3,106 research outputs found
GW method with the self-consistent Sternheimer equation
We propose a novel approach to quasiparticle GW calculations which does not
require the computation of unoccupied electronic states. In our approach the
screened Coulomb interaction is evaluated by solving self-consistent
linear-response Sternheimer equations, and the noninteracting Green's function
is evaluated by solving inhomogeneous linear systems. The frequency-dependence
of the screened Coulomb interaction is explicitly taken into account. In order
to avoid the singularities of the screened Coulomb interaction the calculations
are performed along the imaginary axis, and the results are analytically
continued to the real axis through Pade' approximants. As a proof of concept we
implemented the proposed methodology within the empirical pseudopotential
formalism and we validated our implementation using silicon as a test case. We
examine the advantages and limitations of our method and describe promising
future directions.Comment: 18 pages, 6 figure
Controllability and Fraction of Leaders in Infinite Network
In this paper, we study controllability of a network of linear
single-integrator agents when the network size goes to infinity. We first
investigate the effect of increasing size by injecting an input at every node
and requiring that network controllability Gramian remain well-conditioned with
the increasing dimension. We provide theoretical justification to the intuition
that high degree nodes pose a challenge to network controllability. In
particular, the controllability Gramian for the networks with bounded maximum
degrees is shown to remain well-conditioned even as the network size goes to
infinity. In the canonical cases of star, chain and ring networks, we also
provide closed-form expressions which bound the condition number of the
controllability Gramian in terms of the network size. We next consider the
effect of the choice and number of leader nodes by actuating only a subset of
nodes and considering the least eigenvalue of the Gramian as the network size
increases. Accordingly, while a directed star topology can never be made
controllable for all sizes by injecting an input just at a fraction of
nodes; for path or cycle networks, the designer can actuate a non-zero fraction
of nodes and spread them throughout the network in such way that the least
eigenvalue of the Gramians remain bounded away from zero with the increasing
size. The results offer interesting insights on the challenges of control in
large networks and with high-degree nodes.Comment: 6 pages, 3 figures, to appear in 2014 IEEE CD
Finite size scaling for quantum criticality using the finite-element method
Finite size scaling for the Schr\"{o}dinger equation is a systematic approach
to calculate the quantum critical parameters for a given Hamiltonian. This
approach has been shown to give very accurate results for critical parameters
by using a systematic expansion with global basis-type functions. Recently, the
finite element method was shown to be a powerful numerical method for ab initio
electronic structure calculations with a variable real-space resolution. In
this work, we demonstrate how to obtain quantum critical parameters by
combining the finite element method (FEM) with finite size scaling (FSS) using
different ab initio approximations and exact formulations. The critical
parameters could be atomic nuclear charges, internuclear distances, electron
density, disorder, lattice structure, and external fields for stability of
atomic, molecular systems and quantum phase transitions of extended systems. To
illustrate the effectiveness of this approach we provide detailed calculations
of applying FEM to approximate solutions for the two-electron atom with varying
nuclear charge; these include Hartree-Fock, density functional theory under the
local density approximation, and an "exact"' formulation using FEM. We then use
the FSS approach to determine its critical nuclear charge for stability; here,
the size of the system is related to the number of elements used in the
calculations. Results prove to be in good agreement with previous Slater-basis
set calculations and demonstrate that it is possible to combine finite size
scaling with the finite-element method by using ab initio calculations to
obtain quantum critical parameters. The combined approach provides a promising
first-principles approach to describe quantum phase transitions for materials
and extended systems.Comment: 15 pages, 19 figures, revision based on suggestions by referee,
accepted in Phys. Rev.
Provably convergent Newton-Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics
The relativistic hydrodynamics (RHD) equations have three crucial intrinsic
physical constraints on the primitive variables: positivity of pressure and
density, and subluminal fluid velocity. However, numerical simulations can
violate these constraints, leading to nonphysical results or even simulation
failure. Designing genuinely physical-constraint-preserving (PCP) schemes is
very difficult, as the primitive variables cannot be explicitly reformulated
using conservative variables due to relativistic effects. In this paper, we
propose three efficient Newton--Raphson (NR) methods for robustly recovering
primitive variables from conservative variables. Importantly, we rigorously
prove that these NR methods are always convergent and PCP, meaning they
preserve the physical constraints throughout the NR iterations. The discovery
of these robust NR methods and their PCP convergence analyses are highly
nontrivial and technical. As an application, we apply the proposed NR methods
to design PCP finite volume Hermite weighted essentially non-oscillatory
(HWENO) schemes for solving the RHD equations. Our PCP HWENO schemes
incorporate high-order HWENO reconstruction, a PCP limiter, and
strong-stability-preserving time discretization. We rigorously prove the PCP
property of the fully discrete schemes using convex decomposition techniques.
Moreover, we suggest the characteristic decomposition with rescaled
eigenvectors and scale-invariant nonlinear weights to enhance the performance
of the HWENO schemes in simulating large-scale RHD problems. Several demanding
numerical tests are conducted to demonstrate the robustness, accuracy, and high
resolution of the proposed PCP HWENO schemes and to validate the efficiency of
our NR methods.Comment: 49 page
An adaptive fixed-mesh ALE method for free surface flows
In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.Postprint (published version
Fast interior point solution of quadratic programming problems arising from PDE-constrained optimization
Interior point methods provide an attractive class of approaches for solving linear, quadratic and nonlinear programming problems, due to their excellent efficiency and wide applicability. In this paper, we consider PDE-constrained optimization problems with bound constraints on the state and control variables, and their representation on the discrete level as quadratic programming problems. To tackle complex problems and achieve high accuracy in the solution, one is required to solve matrix systems of huge scale resulting from Newton iteration, and hence fast and robust methods for these systems are required. We present preconditioned iterative techniques for solving a number of these problems using Krylov subspace methods, considering in what circumstances one may predict rapid convergence of the solvers in theory, as well as the solutions observed from practical computations
Sparse Inertial Poser: Automatic 3D Human Pose Estimation from Sparse IMUs
We address the problem of making human motion capture in the wild more
practical by using a small set of inertial sensors attached to the body. Since
the problem is heavily under-constrained, previous methods either use a large
number of sensors, which is intrusive, or they require additional video input.
We take a different approach and constrain the problem by: (i) making use of a
realistic statistical body model that includes anthropometric constraints and
(ii) using a joint optimization framework to fit the model to orientation and
acceleration measurements over multiple frames. The resulting tracker Sparse
Inertial Poser (SIP) enables 3D human pose estimation using only 6 sensors
(attached to the wrists, lower legs, back and head) and works for arbitrary
human motions. Experiments on the recently released TNT15 dataset show that,
using the same number of sensors, SIP achieves higher accuracy than the dataset
baseline without using any video data. We further demonstrate the effectiveness
of SIP on newly recorded challenging motions in outdoor scenarios such as
climbing or jumping over a wall.Comment: 12 pages, Accepted at Eurographics 201
Forces acting on a small particle in an acoustical field in a thermoviscous fluid
We present a theoretical analysis of the acoustic radiation force on a single
small particle, either a thermoviscous fluid droplet or a thermoelastic solid
particle, suspended in a viscous and heat-conducting fluid medium. Our analysis
places no restrictions on the length scales of the viscous and thermal boundary
layer thicknesses and relative to the
particle radius , but it assumes the particle to be small in comparison to
the acoustic wavelength . This is the limit relevant to scattering of
sound and ultrasound waves from micrometer-sized particles. For particles of
size comparable to or smaller than the boundary layers, the thermoviscous
theory leads to profound consequences for the acoustic radiation force. Not
only do we predict forces orders of magnitude larger than expected from
ideal-fluid theory, but for certain relevant choices of materials, we also find
a sign change in the acoustic radiation force on different-sized but otherwise
identical particles. This phenomenon may possibly be exploited in handling of
submicrometer-sized particles such as bacteria and vira in lab-on-a-chip
systems.Comment: Revtex, 23 pages, 4 eps figure
- …