Geophys.J.Int.(2008)174,1029–1036doi:
10.1111/j.1365-246X.2008.03883.x
G J I S e i s m o l o g y
Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling
Hongwei Gao and Jianfeng Zhang ?
State Key Laboratory of Lithosphere Evolution,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China.E-mail:zhangjf@https://www.doczj.com/doc/821273484.html,
Accepted 2008June 10.Received 2008April 4;in original form 2007November 25
S U M M A R Y
The perfectly matched layer (PML)absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme,thus resulting in an irregular-grid PML method.We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations.The irregular-grid PML method is implemented under a discretization of triangular grid cells,which has the ability to absorb incident waves in arbitrary directions.This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries.As a result,the computational domain can be constructed with smaller nodes,for instance,to represent the 2-D half-space by a semi-circle rather than a rectangle.By using a smooth arti?cial boundary,the irregular-grid PML method can also avoid the special treatments to the corners,which lead to complex computer implementations in the conventional PML method.We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media.The numerical simulations of a VTI lamb’s problem,wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.
Key words:Numerical solutions;Computational seismology;Wave propagation.
1I N T RO D U C T I O N
The perfectly matched layer (PML)absorbing boundary condi-tion has proven to be very ef?cient for modelling electromag-netic (B′e renger 1994),acoustic (Liu &Tao 1997)and elastic wave (Collino &Tsogka 2001)propagation in unbounded media.The PML method has been incorporated into a variety of wave propaga-tion algorithms,such as the velocity-stress ?nite-difference method of the ?rst-order system (Marcinkovich &Olsen 2003)and spectral-element method of the second-order system (Komatitsch &Tromp 2003;Festa &Vilotte 2005).The non-splitting PML method (Wang &Tang 2003)is also proposed.However,the current PML models are implemented in rectangular grids with vertical and horizontal edges.This means that the arti?cial boundaries have to be vertical and horizontal.Moreover,special treatments are required for han-dling the corners of the vertical and horizontal edges (Collino &Tsogka 2001;Marcinkovich &Olsen 2003).In practice,the arti-?cial boundaries can be constructed with arbitrary geometries as long as the zones of interest are enclosed.For example,we can take a semi-circle rather than a rectangle as the arti?cial boundaries in simulating the half-space (if a semi-circle PML absorbing layer is
?Corresponding author.
possible).This will result in an over 20per cent reduction of the
nodes in the numerical discretization.
The irregular-grid numerical schemes have proven to be useful in accounting for wave propagation across curved surface and in-terfaces as well as in using spatially varying sampling according to the local velocities (which will result in signi?cant reductions in the computational cost and in the storage requirements).However,it is not straightforward to incorporate the current PML methods with the irregular-grid schemes.An irregular-grid numerical tech-nique that can model elastic wave propagation in both 2-D and 3-D heterogeneous media,including surface and interface topographies,has been presented (Zhang &Liu 1999,2002;Gao &Zhang 2006).There it was called the grid method to distinguish it from the ?nite-element or ?nite-difference method.The grid method has also been extended to account for elastic wave propagation in media with high velocity contrasts (Zhang 2004a),in fractured media (Zhang 2005)and in mixed elastic/poroelastic (Zhang 2001)and ?uid/solid (Zhang 2004b)models.We therefore incorporate the PML model into the grid method,thus resulting in an irregular-grid PML model that has the ability to absorb incident waves in arbitrary directions.The irregular-grid PML method is developed using the local co-ordinate system based PML splitting equations and integral formu-lation of the PML equations under a discretization of triangular grid cells.The integral formulation is obtained following the grid method (Zhang &Liu 1999).The local coordinate system based PML
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splitting equations are formulated in a varying coordinate system whose one axis is always normal to the local arti?cial boundary.Due to the discretization of triangular grid cells and local coordinate sys-tem based splitting,the resulting PML model can be implemented along arbitrary geometrical boundaries on the irregular grids,in the absence of a certain decaying direction.This not only improves the grid method and other irregular-grid numerical schemes(e.g. Moczo1989;Zhang1997)in simulating unbounded media but allows the computational domain to be?exibly constructed,with smaller discretized nodes.The latter signi?cantly reduces the com-putational cost and storage requirements in the numerical simula-tions.Moreover,we can avoid the special treatments to the corners, as occurred in the conventional PML methods,by using a smoothed, curved arti?cial boundary.
Like the grid method,the numerical implementation of the irregular-grid PML method is simply completed by looping through all grid cells inside the PML region,based on the pre-calculated local geometrical coef?cients.This numerical scheme leads to a simpler computer implementation,in contrast to the current PML methods.Owing to that,the local geometrical coef?cients are picked up from a pre-calculated table in each time step,no extra computa-tional costs arise when the irregular-grid PML method is used.By extending the PML splitting equations to consider the anisotropic stiffness tensor,the resulting irregular-grid PML model can handle the anisotropic cases without any extra effort.In this paper,we im-plement the irregular-grid PML model in both2-D elastic isotropic and anisotropic media.
The paper is arranged as follows:?rst,we discuss the local co-ordinate system based PML splitting equations.Then,we present the integral formulation of the PML splitting equations,under a discretization of triangular grid cells,for the nodes inside the PML region and on the interface between the interior and the PML re-gion(we will call the interface the PML interface).Next,we review the numerical implementations when the irregular-grid PML model is incorporated into the grid method.Finally,we present exam-ples which demonstrate the irregular-grid PML method’s ability to absorb surface and body waves and to reduce the computational domain.
2P M L S P L I T T I N G E Q UAT I O N S
Following the PML splitting equations discussed in the conventional PML method(e.g.Collino&Tsogka2001),the local coordinate system based PML splitting equations in2-D anisotropic,elastic media are formulated,in a local coordinate system(x1,x2),with x1-axis being normal to the local arti?cial boundary,in terms of velocity and stress as follows:
ρ?v⊥i
?t
+ρd(x1)v⊥i=
?τi1
?x1
,ρ
?v i
?t
=
?τi2
?x2
,(1)
?τ⊥i j
+d(x1)τ⊥i j=c i jl1?v l
1
,
?τ i j
=c i jl2
?v l
2
,(2)
τi j=τ⊥i j+τ i j,v i=v⊥i+v i,(3) where i,j,l=1,2,we assume the summation convention for repeated indices andρis the density,c ijln are the components of
a fourth-order elastic stiffness tensor,v i,v⊥
i and v
i
andτi j,τ⊥
i j
,
andτ
i j are,respectively,the velocity,split velocity components
and stress,split stress components that are de?ned in the local coordinate system(note thatτi j,etc.are symmetric),
superscript Figure1.Local mesh in the proximity of a curved arti?cial boundary.The
curve g-q-h denotes the arti?cial boundary(i.e.PML interface).A PML
absorbing layer is imposed along the arti?cial boundary.The width between
the upper and lower?gures is created for visualization.The triangles drawn
by solid lines are the grid cells.Coordinate system(x1,x2),for which
x1-axis coincides with the dotted-line segment,is related to grid cell pqk.
The dotted-line segment denotes the normal distance(i.e.a)from the centre
of grid cell pqk to the arti?cial boundary,which is used to compute the
damping factor at the centre of the grid cell.The damping factors become
zero at the centres of the grid cells in the upper?gure(i.e.outside the PML
absorbing layer).F z and F x denote the loads acting on interface1-g-5in
the vertical and horizontal directions,that is,in the total coordinate system.
The dashed lines link the centres of the grid cells,represented by circles,
and the midpoints of the edges of the grid cells.
⊥means that only the derivative perpendicular to the boundary is considered(superscript means that only the derivative parallel
to the boundary is considered)and d(x1)is the damping factor
that gradually increases from zero to a positive number along the
outward-directed normals(i.e.x1-axis).The term c ijln satis?es the
(Green)symmetry conditions,that is,c ijln=c jiln=c ijnl=c lnij.For isotropic cases,it is independent of the coordinate system and is
determined by two Lam′e parameters,that is,c ijln=λδi jδln+μ(δilδjn+δinδjl).In anisotropic cases,we obtain c ijln in the local coordinate system by a coordinate transformation according to the stiffness tensor in the total coordinate system(i.e.the coordinate system with one axis pointing vertical downward)as follows(Ting 1996):
c i jln=T im T jk T lp T nq c o mkpq,m,k,p,q=1,2,(4) where we assume the summation convention for repeate
d indices and T im,etc.denot
e the elements o
f the transformation matrix for
the total coordinate system to the local one and c o
mkpq
denote the
components of the stiffness tensor in the total coordinate system.
We implement the irregular-grid PML method by adding a thin,
even-thickness absorbing layer along the smoothed,curved arti?-
cial boundary.Fig.1shows the PML absorbing layer in the prox-
imity of a curved arti?cial boundary and the local numerical mesh
that accounts for the curved boundary.The mesh is composed of
triangles,thus providing the?exibility for the PML absorbing
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Figure2.Illustration of the local coordinate systems.(x1,x2)is a local
coordinate system related to each grid cell,which is determined by making
x1-axis normal to the arti?cial boundary and pass through the centre of the
grid cell(e.g.node13).(y1,y2)is another local coordinate system related
to each node,which is determined by making y1-axis normal to the arti?cial
boundary and pass through the node(e.g.node k).φandθare angles by
which the local coordinate systems can be rotated to the total coordinate
system(z,x),respectively.Point O denotes the centre of curvature of the
local arti?cial boundary,and r the radius of curvature.
to follow an arbitrary geometrical boundary.To derive the irregular-
grid PML method,two local coordinate systems are used,as illus-
trated in Fig.2.One is the local coordinate system related to each
triangular grid cell,such as(x1,x2)in Fig.2that is determined by
making x1-axis normal to the arti?cial boundary and pass through
the centre of the grid cell(i.e.node13).Another is the local coor-
dinate system related to each node,such as(y1,y2)in Fig.2,that
is determined by making y1-axis normal to the arti?cial boundary
and pass through the node(i.e.node k).However,only the local
geometrical coef?cients that are computed in the local coordinate
system related to the grid cell(i.e.in the x1-x2coordinates),rather
than the two local coordinate systems are used in the numerical
implementation.
We de?ne the damping factors at the centres of the grid cells
inside the PML region(i.e.PML absorbing layer),whose values
are given by d0[1?cos(0.5πa/D)].Here,a is the normal distance
from the centre of the grid cell to the PML interface,as shown in
Fig.1,D is the pre-de?ned thickness of the PML absorbing layer
and d0is a positive constant that reads d0=αc p/D with c p denoting
the P-wave velocity of the local medium andα,a parameter that is
selected in the range6.0<α<8.0.
The split velocity components,v⊥
i and v
i
,are de?ned at the nodes
of the triangular grid cells inside the PML region.Here,superscripts ⊥and denote to coincide with the coordinate axes of the local coordinate system related to the node(i.e.y1-and y2-axes).The
split stress components,τ⊥
i j andτ
i j
,are de?ned at the centres of
the grid cells.Here superscripts⊥and mean to coincide with the coordinate axes of the local coordinate system related to the grid cell (i.e.x1-and x2-axes).The velocity and stress?elds are staggered in time,as is common for the?rst-order systems.3I N T E G R A L F O R M U L AT I O N O F T H E
P M L E Q UAT I O N S
3.1Nodes inside the PML region
We obtain the integral formulation of the split?eld PML method using a triangular discretization in accordance with the grid method (Zhang&Liu1999).Node k inside the PML region,as shown in Fig.1,is considered.First,the PML splitting equations with respect to the local coordinate system related to node k,as(y1,y2)in Fig. 2,are used.Integrating both sides of the PML splitting equations, as shown in eq.(1),over the domain enclosed by the dashed-line contour9-10-11-12-13-4-3-9in Fig.1leads to
ρ
?v⊥i
?t d +
ρd v⊥i d =
9?10···3?9
τi1αd s,
ρ
?v i
?t d =
9?10···3?9
τi2βd s,(5)
whereαandβare direction cosines of the outward-directed normals to the contour.Applying the lumped-mass model to eq.(5),that is, lumping the values ofρandρd inside the grid cells to its nodes and setting the values ofρandρd to zero in the inner domain of the grid cell,the surface integrals of the left-hand sides of eq.(5)reduce
to M k(?v⊥
i
/?t)k,Q k(v⊥i)k and M k(?v i/.?t)k.Here,(?v⊥i/.?t)k and
(?v
i
/.?t)k are the?rst-order time derivatives of v⊥i and v i at node
k and(v⊥
i
)k is the value of v⊥
i
at node k.Due to the fact that the dashed-line contour used cuts one-third of the area of each triangular
grid cell,M k and Q k are equal to one-third of the sums of the value
ρd and
ρd d inside each grid cell of the grid cells around node k,respectively.
The discretization of triangular grid cells leads to linear inter-polating functions of the velocity components inside the grid cells. From the point of view of numerical computation,the stresses com-ponents,τi j,become constants within each grid cell.Thus,the right-hand sides of eq.(5)can be rewritten as
9?10···3?9
τi1αd s=
m
n=1
τi1
s n
αd s≈
m
n=1
(τi1)n(b k)n,
9?10···3?9
τi2βd s=
m
n=1
τi2
s n
βd s≈?
m
n=1
(τi2)n(c k)n,
(6) where subscript n denotes the values of the variables in the n th grid cell around node k,m is the number of grid cells around node k and b k and c k are the geometrical coef?cients of the grid cells. Due to the fact that eq.(5)is derived in the local coordinate sys-tem related to node k,as(y1,y2)in Fig.2,b k and c k should be computed in the y1-y2coordinates.For a typical grid cell kpq, with(z p,x p),(z q,x q)and(z k,x k)denoting,respectively,the coor-dinates of nodes p,q and k in the total coordinate system andθdenoting the rotation angle of(y1,y2)to the total coordinate sys-tem(z,x),as illustrated in Fig.2;the exact b k and c k are given by
b k=0.5[(x q?x p)cosθ?(z q?z p)sinθ],
c k=0.5[(z q?z p)cosθ+(x q?x p)sinθ].(7) However,for a smoothe
d arti?cial boundary,w
e haveθ?φ< 0.5 /.r as illustrated in Fig.2.Here,1/.r is the curvature o
f the local arti?cial boundary and is the length of the edge of the grid cell.We can ignore the difference betweenθand
φwhen r>100 (which can be easily satis?ed in building the numerical models).To replaceθwithφin eq.(7),b k and c k become equal to the geometrical
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1032H.Gao and J.Zhang
coef?cients computed in the local coordinate system related to grid
cell kpq ,as (x 1,x 2)in Fig.2.We call the resulting coef?cients the local geometrical coef?cients,which are determined by substituting the coordinates of three nodes of the grid cell in the total coordinate system and the rotation angle of the local coordinate system related to the grid cell against to the total coordinate system (as φin Fig.2)into eq.(7).The other local geometrical coef?cient b p and c p ,etc.,can be obtained by letting k →p →q →k .
We use the local geometrical coef?cients rather than the exact b k and c k in eq.(6).For the same sake (i.e.the difference between the rotation angles can be ignored),we replace the stresses that are de?ned in the local coordinate system related to node k with those de?ned in the local coordinate system related to each grid cell in eq.(6).This is the reason why we use the approximation signs in eq.(6).The proposed approximations lead to a simpler numerical implementation,that is,the same stresses and same local geometrical coef?cients can be used for the integral formulation at the other nodes of the grid cell,such as node p and q .Moreover,the same local geometrical coef?cients can be used to calculate the stresses as discussed in the following.
From eq.(6),we have the integral formulation of the PML split-ting equations using a triangular discretization as follows:M k
?v ⊥i
?t k
+Q k v ⊥i k =m n =1
(τi 1)n (b k )n ,M k ?v
i ?t k
=?m n =1
(τi 2)n (c k )n ,(8)
where the split velocity components are de?ned in the local coor-dinate system related to each node,and the stress components are de?ned in the local coordinate system related to each grid cell.For a typical grid cell pqk ,by constructing the linear interpolating function passing through the nodes of the triangle and then taking ?rst-order spatial derivatives of the function,we have the triangular-grid ?nite-difference operators (e.g.Cook 1974)as
?v l
1≈D 1v l =?1A r =p ,q ,k b r (v l )r ,?v l ?x 2≈D 2v l =1A
r =p ,q ,k
c r (v l )r ,(9)
where A is the area of triangle,subscript r denotes the node of triangle,and coef?cients b r and c r are the same local geometrical coef?cients,as used in eq.(8).Again,we ignore the small difference between the rotation angles of the local coordinate systems related to the grid cell and its nodes.As a result,we can directly substitute the velocity components de?ned in the local coordinate system related to each node,rather than true ones de?ned in the local coordinate system related to the grid cell,into the ?nite-difference operators of eq.(9).We thus have the discretized version of eq.(2)within each grid cell as
?τ⊥i j
n
+(d )n τ⊥i j n
=c i jl 1D 1v l , ?τ i j n
=c i jl 2D 2v l ,(10)where subscript n denotes the value at the centre of the n th grid cell,
the velocities and stresses used are de?ned in the local coordinate systems related to each node and grid cell,respectively.
Eqs (3),(8)and (10)represent the formulations to update the velocities and stresses for the nodes and grid cells inside the PML region.Like the grid method,the approximations in eqs (8)and (10)are second order.Owing to the use of the local geometrical coef?cients,no coordinate transformations arise.
3.2Nodes on the PML interface
When the nodes are on the PML interface (i.e.the arti?cial bound-ary shown in Fig.1),the difference of the coordinate systems has to be considered in deriving the integral formulation of the PML equations.In the following,node g on the PML interface,as shown in Fig.1,is considered.By following the foregoing derivation,inte-grating both sides of the PML splitting equations with respect to the local coordinate system related to node g ,over the domain enclosed by the contour 1-2-3-4-5-g -1in the lower of Fig.1,leads to M g
?v ⊥
i ?t g +Q g v ⊥i g =m 1
n =1(τi 1)n b g n + 5?g ?1τi 1αd s ,M g ?v
i ?t g
=?m 1
n =1
(τi 2)n c g n + 5?g ?1τi 2βd s ,
(11)where M g and Q g are one-third of the sums of the value
ρd and ρd d within each grid cell of the grid cells around node g inside the PML region,respectively.Integrating both sides of eq.(1)with respect to the total coordinate system over the domain enclosed by the contour 5-6-7-8-1-g -5in the upper of Fig.1leads to M
g
?ˉv ⊥
i ?t g =m 2
n =1
(ˉτi 1)n ˉb g n + 1?g ?5ˉτi 1ˉαd s ,M g ?ˉv
i ?t g
=?m 2
n =1
(ˉτi 2)n ˉc
g n + 1?g ?5ˉτi 2ˉβd s ,(12)
where no damping factors are present since they are zero outside the PML region,M
g is one-third of the sum of the value
ρd within each grid cell of the grid cells around node g outside the PML region and the bars above the variables denote that the variables are de?ned in the total coordinate system.
The sums of the two last terms in the right-hand sides of eq.(12)are equal to the total loads acting on interface 1-g -5in the verti-cal and horizontal directions,respectively,F z and F x as shown in Fig.1.The continuities of the stress and velocity components across the PML interface give
?v ⊥
i ?t g =2 k =1
T ik ?ˉv
⊥k ?t
g , ?v i ?t g
=2 k =1T ik ?ˉv
k ?t g
,
5?g ?1
τi 1αd s =?
2 k =1
T ik
1?g ?5
ˉτk 1ˉαd s
,
5?g ?1
τi 2βd s =?
2 k =1
T ik
1?g ?5
ˉτk 2ˉβ
d s
,(13)
where T ik denote the elements of the transformation matrix for
the total coordinate system to the local one.Based on eq.(13),multiplying the transformation matrix to both sides of eq.(12)
and
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then adding them to eq.(11),respectively,lead to
M g +M
g
?v ⊥i
?t g
+Q g v ⊥i g =m 1
n =1(τi 1)n b g n +2 k =1T ik m 2 n =1
(ˉτk 1)n ˉb g
n
,
M g +M
g
?v i
?t g
=?m 1 n =1(τi 2)n c g n ?2 k =1
T ik m 2 n =1
(ˉτk 2)n ˉc
g
n .(14)
Eq.(14)represents the integral formulation of the PML splitting
equations,using triangular grid discretization for the nodes on the PML interface.Following the discussions on M g and M g below eqs
(11)and (12),we know M g +M g and Q g are one-third of the sums of the value ρd and
ρd d within each grid cell of all the grid cells around node g (no matter whether inside and outside the PML region),respectively.Hence,the left-hand sides of the resulting integral formulation are same for the nodes on the PML interface and inside the PML region.The only difference between the integral formulations is that a coordinate transformation is needed for the grid cells outside the PML region.
Eqs (3)and (14)represent the formulations to update the veloc-ities of the nodes on the PML interface.For the nodes outside the PML region,the integral formulation of eq.(1)are the same as ones used in the grid method,which are the sum of the two equations in eq.(8)with Q k related terms and split velocity ?eld vanishing.The numerical implementation becomes simple when incorporating the irregular-grid PML model into the grid method owing to the similar integral formulation for the nodes inside the PML region,on the PML interface and outside the PML region.
4N U M E R I C A L I M P L E M E N TAT I O N S The numerical implementation of the grid method is completed by looping through each grid cell and adding the results obtained to the memory units corresponding to the nodes (Zhang &Liu 1999).Based on the pre-calculated local geometrical coef?cients and elastic stiffness tensors (which are needed only in anisotropic cases),we can update the split stresses and velocities of the nodes and grid cells inside the PML region,following the same numerical procedure as the grid method,by looping through each grid cell inside the PML region.Hence,we can combine the updates of the stresses and velocities inside and outside the PML region by looping through all grid cells together,when incorporating the irregular-grid PML model into the grid method.
There are two differences between the updates inside and outside the PML region.In particular:(1)two results of the right-hand sides of eq.(8)are summed and then added to one memory unit for the grid cells outside the PML region,whereas the two results are added to the separated memory units for the grid cells inside the PML region and (2)the geometrical coef?cients b k and c k are picked up from the different tables,and the split stress ?elds are computed for the grid cells inside the PML region.Special treatments are needed for the grid cells that have nodes on the PML interface but are outside the PML region.That is,the results obtained using those grid cells should ?rst be subjected to coordinate transformation and then added to the corresponding memory units,as expressed in eq.(14),when the related nodes are on the PML interface.
We can update the split velocity ?elds at the nodes on the PML
interface and inside the PML region based on the results of the right-hand sides of eqs (8)and (14)(which have been obtained by looping through all grid cells)using the centre-difference approximations that read
?v ⊥i
?t t +0.5 t
k =1 t v ⊥i t + t k ? v ⊥i t k ,
v ⊥i t +0.5 t k =12
v ⊥i t + t k + v ⊥i t k ,(15)
where the superscript denotes the time.The split stress ?elds inside the PML region can be updated,based on the results of the right-hand sides of eq.(10)(which are obtained using the triangular-grid ?nite-difference operators of eq.9),by using the same centre difference approximations as eq.(15).We update the velocity and stress ?elds outside the PML region using the same but simpler procedure,as discussed in Zhang &Liu (1999),because the damping terms vanish and no split ?elds are needed.We can thus update the velocities from time level t to t + t and stresses from time level t ?0.5 t to t +0.5 t in the whole domain.
The local geometrical coef?cients and the elastic stiffness tensor (which are needed only in anisotropic cases)are computed and stored in a table in advance.We can then pick up them from the table for the recursive computations.Hence,no extra computational costs arise when the irregular-grid PML method is used,as well as when the anisotropy is considered.The same numerical procedure,for the grid cells inside and outside the PML region,leads to a simple computer implementation when incorporating the irregular-grid PML model into the grid method.
The resulting irregular-grid PML model can also be in other numerical schemes which employ the ?rst-order system.For this sake,the mesh composed of triangles should be generated inside the PML absorbing layer and in its neighbourhood.The updates of the splitting stresses and velocities at the nodes inside the PML region and on the PML interface can be completed by looping through those triangular grid cells,as discussed earlier.The stresses and velocities at nodes that are not enclosed by the triangular grid cells need to be updated using the corresponding numerical schemes.Hence,the irregular-grid PML model can also be used to construct ?exible arti?cial boundaries by the other numerical schemes.5N U M E R I C A L E X A M P L E S 5.1Wave propagation in a VTI half-space
This example considers the anisotropic Lamb’s problem.We use the grid method together with the irregular-grid PML model.A semi-circle is taken as an arti?cial boundary and an even-thickness PML absorbing layer is imposed along the boundary.The numerical mesh is composed of homogeneous right triangles with the right edge of 5m inside and outside the PML region.Due to anisotropy and the lower surface wave velocity,we use a little thicker PML absorbing layer that has 15grid cells in thickness with d 0=224.0s ?1.The medium is a transversely isotropic medium with a symmetry axis normal to the surface.Its ?ve modi?ed Lam′e parameters and density are listed in Table 1,where subscript means the variable parallel
Table 1.Elastic constants of the VTI and TTI media.
Medium λ (GPa)μ (GPa)λ⊥(GPa)μ⊥(GPa)η(GPa)ρ(kg m ?3)VTI 6.99 5.32 3.288.99 5.632340TTI
6.71
9.38
7.29
5.55
10.44
2440
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Z -a x i s (m )
Z -a x i s (m )
X-axis (m)Figure 3.Snapshots of the norm of the velocity for a VTI lamb’s problem with and without absorbing boundaries at 0.317and 0.505s propagation times.Owing to the symmetry,only the half for each case is shown.The left-hand sides are the results obtained using a rectangular non-absorbing boundary,and the right-hand sides are the results obtained using a semi-circle PML absorbing layer,represented by two parallel solid lines.Note the events that are gradually decaying inside the PML absorbing layer.
to the symmetry axis.The VTI medium has a quasi-P wave velocity of 2745m s ?1and a quasi-SV wave velocity of 1508m s ?1in the vertical direction.A Ricker-wavelet vertical force is loaded at the surface with a peak frequency of 20Hz.For contrast,we also compute the case where a rectangular non-absorbing boundary is used.Both results are symmetric.For comparison,we incorporate each half of the two results into a ?gure,as shown in Fig.3.
Fig.3shows snapshots of the norm of the velocity, v =
v 21+v 22,at 0.317and 0.505s propagation times for the two cases.By comparing the right-and left-hand sides,we see that the conical and quasi-P waves that propagate through the PML absorbing layer at 0.317s are gradually decaying,whereas all the surface wave,conical wave and quasi-P and quasi-SV waves are well absorbed by the PML layer,without re?ections,at 0.505s.In this example,a staircase approximation is used to model the semi-circle arti?cial boundary in the numerical discretization.This shows that it is not necessary to accurately follow the prescribed arti?cial boundary in generating the mesh inside the PML https://www.doczj.com/doc/821273484.html,pared with the rect-angular boundary,the curved arti?cial boundary used results in a 21per cent reduction in the computational cost and storage require-ments.We also avoid the complexity resulting from the corners,which will occur in the conventional PML model.
5.2Wave propagation in a homogeneous TTI medium We use the grid method,together with the irregular-grid PML model,
to simulate quasi-P and quasi-SV wave propagation in a homoge-neous TTI medium.The TTI medium is a transversely isotropic medium with a symmetry axis of 30?to the vertical direction.Its ?ve modi?ed Lam′e parameters and density are listed in Table 1,
where subscript means the variable parallel to the symmetry axis.The medium has a quasi-P wave velocity of 3231m s ?1and a quasi-SV wave velocity of 1961m s ?1,in the direction parallel to the symmetry axis.We use an elliptical arti?cial boundary.A PML absorbing layer with a thickness of 15grid cells and d 0=549.0s ?1is imposed along the curved arti?cial boundary.The numerical mesh is composed of homogeneous right triangles with the right edge of 3m inside and outside the PML region.A Ricker-wavelet point source,with a peak frequency of 20Hz,is positioned above of the centre,as indicated by cross in Fig.4.As a result,waves will arrive at the upper and lower arti?cial boundaries at the different propagation times.
Fig.4shows snapshot of the norm of the velocity, v =
v 21+v 22,at 0.325and 0.625s propagation times.We see that quasi-P wave is absorbed and quasi-SV wave is partially absorbed in the upper of the ?gure at 0.325s.Quasi-P wave is fully absorbed,and only a part of quasi-SV wave that doesn’t arrive at the PML absorbing layer can be seen,at 0.625s.
5.3Wave propagation in an isotropic medium with curved surface and interface
We use the grid method together with the irregular-grid PML model to simulate elastic wave propagation in a two-layer isotropic medium with curved interface and surface,as shown in Fig.5.The ?rst and second layer media have P -wave velocities of 3231and 3749m s ?1,S -wave velocities of 1960and 2621m s ?1and densities of 2440and 2920kg m ?3,
respectively.A numerical discretization of inho-mogeneous triangular grid cells is used that accurately model the surface and interface topographies.The edge of the triangular grid
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10001500
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X-axis (m)t=0.325 s t=0.625 s
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PML Layer
Figure 4.Snapshots of the norm of the velocity for a point source in a TTI
medium at 0.325and 0.625s propagation times.Cross indicates the point source.An elliptical PML absorbing layer,represented by two parallel solid lines,is used to simulate the unbounded medium.Note the events that are gradually decaying inside the PML absorbing layer.Quasi-P wave is fully absorbed and only a part of quasi-SV wave can be seen in the lower ?gure.
cell is varying around 3m.A semi-ellipse PML absorbing layer,as shown in Fig.5,is imposed along the curved arti?cial boundary.The thickness of the PML layer is 10grid cells with d 0=692.0s ?1in the ?rst-layer and d 0=803.0s ?1in the second-layer.Again,we use a staircase approximation to simulate the curved arti?cial boundary in the numerical discretization.
A Ricker-wavelet pressure source with a peak frequency of 40Hz is positioned 130m below the surface,as indicated by cross in Fig.5.Fig.5shows snapshots of the vertical component of the velocity at 0.202and 0.307s propagation times.By contrast,Fig.6shows the same snapshots at the same times for the same model as Fig.5,when a rectangular non-absorbing boundary is used.The re?ections and refractions from the curved surface and interface are well modelled owing to the accurate descriptions of the topographies in the numerical discretization.By comparing Figs 5and 6,we see that the direct and transmitted P -waves,as well as converted
S -wave,that arrive at the PML absorbing layer are well absorbed at 0.202s.The re?ected and transmitted S -waves and sur-face and interface waves that arrive at the PML absorbing layer are absorbed without re?ections at 0.307s
in Fig.5,yet a lot of re?ected
Z -a x i s (m )
X-axis (m)
Z -a x i s (m )
Figure 5.Snapshots of the vertical component of the velocity for a two-layer,isotropic,elastic model at 0.202and 0.307s propagation times.The curved surface and interface are represented by solid lines.A semi-elliptical PML absorbing layer,represented by two parallel solid lines,is used to simulate the half-in?nite medium.Cross indicates the pressure source.The re?ections and refractions from the curved surface and interface are well modelled.No re?ections resulting from the arti?cial boundary can be seen.
waves,resulting from the arti?cial boundaries,are seen in the snap-shots of https://www.doczj.com/doc/821273484.html,pared with the rectangular arti?cial boundary
used in Fig.6,the semi-ellipse arti?cial boundary used in Fig.5results in a 22per cent reduction of the discretized nodes.This means a 22per cent reduction in computational cost and storage requirements.
6C O N C L U S I O N S
We have implemented the PML absorbing boundary condition on an arbitrary geometrical boundary,using a triangular discretization,which results in an irregular-grid PML method that has the abil-ity to absorb incident waves in arbitrary directions.The irregular-grid PML method is developed,following the grid method,which can absorb both body and surface waves in elastic isotropic and anisotropic media.The irregular-grid PML method can also be in other numerical schemes that employ the
?rst-order formulation to simulate unbounded media.The method enables the use of fewer nodes since arti?cial absorbing boundaries can be implemented along smooth curved interfaces.The irregular-grid PML method is simple to implement in conjunction with the grid method,and no extra computational effort is introduced for anisotropic media
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500
750
Z -a x i s (m )
0250
500
7501000
250
500
750
Z -a x i s (m )
0250
500750
1000
X-axis (m)t=0.202 s
Surface
t=0.307 s
Surface
Figure 6.The same snapshots as Fig.5when a rectangular non-absorbing boundary is used.The white-line semi-ellipse denotes the PML interface used in Fig.5.
compared with isotropic media.No additional computational cost is required for using the irregular-grid PML method,in contrast to standard PML implementations,and no special treatment of corners is necessary.Numerical experiments demonstrate its desired effects and a signi?cant reduction of the discretized nodes.A C K N O W L E D G M E N T S
Thanks to the National Natural Science Fund of China (under grant 40474046),which supported this work.This work was also sup-ported by the National High-tech R&D Program of China (under
grant 2006AA09A102)and National Basic Research Program of
China (under grant 2005CB422104).
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如何写先进个人事迹 篇一：如何写先进事迹材料 如何写先进事迹材料 一般有两种情况：一是先进个人，如先进工作者、优秀党员、劳动模范等；一是先进集体或先进单位，如先进党支部、先进车间或科室，抗洪抢险先进集体等。无论是先进个人还是先进集体，他们的先进事迹，内容各不相同，因此要整理材料，不可能固定一个模式。一般来说，可大体从以下方面进行整理。 (1)要拟定恰当的标题。先进事迹材料的标题，有两部分内容必不可少，一是要写明先进个人姓名和先进集体的名称，使人一眼便看出是哪个人或哪个集体、哪个单位的先进事迹。二是要概括标明先进事迹的主要内容或材料的用途。例如《王鬃同志端正党风的先进事迹》、《关于评选张鬃同志为全国新长征突击手的材料》、《关于评选鬃处党支部为省直机关先进党支部的材料》等。 (2)正文。正文的开头，要写明先进个人的简要情况，包括：姓名、性别、年龄、工作单位、职务、是否党团员等。此外，还要写明有关单位准备授予他(她)什么荣誉称号，或给予哪种形式的奖励。对先进集体、先进单位，要根据其先进事迹的主要内容，寥寥数语即应写明，不须用更多的文字。 然后，要写先进人物或先进集体的主要事迹。这部分内容是全篇材料
的主体，要下功夫写好，关键是要写得既具体，又不繁琐；既概括，又不抽象；既生动形象，又很实在。总之，就是要写得很有说服力，让人一看便可得出够得上先进的结论。比如，写一位端正党风先进人物的事迹材料，就应当着重写这位同志在发扬党的优良传统和作风方面都有哪些突出的先进事迹，在同不正之风作斗争中有哪些突出的表现。又如，写一位搞改革的先进人物的事迹材料，就应当着力写这位同志是从哪些方面进行改革的，已经取得了哪些突出的成果，特别是改革前后的．经济效益或社会效益都有了哪些明显的变化。在写这些先进事迹时，无论是先进个人还是先进集体的，都应选取那些具有代表性的具体事实来说明。必要时还可运用一些数字，以增强先进事迹材料的说服力。 为了使先进事迹的内容眉目清晰、更加条理化，在文字表述上还可分成若干自然段来写，特别是对那些涉及较多方面的先进事迹材料，采取这种写法尤为必要。如果将各方面内容材料都混在一起，是不易写明的。在分段写时，最好在每段之前根据内容标出小标题，或以明确的观点加以概括，使标题或观点与内容浑然一体。 最后，是先进事迹材料的署名。一般说，整理先进个人和先进集体的材料，都是以本级组织或上级组织的名义；是代表组织意见的。因此，材料整理完后，应经有关领导同志审定，以相应一级组织正式署名上报。这类材料不宜以个人名义署名。 写作典型经验材料-般包括以下几部分： (1)标题。有多种写法，通常是把典型经验高度集中地概括出来，一
How to manage time Time treats everyone fairly that we all have 24 hours per day. Some of us are capable to make good use of time while some find it hard to do so. Knowing how to manage them is essential in our life. Take myself as an example. When I was still a senior high student, I was fully occupied with my studies. Therefore, I hardly had spare time to have fun or develop my hobbies. But things were changed after I entered university. I got more free time than ever before. But ironically, I found it difficult to adjust this kind of brand-new school life and there was no such thing called time management on my mind. It was not until the second year that I realized I had wasted my whole year doing nothing. I could have taken up a Spanish course. I could have read ten books about the stories of successful people. I could have applied for a part-time job to earn some working experiences. B ut I didn’t spend my time on any of them. I felt guilty whenever I looked back to the moments that I just sat around doing nothing. It’s said that better late than never. At least I had the consciousness that I should stop wasting my time. Making up my mind is the first step for me to learn to manage my time. Next, I wrote a timetable, setting some targets that I had to finish each day. For instance, on Monday, I must read two pieces of news and review all the lessons that I have learnt on that day. By the way, the daily plan that I made was flexible. If there’s something unexpected that I had to finish first, I would reduce the time for resting or delay my target to the next day. Also, I would try to achieve those targets ahead of time that I planed so that I could reserve some more time to relax or do something out of my plan. At the beginning, it’s kind of difficult to s tick to the plan. But as time went by, having a plan for time in advance became a part of my life. At the same time, I gradually became a well-organized person. Now I’ve grasped the time management skill and I’m able to use my time efficiently.
英语演讲稿：未来的工作 这篇《英语演讲稿范文：未来的工作》，是特地，希望对大家有所帮助！ 热门演讲推荐：竞聘演讲稿 | 国旗下演讲稿 | 英语演讲稿 | 师德师风演讲稿 | 年会主持词 | 领导致辞 everybody good afternoon:. first of all thank the teacher gave me a story in my own future ideal job. everyone has a dream job. my dream is to bee a boss, own a pany. in order to achieve my dreams, i need to find a good job, to accumulate some experience and wealth, it is the necessary things of course, in the school good achievement and rich knowledge is also very important. good achievement and rich experience can let me work to make the right choice, have more opportunities and achievements. at the same time, munication is very important, because it determines whether my pany has a good future development. so i need to exercise their municative ability. i need to use all of the free time to learn
世界经典哲学类书籍 哲学，是理论化、系统化的世界观，是自然知识、社会知识、思维知识的概括和总结,是世界观和方法论的统一。是社会意识的具体存在和表现形式，是以追求世界的本源、本质、共性或绝对、终极的形而上者为形式，以确立哲学世界观和方法论为内容的社会科学。 《性心理学》 《作为意志和表象的世界》 《理想国》 《西方哲学史》 《自然哲学的数学原理》 《权力意志》 《新工具》 《纯粹理性批判》《文明论概略》 《劝学篇》 《伦理学》 《耶稣传》 《时间简史》 《逻辑哲学论》 《精神现象学》 《物性论》 《感觉的分析》 《精神分析引论》《基督何许人也——基督抹煞论》 《科学的社会功能》《人有人的用处》《科学史》 《人类理智新论》《逻辑学》 《哲学研究》 《新系统及其说明》《道德情操论》 《实践理性批判》《美学》 《判断力批判》 《基督教的本质》《薄伽梵歌》 《伦理学中的形式主义与质料的价值伦理学》《物种起源》 《物理学》《人类的由来》 《人性论》 《人是机器》 《法哲学原理》 《狄德罗哲学选集》 《野性的思维》 《哲学史教程》 《科学与近代世界》 《人类的知识》 《精神分析引论新编》 《自然宗教对话录》 《基督教并不神秘》 《科学中华而不实的 作风》 《一年有半，续一年有 半》 《时间与自由意志》 《哲学辞典》 《历史理性批判文集》 《苏鲁支语录》 《文化科学和自然科 学》 《十六、十七世纪科 学、技术和哲学史》 《科学哲学的兴起》 《灵魂论及其他》 《斯宾诺莎书信集》 《实验心理学史》 《最后的沉思》 《纯粹现象学通论》 《近代心理学历史导 引》 《佛教逻辑》 《神圣人生论》 《逻辑与知识》 《论原因、本原与太 一》 《形而上学导论》 《诗学》 《路标》 《心的概念》 《计算机与人脑》 《十七世纪英格兰的 科学、技术与社会》 《卡布斯教诲录》 《薄伽梵歌论》 《尼各马可伦理学》 《论老年论友谊论责 任》 《实用主义》 《我的哲学的发展》 《拓扑心理学原理》 《在通向语言的途中》 《科学社会学》 《埃克哈特大师文集》 《逻辑大全》 《简论上帝、人及其心 灵健康》 《宗教的本质》 《论灵魂》 《科学的价值》 《内时间意识现象学》 《艺术即经验》 《宗教与科学》 《感觉与可感物》 《行为的结构》 《真理与方法》 《阿维斯塔》 《善的研究》 《人类知识原理》 《伦理学体系》 《科学与方法》 《第一哲学（上下卷）》 《物理学理论的目的 与结构》 《思维方式》 《发生认识论原理》 《爱因斯坦文集》 《伦理学的两个基本问题》 《数理哲学导论 《耶稣传（第一、二卷）》 《美学史》 《原始思维》 《面向思的事情》 《普通认识论》 《莱布尼茨与克拉克论战 书信集》 《对莱布尼茨哲学的批评 性解释》 《物理学和哲学》 《尼采（上下卷）》 《思想录》 《道德原则研究》 《自我的超越性》 《实验医学研究导论》 《巴曼尼得斯篇》 《人类理解论》 《笛卡尔哲学原理》 《人生的亲证》 《认识与谬误》 《哲学史讲演录》 《圣教论》 《哲学作为严格的科学》 《人类知识起源论》 《回忆苏格拉底》 《心的分析》 《任何一种能够作为科学 出现的未来形而上学导论》 《科学与假设》 《宗教经验之种种》 《声音与现象》 《苏格拉底的申辩》 《论个人在历史上的作用 问题》 《论有学识的无知》 《保卫马克思》 《艺术的起源》
小学生个人读书事迹简介怎么写800字 书,是人类进步的阶梯,苏联作家高尔基的一句话道出了书的重要。书可谓是众多名人的“宠儿”。历来,名人说出关于书的名言数不胜数。今天小编在这给大家整理了小学生个人读书事迹,接下来随着小编一起来看看吧! 小学生个人读书事迹1 “万般皆下品,惟有读书高”、“书中自有颜如玉,书中自有黄金屋”,古往今来,读书的好处为人们所重视,有人“学而优则仕”,有人“满腹经纶”走上“传道授业解惑也”的道路……但是,从长远的角度看,笔者认为读书的好处在于增加了我们做事的成功率,改善了生活的质量。 三国时期的大将吕蒙,行伍出身,不重视文化的学习,行文时,常常要他人捉刀。经过主君孙权的劝导,吕蒙懂得了读书的重要性,从此手不释卷,成为了一代儒将,连东吴的智囊鲁肃都对他“刮目相待”。后来的事实证明,荆州之战的胜利,擒获“武圣”关羽,离不开吕蒙的“运筹帷幄,决胜千里”,而他的韬略离不开平时的读书。由此可见,一个人行事的成功率高低,与他的对读书,对知识的重视程度是密切相关的。 的物理学家牛顿曾近说过,“如果我比别人看得更远,那是因为我站在巨人的肩上”,鲜花和掌声面前,一代伟人没有迷失方向,自始至终对读书保持着热枕。牛顿的话语告诉我们,渊博的知识能让我们站在更高、更理性的角度来看问题,从而少犯错误,少走弯路。
读书的好处是显而易见的,但是,在社会发展日新月异的今天,依然不乏对读书,对知识缺乏认知的人,《今日说法》中我们反复看到农民工没有和用人单位签订劳动合同,最终讨薪无果;屠户不知道往牛肉里掺“巴西疯牛肉”是犯法的;某父母坚持“棍棒底下出孝子”,结果伤害了孩子的身心,也将自己送进了班房……对书本,对知识的零解读让他们付出了惨痛的代价,当他们奔波在讨薪的路上,当他们面对高墙电网时,幸福,从何谈起?高质量的生活,从何谈起? 读书,让我们体会到“锄禾日当午,汗滴禾下土”的艰辛;读书,让我们感知到“四海无闲田,农夫犹饿死”的无奈;读书,让我们感悟到“为报倾城随太守,西北望射天狼”的豪情壮志。 读书的好处在于提高了生活的质量,它填补了我们人生中的空白,让我们不至于在大好的年华里无所事事,从书本中,我们学会提炼出有用的信息,汲取成长所需的营养。所以,我们要认真读书,充分认识到读书对改善生活的重要意义,只有这样,才是一种负责任的生活态度。 小学生个人读书事迹2 所谓读一本好书就是交一个良师益友,但我认为读一本好书就是一次大冒险,大探究。一次体会书的过程,真的很有意思,咯咯的笑声,总是从书香里散发;沉思的目光也总是从书本里透露。是书给了我启示,是书填补了我无聊的夜空,也是书带我遨游整个古今中外。所以人活着就不能没有书,只要爱书你就是一个爱生活的人,只要爱书你就是一个大写的人,只要爱书你就是一个懂得珍惜与否的人。可真所谓
关于坚持的英语演讲稿 Results are not important, but they can persist for many years as a commemoration of. Many years ago, as a result of habits and overeating formed one of obesity, as well as indicators of overall physical disorders, so that affects my work and life. In friends to encourage and supervise, the participated in the team Now considered to have been more than three years, neither the fine rain, regardless of winter heat, a day out with 5:00 time. The beginning, have been discouraged, suffering, and disappointment, but in the end of the urging of friends, to re-get up, stand on the playground. 成绩并不重要，但可以作为坚持多年晨跑的一个纪念。多年前，由于庸懒习惯和暴饮暴食，形成了一身的肥胖，以及体检指标的全盘失常，以致于影响到了我的工作和生活。在好友的鼓励和督促下，参加了晨跑队伍。现在算来，已经三年多了，无论天晴下雨，不管寒冬酷暑，每天五点准时起来出门晨跑。开始时，也曾气馁过、痛苦过、失望过，但最后都在好友们的催促下，重新爬起来，站到了操场上。 In fact, I did not build big, nor strong muscles, not a sport-born people. Over the past few years to adhere to it, because I have a team behind, the strength of a strongteam here, very grateful to our team, for a long time, we encourage each other, and with sweat, enjoying common health happy. For example, Friends of the several run in order to maintain order and unable to attend the 10，000 meters race, and they are always concerned about the brothers and promptly inform the place and time, gives us confidence and courage. At the same time, also came on their own inner desire and pursuit for a good health, who wrote many of their own log in order to refuel for their own, and inspiring. 其实我没有高大身材，也没健壮肌肉，天生不属于运动型的人。几年来能够坚持下来，因为我的背后有一个团队，有着强大团队的力量，在这里，非常感谢我们的晨跑队，长期以来，我们相互鼓励着，一起流汗，共同享受着健康带来的快
1.How to build a business that lasts100years 0:11Imagine that you are a product designer.And you've designed a product,a new type of product,called the human immune system.You're pitching this product to a skeptical,strictly no-nonsense manager.Let's call him Bob.I think we all know at least one Bob,right?How would that go? 0:34Bob,I've got this incredible idea for a completely new type of personal health product.It's called the human immune system.I can see from your face that you're having some problems with this.Don't worry.I know it's very complicated.I don't want to take you through the gory details,I just want to tell you about some of the amazing features of this product.First of all,it cleverly uses redundancy by having millions of copies of each component--leukocytes,white blood cells--before they're actually needed,to create a massive buffer against the unexpected.And it cleverly leverages diversity by having not just leukocytes but B cells,T cells,natural killer cells,antibodies.The components don't really matter.The point is that together,this diversity of different approaches can cope with more or less anything that evolution has been able to throw up.And the design is completely modular.You have the surface barrier of the human skin,you have the very rapidly reacting innate immune system and then you have the highly targeted adaptive immune system.The point is,that if one system fails,another can take over,creating a virtually foolproof system. 1:54I can see I'm losing you,Bob,but stay with me,because here is the really killer feature.The product is completely adaptive.It's able to actually develop targeted antibodies to threats that it's never even met before.It actually also does this with incredible prudence,detecting and reacting to every tiny threat,and furthermore, remembering every previous threat,in case they are ever encountered again.What I'm pitching you today is actually not a stand-alone product.The product is embedded in the larger system of the human body,and it works in complete harmony with that system,to create this unprecedented level of biological protection.So Bob,just tell me honestly,what do you think of my product? 2:47And Bob may say something like,I sincerely appreciate the effort and passion that have gone into your presentation,blah blah blah-- 2:56(Laughter) 2:58But honestly,it's total nonsense.You seem to be saying that the key selling points of your product are that it is inefficient and complex.Didn't they teach you 80-20?And furthermore,you're saying that this product is siloed.It overreacts, makes things up as it goes along and is actually designed for somebody else's benefit. I'm sorry to break it to you,but I don't think this one is a winner.
关于工作的优秀英语演讲稿 Different people have various ambitions. Some want to be engineers or doctors in the future. Some want to be scientists or businessmen. Still some wish to be teachers or lawers when they grow up in the days to come. Unlike other people, I prefer to be a farmer. However, it is not easy to be a farmer for Iwill be looked upon by others. Anyway,what I am trying to do is to make great contributions to agriculture. It is well known that farming is the basic of the country. Above all, farming is not only a challenge but also a good opportunity for the young. We can also make a big profit by growing vegetables and food in a scientific way. Besides we can apply what we have learned in school to farming. Thus our countryside will become more and more properous. I believe that any man with knowledge can do whatever they can so long as this job can meet his or her interest. All the working position can provide him with a good chance to become a talent. 1 ————来源网络整理，仅供供参考
个人先进事迹简介 01 在思想政治方面,xxxx同学积极向上,热爱祖国、热爱中国共产党,拥护中国共产党的领导.利用课余时间和党课机会认真学习政治理论,积极向党组织靠拢. 在学习上,xxxx同学认为只有把学习成绩确实提高才能为将来的实践打下扎实的基础,成为社会有用人才.学习努力、成绩优良. 在生活中,善于与人沟通,乐观向上,乐于助人.有健全的人格意识和良好的心理素质和从容、坦诚、乐观、快乐的生活态度,乐于帮助身边的同学,受到师生的好评. 02 xxx同学认真学习政治理论,积极上进,在校期间获得原院级三好生,和校级三好生,优秀团员称号,并获得三等奖学金. 在学习上遇到不理解的地方也常常向老师请教,还勇于向老师提出质疑.在完成自己学业的同时,能主动帮助其他同学解决学习上的难题,和其他同学共同探讨,共同进步. 在社会实践方面,xxxx同学参与了中国儿童文学精品“悦”读书系,插画绘制工作,xxxx同学在班中担任宣传委员,工作积极主动,认真负责,有较强的组织能力.能够在老师、班主任的指导下独立完成学院、班级布置的各项工作. 03 xxx同学在政治思想方面积极进取,严格要求自己.在学习方面刻苦努力,不断钻研,学习成绩优异,连续两年荣获国家励志奖学金；作
为一名学生干部,她总是充满激情的迎接并完成各项工作,荣获优秀团干部称号.在社会实践和志愿者活动中起到模范带头作用. 04 xxxx同学在思想方面,积极要求进步,为人诚实,尊敬师长.严格 要求自己.在大一期间就积极参加了党课初、高级班的学习,拥护中国共产党的领导,并积极向党组织靠拢. 在工作上,作为班中的学习委员,对待工作兢兢业业、尽职尽责 的完成班集体的各项工作任务.并在班级和系里能够起骨干带头作用.热心为同学服务,工作责任心强. 在学习上,学习目的明确、态度端正、刻苦努力,连续两学年在 班级的综合测评排名中获得第1.并荣获院级二等奖学金、三好生、优秀班干部、优秀团员等奖项. 在社会实践方面,积极参加学校和班级组织的各项政治活动,并 在志愿者活动中起到模范带头作用.积极锻炼身体.能够处理好学习与工作的关系,乐于助人,团结班中每一位同学,谦虚好学,受到师生的好评. 05 在思想方面,xxxx同学积极向上,热爱祖国、热爱中国共产党,拥护中国共产党的领导.作为一名共产党员时刻起到积极的带头作用,利用课余时间和党课机会认真学习政治理论. 在工作上,作为班中的团支部书记,xxxx同学积极策划组织各类 团活动,具有良好的组织能力. 在学习上,xxxx同学学习努力、成绩优良、并热心帮助在学习上有困难的同学,连续两年获得二等奖学金. 在生活中,善于与人沟通,乐观向上,乐于助人.有健全的人格意 识和良好的心理素质.
尊敬的领导，老师，亲爱的同学们， 大家好！我是5班的梁浩东。今天早上我坐车来学校的路上，我仔细观察了路上形形色色的人，有开着小车衣着精致的叔叔阿姨，有市场带着倦容的卖各种早点的阿姨，还有偶尔穿梭于人群中衣衫褴褛的乞丐。于是我问自己，十几年后我会成为怎样的自己，想成为社会成功人士还是碌碌无为的人呢，答案肯定是前者。那么十几年后我怎样才能如愿以偿呢，成为一个受人尊重，有价值的人呢？正如我今天演讲的题目是：自主管理。 大家都知道爱玩是我们孩子的天性，学习也是我们的责任和义务。要怎样处理好这些矛盾，提高自主管理呢？ 首先，我们要有小主人翁思想，自己做自己的主人，要认识到我们学习，生活这一切都是我们自己走自己的人生路，并不是为了报答父母，更不是为了敷衍老师。 我认为自主管理又可以理解为自我管理，在学习和生活中无处不在，比如通过老师，小组长来管理约束行为和同学们对自身行为的管理都属于自我管理。比如我们到一个旅游景点，看到一块大石头，有的同学特别兴奋，会想在上面刻上：某某某到此一游话。这时你就需要自我管理，你需要提醒自己，这样做会破坏景点，而且是一种素质低下的表现。你设想一下，如果别人家小孩去你家墙上乱涂乱画，你是何种感受。同样我们把自主管理放到学习上，在我们想偷懒，想逃避，想放弃的时候，我们可以通过自主管理来避免这些，通过他人或者自己的力量来完成。例如我会制定作息时间计划表，里面包括学习，运动，玩耍等内容的完成时间。那些学校学习尖子，他们学习好是智商高于我们吗，其实不然，在我所了解的哪些优秀的学霸传授经验里，就提到要能够自我管理，规范好学习时间的分分秒秒，只有辛勤的付出，才能取得优异成绩。 在现实生活中，无数成功人士告诉我们自主管理的重要性。十几年后我想成为一位优秀的，为国家多做贡献的人。亲爱的同学们，你们们？让我们从现在开始重视和执行自主管理，十几年后成为那个你想成为的人。 谢谢大家！
关于工作的英语演讲稿 【篇一：关于工作的英语演讲稿】 关于工作的英语演讲稿 different people have various ambitions. some want to be engineers or doctors in the future. some want to be scientists or businessmen. still some wish to be teachers or lawers when they grow up in the days to come. unlike other people, i prefer to be a farmer. however, it is not easy to be a farmer for iwill be looked upon by others. anyway,what i am trying to do is to make great contributions to agriculture. it is well known that farming is the basic of the country. above all, farming is not only a challenge but also a good opportunity for the young. we can also make a big profit by growing vegetables and food in a scientific way. besides we can apply what we have learned in school to farming. thus our countryside will become more and more properous. i believe that any man with knowledge can do whatever they can so long as this job can meet his or her interest. all the working position can provide him with a good chance to become a talent. 【篇二：关于责任感的英语演讲稿】 im grateful that ive been given this opportunity to stand here as a spokesman. facing all of you on the stage, i have the exciting feeling of participating in this speech competition. the topic today is what we cannot afford to lose. if you ask me this question, i must tell you that i think the answer is a word---- responsibility. in my elementary years, there was a little girl in the class who worked very hard, however she could never do satisfactorily in her lessons. the teacher asked me to help her, and it was obvious that she expected a lot from me. but as a young boy, i was so restless and thoughtless, i always tried to get more time to play and enjoy myself. so she was always slighted over by me. one day before the final exam, she came up to me and said, could you please explain this to me? i can not understand it. i
第五章老年社会工作 第一节老年社会工作概述 第二节老年社会工作的主要内容 第三节老年社会工作的主要方法 第一节老年社会工作概述 一、老年人与老年期 （一）年龄界定 生理年龄：生理指标与功能确定 心理年龄：心理活动程度确定 社会年龄：与他人交往的角色确定 （二）老年期的划分 低龄老年人：60-69岁 中龄老年人：70-79 高龄老年人：80岁以上 （三）划分的意义 1.三种年龄：不能仅凭日历年龄判断服务需求，而要关注不同个体在生理、心理与社会方面的差异。 2.三个时期：关注老年同期群的共性需要。 二、老年期的特点 （一）生理变化 1.生理变化的特点：九大生理系统老化 2.对开展老年社会工作的影响 （1）要特别关注老年人的身体健康状况； （2）处理好隐私的健康问题，如大小便； （3）帮助机构和家庭策划环境的调整。 （二）心理变化 1.智力、人格、记忆力的变化 智力：结晶智力强，但处理问题速度下降 人格：总结自己生命的意义 记忆力：记忆速度下降，动机决定是否学习 2.对开展老年社工的影响 （1）提供机会但尊重选择 （2）所有事放慢节奏 （3）关注身体健康对心理功能的重要性 （三）社会生活方面的变化 1.对老年社会生活变化的理论解释 （1）角色理论：丧失象征中年的社会角色 （2）活动理论：生活满足感与活动有积极联系 （3）撤离理论：接受减少与社会的交往 （4）延续理论：不能割裂看待老年阶段 （5）社会建构理论：老年是一个独特的个人过程 （6）现代化理论：现代化使老年人地位下降
2.理论在社会工作中的应用 （1）注意角色转变的重大生活事件 （2）注意老年个体的差异性，尊重其对生活意义的不同理解 （3）注意社会隔离可能对老年人造成的伤害 （4）改变总有可能 （5）关注社会变迁对老年人的影响，推动社会政策的调整 三、老年人的需要及问题 （一）老年人的需要 1.健康维护 2.经济保障 3.就业休闲 4.社会参与 5.婚姻家庭 6.居家安全 7.后事安排 8.一条龙照顾 （二）老年人的问题 1.慢性病问题与医疗问题 2.家庭照顾问题 3.宜居环境问题 4.代际隔阂问题 5.社会隔离问题 四、老年社会工作 （一）老年社会工作的对象 1.老年人自身：空巢、残疾、高龄老人，也包括健康老人 2.老年人周围的人：家庭成员、亲属、朋友、邻居等 3.宏观系统：单位与服务组织 （二）老年社会工作的目的 根本目标：老有所养、老有所医、老有所教、老有所学、老有所为、老有所乐 （三）老年社会工作的作用 1.个体层面：维持日常生活、获得社会支持 2.宏观层面：参与制定有关老年人的服务方案与政策 五、老年社会工作的特点 （一）老年歧视等社会价值观会影响社会工作者的态度与行为 （二）反移情是社会工作者的重要课题 （三）社会工作者要善于运用督导机制 （四）需要多学科合作 第二节老年社会工作的主要内容 一、身体健康方面的服务 二、认知与情绪问题的处理 三、精神问题的解决 四、社会支持网络的建立 五、老年人特殊问题的处理 一、身体健康方面的服务
Dear teacher and colleagues: my topic is on “spare time”. It is a huge blessing that we can work 996. Jack Ma said at an Ali's internal communication activity, That means we should work at 9am to 9pm, 6 days a week .I question the entire premise of this piece. but I'm always interested in hearing what successful and especially rich people come up with time .So I finally found out Jack Ma also had said :”i f you don’t put out more time and energy than others ,how can you achieve the success you want? If you do not do 996 when you are young ,when will you ?”I quite agree with the idea that young people should fight for success .But there are a lot of survival activities to do in a day ,I want to focus on how much time they take from us and what can we do with the rest of the time. As all we known ,There are 168 hours in a week .We sleep roughly seven-and-a-half and eight hours a day .so around 56 hours a week . maybe it is slightly different for someone . We do our personal things like eating and bathing and maybe looking after kids -about three hours a day .so around 21 hours a week .And if you are working a full time job ,so 40 hours a week , Oh! Maybe it is impossible for us at