Search results for "statistical"
showing 10 items of 4960 documents
Entropy of glassy polymer melts: Comparison between Gibbs-DiMarzio theory and simulation.
1996
We calculate the free energy of a model for a polymer melt in a computer simulation of the bond-fluctuation model and determine the entropy of the melt over a wide range of temperatures, including the region close to the glass transition. The results are compared with the Gibbs-DiMarzio theory, a theory by Flory for semiflexible polymers, and a modification of their theories due to Milchev. We can describe the data within the framework of the Flory theory with Milchev's correction and discuss the consequences for the understanding of the glass transition. \textcopyright{} 1996 The American Physical Society.
Computer Simulations and Coarse-Grained Molecular Models Predicting the Equation of State of Polymer Solutions
2010
Monte Carlo and molecular dynamics simulations are, in principle, powerful tools for carrying out the basic task of statistical thermodynamics, namely the prediction of macroscopic properties of matter from suitable models of effective interactions between atoms and molecules. The state of the art of this approach is reviewed, with an emphasis on solutions of rather short polymer chains (such as alkanes) in various solvents. Several methods of constructing coarse-grained models of the simple bead–spring type will be mentioned, using input either from atomistic models (considering polybutadiene as an example) or from experiment. Also, the need to have corresponding coarse-grained models of t…
SPATIAL MULTIFRACTALITY OF ELECTRONIC STATES AND THE METAL-INSULATOR TRANSITION IN DISORDERED SYSTEMS
1993
For the investigation of the spatial behavior of electronic wave functions in disordered systems, we employ the Anderson model of localization. The eigenstates of the corresponding Hamiltonian are calculated numerically by means of the Lanczos algorithm and are analyzed with respect to their spatial multifractal properties. We find that the wave functions show spatial multifractality for all parameter cases not too far away from the metal-insulator transition (MIT) which separates localized from extended states in this model. Exactly at the MIT, multifractality is expected to exist on all length scales larger than the lattice spacing. It is found that the corresponding singularity spectrum…
Influence of CO in the structural and electrical properties of Pt nanocontacts: comparison with H2 molecule addition.
2009
Density-functional theory is used to determine the atomic structure and the zero-bias conductance of Pt nanocontacts upon CO addition. Three stable atomic configurations of the nanocontacts, in conjunction with a statistical analysis of their electrical response, are enough to explain the main features of the experimental conductance histograms. Remarkably, the role of nonlocal effects when approaching the exchange-correlation potential within density-functional theory turns out to be crucial for CO molecular-based systems. Finally, a comparison with H(2) molecule addition on Pt nanocontacts is presented.
Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
1995
We report the results of a large scale computer simulation of a binary supercooled Lennard-Jones liquid. We find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time $tD(T)$, where $D(T)$ is the diffusion constant. The time range for which these curves follow the master curve is identified with the $\alpha$-relaxation regime of mode-coupling theory (MCT). This master curve is fitted well by a functional form suggested by MCT. In accordance with idealized MCT, $D(T)$ shows a power-law behavior at low temperatures. The critical temperature of this power-law is t…
Glass transition of hard spheres in high dimensions
2009
We have investigated analytically and numerically the liquid-glass transition of hard spheres for dimensions $d\to \infty $ in the framework of mode-coupling theory. The numerical results for the critical collective and self nonergodicity parameters $f_{c}(k;d) $ and $f_{c}^{(s)}(k;d) $ exhibit non-Gaussian $k$ -dependence even up to $d=800$. $f_{c}^{(s)}(k;d) $ and $f_{c}(k;d) $ differ for $k\sim d^{1/2}$, but become identical on a scale $k\sim d$, which is proven analytically. The critical packing fraction $\phi_{c}(d) \sim d^{2}2^{-d}$ is above the corresponding Kauzmann packing fraction $\phi_{K}(d)$ derived by a small cage expansion. Its quadratic pre-exponential factor is different fr…
Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range co…
2017
Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of …
Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique
2010
We present an approach, framed in information theory, to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system. The approach follows a sequential procedure for nonuniform embedding of multivariate time series, whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states. A corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure. The causal coupling is detected acc…
Chernobyl exposure as stressor during pregnancy and behaviour in adolescent offspring.
2007
Objective: Research in animals has shown that exposure to stressors during pregnancy is associated with offspring behavioural disorders. We aimed to study the effect of in utero exposure to the Chernobyl disaster in 1986, and maternal anxiety presumably associated with that exposure, on behaviour disorder observed at age 14. Method: Exposed (n = 232) and non-exposed Finnish twins (n = 572) were compared. A semi-structured interview was used to assess lifetime symptoms of depression, generalized anxiety disorder, attention deficit hyperactivity disorder, conduct disorder and oppositional defiant disorder symptoms. Results: Adolescents who were exposed from the second trimester in pregnancy o…
Empirically Determined, Psychopathological Subtypes in Children With ADHD
2013
OBJECTIVE: The aim of this study was to empirically determine subgroups of ADHD defined by specific patterns of psychopathology. METHOD: A clinical sample of 223 children with ADHD, aged 5 to 14 years, was examined with the Child Behavior Checklist (CBCL). In addition, comorbid psychiatric disorders, psychosocial risk factors, and socioeconomic status were assessed. RESULTS: Cluster analysis of CBCL subscales yielded a solution with four distinct subgroups. While "externalizers" showed a high rate of comorbid oppositional defiant disorder (ODD) and conduct disorder (CD), "obsessive-compulsives" exhibited thought problems, low rates of comorbid CD, and high symptoms of inattention. "High psy…