1−β(1−q)(u−u M)2]1Z q(16)withZ q= du[1−β(1−q)(u−u M)2]11−qβ(0)= Z q(0)µ+νd[Z q(t)]µ+νZ q(t)=Z q(0) 1−1K2 1(22)2νDβ(0)[Z q(0)]µ−νandµτ≡t 1µArrayµ+ν.As we see,µ/ν=1,>1and<1respectively imply that[x(t)−x M(t)]2 scales like t(normal diffusion),faster than t(superdiffusion)and slower than t(subdiffu-sion).The limitsµ/ν=0andµ/ν=∞correspond to“no diffusion”and ballistic motion, respectively.For(µ,k1)=(1,0),the present set of equations reduces to that of Plastino and Plastino[17].Let us mention that the general solution given in Eq.(21)can be derived from that forµ=1(and arbitrary k1)by defining p(x,t)=[p(x,t)]µ,and ν=ν/µ,as can easily be seenfrom Eq.(3).Finally,by using Eq.(19)withλ=2µ,we can verify thatdx p q(x,t)=[Z q(t)/Z q(0)]µ−1 dx p q(x,0).(25)Consequently,the norm(”total mass”)is generically conserved for all times only ifµ=1 (∀K2)or if K2=1(∀µ).For0≤K2<1(a common case),the norm monotonically increases(decreases)with time ifµ>1(µ<1).If K2>1,it is the other way around.Before ending let us mention that,also when t grows to infinity,the solutions we have found must be physically meaningful.This imposesµ/ν>−1.Indeed,if k2=0,τin Eq.(21)must be positive,which impliesµ/ν>−1.Also,if k2=0,x must scale with an increasing function of t;hence,β(t)must decrease with t,which implies(through Eqs.(19) and(24))2µ/(µ+ν)>0,hence,the already mentioned restriction applies once again.The entire picture which emerges is indicated in Fig.2(we have not focused theµ<0region because that would force us to discuss the stability of the solutions with respect to small departures,and this lies outside of the scope of the present work).Summarizing,on general grounds,we have shown that thermostatistics allowing for nonextensivity constitute a theoretical framework within which a rather nice unification of normal and correlated anomalous diffusions can be achieved.Both types of diffusions have been founded,on equal footing,on primary concepts of(appropriately generalized) Thermodynamics and Information Theory.On specific grounds,we have obtained,for a generic linear force F(x),the physically relevant exact(space,time)-dependent solutions of a considerably generalized Fokker-Planck equation,namely Eq.(3).It is with pleasure that one of us(C.T.)acknowledges warm hospitality by B.Widom at the Baker Laboratory.This work was carried out in the research group of B.Widom, and was supported by the National Science Foundation and the Cornell University Materials Science Center.REFERENCES[1]A.Ott,J.P.Bouchaud,ngevin and W.Urbach,Phys.Rev.Lett.65,2201(1990);J.P.Bouchaud,A.Ott,ngevin and W.Urbach,J.Phys.II France1,1465(1991).[2]C.-K.Peng,J.Mietus,J.M.Hausdorff,S.Havlin,H.E.Stanley and A.L.Goldberger,Phys.Rev.Lett.70,1343(1993).[3]T.H.Solomon,E.R.Weeks and H.L.Swinney,Phys.Rev.Lett.71,3975(1993).[4]F.Bardou,J.P.Bouchaud,O.Emile,A.Aspect and C.Cohen-Tannoudji,Phys.Rev.Lett.72,203(1994).[5]G.M.Zaslavsky,D.Stevens and H.Weitzner,Phys.Rev.E48,1683(1993);G.M.Zaslavsky,Physica D76,110(1994)and Chaos4,25(1994)and references therein.[6]J.Klafter and G.Zumofen,Phys.Rev.E49,4873(1994).[7]H.Spohn,J.Phys.I France3,69(1993).[8]M.F.Shlesinger and B.D.Hughes,Physica A109,597(1981);E.W.Montroll and M.F.Shlesinger,J.Stat.Phys.32,209(1983);E.W.Montroll and M.F.Shlesinger,in”Non-equilibrium Phenomena II:from Stochastic to Hydrodynamics”,eds.J.L.Lebowitz andE.W.Montroll(North-Holland,Amsterdam,1984).[9]P.A.Alemany and D.H.Zanette,Phys.Rev.E49,956(1994).[10]C.Tsallis, A.M.C.Souza and R.Maynard,in”L´e vyflights and related topics inPhysics”,eds.M.F.Shlesinger,G.M.Zaslavsky and U.Frisch(Springer,Berlin,1995), p.269;D.H.Zanette and P.A.Alemany,Phys.Rev.Lett.75,366(1995);C.Tsallis, S.V.F.Levy,A.M.C.Souza and R.Maynard,Phys.Rev.Lett.75(Oct/Nov1995),in press.[11]C.Tsallis,J.Stat.Phys.52,479(1988).[12]E.M.F.Curado and C.Tsallis,J.Phys.A24,L69(1991);Corrigenda:24,3187(1991)and25,1019(1992).[13]A.R.Plastino and A.Plastino,Phys.Lett.A174,384(1993);J.J.Aly,in”N-Body Prob-lems and Gravitational Dynamics”,Proc.of the Meeting held at Aussois-France(21-25 March1993),bes and E.Athanassoula(Publications de l’Observatoire de Paris,1993),p.19;A.R.Plastino and A.Plastino,Phys.Lett.A193,251(1994);L.S.Lucena,L.R.da Silva and C.Tsallis,Phys.Rev.E51,6247(1995);P.Jund,S.G.Kim and C.Tsallis,Phys.Rev.B52,50(1995);C.Tsallis,F.C.S´a Barreto and E.D.Loh,Phys.Rev.E52,1447(1995);B.M.Boghosian,preprint(1995)[E-mail to chao-dyn@ with”get chao-dyn/9505012”on subject line];M.Portesi,A.Plastino and C.Tsallis,Phys Rev E52,3317(1995).[14]T.J.P.Penna,Phys.Rev.E51,R1(1995)and Computer in Physics9,341(1995);D.A.Stariolo and C.Tsallis,p.Phys.,vol.II,ed.D.Stauffer(World Scientific, Singapore,1995),p.343;K.C.Mundim and C.Tsallis,Int.J.Quantum Chem.(1996), in press.[15]G.E.Uhlenbeck and L.S.Ornstein,Phys.Rev.36,823(1930).[16]P.M.Duxbury,private communication(1994);see[13]of P.Jund,S.G.Kim and C.Tsallis,Phys.Rev.B52,50(1995),and[18]of C.Tsallis,F.C.S´a Barreto and E.D.Loh,Phys.Rev.E52,1447(1995).[17]A.R.Plastino and A.Plastino,Physica A(1995),in press.[18]E.P.da Silva,C.Tsallis and E.M.F.Curado,Physica A199,137(1993);Erratum:Physica A203,160(1994).FIGURESFIG.1.Theµ/ν=1/3example:(a)Time dependence ofβ(0)/β(t)=[Z q(t)/Z q(0)]2µfor Z q(0)=0and typical values of K2(indicated at the right of each curve).The curve for K2=0lies on the vertical axis.For K2=0.25,0.5,and2the asymptotic values for t/τ→∞are shown by the dashed lines.(τis defined in Eq.(23).);(b)Time dependence of{β(0)[Z q(0)]2µ}/β(t)=[Z q(t)]2µfor Z q(0)=0,β(0)[Z q(0)]2µ=0,and typical values of K′2≡k2/{2νDβ(0)[Z q(0)]2µ}(indicated at the right of each curve).The curve for K2=∞coincides with the horizontal axis.All curves saturate at afinite value as t→∞,except that for K′2=0,which is proportional to t2µ/(µ+ν)for all t.FIG.2.”Norm conservation”means that N≡ dx p q(x,t)is time-invariant;”Norm creation”means that N monotonically increases(decreases)with time if K2<1(K2>1);”Norm dissipa-tion”means that N monotonically decreases(increases)with time if K2<1(K2>1).”Normal diffusion”,”Superdiffusion”and”Subdiffusion”refer to the fact that,for k2=0,(x−x M)2scales like t,faster than t and slower than t,respectively.The standard Fokker-Planck equation corre-sponds toµ=ν=q=1.For the precise meaning of”unphysical”,see the text.On theµ=1 line we have q=2−ν;consequently,whenνvaries from∞to−1,q varies from−∞to3,which precisely is the interval within which Eq.(4)(and,consistently, dx p q(x,0)=1)can be satisfied.11。
GRE填空复习题之动物篇1.青蛙内外和分子内外题coincide.。
.differ分子的相似和外表的相似does not necessarily____, for example,几乎所有的青蛙都长的差不多, but他们的内部分子是____.2.青蛙/蜥蜴/两栖动物皮肤和毒物题permeable/porous.。
.absorbed#青蛙/amphibian的皮肤是如此的____,所以大自然中的有毒物怎样____皮肤毒害青蛙。
#一种蜥蜴extinct是因为他们的皮如此的____,以至于很容易____poisonous gas.(no5)【注解】amphibian:两栖动物。
permeable:可渗透的'porous:多孔的,可渗透的3.人的眼睛聚焦细节能力把周围转为背景题focus on.。
.background#The human eyes have the ability to ____on object. So when it happens, the environment will diminish to____.4.苍蝇死而复生对野营者骚扰题resurgence一个地方已经很多年没有受到什么(mxx)fly害虫骚扰了,但(mxx)fly最近变多了,导致了很多camper很不爽,指责the____of the fly is due to the purification of 当地的水源。
5.萤火虫发光和人造光能源效率比较题outstrips.。
.rivals/ approach#Natre‘s energy efficiency often____human technology: despite the intensity of the light fireflies produce,the amount of heat is negligible;only recently have humans developed chemical light-producing system whose efficiency____the firefly’s system.【注解】engender:[v]产生,导致,生育manipulate:[v]操纵outstrip:[v]比。
A modified version of this technical report will appear in ACM Computing Surveys,September2009. Anomaly Detection:A SurveyVARUN CHANDOLAUniversity of MinnesotaARINDAM BANERJEEUniversity of MinnesotaandVIPIN KUMARUniversity of MinnesotaAnomaly detection is an important problem that has been researched within diverse research areas and application domains.Many anomaly detection techniques have been specifically developed for certain application domains,while others are more generic.This survey tries to provide a structured and comprehensive overview of the research on anomaly detection.We have grouped existing techniques into different categories based on the underlying approach adopted by each technique.For each category we have identified key assumptions,which are used by the techniques to differentiate between normal and anomalous behavior.When applying a given technique to a particular domain,these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain.For each category,we provide a basic anomaly detection technique,and then show how the different existing techniques in that category are variants of the basic tech-nique.This template provides an easier and succinct understanding of the techniques belonging to each category.Further,for each category,we identify the advantages and disadvantages of the techniques in that category.We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains.We hope that this survey will provide a better understanding of the different directions in which research has been done on this topic,and how techniques developed in one area can be applied in domains for which they were not intended to begin with.Categories and Subject Descriptors:H.2.8[Database Management]:Database Applications—Data MiningGeneral Terms:AlgorithmsAdditional Key Words and Phrases:Anomaly Detection,Outlier Detection1.INTRODUCTIONAnomaly detection refers to the problem offinding patterns in data that do not conform to expected behavior.These non-conforming patterns are often referred to as anomalies,outliers,discordant observations,exceptions,aberrations,surprises, peculiarities or contaminants in different application domains.Of these,anomalies and outliers are two terms used most commonly in the context of anomaly detection; sometimes interchangeably.Anomaly detectionfinds extensive use in a wide variety of applications such as fraud detection for credit cards,insurance or health care, intrusion detection for cyber-security,fault detection in safety critical systems,and military surveillance for enemy activities.The importance of anomaly detection is due to the fact that anomalies in data translate to significant(and often critical)actionable information in a wide variety of application domains.For example,an anomalous traffic pattern in a computerTo Appear in ACM Computing Surveys,092009,Pages1–72.2·Chandola,Banerjee and Kumarnetwork could mean that a hacked computer is sending out sensitive data to an unauthorized destination[Kumar2005].An anomalous MRI image may indicate presence of malignant tumors[Spence et al.2001].Anomalies in credit card trans-action data could indicate credit card or identity theft[Aleskerov et al.1997]or anomalous readings from a space craft sensor could signify a fault in some compo-nent of the space craft[Fujimaki et al.2005].Detecting outliers or anomalies in data has been studied in the statistics commu-nity as early as the19th century[Edgeworth1887].Over time,a variety of anomaly detection techniques have been developed in several research communities.Many of these techniques have been specifically developed for certain application domains, while others are more generic.This survey tries to provide a structured and comprehensive overview of the research on anomaly detection.We hope that it facilitates a better understanding of the different directions in which research has been done on this topic,and how techniques developed in one area can be applied in domains for which they were not intended to begin with.1.1What are anomalies?Anomalies are patterns in data that do not conform to a well defined notion of normal behavior.Figure1illustrates anomalies in a simple2-dimensional data set. The data has two normal regions,N1and N2,since most observations lie in these two regions.Points that are sufficiently far away from the regions,e.g.,points o1 and o2,and points in region O3,are anomalies.Fig.1.A simple example of anomalies in a2-dimensional data set. Anomalies might be induced in the data for a variety of reasons,such as malicious activity,e.g.,credit card fraud,cyber-intrusion,terrorist activity or breakdown of a system,but all of the reasons have a common characteristic that they are interesting to the analyst.The“interestingness”or real life relevance of anomalies is a key feature of anomaly detection.Anomaly detection is related to,but distinct from noise removal[Teng et al. 1990]and noise accommodation[Rousseeuw and Leroy1987],both of which deal To Appear in ACM Computing Surveys,092009.Anomaly Detection:A Survey·3 with unwanted noise in the data.Noise can be defined as a phenomenon in data which is not of interest to the analyst,but acts as a hindrance to data analysis. Noise removal is driven by the need to remove the unwanted objects before any data analysis is performed on the data.Noise accommodation refers to immunizing a statistical model estimation against anomalous observations[Huber1974]. Another topic related to anomaly detection is novelty detection[Markou and Singh2003a;2003b;Saunders and Gero2000]which aims at detecting previously unobserved(emergent,novel)patterns in the data,e.g.,a new topic of discussion in a news group.The distinction between novel patterns and anomalies is that the novel patterns are typically incorporated into the normal model after being detected.It should be noted that solutions for above mentioned related problems are often used for anomaly detection and vice-versa,and hence are discussed in this review as well.1.2ChallengesAt an abstract level,an anomaly is defined as a pattern that does not conform to expected normal behavior.A straightforward anomaly detection approach,there-fore,is to define a region representing normal behavior and declare any observation in the data which does not belong to this normal region as an anomaly.But several factors make this apparently simple approach very challenging:—Defining a normal region which encompasses every possible normal behavior is very difficult.In addition,the boundary between normal and anomalous behavior is often not precise.Thus an anomalous observation which lies close to the boundary can actually be normal,and vice-versa.—When anomalies are the result of malicious actions,the malicious adversaries often adapt themselves to make the anomalous observations appear like normal, thereby making the task of defining normal behavior more difficult.—In many domains normal behavior keeps evolving and a current notion of normal behavior might not be sufficiently representative in the future.—The exact notion of an anomaly is different for different application domains.For example,in the medical domain a small deviation from normal(e.g.,fluctuations in body temperature)might be an anomaly,while similar deviation in the stock market domain(e.g.,fluctuations in the value of a stock)might be considered as normal.Thus applying a technique developed in one domain to another is not straightforward.—Availability of labeled data for training/validation of models used by anomaly detection techniques is usually a major issue.—Often the data contains noise which tends to be similar to the actual anomalies and hence is difficult to distinguish and remove.Due to the above challenges,the anomaly detection problem,in its most general form,is not easy to solve.In fact,most of the existing anomaly detection techniques solve a specific formulation of the problem.The formulation is induced by various factors such as nature of the data,availability of labeled data,type of anomalies to be detected,etc.Often,these factors are determined by the application domain inTo Appear in ACM Computing Surveys,092009.4·Chandola,Banerjee and Kumarwhich the anomalies need to be detected.Researchers have adopted concepts from diverse disciplines such as statistics ,machine learning ,data mining ,information theory ,spectral theory ,and have applied them to specific problem formulations.Figure 2shows the above mentioned key components associated with any anomaly detection technique.Anomaly DetectionTechniqueApplication DomainsMedical InformaticsIntrusion Detection...Fault/Damage DetectionFraud DetectionResearch AreasInformation TheoryMachine LearningSpectral TheoryStatisticsData Mining...Problem CharacteristicsLabels Anomaly Type Nature of Data OutputFig.2.Key components associated with an anomaly detection technique.1.3Related WorkAnomaly detection has been the topic of a number of surveys and review articles,as well as books.Hodge and Austin [2004]provide an extensive survey of anomaly detection techniques developed in machine learning and statistical domains.A broad review of anomaly detection techniques for numeric as well as symbolic data is presented by Agyemang et al.[2006].An extensive review of novelty detection techniques using neural networks and statistical approaches has been presented in Markou and Singh [2003a]and Markou and Singh [2003b],respectively.Patcha and Park [2007]and Snyder [2001]present a survey of anomaly detection techniques To Appear in ACM Computing Surveys,092009.Anomaly Detection:A Survey·5 used specifically for cyber-intrusion detection.A substantial amount of research on outlier detection has been done in statistics and has been reviewed in several books [Rousseeuw and Leroy1987;Barnett and Lewis1994;Hawkins1980]as well as other survey articles[Beckman and Cook1983;Bakar et al.2006].Table I shows the set of techniques and application domains covered by our survey and the various related survey articles mentioned above.12345678TechniquesClassification Based√√√√√Clustering Based√√√√Nearest Neighbor Based√√√√√Statistical√√√√√√√Information Theoretic√Spectral√ApplicationsCyber-Intrusion Detection√√Fraud Detection√Medical Anomaly Detection√Industrial Damage Detection√Image Processing√Textual Anomaly Detection√Sensor Networks√Table parison of our survey to other related survey articles.1-Our survey2-Hodge and Austin[2004],3-Agyemang et al.[2006],4-Markou and Singh[2003a],5-Markou and Singh [2003b],6-Patcha and Park[2007],7-Beckman and Cook[1983],8-Bakar et al[2006]1.4Our ContributionsThis survey is an attempt to provide a structured and a broad overview of extensive research on anomaly detection techniques spanning multiple research areas and application domains.Most of the existing surveys on anomaly detection either focus on a particular application domain or on a single research area.[Agyemang et al.2006]and[Hodge and Austin2004]are two related works that group anomaly detection into multiple categories and discuss techniques under each category.This survey builds upon these two works by significantly expanding the discussion in several directions. We add two more categories of anomaly detection techniques,viz.,information theoretic and spectral techniques,to the four categories discussed in[Agyemang et al.2006]and[Hodge and Austin2004].For each of the six categories,we not only discuss the techniques,but also identify unique assumptions regarding the nature of anomalies made by the techniques in that category.These assumptions are critical for determining when the techniques in that category would be able to detect anomalies,and when they would fail.For each category,we provide a basic anomaly detection technique,and then show how the different existing techniques in that category are variants of the basic technique.This template provides an easier and succinct understanding of the techniques belonging to each category.Further, for each category we identify the advantages and disadvantages of the techniques in that category.We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains.To Appear in ACM Computing Surveys,092009.6·Chandola,Banerjee and KumarWhile some of the existing surveys mention the different applications of anomaly detection,we provide a detailed discussion of the application domains where anomaly detection techniques have been used.For each domain we discuss the notion of an anomaly,the different aspects of the anomaly detection problem,and the challenges faced by the anomaly detection techniques.We also provide a list of techniques that have been applied in each application domain.The existing surveys discuss anomaly detection techniques that detect the sim-plest form of anomalies.We distinguish the simple anomalies from complex anoma-lies.The discussion of applications of anomaly detection reveals that for most ap-plication domains,the interesting anomalies are complex in nature,while most of the algorithmic research has focussed on simple anomalies.1.5OrganizationThis survey is organized into three parts and its structure closely follows Figure 2.In Section2we identify the various aspects that determine the formulation of the problem and highlight the richness and complexity associated with anomaly detection.We distinguish simple anomalies from complex anomalies and define two types of complex anomalies,viz.,contextual and collective anomalies.In Section 3we briefly describe the different application domains where anomaly detection has been applied.In subsequent sections we provide a categorization of anomaly detection techniques based on the research area which they belong to.Majority of the techniques can be categorized into classification based(Section4),nearest neighbor based(Section5),clustering based(Section6),and statistical techniques (Section7).Some techniques belong to research areas such as information theory (Section8),and spectral theory(Section9).For each category of techniques we also discuss their computational complexity for training and testing phases.In Section 10we discuss various contextual anomaly detection techniques.We discuss various collective anomaly detection techniques in Section11.We present some discussion on the limitations and relative performance of various existing techniques in Section 12.Section13contains concluding remarks.2.DIFFERENT ASPECTS OF AN ANOMALY DETECTION PROBLEMThis section identifies and discusses the different aspects of anomaly detection.As mentioned earlier,a specific formulation of the problem is determined by several different factors such as the nature of the input data,the availability(or unavailabil-ity)of labels as well as the constraints and requirements induced by the application domain.This section brings forth the richness in the problem domain and justifies the need for the broad spectrum of anomaly detection techniques.2.1Nature of Input DataA key aspect of any anomaly detection technique is the nature of the input data. Input is generally a collection of data instances(also referred as object,record,point, vector,pattern,event,case,sample,observation,entity)[Tan et al.2005,Chapter 2].Each data instance can be described using a set of attributes(also referred to as variable,characteristic,feature,field,dimension).The attributes can be of different types such as binary,categorical or continuous.Each data instance might consist of only one attribute(univariate)or multiple attributes(multivariate).In To Appear in ACM Computing Surveys,092009.Anomaly Detection:A Survey·7 the case of multivariate data instances,all attributes might be of same type or might be a mixture of different data types.The nature of attributes determine the applicability of anomaly detection tech-niques.For example,for statistical techniques different statistical models have to be used for continuous and categorical data.Similarly,for nearest neighbor based techniques,the nature of attributes would determine the distance measure to be used.Often,instead of the actual data,the pairwise distance between instances might be provided in the form of a distance(or similarity)matrix.In such cases, techniques that require original data instances are not applicable,e.g.,many sta-tistical and classification based techniques.Input data can also be categorized based on the relationship present among data instances[Tan et al.2005].Most of the existing anomaly detection techniques deal with record data(or point data),in which no relationship is assumed among the data instances.In general,data instances can be related to each other.Some examples are sequence data,spatial data,and graph data.In sequence data,the data instances are linearly ordered,e.g.,time-series data,genome sequences,protein sequences.In spatial data,each data instance is related to its neighboring instances,e.g.,vehicular traffic data,ecological data.When the spatial data has a temporal(sequential) component it is referred to as spatio-temporal data,e.g.,climate data.In graph data,data instances are represented as vertices in a graph and are connected to other vertices with ter in this section we will discuss situations where such relationship among data instances become relevant for anomaly detection. 2.2Type of AnomalyAn important aspect of an anomaly detection technique is the nature of the desired anomaly.Anomalies can be classified into following three categories:2.2.1Point Anomalies.If an individual data instance can be considered as anomalous with respect to the rest of data,then the instance is termed as a point anomaly.This is the simplest type of anomaly and is the focus of majority of research on anomaly detection.For example,in Figure1,points o1and o2as well as points in region O3lie outside the boundary of the normal regions,and hence are point anomalies since they are different from normal data points.As a real life example,consider credit card fraud detection.Let the data set correspond to an individual’s credit card transactions.For the sake of simplicity, let us assume that the data is defined using only one feature:amount spent.A transaction for which the amount spent is very high compared to the normal range of expenditure for that person will be a point anomaly.2.2.2Contextual Anomalies.If a data instance is anomalous in a specific con-text(but not otherwise),then it is termed as a contextual anomaly(also referred to as conditional anomaly[Song et al.2007]).The notion of a context is induced by the structure in the data set and has to be specified as a part of the problem formulation.Each data instance is defined using following two sets of attributes:To Appear in ACM Computing Surveys,092009.8·Chandola,Banerjee and Kumar(1)Contextual attributes.The contextual attributes are used to determine thecontext(or neighborhood)for that instance.For example,in spatial data sets, the longitude and latitude of a location are the contextual attributes.In time-series data,time is a contextual attribute which determines the position of an instance on the entire sequence.(2)Behavioral attributes.The behavioral attributes define the non-contextual char-acteristics of an instance.For example,in a spatial data set describing the average rainfall of the entire world,the amount of rainfall at any location is a behavioral attribute.The anomalous behavior is determined using the values for the behavioral attributes within a specific context.A data instance might be a contextual anomaly in a given context,but an identical data instance(in terms of behavioral attributes)could be considered normal in a different context.This property is key in identifying contextual and behavioral attributes for a contextual anomaly detection technique.TimeFig.3.Contextual anomaly t2in a temperature time series.Note that the temperature at time t1is same as that at time t2but occurs in a different context and hence is not considered as an anomaly.Contextual anomalies have been most commonly explored in time-series data [Weigend et al.1995;Salvador and Chan2003]and spatial data[Kou et al.2006; Shekhar et al.2001].Figure3shows one such example for a temperature time series which shows the monthly temperature of an area over last few years.A temperature of35F might be normal during the winter(at time t1)at that place,but the same value during summer(at time t2)would be an anomaly.A similar example can be found in the credit card fraud detection domain.A contextual attribute in credit card domain can be the time of purchase.Suppose an individual usually has a weekly shopping bill of$100except during the Christmas week,when it reaches$1000.A new purchase of$1000in a week in July will be considered a contextual anomaly,since it does not conform to the normal behavior of the individual in the context of time(even though the same amount spent during Christmas week will be considered normal).The choice of applying a contextual anomaly detection technique is determined by the meaningfulness of the contextual anomalies in the target application domain. To Appear in ACM Computing Surveys,092009.Anomaly Detection:A Survey·9 Another key factor is the availability of contextual attributes.In several cases defining a context is straightforward,and hence applying a contextual anomaly detection technique makes sense.In other cases,defining a context is not easy, making it difficult to apply such techniques.2.2.3Collective Anomalies.If a collection of related data instances is anomalous with respect to the entire data set,it is termed as a collective anomaly.The indi-vidual data instances in a collective anomaly may not be anomalies by themselves, but their occurrence together as a collection is anomalous.Figure4illustrates an example which shows a human electrocardiogram output[Goldberger et al.2000]. The highlighted region denotes an anomaly because the same low value exists for an abnormally long time(corresponding to an Atrial Premature Contraction).Note that that low value by itself is not an anomaly.Fig.4.Collective anomaly corresponding to an Atrial Premature Contraction in an human elec-trocardiogram output.As an another illustrative example,consider a sequence of actions occurring in a computer as shown below:...http-web,buffer-overflow,http-web,http-web,smtp-mail,ftp,http-web,ssh,smtp-mail,http-web,ssh,buffer-overflow,ftp,http-web,ftp,smtp-mail,http-web...The highlighted sequence of events(buffer-overflow,ssh,ftp)correspond to a typical web based attack by a remote machine followed by copying of data from the host computer to remote destination via ftp.It should be noted that this collection of events is an anomaly but the individual events are not anomalies when they occur in other locations in the sequence.Collective anomalies have been explored for sequence data[Forrest et al.1999; Sun et al.2006],graph data[Noble and Cook2003],and spatial data[Shekhar et al. 2001].To Appear in ACM Computing Surveys,092009.10·Chandola,Banerjee and KumarIt should be noted that while point anomalies can occur in any data set,collective anomalies can occur only in data sets in which data instances are related.In contrast,occurrence of contextual anomalies depends on the availability of context attributes in the data.A point anomaly or a collective anomaly can also be a contextual anomaly if analyzed with respect to a context.Thus a point anomaly detection problem or collective anomaly detection problem can be transformed toa contextual anomaly detection problem by incorporating the context information.2.3Data LabelsThe labels associated with a data instance denote if that instance is normal or anomalous1.It should be noted that obtaining labeled data which is accurate as well as representative of all types of behaviors,is often prohibitively expensive. Labeling is often done manually by a human expert and hence requires substantial effort to obtain the labeled training data set.Typically,getting a labeled set of anomalous data instances which cover all possible type of anomalous behavior is more difficult than getting labels for normal behavior.Moreover,the anomalous behavior is often dynamic in nature,e.g.,new types of anomalies might arise,for which there is no labeled training data.In certain cases,such as air traffic safety, anomalous instances would translate to catastrophic events,and hence will be very rare.Based on the extent to which the labels are available,anomaly detection tech-niques can operate in one of the following three modes:2.3.1Supervised anomaly detection.Techniques trained in supervised mode as-sume the availability of a training data set which has labeled instances for normal as well as anomaly class.Typical approach in such cases is to build a predictive model for normal vs.anomaly classes.Any unseen data instance is compared against the model to determine which class it belongs to.There are two major is-sues that arise in supervised anomaly detection.First,the anomalous instances are far fewer compared to the normal instances in the training data.Issues that arise due to imbalanced class distributions have been addressed in the data mining and machine learning literature[Joshi et al.2001;2002;Chawla et al.2004;Phua et al. 2004;Weiss and Hirsh1998;Vilalta and Ma2002].Second,obtaining accurate and representative labels,especially for the anomaly class is usually challenging.A number of techniques have been proposed that inject artificial anomalies in a normal data set to obtain a labeled training data set[Theiler and Cai2003;Abe et al.2006;Steinwart et al.2005].Other than these two issues,the supervised anomaly detection problem is similar to building predictive models.Hence we will not address this category of techniques in this survey.2.3.2Semi-Supervised anomaly detection.Techniques that operate in a semi-supervised mode,assume that the training data has labeled instances for only the normal class.Since they do not require labels for the anomaly class,they are more widely applicable than supervised techniques.For example,in space craft fault detection[Fujimaki et al.2005],an anomaly scenario would signify an accident, which is not easy to model.The typical approach used in such techniques is to 1Also referred to as normal and anomalous classes.To Appear in ACM Computing Surveys,092009.Anomaly Detection:A Survey·11 build a model for the class corresponding to normal behavior,and use the model to identify anomalies in the test data.A limited set of anomaly detection techniques exist that assume availability of only the anomaly instances for training[Dasgupta and Nino2000;Dasgupta and Majumdar2002;Forrest et al.1996].Such techniques are not commonly used, primarily because it is difficult to obtain a training data set which covers every possible anomalous behavior that can occur in the data.2.3.3Unsupervised anomaly detection.Techniques that operate in unsupervised mode do not require training data,and thus are most widely applicable.The techniques in this category make the implicit assumption that normal instances are far more frequent than anomalies in the test data.If this assumption is not true then such techniques suffer from high false alarm rate.Many semi-supervised techniques can be adapted to operate in an unsupervised mode by using a sample of the unlabeled data set as training data.Such adaptation assumes that the test data contains very few anomalies and the model learnt during training is robust to these few anomalies.2.4Output of Anomaly DetectionAn important aspect for any anomaly detection technique is the manner in which the anomalies are reported.Typically,the outputs produced by anomaly detection techniques are one of the following two types:2.4.1Scores.Scoring techniques assign an anomaly score to each instance in the test data depending on the degree to which that instance is considered an anomaly. Thus the output of such techniques is a ranked list of anomalies.An analyst may choose to either analyze top few anomalies or use a cut-offthreshold to select the anomalies.2.4.2Labels.Techniques in this category assign a label(normal or anomalous) to each test instance.Scoring based anomaly detection techniques allow the analyst to use a domain-specific threshold to select the most relevant anomalies.Techniques that provide binary labels to the test instances do not directly allow the analysts to make such a choice,though this can be controlled indirectly through parameter choices within each technique.3.APPLICATIONS OF ANOMALY DETECTIONIn this section we discuss several applications of anomaly detection.For each ap-plication domain we discuss the following four aspects:—The notion of anomaly.—Nature of the data.—Challenges associated with detecting anomalies.—Existing anomaly detection techniques.To Appear in ACM Computing Surveys,092009.。
a r X i v :c o n d -m a t /9810372v 1 [c o n d -m a t .s t a t -m e c h ] 27 O c t 1998Anomalous pinning behaviorin an incommensurate two-chain model of frictionTakaaki KawaguchiDepartment of Technology,Faculty of Education,Shimane University,1060Nishikawatsu,Matsue 690-8504,JapanHiroshi MatsukawaDepartment of Physics,Osaka University,1-16Machikaneyama Toyonaka,Osaka 560-0043,Japan(February 1,2008)Pinning phenomena in an incommensurate two-chain model of friction are studied numerically.The pinning effect due to the breaking of analyticity exists in the present model.The pinning behavior is,however,quite different from that for the breaking of the analyticity state of the Frenkel-Kontorova model.When the elasticity of chains or the strength of interchain interaction is changed,pinning force and maximum static frictional force show anomalously complicated behavior accompanied by a successive phase transition and they vanish completely under certain conditions.I.INTRODUCTIONIn recent years,the study of friction has been attract-ing much attention in physics [1].Nano-scale frictional phenomena have been examined experimentally using frictional force microscopes [2],quartz micro-valance techniques [3]and so on.In theoretical studies,the Frenkel-Kontorova (FK)model [4]and its related ones have been employed as a promising model of such nano-scale friction by several researchers [5–8].The FK model,in general,consists of an atomic chain on a substrate with periodic potential.In the chain harmonic force works between neighboring atoms.When the mean atomic distance and the period of the potential is incommen-surate,the FK model shows a phase transition,which has been discussed in detail by Aubry and coworkers [9,10].Hence this phase transition is called the Aubry transition.The Aubry transition has following features.When the amplitude of the substrate potential is smaller than a certain critical value,the lowest phonon exci-tation is gapless and therefore a free sliding mode ap-pears.This means vanishing maximum static frictional force.Above the critical amplitude,however,the atoms in the chain are pinned strongly nearby the potential minima and a finite gap exists in the phonon excita-tion.This state is called the breaking of the analyticity state.Then finite energy is needed to slide the chain,and therefore the maximum static frictional force becomes fi-nite.The extended FK model which consists of interact-ing two deformable chains also have been investigated so far.The static structural properties of two-chain models have been investigated in Refs.[11–14],where each chain is often treated as a continuum elastic line.The con-tinuum approximation works effectively in the study on the commensurate-incommensurate transition [12].How-ever,the pinning effect,that arises from the discrete nature of lattices,are smeared out inevitably.In other words,the Aubry transition never occurs in the contin-uum models.On the basis of a two-chain model withdiscrete lattice structures,Matsukawa and Fukuyama investigated the static and the kinetic frictional forces [15,16].The model proposed in their study consists of two atomic chains,where interchain atomic force works between atoms in one chain and in another and harmonic force works between neighbor atoms in each chain.In some cases of elastic parameters of chains,they found that the maximum static frictional force for the two-chain model becomes larger than that for the FK model with the same strength of the interchain interaction.Fur-thermore,they discussed the relationship between the strength of the maximum static frictional force and the velocity dependence of kinetic frictional force.In this paper,we revisit the two-chain model of fric-tion employed in Ref.[15]and examine the frictional phe-nomena in a wide range of model parameters.In partic-ular,pinned states are investigated thoroughly in con-nection with the breaking of analyticity state due to the Aubry transition.It turns out that the maximum static frictional force shows complicated behavior against the change in elastic parameters and vanishes completely in certain conditions.This anomalous pinning behavior is discussed in relation to the static lattice structures.We also focus on the velocity dependence of the kinetic fric-tional force in sliding states.II.TWO-CHAIN MODEL OF FRICTIONThe two-chain model of friction employed here is sum-marized in the following [15].We consider two atomic chains,i.e.,an upper chain and a lower chain.Each atom has one-dimensional degree of freedom parallel to the chain.Intrachain interaction with harmonic form and interchain interaction are taken into consideration.The effects of energy dissipation are assumed to be pro-portional to the difference between the velocity of each atom and that of the center of gravity of the chain.The upper chain is driven by the external force parallel to thechain.Assuming overdamped motion,we get the equa-tions of motion of the atoms in the upper and the lower chains given bym aγa(˙u i− ˙u i i)=K a(u i+1+u i−1−2u i)+N bj∈b F I(u i−v j)+F ex,(1)m bγb(˙v i− ˙v i i)=K b(v i+1+v i−1−2v i)+N aj∈a F I(v i−u j)−K s(v i−ic b),(2)where u i(v i),m a(m b),γa(γb),K a(K b),and N a(N b) are the position of the i th atom,the atomic mass,the parameter of energy dissipation,the strength of the in-teratomic force,and the number of atoms in the upper (lower)chain,respectively.K s denotes the strength of the interatomic force between the lower chain and the substrate,which is necessary to bind the lower chain. i represents the average with respect to i.F I and F ex are the interchain force between the two atomic chains and the external force,respectively.The interchain atomic potential is chosen as follows:U I=−K Ic b 2,(3)where K I is the strength of the interchain potential,and c b the mean atomic spacing of the lower chain.The in-teratomic force is given by F I(x)=−ddx U I,is approximated in the following twolimiting cases[17].When the atoms in the lower chain are rigid andfixed at the regular sites,which corresponds to the case of K b/K a→∞or K s/K a→∞,the interchain force that acts on the upper chain is approximated by one term in a Fourier series:N bj∈b F I(u i−v j) v j=jc b≃−0.47K I sin 2πu ic a ,(6)where c a is the mean atomic spacing of the upper chain. These approximations on the interchain force are valid only in the above two limiting cases on elastic parame-ters,and they may break in intermediate cases.This is a crucial point in the following discussion.III.NUMERICAL METHODFor the numerical simulation of the model,the Runge-Kutta(RK)formula is employed to solve the equations of motion.The periodic boundary conditions are employed in both chains.Hence,the ratio c a/c b is equal to N b/N a, where N a and N b are the numbers of atoms in the upper and lower bodies.c aN a=233( N a i(˙u i)2+ N b i(˙v i)2)/(N a+N b)<10−10, the RK calculation is stopped,and the state obtained then is considered to be static.The phonon frequency is calculated using a dynamical matrix for this stationary state.The maximum static frictional force is evaluated as the critical force above which the velocity condition is not satisfiing the criterion,the difference be-tween pinned and sliding states is distinguishable.The frictional force is calculated according to Eq.(4)or the method used in Ref.[15].In a sliding state,after the system reaches a steady state,the temporal average is performed in calculating the kinetic frictional force over a time period much longer than a time during which the center of gravity of the system moves by the system length,N a c a(=N b c b).IV.RESULTSA.Pinned states1.Lowest phonon frequencyIn this section we investigate the pinning effect of the two-chain model in the absence of external force.To investigate the feature of pinned states,wefirst calcu-late the lowest-phonon frequency,which is a significant quantity becausefinite lowest-phonon frequency,i.e.,the phonon gap,means the presence of pinning and its square is proportional to the restoring force due to pinning ef-fects.For the comparison with the two-chain model,wefirst show the squared lowest phonon frequency(ω2lpf)of the FK model described by Eqs.(1)and(5)with K I=1in Fig.1.In this case the elastic parameter is K a only,and there exists its critical value.Below the critical K a,ω2lpf becomesfinite,corresponding to the appearance of the breaking of analyticity state due to the Aubry transition. Above the critical K a,ω2lpf vanishes.The change ofω2lpf is continuous at the critical point.Such behavior ofω2lpf for the FK model was reported in Ref.[10].In the present study on the two-chain model we have another elastic parameters in the lower chain.Hence,we focus on the effect of the elastic relaxation of the lower chain,and then K s and K b are chosen as variable elastic parameters.In Fig.2(a)we showω2lpf as a function of an elastic constant K b in the case of strong interchain interaction K I=1,and K s=1.The strength of the interchain interaction(K I=1)is chosen to be greater than the critical value of the Aubry transition for the FK model,K criticalI,FK ≈0.33for K a=1.Because of strong interchaininteraction,the phonon gap isfinite and almost constant in the region of large value of K b(2.4<K b).However, steep valleys appear in the range0.81<K b<2.4.The amount ofω2lpf changes there more than two orders of magnitude.It is considered thatω2lpf vanishes at each valley.Thefinite values ofω2lpf at the bottoms of the val-leys will be due to the numerical accuracy of the present calculation and thefinite magnitude of changing in K b. When K b becomes smaller than a certain value(≈0.81),ω2lpf increases sharply and then becomes almost constant. The vanishing phonon gap at each valley seems to indi-cate a sort of phase transition.When the interchain interaction K I is somewhat weak-ened,but its strength is still greater than K criticalI,FK ,moredrastic behavior of phonon gaps is observed.Figure 2(b)showsω2lpf obtained for K I=0.45and K s=1. Finite phonon gaps exist both in small and large K b regimes,and steep valleys appear in the intermediate regime,0.2<K b<0.6.Such behavior is quite simi-lar to that for K I=1.In a wide regime,0.6<K b<1.4; however,the phonon gap vanishes completely within a numerical accuracy.This regime is quite distinct from other regimes with narrow valleys seen in Fig.2(a)as discussed in the next subsection.The anomalous behav-ior of the phonon gap disappears when a large value of K s is chosen as in Fig.2(c),where K s=10(K I=1).It is obvious that the behavior of the phonon gap depends on the elastic parameter K s as well as K b.In Fig.2(a) the behavior of the phonon gap looks self-similar.If this is the case,the phonon gap reveals more complicated be-havior against a smaller change in K b in the intermediate K b regime.The discontinuous and complicated behavior ofω2lpf against the change in elastic parameters for the two-chain model is obviously quite different from that for the FK model shown in Fig.1.We confirmed that the magnitude of the phonon gap at all K b’s chosen in Figs.2(a)-(c)is entirely insensitive to the enlargement of the system size determined by using a continued-fraction expansion of the golden mean in Eq.(7).2.Maximum static frictional forceNext we calculate the maximum static frictional force numerically by applying the external force to the pinned states.Figures3(a)and(b)show the maximum static frictional force calculated for pinned states shown in Figs. 2(a)and(b),respectively.The maximum static frictional force also shows anomalous behavior,which obviously re-flects the phonon gap structures in Figs.2(a)and(b). In Fig.3(a),where the values of the parameters,K I=1 and K s=1,are the same with those in Fig.2(a),the maximum static frictional force shows multivalley struc-tures.The magnitude of the maximum static frictional force isfinite in the whole K b regime.We note that the values of K b at the local minima and maxima of the max-imum static frictional force do not correspond exactly to those ofω2lpf shown in Fig.2(a).This may be considered to be the effect of the external force,by which the pinned lattice structures are distorted and the depinning thresh-old force would be affected slightly.On the other hand, as seen in Fig.3(b)for K I=0.45and K s=1,the max-imum static frictional force vanishes completely in the characteristic K b regime where the completely vanishing phonon gap is observed in Fig.2(b).In the case that K I=1and K s=10,it is confirmed that the maximum static frictional force as well as the phonon gap in Fig.2 (c)does not show any anomalous behavior and changes smoothly with K b.3.Hull functions and lattice structuresTo investigate further the above anomalous pinning behavior observed for the phonon gap and the maximum static frictional force,we analyze the lattice structures ofthe pinned states by examining hull functions.Although a hull function has been employed to analyze the breaking of analyticity state for the FK model[9,10],it has been reported that hull functions defined in two chains are also useful to analyze the lattice structures both in pinned and sliding states for the two-chain model[17].The hull functions for the two-chain model are defined asu i=ic a+α+h a(ic a+α),(9)v i=ic b+β+h b(ic b+β),(10)where h a and h b are the hull functions in the upper and lower chains,respectively,andαandβare constant phases.The periodicities of the hull functions are ex-pressed ash a(x)=h a(x+c b),h b(x)=h b(x+c a).(11)When the chains are not deformed and hence the atoms are arrayed periodically,the interchain interaction po-tential is sinusoidal as mentioned in Eqs.(5)and(6),and then the position of the potential maximum in one pe-riod is located at the half of the period of the hull func-tion,x=c b/2(c a/2)for h a(x)(h b(x))in our choice,α=β=0.For the convenience of later discussions,we briefly summarize here some features of the hull function for the FK model.When the strength of the interchain interac-tion is less than the critical value of the Aubry transition, the hull function is smooth and continuous.Above the critical point,however,the breaking of analyticity due to the Aubry transition occurs,and then the hull function changes its form from continuous to discrete and shows a complicated structure with many gaps.Among the gaps the largest one is located at the half of the period of the hull function.The continuous form means continuous spatial atomic distribution in the underlying potential, and then no gap exists in the phonon excitation.On the other hand,the discrete one corresponds to a pinned state,which is accompanied by afinite gap in the phonon excitation.The spatial atomic distribution is vanishing at the maxima of the potential and the atoms are con-fined nearby the minima of the potential.Then the hull function shows the largest central gap,which character-izes the breaking of analyticity state for the Aubry tran-sition.Now we consider the case of the two-chain model.Fig-ures4(I)-(VII)show the hull functions h a and h b for sev-eral values of K b indicated by arrows(I)-(VII)in Fig. 2(a),where the magnitudes of the parameters,K I=1 and K s=1,are the same as those in Fig.2(a).The hull function h b in Fig.4(I)(K b=0.1;(I)in Fig.2(a)) shows the largest central gap at x=c a/2≈0.809.This gap structure is essentially the same with that for the Aubry transition in the FK model and indicates that the lower chain is in the conventional breaking of analyticity state due to the Aubry transition.On the other hand, h a shows a discrete feature but does not have a central gap.Such a state in the upper chain where the central gap of the hull function is absent is not well defined in the context of the conventional breaking of analyticity state due to the Aubry transition of the FK model,but it is obviously a sort of breaking of analyticity states be-cause of the presence of gaps of the hull function.These gap structures of h a and h b remain even for K b=0.702 (Fig.4(II)).This reflects the constantω2lpf observed in the small K b regime(K b<0.81)in Fig.2(a).As K b increases further(K b>0.81),however,the central gap of h b is destroyed and no central gap exists both in h a and h b.Some other gaps also vanish or shrink,otherwise enlarge,and furthermore,new gaps appear at several po-sitions.Figures4(III)-(V)show h a and h b at several val-ues of K b whereω2lpf shows a local maximum against the change in K b(see arrows(III)-(V)in Fig.2(a)).It should be noted here that the gap structures of h a and h b shown in(III)-(V)are different from each other.In a K b regime between two nearest-neighbor valleys ofω2lpf,both the gap structures of h a and h b are almost unchanged.Only when K b is changed crossing through the valley ofω2lpf, the gap structures are suddenly changed,i.e.,new gaps appear.In the large K b regime(K b>2.4),as shown in Fig.4(VI),the central gap appears in h a,but it is absent in h b,and the gaps of h b as a whole are highly reduced.This behavior indicates that the upper chain is in the conventional breaking of analyticity state due to the Aubry transition.These gap structures of h a and h b retain up to infinite K b while the amplitude of h b as a whole shrinks as K b is increased(Figs.4(VI)and(VII)). Theω2lpf also does not change in this large K b regime. To see how the change of gap structures of hull functions takes place at the valleys ofω2lpf,in Figs.5(a)and(c), we show hull functions for two nearest-neighbor valleys (local minima)ofω2lpf at K b=1.18and1.58.Note here that the K b for Fig.4(III)is located in the K b regime between these two nearest-neighbor valleys ofω2lpf.For the comparison with these states at valleys,the graph of Fig.4(III)is plotted again in Fig.5(b).In Figs.5 (a)and(c)several gaps of the hull functions observed in Fig.5(b)are destroyed by the appearance of certain states in gaps,i.e.,the formation of new gap structures at the K b’s.As mentioned above the gap structures of hull functions for Fig.5(b)are stable and almost unchanged in the regime of1.18<K b<1.58where no valley ofω2lpf exists.Similar behavior is observed around each valley of ω2lpf.When K b reaches one of the critical value,the old gap structure becomes unstable and new states appear in gaps,which accompany the decrease of the phonon gap and then the pinning force.When K b crosses the critical value,new gap structure becomes stable and the phonon gap increases.Further change of K b moves the system to the next critical value and then the successive phase transition occurs.In Fig.6we show the hull functions h a and h b for several values of K b in the case of weak interchain in-teraction,K I=0.45,and K s=1,which are the same values with those in Fig.2(b).In the small and large K b regimes((I),(II),and(VI),(VII)in Figs.6,respectively) whereω2lpf is almost constant,both the gap structures of h a and h b are unchanged,one of which shows the cen-tral gap.This indicates that one of the upper and lower chains is in the conventional breaking of analyticity state due to the Aubry transition in the large and small K b regime,respectively.In the intermediate regime(Figs. 6(III)-(V)),the gap structures as a whole are rather sen-sitive to the change in K b,but also in this case the gap structures are almost unchanged in a small K b regime between two nearest-neighbor valleys ofω2lpf.Thus,the behavior of h a and h b is similar to that in Fig.4in this regime.However,in the K b regime0.6<K b<1.4, for K I=0.45,whereω2lpf is vanishing,both the hull functions show a peculiar feature.In Fig.7we show several typical h a and h b in this K b regime.It is clearly observed that both hull functions h a and h b are contin-uous and show sinusoidal forms,which are quite similar to that of the hull function for the FK model in the ab-sence of the breaking of analyticity.These correspond to states in which all atoms of both chains locate near its regular sites periodically and are weakly affected by the almost sinusoidal interchain force caused by atoms in the other chain.Since the continuous hull functions mean that the atomic distribution is spatially continuous both in the upper and lower chains,every atom in the upper chain moves smoothly when the upper chain is driven by the external force.Therefore,there are no energy costs against the sliding motion of the upper chain.Hence,the maximum static frictional force vanishes as observed in Fig.2(b).For K s=10and K I=1(Figs.8(I)-(IV)),h a does not show any remarkable changes of gap structures.h b grad-ually changes its gap structure only in a large K b regime (K b>10),but the effect of the change is almost negli-gible because the amplitude of the gaps of h b becomes very small for such large K b’s.Therefore all elastic ef-fects come from the upper chain.The behavior of the hull functions reflects the smooth change in the phonon gap in Fig.1(c).In all regime of K b,h a shows the largest central gap,but h b does not.Thus,in these pinned states the conventional breaking of analyticity due to the Aubry transition occurs in the upper chain for the whole range of K b.Then the magnitude of the central gap in h a is quite larger than those of the gaps in h b and almost un-changed against the change in K b.It can be confirmed that the breaking of analyticity states exist in the present two-chain model,but they are rather complicated and different from the conventional one due to the Aubry transition of the FK model.In the small(large)K b regime,however,the gap structure of h b (h a)is the same as the conventional one observed in the breaking of analyticity state in the FK model,while that of h a(h b)is different.That is,in the two-chain model,it is considered that whether the conventional breaking of analyticity state characterized by the largest central gap exists in the upper or lower chain depends on the elas-ticity of the two chains.When the lower(upper)chain is highly stiffer than the upper(lower)one,i.e.,K b/K a or K s/K a≫1(≪1),the atoms in the upper(lower) chain tend to relax into potential minima created by the atoms in the lower(upper)chain,and then the conven-tional breaking of analyticity state appears in the upper (lower)chain.In the intermediate K b regime,however, quite different states from the conventional breaking of analyticity state observed for the FK model appear.We will again discuss this point later by calculating the en-ergy quantities of the system.It should be noted here that all the hull functions shown in Figs.4-8do not contain irregular points that break a rotational symmetry byπof hull functions.This fact means that atomic configurations obtained above are not disordered,but they exactly reflect the discreteness of hull functions in an incommensurate system.This fea-ture of the pinned atomic configuration is the same as that for the FK model[10].It is helpful here to observe the change of the pinned lattice structures in real space.Figure9shows the lo-cal lattice structure in the pinned state for K I=1and K s=1,which are the same values with those in Figs. 2(a),3(a)and4.Here the atomic displacements from the regular periodic sites in the two chainsδu i andδv i are plotted in Figs.9(a)and(b),respectively for K b’s indicated by arrows(II)-(VI)in Fig.2(a).In the small K b regime(K b<0.8),the lattice structure is essentially unchanged(Figs.9(a)-(1)and(b)-(1)).In the interme-diate regime(0.8<K b<2.4),however,bothδu i andδv i are very sensitive to the change in K b.Figures(2)and (3)in both of Figs.9(a)and(b)correspond to atomic displacements at local maxima of the phonon gapω2lpf in Fig.2(a).It is obvious that the spatial modulation patterns ofδu i andδv i show quasiperiodicity approxi-mately for each K b,but the spatial patterns are different for different values of K b.When K b increases further (K b>2.5),the reconstruction does not occur any more and the lattice structures as observed in Figs.9(a)-(5) and(b)-(5)retain up to infinite K b,but the atomic dis-placement in the lower chainδv i as a whole decreases its magnitude more and more.Similar changes of local lat-tice structures are observed also in the intermediate K b regime for K I=0.45and K s=1.Note here that if the behavior of the phonon gap has a self-similar nature as noticed in Fig.2(a),then infinite sorts of local lattice structures would exist in the intermediate K b regime.4.Analysis of energy and discussion on the pinningmechanismWe discuss further the anomalous pinning behavior by examining the energy of the system.Here it is useful to define the following energy quantities.Elastic energy in the upper chain E ela−a and that in the lower chain E ela−b are given byE ela−a=K a2N bi(v i+1−v i−c b)2.(13)Elastic energy between the lower chain and the substrate E ela−s is given by,E ela−s=K s2N ai N b j[U I(u i−v j)−U I(ic a−jc b)],(16)where the contribution in the case of periodic rigid atomic configurations is subtracted.To evaluate Eqs.(12)-(16) we used the atomic configuration obtained in the cal-culation ofω2lpf.Figures10(a)-(d)show these energy quantities plotted against K b for K I=1and K s=1, which are the same values with those in Figs.2(a),3(a), 4,5and9.When K b is very small(K b≪1),the ab-solute value of the interchain interaction energy|E int|is much greater than E ela−a,but not so much greater than E ela−s.The upper chain deforms little,but the lower chain deforms so large to gain the interchain interaction. In fact the hull function of the lower chain h b shows the central largest gap,but h a does not and its magnitude is small.These behaviors indicate that the upper chain has an almost periodic structure,but the lower chain ad-justs its local period to that of the upper chain to gain the interchain interaction,that is,the lower chain forms a kind of discommensurate structure or the soliton lat-tice.When K b is increased,the deformation of the lower chain and E ela−s decrease.On the other hand,E ela−b increases because its coupling constant,itself,increases. When|E int|becomes comparable to the total elastic en-ergy,the lattice structures of both chains in the small K b regime becomes unstable and another structure ap-pears.The presence of kinks for all energy curves in Fig.10indicates that the structural change is a phase transition of thefirst order.The difference in the lattice structures between phases is observable directly in Figs. 9(a)and(b).The disappearance of the central gap of the hull function h b in Fig.4is attributed to the structural phase transition.Both chains form complicated discom-mensurate structures where both chains deform to make the local commensurate structure in order to gain the interchain interaction.The occurrence of the structural phase transition leads to the sudden decrease(or vanish-ing)of the phonon gap at K b≈0.81as observed in Fig. 2(a).In the intermediate K b regime(0.81<K b<2.4), many,or an infinite number of lattice structures appear there,each of which corresponds to a different discom-mensurate structure.When K b is increased small or infinitesimally,lattice structures change to another one by a structural phase transition.Such phase transitions occur successively in this regime against the change in K b.As the lower chain becomes stiffer,the atomic dis-placement in the lower chainδv i is suppressed,and then E ela−b and E ela−s decrease.Because in this K b regime a slight change in K b causes a structural phase transition, the phonon gap and the hull functions also change their structures correspondingly.It should be noted that the absence of the central gap in both hull functions char-acterizes the lattice structures in this intermediate K b regime,where the successive structural phase transition occurs(Figs.4(III)-(V)).This indicates complicated dis-commensurate structures of both chains.In the large K b regime(K b>2.4),the structural phase transition does not occur and a quite stable lattice structure appears in each chain,which is characterized by the largest cen-tral gap of h a.These behaviors indicate that the lower chain forms an almost periodic structure,but the up-per chain forms a discommensurate structure.In this regime the major contribution to E ela−total comes from E ela−a because the atomic displacementδv i is suppressed andδu i’s arefixed into a locally commensurate configu-ration.Therefore,E ela−a and E int are almost constant. Consequently,almost the same gap structures of the hull functions as those in Fig.4(IV)and the same atomic configurations as those in(5)in Figs.9(a)and9(b)hold up to infinite K b.We note here that these features,such as the kinks for energy and the vanishing of the phonon gap,which mean afirst-order phase transition,are never expected in the case of the FK model because the Aubry transition observed in the FK model is a higher-order phase transition.In Fig.11we show the energy quantities for the pa-rameters K I=0.45and K s=1employed in Figs.2(b), 3(b),6,and7.Also,in this case kinks are observed for all energy curves.Within the K b regime(0.6<K b<1.4) where the phonon gap and maximum static frictional force are vanishing completely,any anomaly such as a kink is not observed.It is considered that one particular lattice structure of both chains appears in this K b regime The energy quantities obtained for K s=10and K I=。