499 research outputs found
Large deviations for cluster size distributions in a continuous classical many-body system
An interesting problem in statistical physics is the condensation of
classical particles in droplets or clusters when the pair-interaction is given
by a stable Lennard-Jones-type potential. We study two aspects of this problem.
We start by deriving a large deviations principle for the cluster size
distribution for any inverse temperature and particle
density in the thermodynamic limit. Here
is the close packing density. While in general the rate
function is an abstract object, our second main result is the
-convergence of the rate function toward an explicit limiting rate
function in the low-temperature dilute limit ,
such that for some
. The limiting rate function and its minimisers appeared in
recent work, where the temperature and the particle density were coupled with
the particle number. In the decoupled limit considered here, we prove that just
one cluster size is dominant, depending on the parameter . Under
additional assumptions on the potential, the -convergence along curves
can be strengthened to uniform bounds, valid in a low-temperature, low-density
rectangle.Comment: Published in at http://dx.doi.org/10.1214/14-AAP1014 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Surface energy and boundary layers for a chain of atoms at low temperature
We analyze the surface energy and boundary layers for a chain of atoms at low
temperature for an interaction potential of Lennard-Jones type. The pressure
(stress) is assumed small but positive and bounded away from zero, while the
temperature goes to zero. Our main results are: (1) As at fixed positive pressure , the Gibbs measures and
for infinite chains and semi-infinite chains satisfy path large
deviations principles. The rate functions are bulk and surface energy
functionals and
. The minimizer of the surface functional
corresponds to zero temperature boundary layers. (2) The surface correction to
the Gibbs free energy converges to the zero temperature surface energy,
characterized with the help of the minimum of
. (3) The bulk Gibbs measure and Gibbs
free energy can be approximated by their Gaussian counterparts. (4) Bounds on
the decay of correlations are provided, some of them uniform in
Electron Energy-Loss Spectroscopy: A versatile tool for the investigations of plasmonic excitations
The inelastic scattering of electrons is one route to study the vibrational
and electronic properties of materials. Such experiments, also called electron
energy-loss spectroscopy, are particularly useful for the investigation of the
collective excitations in metals, the charge carrier plasmons. These plasmons
are characterized by a specific dispersion (energy-momentum relationship),
which contains information on the sometimes complex nature of the conduction
electrons in topical materials. In this review we highlight the improvements of
the electron energy-loss spectrometer in the last years, summarize current
possibilities with this technique, and give examples where the investigation of
the plasmon dispersion allows insight into the interplay of the conduction
electrons with other degrees of freedom
Large deviations for cluster size distributions in a continuous classical many-body system
An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the
pair-interaction is given by a stable Lennard-Jones-type potential. We study two aspects of this problem. We start by deriving a large deviations principle for
the cluster size distribution for any inverse temperature and
particle density in the thermodynamic limit. Here is the close packing density. While in general the rate function is an abstract object, our second main result is the -convergence of the rate function towards an explicit limiting rate function in the low-temperature dilute limit , such that
for some . The limiting rate function and its minimisers appeared in recent work,
where the temperature and the particle density were coupled with the particle number.
In the de-coupled limit considered here, we prove that just one cluster size is dominant,
depending on the parameter . Under additional assumptions on the potential,
the Γ-convergence along curves can be strengthened to uniform bounds, valid in a low-temperature,
low-density rectangle
Model-agnostic Feature Importance and Effects with Dependent Features -- A Conditional Subgroup Approach
Partial dependence plots and permutation feature importance are popular
model-agnostic interpretation methods. Both methods are based on predicting
artificially created data points. When features are dependent, both methods
extrapolate to feature areas with low data density. The extrapolation can cause
misleading interpretations. To overcome extrapolation, we propose conditional
variants of partial dependence plots and permutation feature importance. Our
approach is based on perturbations in subgroups. The subgroups partition the
feature space to make the feature distribution within a group more homogeneous
and between the groups more heterogeneous. The interpretable subgroups enable
additional local, nuanced interpretations of the feature dependence structure
as well as the feature effects and importance values within the subgroups. We
also introduce a data fidelity measure that captures the degree of
extrapolation when data is transformed with a certain perturbation. In
simulations and benchmarks on real data we show that our conditional
interpretation methods reduce extrapolation. In an application we show that
these methods provide more nuanced and richer explanations
Distribution of cracks in a chain of atoms at low temperature
We consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 1/β ∈ (0, ∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-β e surf /2) with e surf > 0 a surface energy
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Surface Energy and Boundary Layers for a Chain of Atoms at Low Temperature
We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard–Jones type. The pressure (stress) is assumed to be small but positive and bounded away from zero, while the temperature β- 1 goes to zero. Our main results are: (1) As β→ ∞ at fixed positive pressure p> 0 , the Gibbs measures μβ and νβ for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals E¯ bulk and E¯ surf. The minimizer of the surface functional corresponds to zero temperature boundary layers; (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of E¯ surf; (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts; (4) Bounds on the decay of correlations are provided, some of them uniform in β. © 2020, The Author(s)
The Akie language of Tanzania a sketch of discourse grammar
Bibliography: p. 177-18
Distribution of cracks in a chain of atoms at low temperature
We consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 1/β ∈ (0, ∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-β e surf /2) with e surf > 0 a surface energy
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