Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods

Molecular dynamics typically incorporates a stochastic-dynamical device, a “thermostat,” in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the “efficiency” of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321–1336, 2007) and a generalization of the “stochastic velocity rescaling” method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates.     

Boundary treatment effects on molecular dynamics simulations of interface thermal resistance

Molecular Dynamics simulations of heat conduction in liquid Argon confined in Silver nano-channels are performed subject to three different thermal conditions. Particularly, different surface temperatures are imposed on Silver domains using a thermostat in all and limited number of solid layers, resulting in heat flux in the liquid domain. Alternatively, energy is injected and extracted from solid layers to create a NVE liquid Argon system, which corresponds to heat flux specification. Imposition of a constant temperature region in the solid domain results in an unphysical temperature jump, indicating the presence of an artificial thermal resistance induced by the thermostat. Thermal resistance analyses for the components of each case are performed to distinguish the artificial and interface thermal resistance effects. Constant wall temperature simulations are shown to exhibit superposition of the artificial and interface thermal resistance values at the liquid/solid interface, while applying thermostat on wall layers sufficiently away from the liquid/solid interface results in consistent predictions of the interface thermal resistance. Injecting and extracting energy from each solid layer eliminates the artificial resistance. However, the method cannot directly specify a desired temperature difference between the two solid domains.     

Mechanism of electric energy production in galvanic and concentration cells

The mechanism of electric energy production in galvanic and concentration cells, which is based on considering the reaction of separate ions, is described. The production electric energy via useful work in concentration and galvanic cells is considered at constant temperature and pressure by analogy to the Van’t Hoff equilibrium box (VHEB) on a molecular level. It is shown that the reaction heat dissipates in a thermostat (or in the environment) and does not participate in electric energy production. The only source of useful work is the thermal thermostat energy (that of the environment). The second law of thermodynamics is satisfied because the useful work arising from cooling of the environment is accompanied by a decrease in the volume of reagents and an increase in the volume of products. Electric energy arises indirectly via heat exchange with a thermostat according to the scheme reaction heat → thermal thermostat energy → useful work → electric energy. Execution of useful work due to thermal thermostat energy provides electric charging of electrodes whose discharging is followed by electric energy release.     

Finding polymorphic structures during vicinal surface growth

A hybrid scheme is developed to describe vicinal surface growth during epitaxy on two different time and length scales. For this purpose this algorithm combines two modules based on a continuum and an atomistic approach. The continuum module is realized by a phase-field-model which traces back to the Burton–Cabrera–Frank theory, the atomistic module is based on the anisotropic Ising model which is mapped onto a lattice-gas model. The latter provides thermal density fluctuations resulting in adatom clustering. With increasing temperature the probability for island nucleation on the terraces decreases according to 1-p where p is an Arrhenius-type activation probability which prevents clusters from becoming islands. Within this framework it is possible to find the transition from a rough surface at low temperatures to an evenly stepped surface at high temperatures where slight step meandering is observed. Furthermore two competing mechanisms of step bunching are investigated within this scale bridging algorithm: alternating anisotropic diffusion and different Ehrlich–Schwoebel barriers at the step edges. It is shown that a simulation of step bunching displaying the full variety of phenomena observed in experiments can only be achieved by the consideration of different time and length scales.     

The Gross–Pitaevskii Functional with a Random Background Potential and Condensation in the Single Particle Ground State

For discrete and continuum Gross–Pitaevskii energy functionals with a random background potential, we study the Gross–Pitaevskii ground state. We characterize a regime of interaction coupling when the Gross–Pitaevskii ground state and the ground state of the random background Hamiltonian asymptotically coincide.     

Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices

Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton’s equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.     

Modelling transient heat conduction in solids at multiple length and time scales: A coupled non-equilibrium molecular dynamics/continuum approach

A method for controlling the thermal boundary conditions of non-equilibrium molecular dynamics simulations is presented. The method is simple to implement into a conventional molecular dynamics code and independent of the atomistic model employed. It works by regulating the temperature in a thermostatted boundary region by feedback control to achieve the desired temperature at the edge of an inner region where the true atomistic dynamics are retained. This is necessary to avoid intrinsic boundary effects in non-equilibrium molecular dynamics simulations. Three thermostats are investigated: the global deterministic Nosé–Hoover thermostat and two local stochastic thermostats, Langevin and stadium damping. The latter thermostat is introduced to avoid the adverse reflection of phonons that occurs at an abrupt interface. The method is then extended to allow atomistic/continuum models to be thermally coupled concurrently for the analysis of large steady state and transient heat conduction problems. The effectiveness of the algorithm is demonstrated for the example of heat flow down a three-dimensional atomistic rod of uniform cross-section subjected to a variety of boundary conditions.     

The random replicator model at nonzero temperature

The random replicator model with interspecies coupling strengths prescribed by the competitive exclusion principle – the Hebb rule – is studied analytically in the presence of fast noise that describes the flow of migrants between the ecosystem and the outer world. The stochastic dynamics leads to stationary states distributed according to the Gibbs distribution permitting thus an equilibrium statistical mechanics analysis. We find that a discontinuous phase transition separates a regime of strong competition, and consequently of low diversity, from more cooperative regimes. The statistical analysis is carried out for the annealed scheme, for which the evolutionary and ecological timescales coincide, as well as for the quenched scheme, for which the features that identify the species are fixed.     

Plastic deformation under high-rate loading: The multiscale approach

A two-level approach has been proposed for describing the plastic deformation under high-rate loading of metals. The characteristics of the motion of dislocations under shear stresses have been investigated at the atomistic level by using the molecular dynamics simulation. The macroscopic motion of a material has been described at the continuum level with the use of the model of continuum mechanics with dislocations, which uses information obtained at the atomistic level on the dislocation dynamics. The proposed approach has been used to study the evolution of the dislocation subsystem under shock-wave loading of an aluminum target. The behavior of the dynamic yield stress with an increase in the temperature has been analyzed. The results of the calculations are in good agreement with experimental data.     

Stability diagram for elastic domains in epitaxial ferroelectric thin films

The statics of isolated elastic domains (twins) in epitaxial thin tetragonal films grown on a cubic substrate is investigated theoretically. Different possible variants of the geometric shape of a domain are studied: plate, trapezoidal, and triangular. The nonuniform internal stresses, which also exist in polydomain epitaxial systems, are calculated by the effective-dislocation method. Hence the elastic energies stored in heterostructures with different domains are determined. The equilibrium width of a domain is calculated by minimizing the total internal energy of the heterostructure. Next, the stability diagram for isolated domains in epitaxial films is constructed from energy considerations. It is shown that in a large part of this diagram trapezoidal domains are energetically more advantageous than plate-shaped domains. The effect of an external electric field on the stability of 90° domains in epitaxial ferroelectric films is investigated. Fiz. Tverd. Tela (St. Petersburg) 39, 127–134 (January 1997)     

Shock compression and thermodynamics of highly nonideal metallic plasma

Using experimental data on compression and heating of dense metallic plasma by powerful shock waves, we have analyzed the effect of strong Coulomb interaction on both discrete and continuum bands of energy spectrum, the role of short-range repulsion, and the effect of degeneracy on the equation of state for a dense, nonideal metallic plasma. Explosive devices have been used to produce plasma for which the degree of ionization, nonideal parameter, and degeneracy varied over wide ranges. In order to increase effects of irreversible energy dissipation, metal targets of low densities have been used. Thermodynamic measurements have been compared to theoretical models taking into account Coulomb interaction, short-range repulsion, and degeneracy of electrons. The plasma models have been shown to be applicable to the equilibrium properties of multiply ionized plasma in a wide region of the phase diagram characterized by extremely high parameters [T⩾10⁴ K, P⩾10 GPa, and ρ=(0.1–1)ρ ₀], which is beyond the traditional domain of plasma physics. Zh. éksp. Teor. Fiz. 114, 1242–1265 (October 1998)     

基于桥域理论的Cu单晶纳米切削跨尺度仿真研究

桥域方法是一种典型的跨尺度仿真研究方法.基于桥域理论,本文分析了原子和连续介质耦合区域的处理问题,即在耦合区采用不同的权重计算系统的能量,通过Lagrange乘子法对原子和连续介质位移进行约束.采用桥域方法,建立了单晶Cu米纳切削的跨尺度仿真模型,获得了单晶Cu纳米切削的材料变形机理.同时,研究了不同切削速度对纳米切削过程和原子受力分布的影响,仿真结果表明:随着切削速度的提高,切削区原子所受的力值增大,切屑变形系数减小,已加工表面变质层厚度增加.本文基于桥域理论,实现了Cu单晶纳米切削跨尺度的建模和仿真, 关键词： 桥域法 纳米切削 单晶Cu 切削速度     

Stability of magnetic domains in an amorphous metal wire

Dimensions and energy of domains in the core of an amorphous metal wire are estimated in the work. Influence of the external magnetic field strength and coercive force on the dimensions of a stable domain is investigated. It is demonstrated that the highest stability to an external magnetic field and the least energy have domains comprising cylinder and cone-shaped domain tops and domains with zigzag domain tops. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–91, January, 2009.     

Lorentz gas interacting with an inhomogeneous thermostat

The equilibrium distribution of a Lorentz gas (“electrons”) interacting with an inhomogenous thermostat (“atoms”) is examined with consideration of 1) the concept of volumes available and forbidden for the gas particles and 2) the solution of the kinetic equation. Analytical calculations for “electrons” and “atoms” repelling each other with the force ≈r⁻⁵ (where r is the distance between the particles) have shown that the coordinate- and velocity-dependent variables in the distribution function cannot be separated. In particular, this leads to the dependence of the average kinetic energy per “electron” on the coordinate: it is higher in the region with higher density of the “atoms”. It is assumed that the Gibbs distribution does not describe the properties of the system under consideration, because in this case the interaction between the system and thermostat cannot be considered small. Scientific-Research Physical-Technical Institute at N. I. Lobachevskii Nizhnii Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–43, June, 1999.     

Van der Waals energy surface of a carbon nanotube sheet

The van der Walls interaction between a carbon nanotube sheet (CNTS) and a rare gas atom, is studied using both atomistic and continuum approaches. We present analytical expressions for the van der Waals energy of continuous nanotubes interacting with a rare gas atom. It is found that the continuum approach does not properly treat the effect of atomistic configurations on the energy surfaces. The energy barriers are small as compared to the thermal energy, which implies the free motion above the CNTS in heights about one nanometer. In contrast to the energy surface of a graphene sheet, the honeycomb lattice structure in the energy surface of a CNTS is imperceivable. Defects alter the energy surface which therefore influence the gas adsorption mechanism.     

A rational method for probing macromolecules dissociation: the antibody-hapten system

The unbinding process of a protein-ligand complex of major biological interest was investigated by means of a computational approach at atomistic classical mechanical level. An energy minimisation-based technique was used to determine the dissociation paths of the system by probing only a relevant set of generalized coordinates. The complex problem was reduced to a low-dimensional scanning along a selected distance between the protein and the ligand. Orientational coordinates of the escaping fragment (the ligand) were also assessed in order to further characterise the unbinding. Solvent effects were accounted for by means of the Poisson–Boltzmann continuum model. The corresponding dissociation time was derived from the calculated barrier height, in compliance with the experimentally reported Arrhenius-like behaviour. The computed results are in good agreement with the available experimental data.     

Free energy change of a dislocation due to a Cottrell atmosphere

The free energy reduction of a dislocation due to a Cottrell atmosphere of solutes is computed using a continuum model. We show that the free energy change is composed of near-core and far-field components. The far-field component can be computed analytically using the linearized theory of solid solutions. Near the core the linearized theory is inaccurate, and the near-core component must be computed numerically. The influence of interactions between solutes in neighbouring lattice sites is also examined using the continuum model. We show that this model is able to reproduce atomistic calculations of the nickel–hydrogen system, predicting hydride formation on dislocations. The formation of these hydrides leads to dramatic reductions in the free energy. Finally, the influence of the free energy change on a dislocation’s line tension is examined by computing the equilibrium shape of a dislocation shear loop and the activation stress for a Frank–Read source using discrete dislocation dynamics.     

Vibrational and rotational energy transfer of CH+ in collisions with 4He and 3He

A quantum mechanical investigation of vibrational and rotational energy transfer in cold and ultra cold collisions of CH⁺ with ³He and ⁴He atoms is presented. Ab initio potential energy calculations are carried out at the BCCD(T) level and a global 3D potential energy surface is obtained using the Reproducing Kernel Hilbert Space (RKHS) method. Close coupling scattering calculations using this surface are performed at collision energy ranging from 10^-6 to 2000 cm^-1. In the very low collision energy limit, the vibrational and rotational quenching cross sections of CH⁺ in collisions with He are found to be of the same order of magnitude. This unusual result is attributed to the large angular anisotropy of the intermolecular potential and to the unusually small equilibrium value of the Jacobi R coordinate of the He–CH⁺ complex. As for the He–N₂ ⁺ collision, we also find a strong isotope effect in the very low collision energy range which is analyzed in terms of scattering length and the differences between these two collisions are also discussed.