Choice of the k-point mesh For a periodic system, integrals in real space over the (infinitely extended) system are replaced by integrals over the (finite) first Brillouin zone in reciprocal space, by virtue of Bloch's theorem. In fhi98md , such integrals are performed by summing the function values of the integrand (for instance: the charge density) at a finite number of points in the Brillouin zone, called the k -point mesh. Choosing a sufficiently dense mesh of integration points is crucial for the convergence of the results, and is therefore one of the major objectives when performing convergence tests. Here it should be noted that there is no variational principle governing the convergence with respect to the k -point mesh. This means that the total energy does not necessarily show a monotonous behavior when the density of the k -point mesh is increased. Monkhorst-Pack mesh In order to facilitate the choice of k -points, the fhi98md package offers the possibility to choose k -points according to the scheme proposed by Monkhorst and Pack . This essentially means that the sampling k -points are distributed homogeneously in the Brillouin zone, with rows or columns of k -points running parallel to the reciprocal lattice vectors that span the Brillouin zone. This option is enabled by setting t_kpoint_rel to .true., which should be the default for total energy calculations. The density of k -points can be chosen by the folding parameters i_facs(1..3) . With these parameters, you specify to cover the entire Brillouin zone by a mesh of points. The details of this procedure are as follows: In fhi98md , the Brillouin zone is spanned by the reciprocal lattice vectors and attached to the origin of the coordinate system. According to this definition, one corner of the Brillouin zone rests in the origin. The entire Brillouin zone is tiled by small polyhedra of the same shape as the Brillouin zone itself. The parameters specify how many tiles you have along the and direction. In each tile, you specify k -points supplied in form of a list. The coordinates of these k -points are given relative to the spanning vectors of a small polyhedron or 'tile', i.e. The supplied k -point pattern is then spread out over the whole Brillouin zone by translations of the tile. In other words, the k -point pattern of a smaller Brillouin zone (which would correspond to a larger unit cell in real space) is 'unfolded' in the Brillouin zone of your system under study. Normally, the pattern consists only of a single point in the center of the tile, leading to the conventional Monkhorst-Pack k -point sets. k -point set for a bulk calculation A k -point set typically used in a bulk calculation could look like Parameter Value nkpt 1 number of k -points supplied xk(1..3),wkpt 0.5 0.5 0.5 1.0 k -points and weights i_facs(1..3) 4 4 4 k -point folding factors t_kpoint_rel .true. frame of reference for k -points xk(1..3) k -point set for a slab calculation For a surface calculation with the z -axis as the surface normal, you want the k -point mesh to lie in the xy -plane. There is no dispersion of the electronic band structure of the slab in z -direction to sample. If there would be, it just means that the repeated slabs are not decoupled as they should be, i.e. the vacuum region was chosen too thin. Therefore the z -coordinate of all k -points should be zero. The input typically looks like Parameter Value nkpt 1 number of k -points supplied xk(1..3) 0.5 0.5 0.0 1.0 k -points and weights i_facs(1..3) 8 8 1 k -point folding factors t_kpoint_rel .true. frame of reference for k -points xk(1..3) Figure: 2D Brillouin zone of a surface with cubic symmetry with a Monkhorst-Pack grid. The thin square indicates the conventional first Brillouin zone, the thick square marks the Brillouin zone as realized in the fhi98md code. The location of one special k -point (out of 64) within its tile is marked by the cross. Note: We recommend to use even numbers for the folding parameters. As a general rule, one should avoid using high symmetry points in the Brillouin zone as sampling points, because this would result in an inferior sampling quality at comparable numerical effort, compared to a similar number of off-axis k -points. Conventionally (in contrast to our above definition), the Brillouin zone is chosen to have the origin in its center. For odd numbers of the folding parameters and the setting '0.5 0.5 ...', some of the 'unfolded' k -points will fall on the zone boundary of the conventional Brillouin zone, which is often a symmetry plane. Likewise, the k -point set may contain a periodic image of the -point. This is normally undesirable. The concept of equivalent k -points Usually one is not interested in the total energies themselves, but in comparing different structures, i.e. accurate energy differences are required. If the two structures have the same unit cell, the comparison should always be done using the same k -point set, so that possible errors from a non-converged k -point sampling tend to cancel out. A similar strategy can also be applied when comparing structures with different unit cells. We allude to this concept here as 'equivalent k -point sampling': The structure with a large unit cell has a smaller Brillouin zone associated with it. The k -points sampling along this smaller Brillouin zone should be chosen as a subset of the k -point mesh in the larger Brillouin zone, such that the position of the k -points in this subset, expressed in Cartesian coordinates in reciprocal space, agree in both calculations (to check whether this is actually the case, inspect the list of k -points appearing in the inp.ini file). This goal can be achieved in a simple way by choosing appropriate i_facs . As an example, imagine you want to compare two slab calculations, one with a , the other with a unit cell. In this case, use Parameter Value i_facs(1..3) 4 8 1 k -point folding factors in the first case, and Parameter Value i_facs(1..3) 2 4 1 k -point folding factors in the second case, leaving the other parameters unchanged. Note: is orthogonal to the real lattice vectors and . If is the long edge of your real space unit cell, spans the short edge of your Brillouin zone. Therefore, the k -point sampling mesh has fewer points in the direction and more points in the direction in the above example. Chadi-Cohen mesh Another convention for choosing a k -point mesh has been proposed by Chadi and Cohen , and has been applied to slab calculations by Cunningham . In contrast to Monkhorst and Pack, the refinement of the k -point mesh to obtain higher sampling density is based on a recursive scheme. However, for cubic symmetry, the outcome of this algorithm can also be interpreted as a special Monkhorst-Pack grid. To discuss differences between the schemes, we resort to the simple case of a two-dimensional mesh for a slab calculation. An example where Cunningham's scheme leads to results different from Monkhorst-Pack are systems with hexagonal symmetry, e.g. slabs with (111) surface of fcc-metals. Here, Cunningham proposes to use a hexagonal k -point mesh. To realize such meshes in the fhi98md code, one has to provide explicitly a list of k -points forming the desired pattern. Cunningham's 6-point pattern in the full Brillouin zone can be obtained as follows Parameter Value nkpt 6 number of k -points xk(1..3),wkpt 0.33333 0.00000 0.0 0.16667 k -points xk(1..3),wkpt 0.66667 0.00000 0.0 0.16667 and weights xk(1..3),wkpt 0.00000 0.33333 0.0 0.16667 xk(1..3),wkpt 0.00000 0.66667 0.0 0.16667 xk(1..3),wkpt 0.66667 0.33333 0.0 0.16667 xk(1..3),wkpt 0.33333 0.66667 0.0 0.16667 i_facs(1..3) 1 1 1 k -point folding factors t_kpoint_rel .true. frame of reference for k -points Figure 3.2: 2D Brillouin zone of a fcc(111) surface with hexagonal symmetry with set of 6 special k -points following Cunningham. The thin polygon indicates the conventional first Brillouin zone, the thick polygon marks the Brillouin zone as realized in the fhi98md code. When a denser mesh in the same cell is desired, Cunningham's 18-point pattern is obtained from the input Parameter Value nkpt 2 number of k -points supplied xk(1..3),wkpt 0.3333 0.3333 0.0 0.5 k -points and weights xk(1..3),wkpt 0.6666 0.6666 0.0 0.5 k -points and weights i_fa(1..3) 3 3 1 folding factors t_kpoint_rel .true. frame of reference for k -points Figure 3.3: 2D Brillouin zone of a fcc(111) surface with hexagonal symmetry with set of 18 special k -points following Cunningham. The thin polygon indicates the conventional first Brillouin zone, the thick polygon marks the Brillouin zone as realized in the fhi98md code. Here we have made use of the 'tiling' strategy employed in fhi98md . An even denser k -point set, consisting of 54 points in the full Brillouin zone, may be obtained by using the 6 k -points of the first example, but as a pattern repeated in each of the nine tiles, i.e. by setting the folding parameters in the first example to 3 3 1. User-supplied k -point sets In some cases (like a band structure calculation), the user might find it more convenient to specify the k -point mesh directly with respect to the coordinate axes in reciprocal space, rather then with respect to the reciprocal lattice vectors. This can be achieved by setting t_kpoint_rel to .false.. The unit of length on the coordinate axes is in this case. The folding parameters can be used as well to enhance the number of k -points, if desired. However, one should keep in mind that the k -point sets specified in that way might have little symmetry, i.e. their number is not significantly reduced by the built-in symmetry reduction algorithm of fhi98start . Reduced k -points and symmetry Apart from the translational symmetry of the Bravais lattice, the crystal structure under investigation may often have additional point group symmetries. These can be used to reduce the number of k -points which are needed in the actual calculation (and thus the memory demand) substantially. To perform the integrals in the Brillouin zone , it is sufficient to sample the contribution from a subset of non-symmetry-equivalent k -points only. Therefore the integrand (e.g. the charge density) is calculated only at these points. The integrand with the full symmetry can be recovered from its representation by non-symmetry-equivalent k -points whenever this is required. The fhi98start utility is set up to automatically exploit these point group symmetries. First, the point group symmetry operations applicable to the unit cell are determined and stored in the form of symmetry matrices. Secondly, fhi98start seeks to reduce the elements of the k -point mesh to the q u subset which is irreducible under those symmetry matrices. Only this subset is forwarded in the inp.ini file for further use in the main computations. The performance of the reduction procedure can be monitored by inspecting the output in the file start.out . An estimate for the sampling quality of the k -point set is given on the basis of the analysis of 'shells' (see Chadi and Cohen for details). For a good k -point set, the contribution from the leading 'shells' should vanish. Some comments for interested users: For a slab k -point set, those shells that contain contributions from lattice vectors with a finite z-component cannot vanish, thus they must be disregarded when judging the quality of the basis set. The quality assessment only makes sense for systems with a band gap. The effect of having a sharp integration boundary, the Fermi surface, for a metal is not accounted for by Chadi and Cohen's shell analysis. Note: Even if there are no point group symmetries, the vectors k and are symmetry-equivalent by virtue of time-inversion symmetry. For this reason, the number of k -points is reduced by at least a factor of two for any reasonable choice of a k -point mesh
If tomorrow is the end of the world，Iwill tell you：I like you although I am not mature enough to responsible for the responsibilitys brought bythis feeling; I am bad at my major, but I can tell you, I will appear in any place you need me; I still remember when I am in trouble, your selfless help, whatever, I will repay it; I know it is impossible for us, so I write these words, just let me remember these memories; at least, this is aproof that I want to be with you; Yes, I want to tell you all this;but I can't do it. I persuade myself to give up my feelings. It is good for you and me, I believe. Time will prove everything. I have something more important to do. yes. I will remember this.....just remember, and I will do what I need to do...
If you read what he posted on the Web, you will agree with me. Note: The yellow highlight was from me. 我为什么逃离科研.pdf What he suffered is a typical burn e d -out that ma ny of us may not realize until much later in life, say, in our 40s or 50s, which would then be called " M idlife C ris i s." It is high schools' fortune to have new blood like h im. ps. I am definitely not as smart as Dr. Zhao. I only thought about quitting research when I was in my late 40s. At t hat time, I thought very hard about what I would do next. At first, I thought about teaching high school math/sciences. In fact, I was offered a summer teaching job after I applied to two top private schools in Honolulu. I chickened out, beca use the students in a summer math class may be from other schools, including public schools so their math abilities would be a mixed bag. Another reason wa s the lack of freedom in ter ms of time, as ma ny research jobs do not requi re you to work in your office... Of course, I did consider teaching h igh school would be a waste of my training as a numerical ocean modeler. So, I finally e n ded up starting my own business, as a freelan ce English editor...
http://www.mdbbs.org/viewthread.php?action=printabletid=26451 http://www.mdbbs.org/viewthread.php?tid=26451extra=page=5 一般情况下， Tdamp 应该是时间步长的50~100倍 。我忘了当时为什么采用这么小的Tdamp了，但是算出来的结果可以接受，还是建议Tdamp=100*时间步长。你的Tdamp=200*时间步长 应该也可以 http://lammps.sandia.gov/doc/fix_nh.html If Tdamp is too small, the temperature can fluctuate wildly; if it is too large, the temperature will take a very long time to equilibrate. A good choice for many models is a Tdamp of around 100 timesteps . Note that this is NOT the same as 100 time units for most units settings. The Pdamp parameter operates like the Tdamp parameter, determining the time scale on which pressure is relaxed. For example, a value of 10.0 means to relax the pressure in a timespan of (roughly) 10 time units (e.g. tau or fmsec or psec - see the units command). If Pdamp is too small, the pressure and volume can fluctuate wildly; if it is too large, the pressure will take a very long time to equilibrate. A good choice for many models is a Pdamp of around 1000 timesteps . Note that this is NOT the same as 1000 time units for most units settings. 涉及命令： fix temp/berendsen fix nvt command fix nvt/cuda command fix npt command fix npt/cuda command fix nph command http://lammps.sandia.gov/threads/msg16782.html Also for Tdamp = 100, I presume you are using real units, not metal (which would be far too large a damping constant)?
榜样的力量是无穷的。 毋庸置疑，武夷山老师的工作效率那篇文章，是我所有博文中推荐数最多的一篇文章，这肯定不是我写得好，而是武夷山老师本人品质令大家敬仰。这不屑说，给我本人以最强烈的震撼。我希望有一天，我也像他一样，受大家欢迎。 那么，从现在开始，像他学习。 花了两天时间，读了一篇文章。是因为我最近要做一个调查问卷分析，一个朋友就把他的一个朋友写的文章发给我了。参考文献应该这么写：Zixiu Guo and John D’Ambra. (2003). Understanding the Role of National Culture on Communication Media Choice Behavior: A Cross-Cultural Comparison within a Multinational Organizational Setting.7th Pacific Asia Conference on Information Systems, 10-13 July 2003, Adelaide, South Australia. 文章主要写跨国公司里各个国家文化对通讯工具的选择方面的偏好。文章用一个总部设在澳大利亚，在泰国、朝鲜、马来西亚有分公司的一个跨国公司为例进行调查。文章假设，澳大利亚是西方国家，以个性追求为主，而分公司是亚洲国家，以集体利益为主。集体利益为重的文化，往往倾向于维持和谐，避免成员之间的冲突。而以个性追求的文化，则更注重信息的明确和具体。因此，在选择通讯工具的时候，以集体利益为重的文化，往往会选择面对面的交流，以丰富的表情来调整语言过程，来达成沟通。而不愿意使用电话、电子邮件，尤其不喜欢书写形式的交流。而以个性追求为主的文化，则强调自我信赖，所以，更愿意选择那些可以记载下来的东西。 可惜数据不支持这个假设，作者对特定的跨国公司做的问卷分析，虽然在问卷回收等方面东西方有些差异，但对通讯工具的选择方面并没有明显的差异，作者分析说是由于一个公司里特定文化对各国文化的吸纳而引起对通讯工具选择方面的同化。我不以为如此，我以为，是各种通讯工具本身明显的差异性引起。比方，通讯工具是否可以即时回答？交流对象是否可以即时出现等等等等，都会直接影响交流方式的选择。这种工具本身性能差异很大的情况下，在寻求文化的影响，我认为很难。 作者还分析了各种任务对通讯工具的选择的影响，我觉得这是主要的影响因素。这种影响因素主要来自通讯工具的性能，而不是使用者本身的文化背景。 作者还用了一些统计分析方法，我应该好好学习，并实践一下。
Believe it or not, I have been struggling with the possibility that my son might get into UVa, the #1 public school in the US. Why? Because he prefers the west coast of the US. Well, the UVa letter finally arrived, via email. It was a rejection! Instead of feeling sorry for the young man, my response/reply was: "Congratulations! " What a luck boy, he (almost) always gets what he wishes for. I think I am a good mother, because I don't believe in pushing a child too hard. Next step? Go to the bank for a big loan at 1.99%!
Sunday, May 27th, 2007, Sunny From these days on, exactly after the external moderation of our specialized subject teaching, I gradually pick up my dream on further study. I always believe that my intelligence is for the research on economics, or after all I can say that I have sufficient confidence on that area. However, there is definitely not a platform for me in the college and I will not get a chance to improve my ability of research easily, so I have to prepare for it by myself. Since I choose to pay more attention on the self-development than the work, I have to refuse some of the responsibilities and give up some chance form the job. Although it seems that I will lose something nowadays, it will be an acceptable beginning for my whole development. The way I chose to improve myself is to study for the master degree in a good university or institution in China. Although the final aim is not for the master degree, the process of achieving it will train my ability, and it will be useful for me to get a chance to do the job I dreamed and to achieve higher degree.
Rationality Model and Choice Optimization: One answer to Aumanns open problem and one introduction to a new mathematical tool working papers 003 Ai WU aiwu5@sina.com.cn School of Management Dalian University of Technology, Dalian 116023, China Abstract: The dynamical process of choice optimization is the realistic starting point of constructing dynamical economics or evolutionary economics. Rationality model is the logical basis for choice optimization. But in fact, as the common theoretical base in modern economics, rationality modeling is a complex problem unsolved. In this paper, a model of natural rationality (R) is introduced, and R is defined as nonlinear function of agents output benefits (OBS) and input costs (ICS). This mathematical model of natural rationality can be considered as one answer to Aumanns open problem. On the basis of the rationality model, mathematical model of natural rationality is compared with model of bounded (or incomplete) rationality and unbounded (or complete) rationality, and their relations are analyzed according to the completeness degree of information. At last, the dynamic optimization process of rational choice on the basis of mathematical model of natural rationality is introduced. Keywords: rational ity model; rational choice; choice optimization; choice process; mathematical tool This papers has been accepted by The International Conference on Computational Intelligence and Software Engineering (CiSE) , and will be indexed by Ei and ISTP . This conference will cover information security, multimedia and graphics technologies, computational intelligence, and software engineering.
If your heart is full of aims, then everyone will be seen as your aim One said that, how my friends considered towards me just took after how i did to them. Perhaps it remains partly true. Yet I narrated the story between Su Dongpo and his intimacy FoYin, a monk. Fo considers Su as a Buddha when Su wonder how he is in Fos mind. While with the same question, Su replies to Fo with badinage that, In my thought, you are no more than shit. However, Fos heart being penetrated with Buddha, he then consider every thing as Buddha and, the vice versa.. When it comes to the English corner, we can say, one should have emptied their mind out of too much aims, whereas its existence does twist the object. If your heart is full of aims, then everyone will be seen as your aim. Many choices doesn't mean a good choice Someone live with crowds but feel lonely. Someone receives many towards while none is accepted inwards. Many means nothing but mere the many, but the right one contains the whole world. --That was a comment on a single doctress amongst piles of buddies. GUCAS English Corner 2008-05-18
标签: choice
