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Ab initio evaluation of Coulomb and exchange parameters for DFT+U calculations

Physical Review B 2007年第15期76卷 155123-155123页

作者： Nicholas J. Mosey Emily A. Carter []Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

Conventional density functional theory (DFT) fails for materials with strongly correlated electrons, such as late transition metal oxides. Large errors in the intra-atomic Coulomb and exchange interactions are the source of this failure. The DFT+U method has provided a means, through empirical parameters, to correct these errors. Here, we present a systematic ab initio approach in evaluating the intra-atomic Coulomb and exchange terms, U and J, respectively, in order to make the DFT+U method a fully first-principles technique. The method is based on a relationship between these terms and the Coulomb and exchange integrals evaluated in the basis of unrestricted Hartree-Fock molecular orbitals that represent localized states of the extended system. We used this ab initio scheme to evaluate U and J for chromia (Cr2O3). The resulting values are somewhat higher than those determined earlier either empirically or in constrained DFT calculations but have the advantage of originating from an ab initio theory containing exact exchange. Subsequent DFT+U calculations on chromia using the ab initio derived U and J yield properties consistent with experiment, unlike conventional DFT. Overall, the technique developed and tested in this work holds promise in enabling accurate and fully predictive DFT+U calculations of strongly correlated electron materials.

关键词： .electrons Empirical evaluation of Coulomb DFT calculations chromia

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Locality and low-dimensions in the prediction of natural experience from fMRI 07

Locality and low-dimensions in the prediction of natural exp...

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Proceedings of the 21st International Conference on Neural Information Processing Systems

作者： François G. Meyer Greg J. Stephens Center for the Study of Brain Mind and Behavior Program in Applied and Computational Mathematics Princeton University Center for the Study of Brain Mind and Behavior Department of Physics Princeton University

ISBN: (纸本)9781605603520

Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding; how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-defined Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke's area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ~ 0.8) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience.

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Synthetic diamond and wurtzite structures self-assemble with isotropic pair interactions

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Physical Review E 2007年第3期75卷 031403-031403页

作者： Mikael C. Rechtsman Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and PRISM Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton New Jersey 08544 USA

Using inverse statistical-mechanical optimization techniques, we have discovered isotropic pair interaction potentials with strongly repulsive cores that cause the tetrahedrally coordinated diamond and wurtzite lattices to stabilize, as evidenced by lattice sums, phonon spectra, positive-energy defects, and self-assembly in classical molecular dynamics simulations. These results challenge conventional thinking that such open lattices can only be created via directional covalent interactions observed in nature. Thus, our discovery adds to fundamental understanding of the nature of the solid state by showing that isotropic interactions enable the self-assembly of open crystal structures with a broader range of coordination number than previously thought. Our work is important technologically because of its direct relevance generally to the science of self-assembly and specifically to photonic crystal fabrication.

关键词： CRYSTALS NANOPARTICLES

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Underconstrained jammed packings of nonspherical hard particles: Ellipses and ellipsoids

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Physical Review E 2007年第5期75卷 051304-051304页

作者： Aleksandar Donev Robert Connelly Frank H. Stillinger Salvatore Torquato Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Mathematics Cornell University Ithaca New York 14853 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science 303, 990 (2004)] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why an isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle (Z¯=2df), does not apply to nonspherical particles. We develop first- and second-order conditions for jamming and demonstrate that packings of nonspherical particles can be jammed even though they are underconstrained (hypoconstrained, Z¯<2df). We apply an algorithm using these conditions to computer-generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings, even close to the sphere point. We also consider packings that are nearly jammed and draw connections to packings of deformable (but stiff) particles. Finally, we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point.

关键词： GRANULAR-MATERIALS AMORPHOUS SOLIDS SPHERE PACKINGS DENSITY RIGIDITY ELASTICITY ALGORITHM DYNAMICS STRESS

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Modeling heterogeneous materials via two-point correlation functions: Basic principles

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Physical Review E 2007年第3期76卷 031110-031110页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. Yeong and Torquato [Phys. Rev. E 57, 495 (1998)] introduced a stochastic optimization technique that enables one to generate realizations of heterogeneous materials from a prescribed set of correlation functions. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide examples of realizable two-point correlation functions and suggest a set of analytical basis functions. We also discuss an exact mathematical formulation of the (re)construction problem and prove that S2(r) cannot completely specify a two-phase heterogeneous material alone. Moreover, we devise an efficient and isotropy-preserving construction algorithm, namely, the lattice-point algorithm to generate realizations of materials from their two-point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions. We will mainly focus on basic principles in this paper. The algorithmic details and applications of the general scheme are given in the second part of this series of two papers.

关键词： RECONSTRUCTING RANDOM-MEDIA PROBABILITY FUNCTIONS NONLINEAR COMPOSITES POROUS-MEDIA BOUNDS MICROSTRUCTURES OPTIMIZATION SCATTERING

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Multidimensional Quantum Tunneling:Direct Instanton Calculation with Application to Polyatomic Molecules

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Communications in computational Physics 2006年第6期1卷 1096-1116页

作者： Jing Shi Program in Applied and Computational Mathematics Princeton UniversityNJ 08544USA

Multidimensional tunneling appears in many problems at nano *** high dimensionality of the potential energy surface(*** degrees of freedom)poses a great challenge in both theoretical and numerical description of *** simulation based on Schrodinger equation is often prohibitively *** propose an accurate,efficient,robust and easy-to-implement numerical method to calculate the ground state tunneling splitting based on imaginary-time path integral(‘instanton’formulation).The method is genuinely multi-dimensional and free from any additional ad hoc assumptions on potential energy *** enables us to calculate the effects of all coupling modes on the tunneling degree of freedom without *** also review in this paper some theoretical background and survey some recent work from other groups in calculating multidimensional quantum tunneling effects in chemical reactions.

关键词： Quantum tunneling path integral chemical reaction

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Oscillator models and collective motion

IEEE Control Systems Magazine

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IEEE Control Systems Magazine 2007年第4期27卷 89-105页

作者： Paley, Derek A. Leonard, Naomi Ehrich Sepulchre, Rodolphe Grünbaum, Daniel Parrish, Julia K. Princeton University Department of Mechanical and Aerospace Engineering Princeton NJ 08544 United States Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Department Electrical Engineering and Computer Science University of Liège Liège Belgium School of Oceanography Department of Biology University of Washington Seattle WA United States Biology Department School of Aquatic and Fishery Sciences University of Washington Seattle WA United States

A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.

关键词： Oscillators (mechanical)

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Variational Boundary Conditions for Molecular Dynamics Simulations of Solids at Low Temperature

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Communications in computational Physics 2006年第1期1卷 135-175页

作者： Xiantao Li Weinan E Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA Department of Mathematics&Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA

Boundary conditions for molecular dynamics simulation of crystalline solids are considered with the objective of eliminating the reflection of phonons.A variational formalism is presented to construct boundary conditions that minimize total phonon *** boundary conditions that involve a few neighbors of the boundary atoms and limited number of time steps are found using the variational *** effects are studied and compared with other boundary conditions such as truncated exact boundary conditions or by appending border atoms where artificial damping forces are *** general it is found that,with the same cost or complexity,the variational boundary conditions perform much better than the truncated exact boundary conditions or by appending border atoms with empirical damping *** issues of implementation are discussed for real *** to brittle fracture dynamics is illustrated.

关键词： Boundary condition molecular dynamics phonon reflection crack propagation

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A class of nonsymmetric preconditioners for saddle point problems

A class of nonsymmetric preconditioners for saddle point pro...

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作者： Botchev, Mike A. Golub, Gene H. Department of Applied Mathematics University of Twente P.O. Box 217 7500 AE Enschede Netherlands Scientific Computing and Computational Mathematics Program Stanford University Stanford CA 94305-9025

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric. © 2006 Society for Industrial and applied mathematics.

关键词： Problem solving

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Uniform accuracy of the quasicontinuum method

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Physical Review B 2006年第21期74卷 214115-214115页

作者： Weinan E Jianfeng Lu Jerry Z. Yang Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The accuracy of the quasicontinuum method is studied by reformulating the summation rules in terms of reconstruction schemes for the local atomic environment of the representative atoms. The necessary and sufficient condition for uniform first-order accuracy and, consequently, the elimination of the “ghost force” is formulated in terms of the reconstruction schemes. The quasi-nonlocal approach is discussed as a special case of this condition. Examples of reconstruction schemes that satisfy this condition are presented. Transition between atom-based and element-based summation rules are studied.

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