Search results for "Statistical physics"
showing 10 items of 1402 documents
Dynamics of a Supercooled Lennard-Jones System: Qualitative and Quantitative Tests of Mode-Coupling Theory
1996
We present the results of a molecular dynamics computer simulation of a supercooled binary Lennard-Jones mixture. By investigating the temperature dependence of the diffusion constant and of the intermediate scattering function, we show that the ideal version of the mode-coupling theory of the glass transition is able to give a good qualitative description of the dynamics of this system. Using the partial structure factors, as determined from the simulation, as input, we solve the mode-coupling equations in the long time limit. From the comparison of the prediction of the theory for the critical temperature, the exponent parameter, the wave-vector dependence of the nonergodicity parameters …
Glass transition in 1,4-polybutadiene: Mode-coupling theory analysis of molecular dynamics simulations using a chemically realistic model.
2006
We present molecular dynamics simulations of the glass transition in a chemically realistic model of 1,4-polybutadiene (PBD). Around 40 K above the calorimetric glass transition of this polymer the simulations reveal a well-developed two-stage relaxation of all correlation functions. We have analyzed the time-scale separation between vibrational degrees of freedom (subpicosecond dynamics) and the alpha relaxation behavior (nanosecond to microsecond dynamics) using the predictions of mode-coupling theory (MCT). Our value for the mode-coupling critical temperature Tc agrees perfectly with prior experimental estimates for PBD. The predictions of MCT for the scaling behavior of the so-called be…
Energy-Stable Numerical Schemes for Multiscale Simulations of Polymer–Solvent Mixtures
2017
We present a new second-order energy dissipative numerical scheme to treat macroscopic equations aiming at the modeling of the dynamics of complex polymer–solvent mixtures. These partial differential equations are the Cahn-Hilliard equation for diffuse interface phase fields and the Oldroyd-B equations for the hydrodynamics of the polymeric mixture. A second-order combined finite volume/finite difference method is applied for the spatial discretization. A complementary approach to study the same physical system is realized by simulations of a microscopic model based on a hybrid Lattice Boltzmann/Molecular Dynamics scheme. These latter simulations provide initial conditions for the numerical…
Inferring causal relations from observational long-term carbon and water fluxes records
2022
AbstractLand, atmosphere and climate interact constantly and at different spatial and temporal scales. In this paper we rely on causal discovery methods to infer spatial patterns of causal relations between several key variables of the carbon and water cycles: gross primary productivity, latent heat energy flux for evaporation, surface air temperature, precipitation, soil moisture and radiation. We introduce a methodology based on the convergent cross-mapping (CCM) technique. Despite its good performance in general, CCM is sensitive to (even moderate) noise levels and hyper-parameter selection. We present a robust CCM (RCCM) that relies on temporal bootstrapping decision scores and the deri…
Universal N -Partite d -Level Pure-State Entanglement Witness Based on Realistic Measurement Settings
2019
Entanglement witnesses are operators that are crucial for confirming the generation of specific quantum systems, such as multipartite and high-dimensional states. For this reason, many witnesses have been theoretically derived which commonly focus on establishing tight bounds and exhibit mathematical compactness as well as symmetry properties similar to that of the quantum state. However, for increasingly complex quantum systems, established witnesses have lacked experimental achievability, as it has become progressively more challenging to design the corresponding experiments. Here, we present a universal approach to derive entanglement witnesses that are capable of detecting the presence …
Embedding Quantum into Classical: Contextualization vs Conditionalization
2014
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type ine…
Multivariate stochastic wave generation
1996
Abstract In this paper, for the case of the fluid particle velocity, a procedure that substantially reduces the computational effort to generate a multivariate stochastic process is proposed. It is shown that, for a fully coherent wave field, it is possible to decompose the Power Spectral Density (PSD) matrix into the eigenvectors of the matrix itself. This leads to generate each field's process as independent, and the time generation increases linearly with the processes' number in the field. A numerical example to evaluate the statistical properties, in terms of correlation and cross-correlation functions, of the processes is also presented.
Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations
2021
While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve …
Detecting nonlinear causal interactions between dynamical systems by non-uniform embedding of multiple time series.
2010
This study introduces a new approach for the detection of nonlinear Granger causality between dynamical systems. The approach is based on embedding the multivariate (MV) time series measured from the systems X and Y by means of a sequential, non-uniform procedure, and on using the corrected conditional entropy (CCE) as unpredictability measure. The causal coupling from X to Y is quantified as the relative decrease of CCE measured after allowing the series of X to enter the embedding procedure for the description of Y. The ability of the approach to quantify nonlinear causality is assessed on MV time series measured from simulated dynamical systems with unidirectional coupling (the Rössler-…
Surrogate Data Analysis for Assessing the Significance of the Coherence Function
2004
In cardiovascular variability analysis, the significance of the coupling between two time series is commonly assessed by setting a threshold level in the coherence function. While traditionally used statistical tests consider only the parameters of the adopted estimator, the required zero-coherence level may be affected by some features of the observed series. In this study, three procedures, based on the generation of surrogate series sharing given properties with the original but being structurally uncoupled, were considered: independent identically distributed (IID), Fourier transform (FT), and autoregressive (AR). IID surrogates maintained the distribution of the original series, while …