7,939 research outputs found
Beyond Wavelets: Exactness theorems and algorithms for physical calculations
This paper develops the use of wavelets as a basis set for the solution of
physical problems exhibiting behavior over wide-ranges in length scale. In a
simple diagrammatic language, this article reviews both the mathematical
underpinnings of wavelet theory and the algorithms behind the fast wavelet
transform. This article underscores the fact that traditional wavelet bases are
fundamentally ill-suited for physical calculations and shows how to go beyond
these limitations by the introduction of the new concept of semicardinality,
which leads to the profound, new result that basic physical couplings may be
computed {\em without approximatation} from very sparse information, thereby
overcoming the limitations of traditional wavelet bases in the treatment of
physical problems. The paper then explores the convergence rate of conjugate
gradient solution of the Poisson equation in both semicardinal and lifted
wavelet bases and shows the first solution of the Kohn-Sham equations using a
novel variational principle.Comment: 16 pages, 8 figures. Will appear in Computer Simulation Studies in
Condensed Matter Physics XII, Eds. D.P. Landau, S.P. Lewis, and H.B.
Schuttler (Springer Verlag, Heidelberg, Berlin 1999
Material limitations of carbon-nanotube inertial balances: on the possibility of intrinsic yoctogram mass resolution at room temperature
We present a theoretical study of the intrinsic quality factor of the
fundamental flexural vibration in a carbon nanotube and its dependence on
temperature, radius, length and tension. In particular, we examine three- and
four-phonon decays of the fundamental flexural mode within quantized elasticity
theory. This analysis reveals design principles for the construction of
ultrasensitive nanotube mass sensors: under tensions close to the elastic
limit, intrinsic losses allow for \emph{single yoctogram} mass resolution at
room temperature, while cooling opens the possibility of \emph{sub-yoctogram}
mass resolution.Comment: 4 pages, 3 figure
Efficient classical density-functional theories of rigid-molecular fluids and a simplified free energy functional for liquid water
Classical density-functional theory provides an efficient alternative to
molecular dynamics simulations for understanding the equilibrium properties of
inhomogeneous fluids. However, application of density-functional theory to
multi-site molecular fluids has so far been limited by complications due to the
implicit molecular geometry constraints on the site densities, whose resolution
typically requires expensive Monte Carlo methods. Here, we present a general
scheme of circumventing this so-called inversion problem: compressed
representations of the orientation density. This approach allows us to combine
the superior iterative convergence properties of multipole representations of
the fluid configuration with the improved accuracy of site-density functionals.
Next, from a computational perspective, we show how to extend the DFT++
algebraic formulation of electronic density-functional theory to the classical
fluid case and present a basis-independent discretization of our formulation
for molecular classical density-functional theory. Finally, armed with the
above general framework, we construct a simplified free-energy functional for
water which captures the radial distributions, cavitation energies, and the
linear and non-linear dielectric response of liquid water. The resulting
approach will enable efficient and reliable first-principles studies of
atomic-scale processes in contact with solution or other liquid environments.Comment: 34 pages, 11 figure
"Kohn-Shamification" of the classical density-functional theory of inhomogeneous polar molecular liquids with application to liquid hydrogen chloride
The Gordian knot of density-functional theories for classical molecular
liquids remains finding an accurate free-energy functional in terms of the
densities of the atomic sites of the molecules. Following Kohn and Sham, we
show how to solve this problem by considering noninteracting molecules in a set
of effective potentials. This shift in perspective leads to an accurate and
computationally tractable description in terms of simple three-dimensional
functions. We also treat both the linear- and saturation- dielectric responses
of polar systems, presenting liquid hydrogen chloride as a case study.Comment: 4 pages, 2 eps-figures, submitted to Physical Review Letter
New physics of grain boundaries in bcc metals from the atomic level: molybdenum as a case study
We present a systematic trend study of the symmetric tilt grain boundaries
about the axis in molybdenum. Our results show that multiple structural
phases, some incorporating vacancies, compete for the boundary ground state. We
find that at low external stress vacancies prefer to bind to the boundaries in
high concentrations, and moreover, that external stress drives structural phase
transitions which correspond to switching the boundaries on and off as
pipe-diffusion pathways for vacancies. Finally, we present physical arguments
which indicate these phenomena are likely to occur in the other bcc transition
metals as well.Comment: 6 pages, 3 figures, 7 tables Replacement made minor changes to (a)
the title and (b) the margin spacin
Universal iso-density polarizable continuum model for molecular solvents
Implicit electron-density solvation models based on joint density-functional
theory offer a computationally efficient solution to the problem of calculating
thermodynamic quantities of solvated systems from firstprinciples quantum
mechanics. However, despite much recent interest in such models, to date the
applicability of such models in the plane-wave context to non-aqueous solvents
has been limited because the determination of the model parameters requires
fitting to a large database of experimental solvation energies for each new
solvent considered. This work presents an alternate approach which allows
development of new iso-density models for a large class of protic and aprotic
solvents from only simple, single-molecule ab initio calculations and readily
available bulk thermodynamic data
Tensor product expansions for correlation in quantum many-body systems
We explore a new class of computationally feasible approximations of the
two-body density matrix as a finite sum of tensor products of single-particle
operators. Physical symmetries then uniquely determine the two-body matrix in
terms of the one-body matrix. Representing dynamical correlation alone as a
single tensor product results in a theory which predicts near zero dynamical
correlation in the homogeneous electron gas at moderate to high densities. But,
representing both dynamical and statistical correlation effects together as a
tensor product leads to the recently proposed ``natural orbital functional.''
We find that this latter theory has some asymptotic properties consistent with
established many-body theory but is no more accurate than Hartee-Fock in
describing the homogeneous electron gas for the range of densities typically
found in the valence regions of solids.
PACS 71.10.-w 71.15.Mb, Accepted for publication in Physical Review BComment: New figures, better converged result
Ideal regularization of the Coulomb singularity in exact exchange by Wigner-Seitz truncated interactions: towards chemical accuracy in non-trivial systems
Hybrid density functionals show great promise for chemically-accurate first
principles calculations, but their high computational cost limits their
application in non-trivial studies, such as exploration of reaction pathways of
adsorbents on periodic surfaces. One factor responsible for their increased
cost is the dense Brillouin-zone sampling necessary to accurately resolve an
integrable singularity in the exact exchange energy. We analyze this
singularity within an intuitive formalism based on Wannier-function
localization and analytically prove Wigner-Seitz truncation to be the ideal
method for regularizing the Coulomb potential in the exchange kernel. We show
that this method is limited only by Brillouin-zone discretization errors in the
Kohn-Sham orbitals, and hence converges the exchange energy exponentially with
the number of k-points used to sample the Brillouin zone for all but
zero-temperature metallic systems. To facilitate the implementation of this
method, we develop a general construction for the plane-wave Coulomb kernel
truncated on the Wigner-Seitz cell in one, two or three lattice directions. We
compare several regularization methods for the exchange kernel in a variety of
real systems including low-symmetry crystals and low-dimensional materials. We
find that our Wigner-Seitz truncation systematically yields the best k-point
convergence for the exchange energy of all these systems and delivers an
accuracy to hybrid functionals comparable to semi-local and screened-exchange
functionals at identical k-point sets.Comment: 14 pages, 9 figure
The Hopgrid algorithm: multilevel synthesis of multigrid and wavelet theory
The multigrid algorithm is a multilevel approach to accelerate the numerical
solution of discretized differential equations in physical problems involving
long-range interactions. Multiresolution analysis of wavelet theory provides an
efficient representation of functions which exhibit localized bursts of short
length-scale behavior. Applications such as computing the electrostatic field
in and around a molecule should benefit from both approaches. In this work, we
demonstrate how a novel interpolating wavelet transform, which in itself is the
synthesis of finite element analysis and wavelet theory, may be used as the
mathematical bridge to connect the two approaches. The result is a specialized
multigrid algorithm which may be applied to problems expressed in wavelet
bases. With this approach, interpolation and restriction operators and grids
for the multigrid algorithm are predetermined by an interpolating
multiresolution analysis. We will present the new method and contrast its
efficiency with standard wavelet and multigrid approaches.Comment: 14 pages, 11 figure
Impact of octahedral rotations on Ruddlesden-Popper phases of antiferrodistortive perovskites
This work presents the most detailed and extensive theoretical study to date
of the structural configurations of Ruddlesden-Popper (RP) phases in
antiferrodistortive (AFD) perovskites and formulates a program of study which
can be pursued for RP phases of any AFD perovskite system. We systematically
investigate the effects of oxygen octahedral rotations on the energies of RP
phases in AFD perovskites (A_n+1 B_n O_3n+1) for n = 1...30, providing
asymptotic results for n --> infinity that give both the form of the
interaction between stacking faults and the behavior of such stacking faults in
isolation. We find an inverse-distance interaction between faults with a
strength which varies by as much as a factor of two depending on the
configuration of the octahedra. We find that the strength of this effect can be
sufficient to (a) stabilize or destabilize the RP phase with respect to
dissociation into the bulk perovskite and the bulk A-oxide and (b) affect the
energy scales of the RP phase sufficiently to constrain the rotational states
of the octahedra neighboring the stacking faults, even at temperatures where
the octahedra in the bulk regions librate freely. Finally, we present evidence
that the importance of the octahedral rotations can be understood in terms of
changes in the distances between oxygen ions on opposing sides of the RP
stacking faults.Comment: 18 pages, 12 figures, 6 table
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