11,034 research outputs found
Thermal scale modeling
Complex system study data indicate that factors associated with multilayer insulation pose major problem in scale modeling, that numerical analysis aids correction for known compromises of scaling criteria, and that probable errors in scale modeling experiments fall within range predicted by statistical analysis
Affordable, Entropy Conserving and Entropy Stable Flux Functions for the Ideal MHD Equations
In this work, we design an entropy stable, finite volume approximation for
the ideal magnetohydrodynamics (MHD) equations. The method is novel as we
design an affordable analytical expression of the numerical interface flux
function that discretely preserves the entropy of the system. To guarantee the
discrete conservation of entropy requires the addition of a particular source
term to the ideal MHD system. Exact entropy conserving schemes cannot dissipate
energy at shocks, thus to compute accurate solutions to problems that may
develop shocks, we determine a dissipation term to guarantee entropy stability
for the numerical scheme. Numerical tests are performed to demonstrate the
theoretical findings of entropy conservation and robustness.Comment: arXiv admin note: substantial text overlap with arXiv:1509.06902;
text overlap with arXiv:1007.2606 by other author
Curvature Dependence of Hydrophobic Hydration Dynamics
We investigate the curvature-dependence of water dynamics in the vicinity of
hydrophobic spherical solutes using molecular dynamics simulations. For both,
the lateral and perpendicular diffusivity as well as for H-bond kinetics of
water in the first hydration shell, we find a non-monotonic solute-size
dependence, exhibiting extrema close to the well-known structural crossover
length scale for hydrophobic hydration. Additionally, we find an apparently
anomalous diffusion for water moving parallel to the surface of small solutes,
which, however, can be explained by topology effects. The intimate connection
between solute curvature, water structure and dynamics has implications for our
understanding of hydration dynamics at heterogeneous biomolecular surfaces.Comment: 10 pages, 9 figure
Solvent fluctuations induce non-Markovian kinetics in hydrophobic pocket-ligand binding
We investigate the impact of water fluctuations on the key-lock association
kinetics of a hydrophobic ligand (key) binding to a hydrophobic pocket (lock)
by means of a minimalistic stochastic model system. It describes the collective
hydration behavior of the pocket by bimodal fluctuations of a water-pocket
interface that dynamically couples to the diffusive motion of the approaching
ligand via the hydrophobic interaction. This leads to a set of overdamped
Langevin equations in 2D-coordinate-space, that is Markovian in each dimension.
Numerical simulations demonstrate locally increased friction of the ligand,
decelerated binding kinetics, and local non-Markovian (memory) effects in the
ligand's reaction coordinate as found previously in explicit-water molecular
dynamics studies of model hydrophobic pocket-ligand binding [1,2]. Our
minimalistic model elucidates the origin of effectively enhanced friction in
the process that can be traced back to long-time decays in the
force-autocorrelation function induced by the effective, spatially fluctuating
pocket-ligand interaction. Furthermore, we construct a generalized 1D-Langevin
description including a spatially local memory function that enables further
interpretation and a semi-analytical quantification of the results of the
coupled 2D-system
Greenback-Gold Returns and Expectations of Resumption, 1862-1879
We propose a unified framework for studying the greenback-gold price during the U.S. suspension of convertibility from 1862 to 1879. The gold price is viewed as a floating exchange rate, with a fixed destination given by gold standard parity because of the prospect of resumption. We test this perspective using daily data for the entire period, and measure the effect of news during and after the Civil War. New evidence of a decline in the volatility of gold returns after the Resumption Act of 1875 provides statistical support for the importance of expectations of resumption.greenbacks, gold standard, regime switching
Diagnosing Deconfinement and Topological Order
Topological or deconfined phases are characterized by emergent, weakly
fluctuating, gauge fields. In condensed matter settings they inevitably come
coupled to excitations that carry the corresponding gauge charges which
invalidate the standard diagnostic of deconfinement---the Wilson loop. Inspired
by a mapping between symmetric sponges and the deconfined phase of the
gauge theory, we construct a diagnostic for deconfinement that has the
interpretation of a line tension. One operator version of this diagnostic turns
out to be the Fredenhagen-Marcu order parameter known to lattice gauge
theorists and we show that a different version is best suited to condensed
matter systems. We discuss generalizations of the diagnostic, use it to
establish the existence of finite temperature topological phases in
dimensions and show that multiplets of the diagnostic are useful in settings
with multiple phases such as gauge theories with charge matter.
[Additionally we present an exact reduction of the partition function of the
toric code in general dimensions to a well studied problem.]Comment: 11 pages, several figure
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis
of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD
equations as they are particularly useful for mathematically modeling a wide
variety of magnetized fluids. In order to be self-contained we first motivate
the physical properties of a magnetic fluid and how it should behave under the
laws of thermodynamics. Next, we introduce a mathematical model built from
hyperbolic partial differential equations (PDEs) that translate physical laws
into mathematical equations. After an overview of the continuous analysis, we
thoroughly describe the derivation of a numerical approximation of the ideal
MHD system that remains consistent to the continuous thermodynamic principles.
The derivation of the method and the theorems contained within serve as the
bulk of the review article. We demonstrate that the derived numerical
approximation retains the correct entropic properties of the continuous model
and show its applicability to a variety of standard numerical test cases for
MHD schemes. We close with our conclusions and a brief discussion on future
work in the area of entropy consistent numerical methods and the modeling of
plasmas
An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs
We extend the entropy stable high order nodal discontinuous Galerkin spectral
element approximation for the non-linear two dimensional shallow water
equations presented by Wintermeyer et al. [N. Wintermeyer, A. R. Winters, G. J.
Gassner, and D. A. Kopriva. An entropy stable nodal discontinuous Galerkin
method for the two dimensional shallow water equations on unstructured
curvilinear meshes with discontinuous bathymetry. Journal of Computational
Physics, 340:200-242, 2017] with a shock capturing technique and a positivity
preservation capability to handle dry areas. The scheme preserves the entropy
inequality, is well-balanced and works on unstructured, possibly curved,
quadrilateral meshes. For the shock capturing, we introduce an artificial
viscosity to the equations and prove that the numerical scheme remains entropy
stable. We add a positivity preserving limiter to guarantee non-negative water
heights as long as the mean water height is non-negative. We prove that
non-negative mean water heights are guaranteed under a certain additional time
step restriction for the entropy stable numerical interface flux. We implement
the method on GPU architectures using the abstract language OCCA, a unified
approach to multi-threading languages. We show that the entropy stable scheme
is well suited to GPUs as the necessary extra calculations do not negatively
impact the runtime up to reasonably high polynomial degrees (around ). We
provide numerical examples that challenge the shock capturing and positivity
properties of our scheme to verify our theoretical findings
Random polarization dynamics in a resonant optical medium
Random optical-pulse polarization switching along an active optical medium in
the -configuration with spatially disordered occupation numbers of its
lower energy sub-level pair is described using the idealized integrable
Maxwell-Bloch model. Analytical results describing the light
polarization-switching statistics for the single self-induced transparency
pulse are compared with statistics obtained from direct Monte-Carlo numerical
simulations.Comment: 7 pages, 3 figure
Kerr effect as a tool for the investigation of dynamic heterogeneities
We propose a dynamic Kerr effect experiment for the distinction between
dynamic heterogeneous and homogeneous relaxation in glassy systems. The
possibility of this distinction is due to the inherent nonlinearity of the Kerr
effect signal. We model the slow reorientational molecular motion in
supercooled liquids in terms of non-inertial rotational diffusion. The Kerr
effect response, consisting of two terms, is calculated for heterogeneous and
for homogeneous variants of the stochastic model. It turns out that the
experiment is able to distinguish between the two scenarios. We furthermore
show that exchange between relatively 'slow' and 'fast' environments does not
affect the possibility of frequency-selective modifications. It is demonstrated
how information about changes in the width of the relaxation time distribution
can be obtained from experimental results.Comment: 23 pages incl. 6 figures accepted for publication in The Journal of
Chemical Physic
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