统计力学、物质结构类最新论文题录 诸平 统计力学、物质结构（ 82-XX Statistical mechanics, structure of matter ）类与数学相关的论文，在 MSC2010 分类标准中是82-XX,详细分类如下： 82-XX Statistical mechanics, structure of matter 82-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistical mechanics 82-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics 82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics 82-03 History of statistical mechanics 82-04 Software, source code, etc. for problems pertaining to statistical mechanics 82-05 Experimental work for problems pertaining to statistical mechanics 82-06 Proceedings, conferences, collections, etc. pertaining to statistical mechanics 82-08 Computational methods 82Bxx Equilibrium statistical mechanics 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) 82Dxx Applications of statistical mechanics to specific types of physical systems 但是，在 MSC2020 分类当中，变化最大的就是82-08 计算方法（ 82-08 Computational methods）类，将其调整为3位数分类82Mxx类（ 82Mxx Computational methods），其中包括11个5位数分类（ 5-digit classification ）。 MSC2020 82-XX分类如下，与MSC2010分类相比较，少了原来的82-08计算方法，多了下面3个分类号 82-10 Mathematical modeling or simulation for problems pertaining to statistical mechanics 82-11 Research data for problems pertaining to statistical mechanics 82Mxx Basic methods in statistical mechanics 调整后82-XX分类内容如下，这也是最新版的“数学主题分类”标准（ MSC2020 ） 82-XX Statistical mechanics, structure of matter 82-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistical mechanics 82-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics 82-02 Research exposition (monographs, survey articles) pertaining to statistical mechanics 82-03 History of statistical mechanics 82-04 Software, source code, etc. for problems pertaining to statistical mechanics 82-05 Experimental work for problems pertaining to statistical mechanics 82-06 Proceedings, conferences, collections, etc. pertaining to statistical mechanics 82-10 Mathematical modeling or simulation for problems pertaining to statistical mechanics 82-11 Research data for problems pertaining to statistical mechanics 82Bxx Equilibrium statistical mechanics 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) 82Dxx Applications of statistical mechanics to specific types of physical systems 82Mxx Basic methods in statistical mechanics 新增加的82Mxx包括 82M20 82M60 82M15 82M36 82M99 82M12 82M10 82M30 82M22 82M37 82M31 详细分类如下 82Mxx Basic methods in statistical mechanics 82M10 Finite element, Galerkin and related methods applied to problems in statistical mechanics 82M12 Finite volume methods applied to problems in statistical mechanics 82M15 Boundary element methods applied to problems in statistical mechanics 82M20 Finite difference methods applied to problems in statistical mechanics 82M22 Spectral, collocation and related (meshless) methods applied to problems in statistical mechanics 82M30 Variational methods applied to problems in statistical mechanics 82M31 Monte Carlo methods applied to problems in statistical mechanics 82M36 Computational density functional analysis in statistical mechanics 82M37 Computational molecular dynamics in statistical mechanics 82M60 Stochastic analysis in statistical mechanics 82M99 None of the above, but in this section 下面就是 MathSciNet 数据库 2020年6月份收录的与 82-XX 相关的最新论文题录（36条），仅供参考。 MR4076084 Chen, Linxiao ; Turunen, Joonas Critical Ising model on random triangulations of the disk: enumeration and local limits. Comm. Math. Phys. 374 (2020), no. 3, 1577–1643. MR4076077 Ott, Sébastien Sharp asymptotics for the truncated two-point function of the Ising model with a positive field. Comm. Math. Phys. 374 (2020), no. 3, 1361–1387. MR4075267 Dorlas, T. C. ; Rebenko, A. L. ; Savoie, B. Correlation of clusters: partially truncated correlation functions and their decay. J. Math. Phys. 61 (2020), no. 3, 033303, 28 pp. MR4073214 Łapiński, Tomasz M. Approximations of the sum of states by Laplace's method for a system of particles with a finite number of energy levels and application to limit theorems. Math. Phys. Anal. Geom. 23 (2020), no. 1, Paper No. 9, 23 pp. MR4073203 Geng, Zhiyuan ; Tong, Jiajun Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions. Calc. Var. Partial Differential Equations 59 (2020), no. 2, Paper No. 57, 35 pp. MR4072688 Cicalese, Marco ; Gloria, Antoine ; Ruf, Matthias From statistical polymer physics to nonlinear elasticity. Arch. Ration. Mech. Anal. 236 (2020), no. 2, 1127–1215. MR4072185 Tkachov, Pasha Hydrodynamics of a particle model in contact with stochastic reservoirs. J. Math. Phys. 61 (2020), no. 3, 033301, 22 pp. MR4069336 Chodrow, Philip S. ; Mucha, Peter J. Local symmetry and global structure in adaptive voter models. SIAM J. Appl. Math. 80 (2020), no. 1, 620–638. MR4068310 Benjamini, Itai ; Fontes, Luiz Renato ; Hermon, Jonathan ; Machado, Fábio Prates On an epidemic model on finite graphs. Ann. Appl. Probab. 30 (2020), no. 1, 208–258. MR4068246 Bebiano, N. ; da Providência, J. ; da Providência, J. P. Toward non-Hermitian quantum statistical thermodynamics. J. Math. Phys. 61 (2020), no. 2, 022102, 11 pp. MR4066233 Paul, Jithu ; Gendelman, O. V. Kapitza resistance in basic chain models with isolated defects. Phys. Lett. A 384 (2020), no. 10, 126220, 8 pp. MR4066222 Golovinski, P. A. Dynamics of driven Brownian inverted oscillator. Phys. Lett. A 384 (2020), no. 10, 126203, 6 pp. MR4065814 Liu, Li-Min ; Cui, Ying-Ying ; Xu, Jie ; Li, Chao ; Gao, Qing-Hui The non-Markovian property of q -Gaussian process. Comput. Math. Appl. 79 (2020), no. 6, 1802–1812. MR4065611 Chávez, C. Abraham T. ; Curilef, Sergio Tricorn-like structures in an optically injected semiconductor laser. Chaos 30 (2020), no. 2, 023130, 6 pp. MR4065435 Ding, Ounan ; Shinar, Tamar ; Schroeder, Craig Affine particle in cell method for MAC grids and fluid simulation. J. Comput. Phys. 408 (2020), 109311, 29 pp. MR4065358 Boudjemaa, Abdelaali ; Keltoum, Redaouia Effects of weak disorder on two-dimensional bilayered dipolar Bose-Einstein condensates. Chaos Solitons Fractals 131 (2020), 109543, 6 pp. MR4065310 dos Santos, Maike A. F. Mittag-Leffler functions in superstatistics. Chaos Solitons Fractals 131 (2020), 109484, 6 pp. MR4065306 Luo, Xiang Solitons, breathers and rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates. Chaos Solitons Fractals 131 (2020), 109479, 8 pp. MR4065268 Liu, Yifei ; Liu, Yingkai ; Prodan, Emil Braiding flux-tubes in topological quantum and classical lattice models from class-D. Ann. Physics 414 (2020), 168089, 23 pp. MR4064873 Nussinov, Z. Macroscopic length correlations in non-equilibrium systems and their possible realizations. Nuclear Phys. B 953 (2020), 114948, 91 pp. MR4064822 Gromov, E. M. ; Malomed, B. A. Interplay of the pseudo-Raman term and trapping potentials in the nonlinear Schrödinger equation. Commun. Nonlinear Sci. Numer. Simul. 85 (2020), 105220, 11 pp. MR4064820 Chen, Junbo ; Zeng, Jianhua One-dimensional localized modes of spin-orbit-coupled Bose-Einstein condensates with spatially periodic modulated atom-atom interactions: nonlinear lattices. Commun. Nonlinear Sci. Numer. Simul. 85 (2020), 105217, 11 pp. MR4064819 Bai, Feng ; Han, Daozhi ; He, Xiaoming ; Yang, Xiaofeng Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields. Commun. Nonlinear Sci. Numer. Simul. 85 (2020), 105213, 23 pp. MR4064398 Joshi, Abhishek ; Majumdar, Pinaki A classical fluctuation theory of the superfluid, Mott, and normal phases of correlated bosons. Eur. Phys. J. B 93 (2020), no. 2, Paper No. 33, 15 pp. MR4064396 Zakharov, Mikhail Y. ; Demidov, Denis ; Shepelyansky, Dima L. Thermoelectric properties of Wigner crystal in two-dimensional periodic potential. Eur. Phys. J. B 93 (2020), no. 2, Paper No. 31, 9 pp. MR4064394 Azizi, Farshad ; Rezania, Hamed Spin transport properties of anisotropic Heisenberg antiferromagnet on honeycomb lattice in the presence of magnetic field. Eur. Phys. J. B 93 (2020), no. 2, Paper No. 29, 11 pp. MR4064393 Gupta, Deepak ; Maritan, Amos Thermodynamic uncertainty relations in a linear system. Eur. Phys. J. B 93 (2020), no. 2, Paper No. 28, 8 pp. MR4064390 Zhang, Chao ; Rieger, Heiko Phase diagrams of the disordered Bose-Hubbard model with cavity-mediated long-range and nearest-neighbor interactions. Eur. Phys. J. B 93 (2020), no. 2, Paper No. 25, 7 pp. MR4064214 Vroylandt, Hadrien ; Proesmans, Karel ; Gingrich, Todd R. Isometric uncertainty relations. J. Stat. Phys. 178 (2020), no. 4, 1039–1053. MR4064209 Méndez, A. R. ; García-Perciante, A. L. ; Chacón-Acosta, G. Thermal dissipation in two dimensional relativistic Fermi gases with a relaxation time model. J. Stat. Phys. 178 (2020), no. 4, 936–953. MR4064207 Benoist, T. ; Panati, A. ; Pautrat, Y. Heat conservation and fluctuations between quantum reservoirs in the two-time measurement picture. J. Stat. Phys. 178 (2020), no. 4, 893–925. MR4062992 Okuyama, Kazumi Replica symmetry breaking in random matrix model: a toy model of wormhole networks. Phys. Lett. B 803 (2020), 135280, 4 pp. MR4062465 Hilfiker, Lorenz ; Runkel, Ingo Existence and uniqueness of solutions to Y -systems and TBA equations. Ann. Henri Poincaré 21 (2020), no. 3, 941–991. MR4062463 Garrod, Barnaby ; Tribe, Roger ; Zaboronski, Oleg Examples of interacting particle systems on Z as Pfaffian point processes: coalescing-branching random walks and annihilating random walks with immigration. Ann. Henri Poincaré 21 (2020), no. 3, 885–908. MR4065527 Accardi, Luigi ; Guerrero-Poblete, Fernando Quantum Markov semigroups of low density limit: the generic case. Open Syst. Inf. Dyn. 26 (2019), no. 4, 1950021, 30 pp. MR4062009 Ebert, Dietmar ; Blaschke, David Thermodynamics of a generalized graphene-motivated (2 +1 ) D Gross-Neveu model beyond the mean field within the Beth-Uhlenbeck approach. PTEP. Prog. Theor. Exp. Phys. 2019, no. 12, 123I01, 30 pp.
投到Journal of Mountain Science 的文章利用气温计算山区裸地地表温度的新方法（New methods for calculating bare land surface temperature over mountainous terrain） 在第一轮审稿时共收到三份审稿意见, 三份意见均较为详细，所有审稿意见加在一起有四页多，意稿人对这种简单的新方法均表现出浓厚的兴趣并给予了充分的肯定，同时提出了很多具体的建议以便作者进一步修改和完善。三位审稿人分别来位于意大利的欧洲研究院（Academia Europaea）高山研究所， 意大利那不勒斯第二大学,西班牙国家研究委员会比利牛斯生态研究所。 在这里贴出这三份审稿意见的目的是希望国内的学者能够从中学习到一些撰写审稿意见的方法, 同时, 给从事相关研究的国内学者提供一些合作交流的线索。 第一位审稿人先对文章进行了总体评价，然后针对文章各章节给出相应评价和具体意见，这样的审稿意见让作者更容易理解，在修改时也更容易操作。 Reviewer 1 Accademia Europea, Institute for Alpine Environments The manuscript is well written. However, it proposes a rather simple method compared with the major literature on the field. The method could be useful in data-poor regions. I would have suggested reject in a major journal with very high IF, but I think good works, even if made with a few data and simple approaches, deserve a publication in a good journal as JMS. General comments : The article proposes a new methodology to improve the estimation of land surface temperature (LST) over mountainous terrain, on the basis of topographic information and air temperature. The proposed method is very simple and based on few, easily available data. Performances are relatively poor, compared to other, more complex, methods. Nevertheless, the method improves significantly results, compared to an approach based only on air temperature. The method could be useful in data-poor regions. The paper is very well written and results are well supported by observations. However, there are several aspects in the methodology that can be improved. I understand that the Authors want to keep the method simple and with little data requirements (only T air observations), but several improvements are possible that could, at least, be mentioned as possible future developments in the Discussion. In particular: •Only bare soil is considered. However, as acknowledged, vegetation strongly influences LST. How vegetation can be considered in the method? •A better validation of the method could be given by remote sensing data. Why do not validate the model also against such a data? •Effect of long wave radiation and could cover. Simple methods are available to infer long wave radiation to further improve the method. I think the paper is in line with the aims and targets of JMS. To conclude, I suggest a moderate revision for the paper. Specific comments: Introduction Introduction is well written: I suggest underlining the importance of LST estimation in mountain regions for processes as permafrost. I suggest also mentioning the possibility of estimating LST by proximal sensing (thermal cameras). Site and data Here I have a major methodological observation. Did you measure LST just below the soil or at the soil surface? In the last case, how has been the instrument sheltered from the Sun? Incorrect solar sheltering and simply the fact that the instrument is made in a different material with respect to the soil, can alter observation of several K. Please explain better the experimental setup. Methodology If a temperature lapse rate of -6.5 C/100 m is always assumed, large errors in Ta estimation are possible. In fact, over long time scales this assumption is safe, but locally and at the instantaneous time scale, lapse rate could change a lot (i.e. morning thermal inversion, etc …) In the methods, the diurnal Ta excursion is used. The method performs also worse for cloudy days. This could be because the effects of incoming long wave radiation from the clouds are not take in account. Way do not consider simple parametrizations as the one of Brutsaert (1975) and following modifications for clouds? Brutsaert, W. (1975). On a Derivable Formula for Long-Wave Radiation from Clear Skies. Water Resour. Res., 11(5), 742–744. Validation Given the simplicity of the method, it works relatively well, even below pefromances of more complex methods. A better validation of the method could be given by thermal cameras observations or by MODIS (500 m resolution) LANDSAT LST (60 m resolution) observations. The latter are available for free. Why do not validate the model also against such a data Reviewer 2 Seconda Università di Napoli, Dipartimento di Ingegneria Civile, Design, Edilizia e Ambiente The paper proposes a simple method to calculate bare soil surface temperature from air temperature measurements. The topic is of interest for the readership of JMS, as soil surface temperature affects several processes occurring at soil surface, such as soil-atmosphere energy and water exchange, snow melt etc. The manuscript is clearly organized, but the English language must be improved with the help of a native speaker (for instance, there is continuously skipping from present tense to past tense, that should be homogenized throughout the manuscript). Although the proposed method could be useful for practical applications, the presentation of the results does not allow the reader to judge if the drawn conclusions are actually supported by the data. In particular, after describing the proposed mathematical relationships allowing calculation of soil temperature from air temperature, solar elevation and land slope and aspect angles, the authors make their discussion by comparing the obtained results only with the naive assumption of considering soil surface temperature equal to air temperature, and conclude that their model is closer to actual measured soil temperature. I have several concerns about this line of evaluating model performance: - I wonder if this kind of comparison is enough to draw the conclusion that equations (1) and (2) are suitable for estimating LST. The authors should provide more information about the errors of the model, e.g. at what time of the day, and in what part of the year, the discrepancies between model and measurements are maximum? - Would it be possible to introduce the effect of cloud cover to further improve the performance of the equation? - To what extent the errors still present in the modeled LST affect the estimates of water and energy exchanges at soil surface? - Although the authors state that other existing approaches for estimating soil surface temperature do not provide data at the required spatial resolution, some comparison with the performance of other models should be made. - The presented data refer to high altitude sites, and the authors, in their introduction, mention permafrost dynamics as one of the possible fields of application of the method; nonetheless, there is no mention to insulation snow effect on the relationship between air temperature and soil temperature (see Wang et al., 2016, for a recent review of existing models). Given all these issues, me recommendation is that the manuscript is not acceptable in its present form, and major revisions are needed before re-evaluating it for possible publication in JMS. References Wang W, et al., 2016 Evaluation of air–soil temperature relationships simulated by land surface models during winter across the permafrost region, The Cryosphere, 10: 1721–173 Reviewer 3 Spanish Research council, CSIC, Pyrenean Institute of Ecology Dear Editor, The manuscript deals with a research that is rather simple, but may result useful for other researchers and, hence, to be of interest for JSM. Below I indicate a short number of comments that may facilitate the lecture of the manuscript and also some questions that authors should consider before being accepted the manuscript. Comments to the Author The manuscript New methods for calculating bare land surface temperature over mountainous terrain test two equation to obtain bare land suface temperature in mountain areas. Analyses are rather simple and the results are depicted very briefly. In general, I think that this topic may be of interest for different field of research in mountain areas (ecology, erosion, etc) and hence of interest for Journal of Mountain Science. Below I indicate a number of comments that authors should address and/or clarify in a revised version: 1- In the abstract all acronyms should be introduced with the full name for better understanding. 2- Figure captions should be reworked to be self-explanatory. In its current form they do not result very informative if you do not read the full manuscript. 3- The section Validation includes the full results. I would move the first paragraph to methods, and the rest to a results section. 4- An important question is that authors are correlating two series (observed and simulated data) with a very strong seasonality, that always will lead to spuriously increase the correlation values. I think that error estimators should be provided to series with the seasonal signal removed, or alternatively present the error estimators for each month, removing in this way the seasonal cycle. 5- In relation with comment 4, I think it would be of interest to show if the equations work better or worse in different times of the year, so providing (and discussing) error estimators for each month would be of interest. 6- It would be of interest stress the RMSE as a percentage of average Temperature to have an idea which % of error are associated to both equations ( a standardized RMSE). 6- What about snowpack? Were the study sites covered by snow? How did it affect the analysis? 7- Perhaps, it would be good to discuss how these equations may work on bare rock instead of bare soils. Probably, it will be necessary to use completely different parameters as differences between air temperature and surface will be much larger.
http://www.southampton.ac.uk/~rpb/thesis/node1.html vortex domain stray field nature05240.pdf nnano.2013.180.pdf formula JApplPhys_97_074504.pdf magnetic field calculation formula http://www.netdenizen.com/emagnet/index.htm from a rectange condutor wire http://www.ntmdt.com/spm-basics/view/magnetic-field-rectangular-wire
转自： http://i.eol.cn/blog_read.php?topicid=693401 有三个方法： Linear Response Theory Frozen Phonon method Finite Displacement method Linear response 方法（或者称为 density perturbation functional theory ， DFPT ），直接计算出原子的移动而导致 的势场变化，再进一步构造出动力学矩阵。这种方法在计算谱时， Born effective charge （对极性的材料）和声子谱都能计算出。 现在很流行， CASTEP ，Quantum-Expresso，Abinit等等都在用，后面两个原理差不多； Linear Response 优点： 晶体晶胞没有大小限制，即使用包含一个原子的Primitive cell，计算得到的Dynamical Matrix也是很准确的，主要原理：Hellmann-Feymann theorem and Perturbation theory， 原子施加很小的位移，计算波函数， 电子 密度对位移的响应函数，主要方法见Gonze1997年的两个PRB文章。计算速度一般，特别是采用Normal Conserving PPs的时候，单原子晶胞RAM占用量在3-4G之间，CASTEP里面只支持NCPP的Linear response 计算，USPPs不支持。 另外一个是Finite displacement (直接的方法)： 构造超原胞，把原子移动一下，计算原胞中所有原子所受的力（这个根据体系的周期性，要多移动几个原子），然后根据这个力构造力常数矩阵。 而且一般情况下对 LO-TO 的 split 不能计算出（只有在计算了 Born effective charge 之后， 进一步考虑了 non-analyticity term ，才能计算出）。phonon, phonony等就是结合vasp或者其他计算软件如wien2k等计算声子谱的。 Finite displacement 优点： RAM占用量和计算量在Cell一样的情况下，可节约2倍的RAM和CPU时间，但这个方法最大的缺点是需要生成一个Supercell 来获得比较可靠的力常数，虽然鉴于力常数是短程 作用 ，在最邻近原子以外衰减很快，但所需要的Supercell大小也很大，一般截止半径大小是4A以上，对于金属这个半径可能会小一下，因为金属的电子Coulomb屏蔽很显著，但对于其他的晶体结构，以及晶体结构较复杂的体系，这种方法自动生成的Cell一般都包含100原子以上，基本上没有人能采用单机计算Phonon， 如BCC， Ba元素，Primitive cell只包含一个原子， %BLOCK LATTICE_CART -2.445170154155672 2.445170154155674 2.445170154155673 2.445170154155672 -2.445170154155673 2.445170154155673 2.445170154155672 2.445170154155672 -2.445170154155672 %ENDBLOCK LATTICE_CART %BLOCK POSITIONS_FRAC Ba 0.0000000000000000 0.0000000000000000 0.0000000000000000 在采用有限位移方法计算 声子 时晶胞是： %BLOCK PHONON_SUPERCELL_MATRIX 2 0 0 0 2 0 0 0 2 即2*2*2的supercell，里面包含8个Ba原子，采用AMD Dual Core，2G RAM，计算需要2h左右即可完成。 另外一个最大的优点是可以用Ultra soft Pseudo potentials， 这个可以极大的节约时间，减小kinetic energy curoff数值。 Finite Displacement方法只计算Brillouin Zone G点的Normal Modes，其他k点的Dynamical Matrix利用Fourier Transofrmation得到，C（k）=Sum C（R）*Exp（-ikR），只要Cell足够大，可以获得和Linear Response 一样可靠的Dynamical Matrix。 Linear Response计算有带隙的晶体最好，也是最省事的方法，但计算金属，采用Finite element方法最好，Linear response对金属体系基本上失效的。 可能原因： Perturbation theory本身对于金属不成立(金属能隙太小）； Fermi 面Smearing方法本身对计算力常数不利；（目前有几个常用的Smeaing方法，Gaussan函数，或者有限 温度 下的Fermi Dirac函数） 后者基本上可以排除，采用Linear response，同事采用NCPP+fix occupation的方法计算得到的Phonon和NCPP+ Smearing方法是一样子的，因此可以推断是Linear Response theory对metal不适用，CASTEP小组在其网页上也指出Lnear Response theory对Magnetic和Metal不适用。因此CASTEP不支持金属体系NCPP+Linear Response计算，也是有原因的。 采用Quantum-Expresso计算PHONON，可以完全得到与CASTEP一致的结论，即Linear Response不适用于金属体系 。 下面给出Na的例子，有实验数据，势函数计算 结果 ，NCPP+ Linear response，USPP+Finite element 结果 ，可以看到Linear response精度连势函数都不如，数值完全是错误的 声子计算的几种方法： 转自： http://emuch.net/html/200802/723527.html Practical schemes for phonon calculations （见castep说明） A good review of the existing schemes can be found in Baroni et al. (2001). The theoretical study of phonon properties has to rely on one of the three available methods for determining the force constants matrix: analytical calculations, supercell calculations or linear response calculations. The analytical approach is only viable when the energy model is sufficiently simple to allow a direct evaluation of the second derivatives of the energy with respect to atomic displacements (e.g., empirical pair potential models). Therefore, it is unsuitable for first principles calculations. Further alternatives such as extracting vibrational properties from molecular dynamics runs (Arias et al. 1992) are less transparent and noticeably more expensive. The supercell method involves perturbing the positions of the atoms slightly and calculating the reaction forces (Ackland et al. 1997). It is necessary to use supercells of the original cell when interatomic interaction in the system is long ranged. The main advantage of this method (and of the closely related frozen phonon technique) is that there is no need for a new formalism; any total energy scheme like CASTEP can be used to evaluate the forces at a number of carefully selected distorted configurations. The original frozen phonon scheme requires a displacement with the given wave vector and has been successfully used since the early 1980s (Yin and Cohen 1982, Ho et al. 1984). The force constants matrix evaluation in this formalism has been used to calculate interplanar force constants (Wei and Chou 1994) and thus phonon dispersion along high symmetry directions. More recent applications are based on the full reconstruction of the force constants matrix (Ackland et al. 1997, Parlinski et al. 1997, and references in Baroni et al. 2001). Linear response calculations seek to evaluate the dynamical matrix directly for a set of q vectors. The starting point of the linear response approach is evaluation of the second-order change in the total energy induced by atomic displacements. The main advantage of the scheme is that there is no need to artificially increase the cell size in order to accommodate small values of the q vectors, as in the frozen phonon method, or to overcome the long range interaction problem (force constants matrix from supercell calculations). A more detailed description of the linear response method can be found in Baroni et al. 2001. The CASTEP implementation is described in the Linear Response topic. 第一性原理计算声子方法及常见程序： 一，直接法： 直接法，或称frozen-phonon方法，是通过在优化后的平衡结构中引入原子位移，计算作用在原子上的Hellmann-Feynman力，进而由动力学矩阵算出声子色散曲线。用该方法计算声子色散曲线最早开始于80年代初。由于计算简便，不需要特别编写的计算程序，很多小组都采用直接法计算材料性质。直接法的缺陷在于它要求声子波矢与原胞边界(super size)正交，或者原胞足够大使得Hellmann-Feynman力在原胞外可以忽略不计。这使得对于复杂系统，如对称性高的晶体、合金、超晶格等材料需要采用超原胞。超原胞的采用使计算量急剧增加，极大的限制了该方法的使用。这种方法不能很好的预言LO-TO splitting,只有在计算了Born effective charge和dielectric constant之后，进一步考虑了 non-analyticity term，才能计算出;但Direct Method本身并不能给出Born effective charge和dielectric constant.所以这也是它的一个缺陷.目前,vasp+phonon用的就是这种方法. vasp+phonon（或者PHON或者fropho） VASP能计算声子谱的都是采用一种直接的方法：构造超原胞，把原子移动一下，计算原胞中所有原子所受的力（这个根据体系的周期性，要多移动几个原子），然后根据这个力构造力常数矩阵。 1，PHONON Software by Krzysztof PARLINSKI Phonon is a software (see list of Publications) for calculating phonon dispersion curves, and phonon density spectra of crystals, crystals with defects, surfaces, adsorbed atoms on surfaces, etc. from either a set of force constants, or from a set of Hellmann-Feynman forces calculated within an ab initio program (not included). One can use VASP, Wien2k, MedeA of Materials Design , Siesta, or other ab initio code which is able to optimize a supercell and calculate the Hellmann-Feynman forces. Phonon builds a crystal structure, using one of the 230 crystallographic space groups, finds the force constant from the Hellmann-Feynman forces, builds the dynamical matrix, diagonalizes it, and calculates the phonon dispersion relations, and their intensities. Phonon finds the polarization vectors, and the irreducible representations (Gamma point) of phonon modes, and calculates the total and partial phonon density of states. It plots the internal energy, free energy, entropy, heat capacity and tensor of mean square displacements (Debey-Waller factor). Phonon finds the dynamical structure factor for the coherent inelastic neutron scattering and the incoherent doubly differential scattering cross section for a single crystal and polycrystal. For polar cystals the LO/TO mode splitting can be included. Homepage： http://wolf.ifj.edu.pl/phonon/index.html 2，PHON A program to calculate phonons using the small displacement method This program calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like Helmholtz free energy, entropy, specific heat and internal energy of the harmonic crystal. The procedure similar to the one described in Ref. , i.e. is based on the small displacement method. It needs a code capable to calculate forces on the atoms of the crystal. Homepage： http://chianti.geol.ucl.ac.uk/~dario/ E-mail: d.alfe@ucl.ac.uk Telephone: +44 (0)20 7679 2361 Fax: +44 (0)20 7679 5166 3，fropho is the open source implementation of the frozen phonon method. Function: Phonon band structure Phonon DOS (Vibrational spectra) Thermal properties Mulliken notation assignment of vibration mode fropho is the frozen phonon analyzer mainly for first principles (ab initio) calculation. Periodic boundary condition is assumed. fropho gives good combinations with VASP code or another codes which can derive Hellmann-Feynman forces. Homepage： http://fropho.sourceforge.net/ Download: http://sourceforge.net ... oup_id=161614 Contact: atz.togo@gmail.com Authour: Atsushi Togo 二，DFPT方法： 1987年，Baroni、Giannozzi和Testa提出了一种新的晶格动力学性质计算方法--微扰密度泛函方法(Density Function Perturbation Theory)。DFPT通过计算系统能量对外场微扰的响应来求出晶格动力学性质。该方法最大的优势在于它不限定微扰的波矢与原胞边界(super size)正交，不需要超原胞也可以对任意波矢求解。因此可以应用到复杂材料性质的计算上。此外，能量对外场微扰的响应不仅可以推导出声子的晶体性质，还能求出弹性系数、声子展宽、拉曼散射截面等性质,这种方法本身就能算出Born effective charge dielectric constant,可以很好的预言LO-TO splitting甚至Kohn anomalies。这些优势使 得DFPT一经提出就被广泛应用到了半导体、金属和合金、超导体等材料的计算上。 比较常用的程序是pwscf和abinit，castep等采用的是一种linear response theory 的方法（或者称为 density perturbation functional theory，DFPT），直接计算出原子的移动而导致 的势场变化，再进一步构造出动力学矩阵。
转贴（来自西交大论坛）： 在CASTEP计算完毕输出文件output－files中如果体系采用了自旋极化计算方法，一般有下面结果输出： 2* Integrated Spin Density = 0.934374E-01 2*Integrated |Spin Density| = 0.104526 Final energy, E? ? = -14786.05701927??eV Final free energy (E-TS) = -14786.10608945??eV (energies not corrected for finite basis set) NB est. 0K energy (E-0.5TS) = -14786.08155436??eV 注意到红色字体部分，2× Integrated Spin Density表示自旋极化DOS积分结果，也就是自旋up和down通道积分后然后加到一起； 2*Integrated |Spin Density|表示自旋极化DOS绝对值积分相加；2表示自旋磁矩g因子。通过这个参数可以初步判断结构的磁性： After the last SCF iteration CASTEP prints out total spin (number of unpaired electrons) and also integrated |spin|. If the two numbers are very close and are very small, then the system is paramagnetic. If they are close and finite, the system is ferromagnetic. If integrated |spin| is finite, but integrated spin itself is close to zero - system is antiferromagnetic. Finally, if both numbers are finite, and the difference between them is also finite, you have a ferrimagnetic. 2* Integrated Spin Density = 0.934374E-01 2*Integrated |Spin Density| = 0.104526 这个不就是very small and finite的情况，0.0934, 0.104；这个体系就是Paramagnetic！ 其他可能出现的铁磁性，亚铁磁性，反铁磁性都可以按照上面积分的定义来考虑。 Ferromagnetic情况，绝对值的DOS积分显然是Up spin 电子和down spin电子磁矩的和，Finite；DOS积分直接代数相加，就是晶胞中的净剩磁矩，在铁磁性材料里面还是Finite，当然一般材料磁矩平均到每个原子上面最大也就是6－7Bohr，因此是个Finite value。 Antiferromagnetic情况下，绝对值的积分是2×Up spin了，但积分数值代数和是接近0的，因此是very small 第一组：2*Integrated Spin Density =??1.00034 2*Integrated |Spin Density| =??2.85159 第二组：2*Integrated Spin Density = -0.216329E-07 2*Integrated |Spin Density| = 0.320014E-05 那么请大家帮忙看一下这个能说明什么啊？ 新手求助 这是我在一个体系中去掉一个空位出现的情况 Spin density＝DOS（spin up)-DOS （Spin down） 2意义表示电子自旋磁矩前面的g因子； Integrated Spin Density 表示DOS（spin up)-DOS （Spin down）积分后面积的矢量和，或者说沿特定方向的净自旋极化电子数目，如1.00034 就是说spin up有这么多净自旋极化电子多出来； Integrated |Spin Density|意义很简单了，表示所有通道中净自旋极化电子数目，是上面DOS（spin up)-DOS （Spin down）曲线绝对值的积分了； 因此在DOS（spin up)-DOS （Spin down）曲线中： N（up）－N（down）＝1.0034 N(up)+N(down)=2.85159 这个应该是FM情况； 同理对于第二组：2*Integrated Spin Density = -0.216329E-07 2*Integrated |Spin Density| = 0.320014E-05 应该是Paramagnetic情况！
蒙特·卡罗方法（Monte Carlo method），也称统计模拟方法，是二十世纪四十年代中期由于科学技术的发展和电子计算机的发明，而被提出的一种以概率统计理论为指导的一类非常重要的数值计算方法。是指使用随机数（或更常见的伪随机数）来解决很多计算问题的方法。蒙特·卡罗方法的名字来源于摩纳哥的一个城市蒙地卡罗，该城市以赌博业闻名，而蒙特·卡罗方法正是以概率为基础的方法。 基本背景： 1946年，美国拉斯阿莫斯国家实验室的三位科学家John von Neumann,Stan Ulam 和 Nick Metropolis共同发明，被称为蒙特卡洛方法。它的具体定义是：在广场上画一个边长一米的正方形，在正方形内部随意用粉笔画一个不规则的形状，现在要计算这个不规则图形的面积，怎么计算列?蒙特卡洛(Monte Carlo)方法告诉我们，均匀的向该正方形内撒N（N 是一个很大的自然数）个黄豆，随后数数有多少个黄豆在这个不规则几何形状内部，比如说有M个，那么，这个奇怪形状的面积便近似于M/N，N越大，算出来的值便越精确。在这里我们要假定豆子都在一个平面上，相互之间没有重叠。 蒙特卡洛方法可用于近似计算圆周率：让计算机每次随机生成两个0到1之间的数，看这两个实数是否在单位圆内。生成一系列随机点，统计单位圆内的点数与总点数，（圆面积和正方形面积之比为PI:4，PI为圆周率），当随机点取得越多（但即使取10的9次方个随机点时，其结果也仅在前4位与圆周率吻合）时，其结果越接近于圆周率。
作者： 王希胤 学科专业： 生物学(生物信息学) 授予学位： 博士 学位授予单位： 北京大学 北京大学 导师姓名： 罗静初 郝柏林 学位年度： 2005 确定染色体同源片段是基因组学研究的一个重要方面，有助于揭示基因组在历史上发生的多种多样的进化事件，如DNA复制、染色体重排、基因丢失等。研究发现，谷物之间、哺乳动物之间、分属不同种的酵母之间都存在大规模的染色体同源片段；物种内部也常发现由于大规模基因组复制而形成的同源片段；约80％的拟南芥基因组处于复制区，分析表明，拟南芥的进化过程中，至少发生了一次或三次多倍化事件。 水稻基因组中也发现了许多大的复制片段，但对于这些复制片段的规模、复制事件的性质和发生时间，存在很大分歧。基于粳稻基因组草图数据分析，Goff等推测四千到五千万年前发生了一次多倍化事件。而VandePeer等发现仅15％基因位于复制区，而且大部分与水稻2号染色体相关，因此认为水稻在历史上只有一、两条染色体发生了复制，从而有一个非整倍体祖先，并推断相应非整倍化事件发生在七千万年前；尽管后来他们找到了较多复制片段，但依然维持已有结论。几乎在同时而且同样基于粳稻基因组数据，Paterson等利用不同方法发现61.9％水稻基因位于复制区，远多于VandePeer等的发现；他们认为这可能源于约七千万年前一次多倍化事件。 这种争议主要在于是多倍化还是非整倍化，也就是复制发生的规模，这可能是由于采用的方法不同造成的。实际上，大规模复制之后，由于大量染色体重排、基因丢失、基因插入等，使染色体片段间同源关系变得面目全非，从现存的遗迹识别同源性并相当困难。目前，已有多种推断染色体间同源关系的方法，或基于遗传图谱、或基于序列比较、或基于基因共群性(synteny)、或基于基因共线性(colinearity)，等等。基于共线性的方法有很多优点，由于考虑了基因顺序和密度，所确定的同源片段较为可靠，而且运算效率较高。VandePeer等发展了名为ADHoRe的共线性方法，并用于水稻基因组分析。然而，现有共线性方法有一些缺陷，最大问题在于参数选择基于经验，没有深入合理的理论分析。例如，相邻同源基因对之间的距离是一个重要参数，经验方法难以取定一个合适的值，而把不适当的值用于寻找同源区域，会使结果严重地偏离实际情况。 本文发展了一个新的基于共线性的确定同源片段方法，其主要特点是：合理的统计推断、较强的适应性、计算的高效性。该方法的参数选择，尤其是相邻同源基因对距离确定，依据基因组特点做了合理的理论分析，对推断的同源区显著性也做了深入的统计学检验。本文开发了一个新的动态规划算法并编写了程序 ColinearScan实现这个共线性方法。 利用ColinearScan分析370Mb水稻籼稻亚种基因组序列，发现337个复制片段涉及全部12条染色体的76％水稻基因位于这些复制区。基于上述结果，以及对共线性基因系统发育学分析，本文推断在七千万年前，水稻祖先发生了一次全基因组复制，即多倍化事件。本文支持Paterson等的结论，而与VandePeer等的结论不一致。根据分析，我们认为VandePeer等所得结论与Paterson和本文研究结果不一致的原因在于不适当的参数选择以及过于严格的线性回归分析方法。解决这个分歧的意义在于，确定了一次发生于主要的谷物，如玉米、小麦、大麦、高粱、谷子、甘蔗等，分化之前的多倍化事件，这个多倍化影响了这些人类赖以生存的主要作物的基因组结构。本文研究结果得到了Paterson和VandePeer小组的高度评价，后者在发表于 NewPhytologist的评述文章中，承认其分析存在问题，并重做了水稻基因组分析，得到了和笔者的工作相近的结果(见附录)。 基于水稻基因组复制图样和水稻与高粱的比较基因组图谱，本文重构了两个物种的染色体结构进化图谱，推断谷物的共同祖先在多倍化发生之前有6条染色体。这对研究谷物染色体进化有重要意义。 另外，本文还确定了拟南芥基因组中的复制片段，发现约82.6％的拟南芥基因组处于复制区，而且这些复制区常常是多拷贝的。按照这个发现，本文支持拟南芥基因组曾经发生三次多倍化的可能性。本文还全面分析和确定了水稻和拟南芥之间的染色体同源片段，这些具有共线性基因的同源片段覆盖水稻和拟南芥基因组的 61.25％和87.35％；然而，几乎所有这些片段长度都小3Mb，所以很难建构单、双子中植物之间可用于基因定位信息共享的比较遗传图谱。 已测序的植物基因组：Sequenced plant genomes 2010-09-01 16:27:14 |分类： 生物信息分析 |标签： 基因组 | 字号 大 中 小 订阅 一直想找到这样的一个网站，可以把目前已经测序的植物基因组信息做个收集和整理。看来，天下有心人真不少，终于还是让我找到组织了。唯一遗憾的是，这样的网站还是一如既往的由咱中国以外的科学家们在做收集和维护，算是点点遗憾。以下是网址，感兴趣的同学可以去看看！ This site attempts to track all plant genomes with published sequences, and at least some of the genomes currently in the process of being sequenced. Genomes are divided into four states: Published: A complete genome sequence is available, and anyone can publish papers on it without restriction. Unpublished: The complete sequence (or a substantially complete sequence) is available, but whole genome analysis cannot be published until the group that sequenced the genome publishes their own paper describing it. These restrictions are outlines by the Fort Lauderdale Convention . Incomplete: A partial assembly is available, but sequencing and/or assembly and/or gene annotation is ongoing. Unreleased: Genome sequencing has at least begun, but no data has been made publicly available. http://synteny.cnr.berkeley.edu/wiki/index.php/Sequenced_plant_genomes
转自： http://i.eol.cn/blog_read.php?topicid=693401 有三个方法： Linear Response Theory Frozen Phonon method Finite Displacement method Linear response 方法（或者称为 density perturbation functional theory ， DFPT ），直接计算出原子的移动而导致 的势场变化，再进一步构造出动力学矩阵。这种方法在计算谱时， Born effective charge （对极性的材料）和声子谱都能计算出。 现在很流行， CASTEP ，Quantum-Expresso，Abinit等等都在用，后面两个原理差不多； Linear Response 优点： 晶体晶胞没有大小限制，即使用包含一个原子的Primitive cell，计算得到的Dynamical Matrix也是很准确的，主要原理：Hellmann-Feymann theorem and Perturbation theory， 原子施加很小的位移，计算波函数， 电子 密度对位移的响应函数，主要方法见Gonze1997年的两个PRB文章。计算速度一般，特别是采用Normal Conserving PPs的时候，单原子晶胞RAM占用量在3-4G之间，CASTEP里面只支持NCPP的Linear response 计算，USPPs不支持。 另外一个是Finite displacement (直接的方法)： 构造超原胞，把原子移动一下，计算原胞中所有原子所受的力（这个根据体系的周期性，要多移动几个原子），然后根据这个力构造力常数矩阵。 而且一般情况下对 LO-TO 的 split 不能计算出（只有在计算了 Born effective charge 之后， 进一步考虑了 non-analyticity term ，才能计算出）。phonon, phonony等就是结合vasp或者其他计算软件如wien2k等计算声子谱的。 Finite displacement 优点： RAM占用量和计算量在Cell一样的情况下，可节约2倍的RAM和CPU时间，但这个方法最大的缺点是需要生成一个Supercell 来获得比较可靠的力常数，虽然鉴于力常数是短程 作用 ，在最邻近原子以外衰减很快，但所需要的Supercell大小也很大，一般截止半径大小是4A以上，对于金属这个半径可能会小一下，因为金属的电子Coulomb屏蔽很显著，但对于其他的晶体结构，以及晶体结构较复杂的体系，这种方法自动生成的Cell一般都包含100原子以上，基本上没有人能采用单机计算Phonon， 如BCC， Ba元素，Primitive cell只包含一个原子， %BLOCK LATTICE_CART -2.445170154155672 2.445170154155674 2.445170154155673 2.445170154155672 -2.445170154155673 2.445170154155673 2.445170154155672 2.445170154155672 -2.445170154155672 %ENDBLOCK LATTICE_CART %BLOCK POSITIONS_FRAC Ba 0.0000000000000000 0.0000000000000000 0.0000000000000000 在采用有限位移方法计算 声子 时晶胞是： %BLOCK PHONON_SUPERCELL_MATRIX 2 0 0 0 2 0 0 0 2 即2*2*2的supercell，里面包含8个Ba原子，采用AMD Dual Core，2G RAM，计算需要2h左右即可完成。 另外一个最大的优点是可以用Ultra soft Pseudo potentials， 这个可以极大的节约时间，减小kinetic energy curoff数值。 Finite Displacement方法只计算Brillouin Zone G点的Normal Modes，其他k点的Dynamical Matrix利用Fourier Transofrmation得到，C（k）=Sum C（R）*Exp（-ikR），只要Cell足够大，可以获得和Linear Response 一样可靠的Dynamical Matrix。 Linear Response计算有带隙的晶体最好，也是最省事的方法，但计算金属，采用Finite element方法最好，Linear response对金属体系基本上失效的。 可能原因： Perturbation theory本身对于金属不成立(金属能隙太小）； Fermi 面Smearing方法本身对计算力常数不利；（目前有几个常用的Smeaing方法，Gaussan函数，或者有限 温度 下的Fermi Dirac函数） 后者基本上可以排除，采用Linear response，同事采用NCPP+fix occupation的方法计算得到的Phonon和NCPP+ Smearing方法是一样子的，因此可以推断是Linear Response theory对metal不适用，CASTEP小组在其网页上也指出Lnear Response theory对Magnetic和Metal不适用。因此CASTEP不支持金属体系NCPP+Linear Response计算，也是有原因的。 采用Quantum-Expresso计算PHONON，可以完全得到与CASTEP一致的结论，即Linear Response不适用于金属体系 。 下面给出Na的例子，有实验数据，势函数计算 结果 ，NCPP+ Linear response，USPP+Finite element 结果 ，可以看到Linear response精度连势函数都不如，数值完全是错误的 声子计算的几种方法： 转自： http://emuch.net/html/200802/723527.html Practical schemes for phonon calculations （见castep说明） A good review of the existing schemes can be found in Baroni et al. (2001). The theoretical study of phonon properties has to rely on one of the three available methods for determining the force constants matrix: analytical calculations, supercell calculations or linear response calculations. The analytical approach is only viable when the energy model is sufficiently simple to allow a direct evaluation of the second derivatives of the energy with respect to atomic displacements (e.g., empirical pair potential models). Therefore, it is unsuitable for first principles calculations. Further alternatives such as extracting vibrational properties from molecular dynamics runs (Arias et al. 1992) are less transparent and noticeably more expensive. The supercell method involves perturbing the positions of the atoms slightly and calculating the reaction forces (Ackland et al. 1997). It is necessary to use supercells of the original cell when interatomic interaction in the system is long ranged. The main advantage of this method (and of the closely related frozen phonon technique) is that there is no need for a new formalism; any total energy scheme like CASTEP can be used to evaluate the forces at a number of carefully selected distorted configurations. The original frozen phonon scheme requires a displacement with the given wave vector and has been successfully used since the early 1980s (Yin and Cohen 1982, Ho et al. 1984). The force constants matrix evaluation in this formalism has been used to calculate interplanar force constants (Wei and Chou 1994) and thus phonon dispersion along high symmetry directions. More recent applications are based on the full reconstruction of the force constants matrix (Ackland et al. 1997, Parlinski et al. 1997, and references in Baroni et al. 2001). Linear response calculations seek to evaluate the dynamical matrix directly for a set of q vectors. The starting point of the linear response approach is evaluation of the second-order change in the total energy induced by atomic displacements. The main advantage of the scheme is that there is no need to artificially increase the cell size in order to accommodate small values of the q vectors, as in the frozen phonon method, or to overcome the long range interaction problem (force constants matrix from supercell calculations). A more detailed description of the linear response method can be found in Baroni et al. 2001. The CASTEP implementation is described in the Linear Response topic. 第一性原理计算声子方法及常见程序： 一，直接法： 直接法，或称frozen-phonon方法，是通过在优化后的平衡结构中引入原子位移，计算作用在原子上的Hellmann-Feynman力，进而由动力学矩阵算出声子色散曲线。用该方法计算声子色散曲线最早开始于80年代初。由于计算简便，不需要特别编写的计算程序，很多小组都采用直接法计算材料性质。直接法的缺陷在于它要求声子波矢与原胞边界(super size)正交，或者原胞足够大使得Hellmann-Feynman力在原胞外可以忽略不计。这使得对于复杂系统，如对称性高的晶体、合金、超晶格等材料需要采用超原胞。超原胞的采用使计算量急剧增加，极大的限制了该方法的使用。这种方法不能很好的预言LO-TO splitting,只有在计算了Born effective charge和dielectric constant之后，进一步考虑了 non-analyticity term，才能计算出;但Direct Method本身并不能给出Born effective charge和dielectric constant.所以这也是它的一个缺陷.目前,vasp+phonon用的就是这种方法. vasp+phonon（或者PHON或者fropho） VASP能计算声子谱的都是采用一种直接的方法：构造超原胞，把原子移动一下，计算原胞中所有原子所受的力（这个根据体系的周期性，要多移动几个原子），然后根据这个力构造力常数矩阵。 1，PHONON Software by Krzysztof PARLINSKI Phonon is a software (see list of Publications) for calculating phonon dispersion curves, and phonon density spectra of crystals, crystals with defects, surfaces, adsorbed atoms on surfaces, etc. from either a set of force constants, or from a set of Hellmann-Feynman forces calculated within an ab initio program (not included). One can use VASP, Wien2k, MedeA of Materials Design , Siesta, or other ab initio code which is able to optimize a supercell and calculate the Hellmann-Feynman forces. Phonon builds a crystal structure, using one of the 230 crystallographic space groups, finds the force constant from the Hellmann-Feynman forces, builds the dynamical matrix, diagonalizes it, and calculates the phonon dispersion relations, and their intensities. Phonon finds the polarization vectors, and the irreducible representations (Gamma point) of phonon modes, and calculates the total and partial phonon density of states. It plots the internal energy, free energy, entropy, heat capacity and tensor of mean square displacements (Debey-Waller factor). Phonon finds the dynamical structure factor for the coherent inelastic neutron scattering and the incoherent doubly differential scattering cross section for a single crystal and polycrystal. For polar cystals the LO/TO mode splitting can be included. Homepage： http://wolf.ifj.edu.pl/phonon/index.html 2，PHON A program to calculate phonons using the small displacement method This program calculates force constant matrices and phonon frequencies in crystals. From the frequencies it also calculates various thermodynamic quantities, like Helmholtz free energy, entropy, specific heat and internal energy of the harmonic crystal. The procedure similar to the one described in Ref. , i.e. is based on the small displacement method. It needs a code capable to calculate forces on the atoms of the crystal. Homepage： http://chianti.geol.ucl.ac.uk/~dario/ E-mail: d.alfe@ucl.ac.uk Telephone: +44 (0)20 7679 2361 Fax: +44 (0)20 7679 5166 3，fropho is the open source implementation of the frozen phonon method. Function: Phonon band structure Phonon DOS (Vibrational spectra) Thermal properties Mulliken notation assignment of vibration mode fropho is the frozen phonon analyzer mainly for first principles (ab initio) calculation. Periodic boundary condition is assumed. fropho gives good combinations with VASP code or another codes which can derive Hellmann-Feynman forces. Homepage： http://fropho.sourceforge.net/ Download: http://sourceforge.net ... oup_id=161614 Contact: atz.togo@gmail.com Authour: Atsushi Togo 二，DFPT方法： 1987年，Baroni、Giannozzi和Testa提出了一种新的晶格动力学性质计算方法--微扰密度泛函方法(Density Function Perturbation Theory)。DFPT通过计算系统能量对外场微扰的响应来求出晶格动力学性质。该方法最大的优势在于它不限定微扰的波矢与原胞边界(super size)正交，不需要超原胞也可以对任意波矢求解。因此可以应用到复杂材料性质的计算上。此外，能量对外场微扰的响应不仅可以推导出声子的晶体性质，还能求出弹性系数、声子展宽、拉曼散射截面等性质,这种方法本身就能算出Born effective charge dielectric constant,可以很好的预言LO-TO splitting甚至Kohn anomalies。这些优势使 得DFPT一经提出就被广泛应用到了半导体、金属和合金、超导体等材料的计算上。 比较常用的程序是pwscf和abinit，castep等采用的是一种linear response theory 的方法（或者称为 density perturbation functional theory，DFPT），直接计算出原子的移动而导致 的势场变化，再进一步构造出动力学矩阵。
用户咨询：期刊《 INTERNATIONAL JOURNAL OF SUSTAINABLE DEVELOPMENT AND WORLD ECOLOGY 》2010年的文章数为68篇，为什么计算影响因子的时候只算了64篇？ 用户说还挺急的，等着回复， 手忙脚乱地现查了一通，完全是临时抱佛脚 Web of Knowledge网站上有关于影响因子计算的详细介绍 其实影响因子（Impact Factor）的计算并不涉及当年的文章数，其计算方法为前两年文章在当年的引用次数除以前两年的文章数；涉及到当年文章数的是即年指标（Immediacy Index），计算方法为当年文章在当年被引用的次数除以当年的文章数。用户问题中提到的“68”和“64”，就出现在这个地方。 经检索，2010年该刊文章数确实为68篇。 查68篇文献的类型，发现其中62篇为article，2篇为review，3篇为editorial material，1篇为correction。JCR中“64”对应的是citable items，那么推测editorial material和correction应该就是uncitable的啦
1954 年 , 古登堡 和里克特，首先提出使用震级－频度的经验公式来描述世界各地区地震活动性的差异，这个公式的常用形式（简称 G-R 关系）为： lg N ( M )=ɑ- bM ， 式中 N ( M ) 是以震级 M 为中心的小区间 ( M ± △M ) 在一定时期内发生地震的次数； ɑ 和 b 是常数， ɑ 表征在统计时间、区域内的地震活动水平 , b 值表示该地大小地震数的比例关系，大地震数目相对多时， b 值则小， b 值大小和该地区的介质强度以及应力大小有关。古登堡等对全球地震统计得到：在 环太平洋 岛弧地带 ， ɑ 和 b 值均高；大陆内部， ɑ 、 b 值较低。 震级与频度关系 ｌｇ Ｎ ＝ ａ － ｂＭ ，是地震学者研究地震活动性时引用最多的一个经验关系式，而且在地震预报和地震危险性分析中也得到了广泛的应用。在计算 b 值时，根据一定时空范围内的地震目录数据，采用最小二乘法或其它数学统计方法确定。 仔细推敲，以前常用的 b 值计算方法存在如下问题： 1 、 b 值的计算与统计的空间范围有关，选择的空间范围不同，得到的 b 值肯定不同。正确的方法应选择特定孕震区域范围内的地震事件，由于过去无法划分这样的孕震区域，故 b 值计算结果有很大的人为性。 2 、 b 值的计算与统计的时间起点有关，正确的方法应统计在一个特定的孕震区域内、一个孕震周期内的地震事件。由于过去无法确定其时间起点，故 b 值计算结果有很大的人为性。 鉴于 b 值计算结果的不确定性，在用 b 值进行强震预测时应小心从事。
2004 年创刊的International Journal of Computational Methods《国际计算方法杂志》ISSN: 0219-8762，季刊，新加坡世界科学出版社（WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE, SINGAPORE, 596224）出版，2009年入选 Web of Science的Science Citation Index Expanded，目前在SCI数据库可以检索到该期刊2008年的第5卷1-4期到第6卷1-4期共66篇论文。 该刊是 EI 收录期刊， EI 从 2006 年开始收录， EI 共收录了该刊 2006-2009 年 122 篇论文。 66篇包括学术论文64篇、评论2篇。 66篇文章的主要国家分布：印度18篇，中国12篇，英国7篇，新加坡6篇，伊朗5篇，美国4篇，日本、马来西亚、巴基斯坦、泰国各3篇等。 中国学者2008-2009年在该期刊发表论文的主要单位有华中科技大学（HUAZHONG UNIV SCI TECHNOL ）2篇、江苏大学（JIANGSU UNIV）2篇、香港城市大学（City Univ Hong Kong）1篇、天津大学（Tianjin Univ）1篇、华东交通大学（E China Jiaotong Univ）1篇、哈尔滨工业大学（Harbin Inst Technol）1篇、清华大学（Tsinghua Univ）1篇、西北工业大学（NW Polytech Univ）1篇、上海交通大学（ Shanghai Jiao Tong Univ ） 1 篇。 66篇文章共被引用42次，其中2008年被引用2次，2009年被引用39次，2010年被引用1次，平均引用0.64次， H指数为2（有2篇文章每篇最少被引用2次）。 International Journal of Computational Methods《国际计算方法杂志》投稿指南： The journal is devoted to all aspects of modern computational methods including mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; adaptive analysis techniques and algorithms; implementation, coding and parallelization issues; novel and practical applications. The articles can involve theory, algorithm, programming, coding, numerical simulation and/or novel application of computational techniques to problems in engineering, science, and other disciplines related to computations. Examples of fields covered by the journal are: Computational mechanics for solids and structures, Computational fluid dynamics, Computational heat transfer, Computational inverse problem, Computational mathematics, Computational meso/micro/nano mechanics, Computational biology, Computational penetration mechanics, Meshfree methods, Particle methods, Molecular and Quantum methods, Advanced Finite element methods, Advanced Finite difference methods, Advanced Finite volume methods, High-performance computing techniques. 网址： http://www.worldscinet.com/ijcm/ijcm.shtml 编委会： http://www.worldscinet.com/ijcm/mkt/editorial.shtml 作者指南： http://www.worldscinet.com/ijcm/mkt/guidelines.shtml 在线投稿： http://www.worldscinet.com/ijcm/editorial/submitpaper.shtml
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