Mean-square displacement of a stochastic oscillator: Linear vs quadratic noise

2012 ◽  
Vol 391 (11) ◽  
pp. 3033-3042 ◽  
Author(s):  
M. Gitterman
Keyword(s):  
Mean Square Displacement ◽  
Mean Square ◽  
Stochastic Oscillator ◽  
Quadratic Noise

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.

Molecular Dynamics Study of Microscopic Mechanism of Diffusion in Li2SiO3 System

1991 ◽  
Vol 46 (7) ◽  
pp. 616-620 ◽  
Author(s):  
Junko Habasaki
Keyword(s):  
Molecular Dynamics ◽  
Coordination Number ◽  
Md Simulation ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Lithium Ions ◽  
Microscopic Mechanism ◽  
Trapping Model ◽  
The Mean

MD simulation has been performed to learn the microscopic mechanism of diffusion of ions in the Li2SiO3 system. The motion of lithium ions can be explained by the trapping model, where lithium is trapped in the polyhedron and moves with fluctuation of the coordination number. The mean square displacement of lithium was found to correlate well with the net changes in coordination number.

Temperature dependence of asymmetry parameter and mean square displacement of the iron sites in FeSO4⋅4H2O

1977 ◽  
Vol 66 (12) ◽  
pp. 5798-5800 ◽  
Author(s):  
M. S. Nascimento ◽  
V. K. Garg
Keyword(s):  
Temperature Dependence ◽  
Asymmetry Parameter ◽  
Mean Square Displacement ◽  
Mean Square

Swimming of the Trophont Zooid of Vorticella Convallaria

2021 ◽  
Author(s):  
Dilziba Kizghin ◽  
Sangjin Ryu ◽  
Younggil Park ◽  
Sunghwan Jung
Keyword(s):  
Mean Square Displacement ◽  
Swimming Velocity ◽  
Mean Square ◽  
Ciliated Protozoan ◽  
Swimming Motility ◽  
Swimming Motion ◽  
Swimming Pattern ◽  
Freshwater Habitats ◽  
Gap Height ◽  
Swimming Trajectories

Abstract Vorticella convallaria is a ciliated protozoan found in freshwater habitats. In the sessile or stalked trophont form, V. convallaria is shaped somewhat like a balloon as it has a body or zooid (the head of the balloon) that is about 40 μm large with cilia around its oral part, and a stalk (the string of a balloon) anchoring the zooid to a solid surface. When a trophont zooid of V. convallaria detached from the stalk, the zooid swims around in water by creating water flow using its oral cilia. In contrast to the stalk contraction of V. convallaria that has been well studied, the swimming motility of V. convallaria is little known. In this study, we measured the swimming trajectories of the stalkless trophont zooid of V. convallaria using video microscopy and Hele-Shaw cells with a gap height of 25 μm, traced the swimming zooid using image processing, and analyzed the swimming motion in terms of swimming velocity and mean square displacement. The stalkless trophont zooid of V . convallaria was found to swim in circular patterns with intermittent ballistic motions in the confinement, and the average swimming speed ranged from 20 μm/s to 110 μm/s. Since the swimming pattern of V. convallaria appeared to be affected by the level of confinement, we will continue characterizing the ciliate’s swimming in the Hele-Shaw cell with different gap heights. Our study is expected to reveal the swimming motility of V. convallaria and to advance general understanding of swimming of microorganisms.

THE EFFECT OF PREMELTING: STUDY FOR SEMI-INFINITE CRYSTALS AND NANO-SYSTEMS

1994 ◽  
Vol 08 (24) ◽  
pp. 3411-3422 ◽  
Author(s):  
W. SCHOMMERS
Keyword(s):  
Pair Correlation ◽  
Mean Square Displacement ◽  
Phonon Density ◽  
Mean Square ◽  
Phonon Density Of States ◽  
Molecular Dynamics Calculations ◽  
Theory Of Melting ◽  
The Mean ◽  
Dynamical Properties ◽  
Reliable Interaction

The effect of premelting is of particular interest in connection with the theory of melting. In this paper, we discuss the structural and dynamical properties of the surfaces of semi-infinite crystals as well as of nano-clusters, which show the effect of premelting. The investigations are based on molecular-dynamics calculations: different models are used for the systematic study of the effect of premelting. In particular, the behaviour of the following functions have been studied: pair correlation function, generalized phonon density of states, and the mean-square displacement as a function of time. The calculations have been done for krypton since for this substance a reliable interaction potential is available.

scholarly journals Distributions of diffusion measures from a local mean-square displacement analysis

2012 ◽  
Vol 86 (2) ◽  
Author(s):  
Amitabha Nandi ◽  
Doris Heinrich ◽  
Benjamin Lindner
Keyword(s):  
Mean Square Displacement ◽  
Mean Square ◽  
Displacement Analysis ◽  
Local Mean

scholarly journals Very simple method for the calculation of the mean square displacement of crystal atoms

1971 ◽  
Vol 32 (11-12) ◽  
pp. 939-940 ◽  
Author(s):  
P. Masri ◽  
L. Dobrzynski
Keyword(s):  
Mean Square Displacement ◽  
Mean Square ◽  
Simple Method ◽  
The Mean
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