scholarly journals Chaos and Its Impact on the Foundations of Statistical Mechanics

1996 ◽  
Vol 49 (1) ◽  
pp. 51 ◽  
Author(s):  
Gary P Morriss ◽  
Lamberto Rondoni
Keyword(s):  
Periodic Orbit ◽  
Lorentz Gas ◽  
Analytic Formula ◽  
Numerical Techniques ◽  
Lyapunov Numbers ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
Definition Of ◽  
Dynamics Simulations ◽  
Good Agreement

In this work we present a brief derivation of the periodic orbit expansion for simple dynamical systems, and then we apply it to the study of a classical statistical mechanical model, the Lorentz gas, both at equilibrium and in a nonequilibrium steady state. The results are compared with those obtained through standard molecular dynamics simulations, and they are found to be in good agreement. The form of the average using the periodic orbit expansion suggests the definition of a new dynamical partition function, which we test numerically. An analytic formula is obtained for the Lyapunov numbers of periodic orbits for the nonequilibrium Lorentz gas. Using this formula and other numerical techniques we study the nonequilibrium Lorentz gas as a dynamical system and obtain an estimate of the upper bound on the external field for which the system remains ergodic.

scholarly journals Torque and buckling in stretched intertwined double-helix DNAs

2017 ◽  
Author(s):  
Sumitabha Brahmachari ◽  
John F. Marko
Keyword(s):  
Experimental Data ◽  
Mechanical Model ◽  
Double Helix ◽  
Magnetic Tweezers ◽  
Applied Force ◽  
Linking Number ◽  
Opposite Trend ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
Good Agreement

We present a statistical-mechanical model for the behavior of intertwined DNAs, with a focus on their torque and extension as a function of their catenation (linking) number and applied force, as studied in magnetic tweezers experiments. Our model produces results in good agreement with available experimental data, and predicts a catenation-dependent effective twist modulus distinct from what is observed for twisted individual double-helix DNAs. We find that buckling occurs near to the point where experiments have observed a kink in the extension versus linking number, and that the subsequent “supercoiled braid” state corresponds to a proliferation of multiple small plectoneme structures. We predict a discontinuity in extension at the buckling transition corresponding to nucleation of the first plectoneme domain. We also find that buckling occurs for lower linking number at lower salt; the opposite trend is observed for supercoiled single DNAs.

Multicanonical Molecular Dynamics Simulation Study of the Liquid-Solid and Solid-Solid Transitions in Lennard-Jones Clusters

2011 ◽  
Author(s):  
Toshihiro Kaneko ◽  
Kenji Yasuoka ◽  
Ayori Mitsutake ◽  
Xiao Cheng Zeng
Keyword(s):  
Molecular Dynamics ◽  
Heat Capacity ◽  
Transition Temperature ◽  
Peak Position ◽  
Temperature Curve ◽  
Dynamics Simulation ◽  
Lennard Jones ◽  
Dynamics Simulations ◽  
First Time ◽  
Good Agreement

Multicanonical molecular dynamics simulations are applied, for the first time, to study the liquid-solid and solid-solid transitions in Lennard-Jones (LJ) clusters. The transition temperatures are estimated based on the peak position in the heat capacity versus temperature curve. For LJ31, LJ58 and LJ98, our results on the solid-solid transition temperature are in good agreement with previous ones. For LJ309, the predicted liquid-solid transition temperature is also in agreement with previous result.

Periodic orbit expansions for the Lorentz gas

1994 ◽  
Vol 75 (3-4) ◽  
pp. 553-584 ◽  
Author(s):  
Gary P. Morris ◽  
Lamberto Rondoni
Keyword(s):  
Periodic Orbit ◽  
Lorentz Gas

scholarly journals Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical Chains

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Christian B. Mendl ◽  
Folkmar Bornemann
Keyword(s):  
Transfer Operator ◽  
Classical System ◽  
Free Energy Density ◽  
Classical Particle ◽  
Thermodynamic Quantities ◽  
Nls Equation ◽  
Classical Systems ◽  
Particle Chain ◽  
Dynamics Simulations ◽  
Good Agreement

AbstractThis work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.

Size-Dependent Elasticity of Silicon Nanowires

2009 ◽  
Vol 60-61 ◽  
pp. 315-319 ◽  
Author(s):  
W.W. Zhang ◽  
Qing An Huang ◽  
H. Yu ◽  
L.B. Lu
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Silicon Nanowires ◽  
First Principles ◽  
Si Nanowires ◽  
Size Dependent ◽  
Reconstructed Surfaces ◽  
Strain Relationship ◽  
Dynamics Simulations ◽  
Good Agreement

Molecular dynamics simulations are carried out to characterize the mechanical properties of [001] and [110] oriented silicon nanowires, with the thickness ranging from 1.05nm to 3.24 nm. The nanowires are taken to have ideal surfaces and (2×1) reconstructed surfaces, respectively. A series of simulations for square cross-section Si nanowires have been performed and Young’s modulus is calculated from energy–strain relationship. The results show that the elasticity of Si nanowires is strongly depended on size and surface reconstruction. Furthermore, the physical origin of above results is analyzed, consistent with the bond loss and saturation concept. The results obtained from the molecular dynamics simulations are in good agreement with the values of first-principles. The molecular dynamics simulations combine the accuracy and efficiency.

Computer-Generated Structural Models for a-Si:H

1988 ◽  
Vol 141 ◽  
Author(s):  
Laurent J. Lewis ◽  
Normand Mousseau ◽  
FranÇois Drolet
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Amorphous Silicon ◽  
Periodic Boundary ◽  
Hydrogenated Amorphous Silicon ◽  
Structural Models ◽  
Periodic Boundary Conditions ◽  
Dynamics Simulations ◽  
Hydrogenated Amorphous ◽  
Good Agreement

AbstractA new algorithm for generating fully-coordinated hydrogenated amorphous silicon models with periodic boundary conditions is presented. The hydrogen is incorporated into an a-Si matrix by a bond-switching process similar to that proposed by Wooten, Winer, and Weaire, making sure that four-fold coordination is preserved and that no rings with less than 5 members are created. After each addition of hydrogen, the structure is fully relaxed. The models so obtained, to be used as input to molecular dynamics simulations, are found to be in good agreement with experiment. A model with 12 at.% H is discussed in detail.

ALTERNATIVE COEFFICIENT OF CONCORDANCE IN CASE OF CONNECTED RANKS

2021 ◽  
pp. 40-45
Author(s):  
Ю.В. Лубенец
Keyword(s):  
Expert Opinion ◽  
Special Kind ◽  
Statistical Characteristics ◽  
Expert Survey ◽  
Complete Consistency ◽  
Expert Opinions ◽  
Coefficient Of Concordance ◽  
Definition Of ◽  
Two Stages ◽  
Good Agreement

Рассматривается оценка согласованности мнений экспертов при проведении экспертного опроса. Наиболее часто в качестве такой оценки применяется коэффициент конкордации Кендалла. Однако этот коэффициент не может в полной мере применяться для установления хорошей согласованности мнений экспертов, поскольку он показывает только отклонение от случаев полной несогласованности. Для устранения данного недостатка может рассматриваться альтернативный коэффициент конкордации, оценивающий близость сумм рангов альтернатив к случаю полной согласованности. Здесь дается определение этого коэффициента при наличии связанных рангов. Сложность определения заключается в том, что в этом случае наблюдается несколько случаев полной согласованности с различными суммами рангов. Определение альтернативного коэффициента конкордации при наличии связанных рангов проводится в два этапа. Сначала вводится его определение для упорядоченных таблиц специального вида и показывается его совпадение с коэффициентом конкордации Кендалла в этом случае. После дается определение альтернативного коэффициента конкордации в общем случае и показывается более простая формула его вычисления. Далее приводятся некоторые примеры сравнений значений рассматриваемых коэффициентов конкордации, их статистических характеристик и гистограмм The article considers evaluation of expert opinion consistency when conducting an expert survey. The most commonly used score is Kendall's coefficient of concordance. However, this coefficient cannot be fully applied to establish good agreement of expert opinions, as it only shows deviations from cases of complete inconsistency. To eliminate this drawback, an alternative concordance coefficient can be considered, which estimates the proximity of the sums of the ranks of the alternatives to the case of complete consistency. The article gives the definition of this coefficient in the presence of connected ranks. The difficulty of this definition lies in the fact that in this case there are several cases of complete consistency with different sums of ranks. Definition of the alternative coefficient of concordance in the presence of tied ranks is carried out in two stages. First, its definition for ordered tables of a special kind is introduced and its coincidence with Kendall's coefficient of concordance in this case is shown. After that, the definition of the alternative coefficient of concordance in the general case is given and a simpler formula for its calculation is shown. Below are some examples of comparisons of the values of the considered concordance coefficients, their statistical characteristics, and histograms

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