Derivation and validation of mesoscopic theories for diffusion of interacting molecules

A mesoscopic theory for diffusion of molecules interacting with a long-range potential is derived for Arrhenius microscopic dynamics. Gradient Monte Carlo simulations are presented on a one-dimensional lattice to assess the validity of the mesoscopic theory. Results are compared for Metropolis and Arrhenius microscopic dynamics. Non-Fickian behavior is demonstrated and it is shown that microscopic dynamics dictate the steady-state concentration profiles.     

Equivalence of the method of the kinetic equation and the fluctuating-frequency method in the theory of the broadening of spectral lines

A new expression for the Stark profiles of spectral lines in plasma has been obtained by the method of the kinetic equation taking into account the dynamics of the plasma microfield. The result represents a dynamic line profile in the form of simple functionals of a static profile. The relation of the new solution with the known fluctuating-frequency method has been analyzed. It has been shown that this method is a discrete analog of the method of the kinetic equation and passes to the latter method in the limit of the continuous fluctuations. Simple formulas (4), (5), and (21) for dynamic line profiles provide ultrafast calculations of the profiles of spectral lines taking into account the dynamics of the plasma microfield.     

A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation

Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel (K-S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.     

非晶态金属Al中微团簇多面体结构及其演变规律的模拟研究

对50 000个金属Al原子从液态急冷形成非晶态结构的过程进行了分子动力学模拟研究.采用原子键型和原子团簇类型指数法,发现在其微观结构的转变过程中,与不断增加的1551键型密切相关的二十面体及其缺陷结构的形成起了非常突出的作用.通过各种键型原子团簇的计算,获得团簇多面体结构的分布数据.在可视化的显示下,得到一幅十分清晰的关于团簇多面体结构的特征及其演变的图景.建立了一种简单而有效的团簇多面体结构研究方法.同时也对模拟计算结果的微观机理给出了相应的讨论,这对于深入理解非晶态结构的形成机制及其微观过程,将有重     

Tunable-slip boundaries for coarse-grained simulations of fluid flow

On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit "slip" at the surface, which is characterized by a finite slip length (partial slip). We present a new, systematic way of implementing partial-slip boundary conditions with arbitrary slip length in coarse-grained computer simulations. The main idea is to represent the complex microscopic interface structure by a spatially varying effective viscous force. An analytical equation for the resulting slip length can be derived for planar and for curved surfaces. The comparison with computer simulations of a DPD (dissipative particle dynamics) fluid shows that this expression is valid from full slip to no slip.     

纳米尺度圆柱绕流现象的分子动力学模拟研究

本文采用分子动力学模拟方法,利用Lennard-Jones(L-J)势能模型,模拟了Re为28时Ar流体流过Pt纳米圆柱的绕流现象.采用小步长时均值作为涡的瞬时值的方法,在纳米尺度、纳秒量级下得到了涡的周期性产生、组合、发展和脱落现象;在大步长时均条件下,得到了稳定的对称涡,表现出了绕流现象在不同时间范围内的不同特征.绕流过程还体现了流体的密度变化,圆柱上游密度大于下游密度、对称的两侧离轴线越远密度越大.结果表明,分子动力学模拟方法可以有效地细节刻画圆柱绕流现象.     

Temperature Dependent Relativistic Microscopic Optical Potential and Mean Free Paths of Nucleons

The microscopic optical potential,mean free paths and Schrodinger equivalent potential of nucleons at finite temperature in nuclear matter are studied based on Walecka's model and thermo field dynamics.We let only the Hartree-Fock self-energy of nucleon represent to be the real part of the microscopic optical potential and the fourth order of meson exchange diagrams,i.e. the core polarization represent the imaginary part of microscopic optical potential in nuclear matter.The microscopic optical potential of finite nuclei is obtained with the local density approximation.     

Vacancy-solute complexes and their clusters in iron

In this contribution, several vacancy-solute complexes in iron are investigated theoretically from the viewpoint of positron annihilation. In particular, V-Si, V-P, V-Cr, V-Mn, V-Ni, V-Cu and V-Mo complexes are examined. In addition, nano-sized vacancy-Cu clusters in the Fe matrix are also studied. We concentrate on positron lifetimes and coincidence Doppler broadening profiles that bring complementary information about the studied complexes and their clusters. Positron calculations are carried out using the atomic superposition method employing realistic atomic configurations obtained recently using an ab initio pseudopotential method (vacancy-solute complexes) and Monte Carlo/molecular dynamics methods (vacancy-Cu clusters). The main aim of this study is to predict as to what extent such defects are detectable and differentiable using positron annihilation techniques. The results obtained are discussed in the context of experimental data available in the literature.     

Magnetic field effects on the electric modulus properties of nematic mixture E7

The molecular dynamics of the homogeneously aligned nematic liquid crystal mixture E7 subject to a magnetic field has been studied. The dielectric spectra study has revealed a low bias magnetic field effect on the evolution of dielectric relaxation spectra occurred at lower (∼kHz) (δ-relaxation) and higher (∼MHz) (α-relaxation) frequency regions. The complex electric modulus, which converted from experimental dielectric spectra, has been analyzed with theoretical model of Debye relaxation. The obtained fitting parameters of relaxation time and strength of dielectric components are shown to vary systematically with the strength of applied magnetic field. A microscopic molecular dynamic model has been proposed to describe the two-step variation of E7 molecular under the bias magnetic field. The results provide implication for magneto-modulation of liquid crystal molecular dynamics under the bias magnetic field.     

A generic travelling wave solution in dissipative laser cavity

A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the not-so-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussian with variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics and localization in semiconductor laser cavity.     

Entropy production and nonequilibrium stationarity in quantum dynamical systems. Physical meaning of van Hove limit

With aid of the so-called dilation method, a concise formula is obtained for the entropy production in the algebraic formulation of quantum dynamical systems. In this framework, the initial ergodic state of an external force system plays a pivotal role in generating dissipativity as a conditional expectation. The physical meaning of van Hove limit is clarified through the scale-changing transformation to control transitions between microscopic and macroscopic levels. It plays a crucial role in realizing the macroscopic stationarity in the presence of microscopic fluctuations as well as in the transition from non-Markovian (groupoid) dynamics to Markovian dissipative processes of state changes. The extension of the formalism to cases with spatial and internal inhomogeneity is indicated in the light of the groupoid dynamical systems and noncommutative integration theory.     

Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates

The dynamics of the weak nonlinear matter solitary waves in a spin-1condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the (KdV) equation may be useful tounderstand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.     

The time-local view of nonequilibrium statistical mechanics. II. Generalized Langevin equations

On a semiphenomenological level, generalized Langevin equations are usually obtained by adding a random force (RF) term to macroscopic deterministic equations assumed to be known. Here this procedure is made rigorous by conveniently redefining the RF, which is shown to be colored noise weakly correlated with the observables at earlier times due to the finite lifetime of microscopic events. Corresponding fluctuation-dissipation theorems are derived. Explicit expressions for the spectral density of the fluctuations are obtained in a particularly simple form, with the deviation of the line shape from the Lorentzian being related most explicitly to the spectral density of the RF. Well-known low-frequency expressions and the Einstein relation of (generalized) Brownian motion theory are modified so as to include lifetime effects. New sum rules are obtained relating dissipative quantities to contour integrals (in the complex frequency domain) over spectral densities or corresponding response functions. The Heisenberg dynamics of a complete set of macroobservables is shown to be equivalent to a generalized Orstein-Uhlenbeck stochastic process which is a non-Markovian process due to the lifetime effects.     

Femtosecond dynamics of electron-vibrational heating and desorption

The dynamics of vibrational heating and desorption induced by multiple inelastic hot electron scatterings is investigated by a microscopic quantum mechanical approach. Numerical simulations are found to be in good agreement with experimental results of O₂ desorbed from Pt(111) by femtosecond laser pulses. The subpicosecond response time of the desorption probability is shown to arise directly from the dynamics of vibrational heating of the molecule-surface bond.     

Dynamics of paramagnetic agents by off-resonance rotating frame technique

Off-resonance rotating frame technique offers a novel tool to explore the dynamics of paramagnetic agents at high magnetic fields (B0 > 3T). Based on the effect of paramagnetic relaxation enhancement in the off-resonance rotating frame, a new method is described here for determining the dynamics of paramagnetic ion chelates from the residual z-magnetizations of water protons. In this method, the dynamics of the chelates are identified by the difference magnetization profiles, which are the subtraction of the residual z-magnetization as a function of frequency offset obtained at two sets of RF amplitude omega(1) and pulse duration tau. The choices of omega(1) and tau are guided by a 2-D magnetization map that is created numerically by plotting the residual z-magnetization as a function of effective field angle theta and off-resonance pulse duration tau. From the region of magnetization map that is the most sensitive to the alteration of the paramagnetic relaxation enhancement efficiency R(1rho)/R1, the ratio of the off-resonance rotating frame relaxation rate constant R(1rho) verse the laboratory frame relaxation rate constant R(1), three types of difference magnetization profiles can be generated. The magnetization map and the difference magnetization profiles are correlated with the rotational correlation time tauR of Gd-DTPA through numerical simulations, and further validated by the experimental data for a series of macromolecule conjugated Gd-DTPA in aqueous solutions. Effects of hydration water number q, diffusion coefficient D, magnetic field strength B0 and multiple rotational correlation times are explored with the simulations of the magnetization map. This method not only provides a simple and reliable approach to determine the dynamics of paramagnetic labeling of molecular/cellular events at high magnetic fields, but also a new strategy for spectral editing in NMR/MRI based on the dynamics of paramagnetic labeling in vivo.     

Nonlinear and stochastic dynamics in the heart

In a normal human life span, the heart beats about 2–3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.