scholarly journals Ordering in Two-Dimensional Lennard-Jones Clusters

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Barnana Pal
Keyword(s):  
Phase Diagram ◽  
Particle Concentration ◽  
Cluster Formation ◽  
Mean Square Displacement ◽  
Nearest Neighbour ◽  
Mean Square ◽  
Two Dimensional ◽  
Neighbour Distance ◽  
Lennard Jones ◽  
The Monte Carlo Method

Cluster formation in a two-dimensional Lennard-Jones system under different conditions of temperature () and particle concentration () has been studied using the Monte-Carlo method with the introduction of real thermal motion of the constituent particles through a modification of the conventional Metropolis algorithm. The - phase diagram determined from the study of the root mean square displacement of the particles shows features characteristics of the - diagram for phase equilibrium in real systems. The solid-like to liquid-like transition takes place when the average nearest neighbour distance increases by ~1% of the equilibrium value in the low-temperature solid-like configuration. The Lindemann parameter () is found to decrease with the increase of to reach a steady value of for .

Computer analysis of polarized spacing patterns with special reference to the larvae of the black fly, Simulium vittatum

1987 ◽  
Vol 65 (3) ◽  
pp. 602-604 ◽  
Author(s):  
M. Eymann ◽  
J. M. Schmidt ◽  
W. G. Friend
Keyword(s):  
Computer Analysis ◽  
Statistical Significance ◽  
Present Form ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Neighbour Distance ◽  
Analysis Techniques ◽  
Simulium Vittatum ◽  
Spacing Pattern ◽  
Average Individual

A computer analysis of spacing patterns which makes fewer assumptions than either nearest-neighbour distance or plot frequency analysis techniques is described. This analysis determines if the spacing pattern is polarized in any direction, and can compensate for the possible effect of the size and shape of the organism on the spacing pattern. The output of the analysis is a two-dimensional frequency distribution which represents the likelihood of finding a neighbour near an average individual. This output can be represented by a two-dimensional map. The method requires a sample size greater than 50, and in its present form cannot assign statistical significance to the resulting probability distribution.

scholarly journals VIRIAL THEOREM FOR ROTATING SELF-GRAVITATING BROWNIAN PARTICLES AND TWO-DIMENSIONAL POINT VORTICES

2012 ◽  
Vol 26 (12) ◽  
pp. 1241002 ◽  
Author(s):  
PIERRE-HENRI CHAVANIS
Keyword(s):  
Virial Theorem ◽  
Mean Square Displacement ◽  
Point Vortices ◽  
Mean Square ◽  
Two Dimensional ◽  
Exact Analytical Expression ◽  
Brownian Particles ◽  
The Mean ◽  
Gravitating Systems ◽  
Interacting Brownian Particles

We derive the virial theorem for an overdamped system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a closed form that can be used to obtain general results about the dynamics without being required to solve the Smoluchowski–Poisson system explicitly. In particular, we obtain the exact analytical expression of the mean square displacement 〈r2〉(t) of the interacting Brownian particles. We exhibit a critical temperature below which the system collapses, and above which it evaporates, and we determine how this temperature is affected by a solid rotation. We also develop an analogy between self-gravitating systems and two-dimensional point vortices. We derive a virial-like relation for point vortices at statistical equilibrium relating the angular velocity to the angular momentum and the temperature.

Liquid-vapor phase diagram and cluster formation of two-dimensional ionic fluids

2012 ◽  
Vol 137 (5) ◽  
pp. 054711 ◽  
Author(s):  
Gloria Arlette Méndez-Maldonado ◽  
Minerva González-Melchor ◽  
José Alejandre
Keyword(s):  
Phase Diagram ◽  
Vapor Phase ◽  
Cluster Formation ◽  
Two Dimensional ◽  
Ionic Fluids ◽  
Liquid Vapor

SELFTRAPPING DYNAMICS IN TWO-DIMENSIONAL NONLINEAR LATTICES

1999 ◽  
Vol 13 (24) ◽  
pp. 837-847 ◽  
Author(s):  
M. I. MOLINA
Keyword(s):  
Mean Square Displacement ◽  
Critical Value ◽  
Mean Square ◽  
Two Dimensional ◽  
Nonlinear Lattices ◽  
Long Time ◽  
Average Probability ◽  
The Mean ◽  
Time Average ◽  
Dnls Equation

We compute numerically the selftrapping dynamics for an electron or excitation initially located on a single site of a two-dimensional nonlinear lattice of arbitrary nonlinear exponent. The time evolution is given by the Discrete Nonlinear Schrödinger (DNLS) equation and we focus on the long-time average probability at the initial site and the mean square displacement in terms of both the exponent and strength of the nonlinearity. For the square and triangular nonlinear lattices, we find selftrapping for nonlinearity parameters greater than an exponent-dependent critical value, whose magnitude increases (decreases) with the nonlinear exponent when this is larger (smaller) than one, approximately.

scholarly journals Effect of Terminal Groups on Thermomechanical and Dielectric Properties of Silica–Epoxy Composite Modified by Hyperbranched Polyester

Polymers ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2451
Author(s):  
Jianwen Zhang ◽  
Dongwei Wang ◽  
Lujia Wang ◽  
Wanwan Zuo ◽  
Lijun Zhou ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Dielectric Properties ◽  
Binding Energy ◽  
Epoxy Resin ◽  
Volume Fraction ◽  
Epoxy Composite ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Hyperbranched Polyester ◽  
Free Volume Fraction

To study the effect of hyperbranched polyester with different kinds of terminal groups on the thermomechanical and dielectric properties of silica–epoxy resin composite, a molecular dynamics simulation method was utilized. Pure epoxy resin and four groups of silica–epoxy resin composites were established, where the silica surface was hydrogenated, grafted with silane coupling agents, and grafted with hyperbranched polyester with terminal carboxyl and terminal hydroxyl, respectively. Then the thermal conductivity, glass transition temperature, elastic modulus, dielectric constant, free volume fraction, mean square displacement, hydrogen bonds, and binding energy of the five models were calculated. The results showed that the hyperbranched polyester significantly improved the thermomechanical and dielectric properties of the silica–epoxy composites compared with other surface treatments, and the terminal groups had an obvious effect on the enhancement effect. Among them, epoxy composite modified by the hyperbranched polyester with terminal carboxy exhibited the best thermomechanical properties and lowest dielectric constant. Our analysis of the microstructure found that the two systems grafted with hyperbranched polyester had a smaller free volume fraction (FFV) and mean square displacement (MSD), and the larger number of hydrogen bonds and greater binding energy, indicating that weaker strength of molecular segments motion and stronger interfacial bonding between silica and epoxy resin matrix were the reasons for the enhancement of the thermomechanical and dielectric properties.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

scholarly journals Tentative Peptide‒Lipid Bilayer Models Elucidating Molecular Behaviors and Interactions Driving Passive Cellular Uptake of Collagen-Derived Small Peptides

Molecules ◽  
2021 ◽  
Vol 26 (3) ◽  
pp. 710
Author(s):  
Pathomwat Wongrattanakamon ◽  
Wipawadee Yooin ◽  
Busaban Sirithunyalug ◽  
Piyarat Nimmanpipug ◽  
Supat Jiranusornkul
Keyword(s):  
Lipid Bilayer ◽  
Lipid Bilayers ◽  
Mean Square Displacement ◽  
Dynamics Simulation ◽  
Coordinate Frame ◽  
Mean Square ◽  
Binding Modes ◽  
Small Peptides ◽  
Collagen Peptides ◽  
Electron Density Profiles

Collagen contains hydroxyproline (Hyp), which is a unique amino acid. Three collagen-derived small peptides (Gly-Pro-Hyp, Pro-Hyp, and Gly-Hyp) interacting across a lipid bilayer (POPC model membrane) for cellular uptakes of these collagen-derived small peptides were studied using accelerated molecular dynamics simulation. The ligands were investigated for their binding modes, hydrogen bonds in each coordinate frame, and mean square displacement (MSD) in the Z direction. The lipid bilayers were evaluated for mass and electron density profiles of the lipid molecules, surface area of the head groups, and root mean square deviation (RMSD). The simulation results show that hydrogen bonding between the small collagen peptides and plasma membrane plays a significant role in their internalization. The translocation of the small collagen peptides across the cell membranes was shown. Pro-Hyp laterally condensed the membrane, resulting in an increase in the bilayer thickness and rigidity. Perception regarding molecular behaviors of collagen-derived peptides within the cell membrane, including their interactions, provides the novel design of specific bioactive collagen peptides for their applications.

ELASTIC PROPERTIES OF STRAINED FCC AND HCP IRON

1993 ◽  
Vol 07 (01n03) ◽  
pp. 207-211
Author(s):  
T. KRAFT ◽  
M. METHFESSEL ◽  
M. VAN SCHILFGAARDE ◽  
M. SCHEFFLER
Keyword(s):  
Energy Cost ◽  
Interplanar Distance ◽  
Orbital Method ◽  
Full Potential ◽  
Local Spin Density Approximation ◽  
Nearest Neighbour ◽  
Density Approximation ◽  
Neighbour Distance ◽  
Large Lattice ◽  
Fcc Phase

Using the full-potential linear muffin-tin orbital method within the local spin-density approximation we analyse the influence of the nearest neighbour distance on fcc(111) or hcp(0001) iron layers. The LDA-LSDA error in describing ferromagnetic phases is determined to be at least 15 mRy/atom. As a consequence of this error, our calculations favour paramagnetic ground states. In this sense, the reported results have some model character. However, our analysis of the elastic energy cost under distortions should hold for transition metals in general. Allowing relaxations of the interplanar distance the fcc phase can become energetically favourable over the hcp phase at large lattice mismatches. The main reason for this behaviour is the enhanced stiffness of the hcp interplanar bonds due to the shortening of the axial c/a ratio.

Specific heat of ordered and isotopically disordered lattices

1978 ◽  
Vol 56 (10) ◽  
pp. 1390-1394
Author(s):  
K. P. Srivastava
Keyword(s):  
Specific Heat ◽  
Low Temperatures ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Volume ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Appreciable Difference ◽  
Substantial Change ◽  
Neighbour Interaction

An extensive numerical study on specific heat at constant volume (Cv) for ordered and isotopically disordered lattices has been made. Cv at various temperatures for ordered and disordered linear and two-dimensional lattices have been compared and no appreciable difference in Cv between these two structures has been observed. Effect of concentration of light atoms on Cv for three-dimensional isotopically disordered lattices has also been shown.In spite of taking next-nearest-neighbour interaction into account, no substantial change in Cv between the ordered and isotopically disordered linear lattices has been found. It is shown that the low lying modes contribute substantially at low temperatures.

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