Simulation of DNA electrophoresis in systems of large number of solvent particles by coarse-grained hybrid molecular dynamics approach

Simulation of DNA electrophoresis facilitates the design of DNA separation devices. Various methods have been explored for simulating DNA electrophoresis and other processes using implicit and explicit solvent models. Explicit solvent models are highly desired but their applications may be limited by high computing cost in simulating large number of solvent particles. In this work, a coarse-grained hybrid molecular dynamics (CGH-MD) approach was introduced for simulating DNA electrophoresis in explicit solvent of large number of solvent particles. CGH-MD was tested in the simulation of a polymer solution and computation of nonuniform charge distribution in a cylindrical nanotube, which shows good agreement with observations and those of more rigorous computational methods at a significantly lower computing cost than other explicit-solvent methods. CGH-MD was further applied to the simulation of DNA electrophoresis in a polymer solution and in a well-studied nanofluidic device. Simulation results are consistent with observations and reported simulation results, suggesting that CGH-MD is potentially useful for studying electrophoresis of macromolecules and assemblies in nanofluidic, microfluidic, and microstructure array systems that involve extremely large number of solvent particles, nonuniformly distributed electrostatic interactions, bound and sequestered water molecules.     

Ambiguous Discrimination of General Quantum Operations

We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations.     

Nonlocal symmetry,optimal systems,and explicit solutions of the mKdV equation

The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.     

基于动态本构模型的整流罩铰链系统自冲击分析

整流罩铰链系统结构分析是大型整流罩分离分析的重要环节,也是国内新一代运载火箭研制过程中的关键技术之一。基于30CrMnSiA和ZTC4-1的力学性能试验研究,得到材料的动态本构模型,并建立整流罩及动态本构模型下的铰链系统有限元模型。通过非线性显式动力学分析方法,对铰链系统自冲击过程进行仿真,得到冲击作用下铰链系统的应力和应变情况,并通过内力分析得到自冲击过程中铰链系统的主要内力形式。最后,通过比较铰链系统动态本构与准静态本构下的自冲击响应,验证并说明了动态本构模型对铰链系统自冲击仿真的影响。计算结果表明,自冲击作用会使铰链系统发生塑性变形,且动态本构模型有利于反映真实结果,为新一代运载火箭的研制提供一定的参考价值。     

黏塑性本构计算的稳定性分析

提出本构方程计算方法的稳定性问题,针对黏塑性本构计算的显式精确算法的稳定性进行分析,发现该算法并非无条件稳定,使用小扰动方法给出了其计算稳定的必要条件,稳定性条件对数值计算中的时间步长提出限制要求。通过有限元算例验证了分析的正确性,计算结果也表明理论推导得到的稳定性公式能够准确预测满足计算稳定性条件要求的最大时间步长与各参数之间关系。     

ON SOLUTIONS OF QUATERNION MATRIX EQUATIONS XF-AX=BY AND XF-A=BY

In this paper,the quaternion matrix equations XF-AX=BY and XF-A=BY are investigated.For convenience,they were called generalized Sylvesterquaternion matrix equation and generalized Sylvester-j-conjugate quaternion matrix equation,which include the Sylvester matrix equation and Lyapunov matrix equation as special cases.By applying of Kronecker map and complex representation of a quaternion matrix,the sufficient conditions to compute the solution can be given and the expressions of the explicit solutions to the above two quaternion matrix equations XF-AX=BY and XF-A=BY are also obtained.By the established expressions,it is easy to compute the solution of the quaternion matrix equation in the above two forms.In addition,two practical algorithms for these two quaternion matrix equations are give.One is complex representation matrix method and the other is a direct algorithm by the given expression.Furthermore,two illustrative examples are proposed to show the efficiency of the given method.     

一类阶为偶数的高斯和显式计算的注记

给出指数2情形下阶数为2l_1~(r1)l_1~(r2)的高斯和的显式计算公式.证明方法直接利用Stickelberger理想分解定理,进而结果独立于其他指数2情形高斯和的结果而成立.     

A reliable and efficient first principles-based method for predicting pKa values. III. Adding explicit water molecules: Can the theoretical slope be reproduced and pKa values predicted more accurately?

A popular method for predicting pK(a) values for organic molecules in aqueous solution is to establish empirical linear least-squares fits between calculated deprotonation energies and known experimental pK(a) values. In virtually all such calculations, the empirically observed slope of the pK(a) vs. ΔE fit is significantly less than the theoretical value, 1/(2.303RT) (which is 0.73 mol/kcal at room temperature). In our own continuum solvation calculations (Zhang et al., J Phys Chem A 2010, 114, 432), the empirical slope for carboxylic acids was only 0.23 mol/kcal, despite the excellent fit to the experimental pK(a) values. There has been much speculation about the reason for this phenomenon. Although the ΔE - pK(a) relation neglects entropic effects, these are expected to largely cancel. The most likely cause for the strange behavior of the fitted slope is explicit solute-solvent (water) interactions, especially involving the ions, which cannot be described accurately by continuum solvation models. We used our previously developed pK(a) protocol (OLYP/6-311+G(d,p)//3-21G(d) with the COSMO solvation model) to investigate the effect of adding one or two explicit water molecules to the system. The slopes for organic acids (especially carboxylic acids) are much closer to the theoretical value when explicit water molecules are added to both the neutral molecule and the anion. However, explicit water molecules have almost no effect on the slopes for organic bases. Adding explicit water molecules to the ions only produces intermediate results. Unfortunately, linear fits involving explicit water molecules have much larger errors than with continuum solvation models alone and are also much more expensive. Consequently, they are not suitable for large-scale pK(a) calculations. The results compared with literature values showed that our predicted pK(a) s are more accurate.     

Placevent: An algorithm for prediction of explicit solvent atom distribution—Application to HIV‐1 protease and F‐ATP synthase

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the three‐dimensional (3D) continuous distribution resulting from a 3D reference interaction site model (3D‐RISM) calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure and the solvent composition. We show examples of predicting water molecules near the KNI‐272 bound form of HIV‐1 protease and predicting both sodium ions and water molecules near the rotor ring of F‐adenosine triphosphate (ATP) synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.39–0.65 Å. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D‐RISM output within minutes. It is extremely useful for examining multiple specific solvent–solute interactions, as a convenient method for generating initial solvent structures for molecular dynamics calculations, and may assist in refinement of experimental structures. © 2012 Wiley Periodicals, Inc.     

Solitons for the cubic-quintic nonlinear Schrdinger equation with varying coefficients

In this paper,by means of similarity transfomations,we obtain explicit solutions to the cubic-quintic nonlinear Schrdinger equation with varying coefficients,which involve four free functions of space.Four types of free functions are chosen to exhibit the corresponding nonlinear wave propagations.