Noise-driven numerical irreversibility in molecular dynamics technique

It is widely believed that, in molecular dynamics (MD) simulations, round-off errors can cause numerical irreversibility since, in the standard MD, floating-point real number arithmetic is employed and round-off errors cannot be avoided. To investigate the characteristic of this numerical irreversibility, the ‘bit-reversible algorithm’, which is completely time-reversible and is free from any round-off error, is made use of as a test bed. Through this study, it is clearly demonstrated that, other than the extent of the stability of the system, the appearance of irreversibility is related to the ‘quantity’ of the controlled noise. By means of the bit-reversible simulation added to the controlled noise of an appropriate ‘quantity’, the characteristic of the numerical irreversibility in the standard MD is revealed.     

On a nonlinear iterative method in applied mechanics, part II

In Part I of this paper, a particular iterative method used in applied mechanics is shown to belong to a general class of methods termed SOR-Newton-(m_k) iterative methods. The purpose here is to make a case study of the method and compare its performance with Newton iteration and Newton-SOR iteration. The numerical experiments are designed to examine the range of convergence of the m_k = 1 step method, rates of convergence, and the effect of relaxation.     

Quantum quasi-Markov processes in eventum mechanics dynamics, observation, filtering and control

Quantum mechanical systems exhibit an inherently probabilistic behavior upon measurement which excludes in principle the singular case of direct observability. The theory of quantum stochastic time continuous measurements and quantum filtering was earlier developed by the author on the basis of non-Markov conditionally-independent increment models for quantum noise and quantum nondemolition observability. Here this theory is generalized to the case of demolition indirect measurements of quantum unstable systems satisfying the microcausality principle. The exposition of the theory is given in the most general algebraic setting unifying quantum and classical theories as particular cases. The reduced quantum feedback-controlled dynamics is described equivalently by linear quasi-Markov and nonlinear conditionally-Markov stochastic master equations. Using this scheme for diffusive and counting measurements to describe the stochastic evolution of the open quantum system under the continuous indirect observation and working in parallel with classical indeterministic control theory, we derive the Bellman equations for optimal feedback control of the a posteriori stochastic quantum states conditioned upon these measurements. The resulting Bellman equation for the diffusive observation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian problem which emphasizes many similarities with the corresponding classical control problem.     

Molecular dynamics

Molecular dynamics is a model for the structure and meaning of object based programming systems. In molecular dynamics the memory state of a system is modeled as a fluid consisting of a collection of molecules. Each molecule is a collection of atoms with bindings between them. A computation is modeled as an evolution of the memory fluid. Evolution of the memory fluid takes place by means of chains of actions. Actions transform the structure of molecules in a way similar to chemical reactions.     

分数阶动力学的分析力学方法及其应用

综述我们在分数阶动力学分析力学方法的研究进展,包括：分数阶动力学系统的分析力学表示,构造分数阶动力学模型的分析力学方法,构造分数阶动力学模型团簇的分析力学方法,三类分数阶Lie群无限小变换方法,分数阶动力学系统的对称性、对称性摄动和共形不变性的分析力学方法,分数阶动力学系统的代数结构与Poisson积分的分析力学方法,构造分数阶动力学系统积分不变量的分析力学方法,分数阶动力学系统梯度表示的分析力学方法,分数阶动力学系统稳定性的分析力学方法,分数阶微分方程的分析力学方法等,介绍了对于物理学、力学、生物学、非线性科学等领域的10多种分数阶动力学模型的应用,并指出了若干进一步研究的问题.     

The origins of entropy and irreversibility

The origins of entropy and irreversibility in thermodynamics are re-examined once more, in the light of 45 years of influence from information-theoretic concepts. Familiar, but elusive notions of the approach to equilibrium, and time-dependent entropy, are subjected to renewed scrutiny.     

Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations

A complete classification of all explicit self-adjoint decomposition algorithms with up to 11 stages is given and the derivation process used is described. As a result, we have found 37 (6 non-gradient plus 31 force-gradient) new schemes of orders 2 to 6 in addition to 8 (4 non- and 4 force-gradient) integrators known earlier. It is shown that the derivation process proposed can be extended, in principle, to arbitrarily higher stage numbers without loss of generality. In practice, due to the restricted capabilities of modern computers, the maximal number of stages, which can be handled within the direct decomposition approach, is limited to 23. This corresponds to force-gradient algorithms of order 8. Combining the decomposition method with an advanced composition technique allows to increase the overall order up to a value of 16. The implementation and application of the introduced algorithms to numerical integration of the equations of motion in classical and quantum systems is considered as well. As is predicted theoretically and confirmed in molecular dynamics and celestial mechanics simulations, some of the new algorithms are particularly outstanding. They lead to much superior integration in comparison with known decomposition schemes such as the Verlet, Forest-Ruth, Chin, Suzuki, Yoshida, and Li integrators.     

红曲红素的分子动力模拟及其量化计算

采用分子力学及分子动力学理论,分子模拟红曲红素的化学结构,得到1 atm,298.15 K时的优势构象及其能量(-1 245.278 kcaL/mol)。应用密度泛函理论的量化计算,研究分子的电荷分布,结果表明,C1、C3、C4、C5、C6、C7、C9、C10、C11、C12、O21组成的共扼体系所含净电荷数为-0.418 45,约占分子总负电荷数的14.3%;正电荷主要分布于C3、C16、C19,其电荷数分别为0.129 57、0.116 4、0.156 964。借助理论计算可推测红曲红素分子有3个反应活性部位,即由C19-O20-O28-C2组成的内酯基,以及C3-O21、C16-O17构成的2对羰基;并解释了红曲红素分子的衍生化机理,为红曲红素衍生物的进一步开发提供理论指导。     

Molecular dynamics simulation of ribosome jam

We propose a coarse-grained molecular dynamics model of ribosome molecules to study the dependence of translation process on environmental parameters. We found the model exhibits traffic jam property, which is consistent with an ASEP model. We estimated the influence of the temperature and concentration of molecules on the hopping probability used in the ASEP model. Our model can also treat environmental effects on the translation process that cannot be explained by such cellular automaton models.     

The concept of fracture mechanics applied to the progressive failure of structural members

Because of the imperfections inherent in all real materials and because of possible overloads, a structure which is thought to be capable of safely carrying its design load may suddenly fail. A flaw may grow from its initial size at design stress levels to a size intolerable to the structure. If the flaw is undetected before it reaches the critical size, a catastrophic failure may result.

An approximate method of analysis is suggested in this work. Refinements involving special treatment of stress singularities may be added if desired. The basic idea is that a structure or structural member is considered to be an assemblage of finite parts (as in finite element approaches). When, for one cause or another, one of these parts fails, it is considered to lose its effectiveness in the structure completely. A structure with no redundancy in its design would collapse immediately if the loads were held constant. In a structure which has been designed with some redundancy (as with panels, beams, etc), the effect of successive failure or portions on the integrity of the overall structure can be analyzed.

In this report, calculations of the loss of load carrying capacity and of stiffness of a particular structure are presented as an example of the approach. The discrete parts into which the structure is divided for the analysis are allowed to fail one-at-a-time. The compliance of the structure increases as the individual failures progress. The purpose of the research was to develop a structural toughness term involving the rate of increase of compliance with volume of material failed. It was anticipated that the point of instability of the structure could be related to the toughness. However, the limited computations do not permit generalization of the results of this report to other structures or loadings. To accomplish a general definition of structural toughness requires additional research.     

A coupling algorithm for partitioned solvers applied to bubble and droplet dynamics

Bubbles and droplets both consist of a liquid in contact with a gas. In this paper, we consider the interface between the incompressible liquid and the gas as a zero thickness structure. The position of the interface is determined by the equilibrium between surface tension effects and the fluid pressure difference across the interface. So, the structure interacts with the fluids on either side. The behaviour of a limited number of bubbles and droplets can therefore be simulated as a Fluid-Structure Interaction (FSI) problem.Most existing techniques frequently used for studying bubble and droplet dynamics, such as Level Set or Volume Of Fluid, use monolithic schemes. The flow on both sides of the interface and the position of the interface are calculated in a single code. In this contribution, a partitioned approach is presented. The position of the interface is calculated with a structural solver. Given a displacement of the interface, a separate flow solver calculates the flow on the liquid side of the interface with the Arbitrary Lagrangian-Eulerian (ALE) technique. The structural solver uses a reduced order model of the flow solver to obtain implicit coupling between both solvers. This reduced order model is built up during the coupling iterations of a time step. Grid and time converged solutions of two axisymmetric problems are calculated: an oscillating water droplet in air and the growth and detachment of an air bubble from the outlet of a vertical needle, submerged in quiescent water.