scholarly journals Entropy of Simulated Liquids Using Multiscale Cell Correlation

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 750
Author(s):  
Hafiz Saqib Ali ◽  
Jonathan Higham ◽  
Richard H. Henchman
Keyword(s):  
Degrees Of Freedom ◽  
Probability Distributions ◽  
Mean Field ◽  
Vibrational Entropy ◽  
Amber Force Field ◽  
Equal Importance ◽  
The Mean ◽  
Dynamics Simulations ◽  
Consistent Treatment ◽  
Better Than

Accurately calculating the entropy of liquids is an important goal, given that many processes take place in the liquid phase. Of almost equal importance is understanding the values obtained. However, there are few methods that can calculate the entropy of such systems, and fewer still to make sense of the values obtained. We present our multiscale cell correlation (MCC) method to calculate the entropy of liquids from molecular dynamics simulations. The method uses forces and torques at the molecule and united-atom levels and probability distributions of molecular coordinations and conformations. The main differences with previous work are the consistent treatment of the mean-field cell approximation to the approriate degrees of freedom, the separation of the force and torque covariance matrices, and the inclusion of conformation correlation for molecules with multiple dihedrals. MCC is applied to a broader set of 56 important industrial liquids modeled using the Generalized AMBER Force Field (GAFF) and Optimized Potentials for Liquid Simulations (OPLS) force fields with 1.14*CM1A charges. Unsigned errors versus experimental entropies are 8.7 J K − 1 mol − 1 for GAFF and 9.8 J K − 1 mol − 1 for OPLS. This is significantly better than the 2-Phase Thermodynamics method for the subset of molecules in common, which is the only other method that has been applied to such systems. MCC makes clear why the entropy has the value it does by providing a decomposition in terms of translational and rotational vibrational entropy and topographical entropy at the molecular and united-atom levels.

QUANTUM CORRECTIONS TO THE CRANKING MODEL

1992 ◽  
Vol 01 (01) ◽  
pp. 95-130 ◽  
Author(s):  
ABRAHAM KLEIN ◽  
NIELS R. WALET ◽  
G. DO DANG
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Correction ◽  
Mean Field ◽  
Original System ◽  
Quantum Corrections ◽  
Transition Rates ◽  
Rotation Symmetry ◽  
Exchange Effects ◽  
Self Consistent ◽  
The Mean

A method is described for the restoration of translation or rotation symmetry to a system of fermions, starting from a self-consistent cranking solution and valid when either momentum or angular momentum is large enough so that semi-classical approximations are valid. The quantum fluctuations that restore the broken symmetry are described in terms of the particle-hole degrees of freedom of the original system rather than by mapping these variables onto a boson space, as in most previous work. Only the leading quantum correction to the mean field solution is worked out in detail. New results include the treatment of direct and exchange effects on an equal footing and a method for computing transition rates.

scholarly journals 1/Nc EXPANSION FOR THE PARTITION FUNCTION IN FOUR-FERMION MODELS

1996 ◽  
Vol 11 (19) ◽  
pp. 1579-1587 ◽  
Author(s):  
A. BARDUCCI ◽  
R. CASALBUONI ◽  
M. MODUGNO ◽  
G. PETTINI ◽  
R. GATTO
Keyword(s):  
Partition Function ◽  
Low Temperatures ◽  
Degrees Of Freedom ◽  
Mean Field ◽  
Field Approximation ◽  
Functional Integral ◽  
Mean Field Approximation ◽  
Thermodynamical Potential ◽  
Low Mass ◽  
The Mean

We present a derivation of the bosonic contribution to the thermodynamical potential of four-fermion models by means of a 1/N c -expansion of the functional integral defining the partition function. This expansion turns out to be particularly useful in correcting the mean field approximation especially at low temperatures, where the relevant degrees of freedom are low-mass bosonic excitations (pseudo-Goldstones).

scholarly journals Multiphase Organization Is a Second Phase Transition Within Multi-Component Biomolecular Condensates

2021 ◽  
Author(s):  
Konstantinos Mazarakos ◽  
Huan-Xiang Zhou
Keyword(s):  
Phase Transition ◽  
Mean Field Theory ◽  
Mean Field ◽  
Individual Species ◽  
Second Phase ◽  
Dense Phase ◽  
Main Driver ◽  
The Mean ◽  
Dynamics Simulations ◽  
The Individual

We present a mean-field theory for the multiphase organization of multi-component biomolecular condensates and validate the theory by molecular dynamics simulations of model mixtures. A first phase transition results in the separation of the dense phase from the bulk phase. In a second phase transition, the components in the dense phase demix to localize in separate regions that attach to each other. The second phase transition occurs when the strength of cross- species attraction goes below the mean strength of the self-attraction of the individual species and reaches a critical value. At a given strength of cross-species attraction, both of the phase transitions can be observed by decreasing temperature, leading first to phase separation and then to demixing of the dense phase. The theory and simulations establish the disparity in strength between self and cross-species attraction as a main driver for the multiphase organization of multi-component biomolecular condensates.

NUCLEON PROPERTIES FROM MODIFIED SIGMA MODEL

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2673-2681 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Original Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

Birse and Banerjee model is extended to include higher-order mesonic interactions. The field equations have been solved in the mean-field approximation and a good agreement with the data for the nucleon properties has been obtained. The agreement is better than that obtained by the original model of Birse and Banerjee which indicates the important of the inclusion of higher-order meson correlations.

scholarly journals On the Critical Value for ‘Percolation’ of Minimum-Weight Trees in the Mean-Field Distance Model

1998 ◽  
Vol 7 (1) ◽  
pp. 1-10 ◽  
Author(s):  
DAVID ALDOUS
Keyword(s):  
Fixed Point ◽  
Probability Distributions ◽  
Minimum Weight ◽  
Mean Field ◽  
Critical Value ◽  
Edge Weight ◽  
Maximal Size ◽  
Distance Model ◽  
The Mean

Consider the complete n-graph with independent exponential (mean n) edge-weights. Let M(c, n) be the maximal size of subtree for which the average edge-weight is at most c. It is shown that M(c, n) makes the transition from o(n) to Ω(n) around some critical value c(0), which can be specified in terms of a fixed point of a mapping on probability distributions.

scholarly journals Noise and disorder: Phase transitions and universality in a model of opinion formation

2016 ◽  
Vol 27 (06) ◽  
pp. 1650060 ◽  
Author(s):  
Nuno Crokidakis
Keyword(s):  
Phase Transitions ◽  
Probability Distributions ◽  
Mean Field ◽  
Universality Class ◽  
Formation Model ◽  
Opinion Formation ◽  
Discrete Probability ◽  
Wide Range ◽  
The Mean ◽  
Discrete Probability Distributions

In this work, we study a three-state opinion formation model considering two distinct mechanisms, namely independence and conviction. Independence is introduced in the model as a noise by means of a probability of occurrence q. On the other hand, conviction acts as a disorder in the system, and it is introduced by two discrete probability distributions. We analyze the effects of such two mechanisms on the phase transitions of the model, and we found that the critical exponents are universal over the order–disorder frontier, presenting the same universality class of the mean-field Ising model. In addition, for one of the probability distributions, the transition may be eliminated for a wide range of the parameters.

THE NUCLEAR MATTER COMPRESSIBILITY FUNCTION IN A PARAMETERIZED COUPLING MODEL

2007 ◽  
Vol 16 (02n03) ◽  
pp. 269-275 ◽  
Author(s):  
VERÔNICA A. DEXHEIMER ◽  
CÉSAR A. Z. VASCONCELLOS ◽  
BARDO E. J. BODMANN
Keyword(s):  
Field Theory ◽  
Degrees Of Freedom ◽  
Mean Field Theory ◽  
Mean Field ◽  
Compression Modulus ◽  
Coupling Model ◽  
Baryon Number ◽  
Nucleon Mass ◽  
Derivative Coupling ◽  
The Mean

In the framework of an effective derivative-coupling model with scalar and vector mesons coupled to the octet of baryons and leptonic degrees of freedom, we have calculated in detail the nuclear property known as the compressibility function, using the mean-field theory formalism and taking into account chemical equilibrium, baryon number and electric charge conservation. The parameters of the model are chosen in order to reproduce phenomenology: an effective nucleon mass between 0.7–0.8 MN and a compression modulus between 200–300 MeV.

ANTIFERROMAGNETISM AND HOLE CONCENTRATION IN THE LINEAR SPIN WAVE APPROXIMATION OF THE t-J MODEL

1994 ◽  
Vol 08 (02) ◽  
pp. 131-136 ◽  
Author(s):  
A. BELKASRI ◽  
J.L. RICHARD
Keyword(s):  
Spin Wave ◽  
Order Parameter ◽  
Degrees Of Freedom ◽  
Hole Concentration ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Antiferromagnetic State ◽  
Wave Approximation ◽  
The Mean

The interplay between antiferromagnetic state and low doping regime is studied within the framework of the t-J model. The staggered magnetization is calculated in the mean field approximation by separating spin and charge degrees of freedom. We have obtained that this order parameter decreases with increasing doping and vanishes for some critical hole concentration.

USING THE POTTS GLASS FOR SOLVING THE CLUSTERING PROBLEM

1995 ◽  
Vol 06 (02) ◽  
pp. 119-132 ◽  
Author(s):  
MATS BENGTSSON ◽  
PERTTI ROIVAINEN
Keyword(s):  
Vector Quantization ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Local Minima ◽  
Clustering Problem ◽  
The Mean ◽  
Free Parameters ◽  
Clustering Problems ◽  
Better Than

We present an application of a Potts glass to the clustering problem. Simulated annealing in the mean field approximation is used in order to avoid local minima. The resulting updating equations are completely parallel, and very easy to implement. The model has no free parameters except for the annealing parameters. We show how the model can be implemented for some special clustering problems. The T→0 limit of the Potts glass is identical to the vector quantization algorithm with certain increments. A comparative study of the Potts glass and vector quantization is also made, and it is shown that for difficult clustering problems, the Potts glass is far better than vector quantization.

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