Regularity and asymptotic behavior of solutions of nonautonomous differential equations

The existence of a nonautonomous approximate inertial manifold is shown for problems of the formu + Au + N(t,u)=0, in whichA is a self-adjoint operator with compact resolvent in a Hilbert spaceH. The operatorN(t, u) = G(u) + F(t, u) is nonlinear withG a monotone gradient that is locally Lipschitz fromD(A ^1/2) intoH, andF:⁺×HH a Lipschitz perturbation that is Hölder continuous int. Weak solutions are shown to be uniformly locally Hölder continuous intoD(A) with equicontinuity in families of solutions with ¦u(0)¦ r.A priori estimates of ¦Au(t)¦ are also verified and used in a skew-product flow to show there is a global attractor whose component elements form a equicontinuous family of solutions.     

微粗糙结构表面液滴浸润特性的多体耗散粒子动力学研究

超疏水表面因其优异的自洁作用一直是表面科学领域关注的重点.本文使用多体耗散粒子动力学(many-body dissipative particle dynamics, MDPD)方法模拟研究了不同粗糙结构下液滴的浸润特性, 并与Cassie-Baxter理论进行了对比. 研究使用了一种具有长吸短斥作用的流固作用函数来获得不同的液滴浸润性, 并利用一种简洁的数值方法来测量接触角. 模拟结果表明本研究方法能够稳定地捕捉到液滴在粗糙表面的静态和动态特性. 模拟了粗糙结构对三相接触线运动的黏滞作用, 与物理实验结果相符合, 表明Cassie-Baxter理论在实际应用中尚存在一定局限性. 研究分析了在动态铺展过程中的能量转化关系, 并指出在低值表面容易引起液滴反弹.     

生物表面活性剂鼠李糖脂及其复配体系界面行为和性质的介观模拟

采用介观模拟耗散颗粒动力学（DPD）方法研究不同结构的鼠李糖脂在油/水界面行为差异和结构对活性的影响,并探讨了其与不同类型表面活性剂如十二烷基硫酸钠（SDS）、十二烷基苯磺酸钠（SDBS）、脂肪醇聚氧乙烯醚（AEO3）复配时体系的界面性质,给出不同结构的鼠李糖脂的行为特点及与常用合成表面活性剂在油/水界面的相互作用规律...     

Blow-up phenomena and global existence for the nonuniform weakly dissipative b-equation

We first establish the local well-posedness for the nonuniform weakly dissipative b-equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. We then study the blow-up phenomena and the long time behavior of the solutions. Two blow-up results are established for certain initial profiles. Moreover, two sufficient conditions for the decay of the solutions are presented.     

Ergodic BSDEs under weak dissipative assumptions

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying forward equation, which, on the contrary, is assumed to be non-degenerate.We show the existence of solutions by the use of coupling estimates for a non-degenerate forward stochastic differential equation with bounded measurable nonlinearity. Moreover we prove the uniqueness of “Markovian” solutions by exploiting the recurrence of the same class of forward equations.Applications are then given for the optimal ergodic control of stochastic partial differential equations and to the associated ergodic Hamilton-Jacobi-Bellman equations.     

A hybrid legendre tau method for the solution of a class of nonlinear wave equations with nonlinear dissipative terms

This article presents a technique based on the hybrid Legendre tau‐finite difference method to solve the fourth order wave equation which arises in the elasto‐plastic‐microstructure models for longitudinal motion of an elasto‐plastic bar. Illustrative examples and numerical results obtained using new technique demonstrate that the proposed approach is efficient in treating longitudinal equation of ealsto‐plastic bar. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1055–1071, 2011     

A 3D‐2D asymptotic analysis of viscoelastic problem with nonlinear dissipative and source terms

The purpose of this article is to study the asymptotic analysis of the solutions of a linear viscoelastic problem with a dissipative and source terms in a three‐dimensional thin domain Ω^ε. Firstly, we give the strong formulation of the problem and the existence and uniqueness theorem of the weak solution. Then, we establish some estimates independent of the parameter ε. These last will be useful to obtain the limit problem with a specific weak form of the Reynolds equation.     

Evidence for the purely electronic character of primary electron transfer in purple bacteria Rh. Sphaeroides

A quantum-chemical calculation of the excited electronic states of a Rh. Sphaeroides reaction centre was performed. We discovered a new excited electronic state which can participate in electron transfer (ET). The energy gradient calculations showed that photoexcitation activates only high-frequency vibrational modes. This contradicts the widely accepted picture of ET resulting from vibrational wave packet motion. An alternative model is suggested where ET has a purely dissipative character and occurs only due to pigment--protein interaction. With this model, we demonstrate that oscillations in the femtosecond spectra can be caused by the new electronic state and non-Markovian character of dissipative dynamics.     

Dissipative particle dynamics simulation for the effect of interaction on the self-assembly behaviours of heterogemini surfactant in aqueous solution

Self-assembly behaviours of heterogemini surfactant in aqueous solution have been explored by means of dissipative particle dynamics simulation. Five kinds of heterogemini molecules are involved and a variety of novel morphologies have been obtained. Results based on detailed analyses show that head–tail and tail–water interactions play different roles in the formation of six kinds of self-assembly morphologies. The key factors are tail–water and head–tail repulsions separately for morphology with small (sphere) and relatively large scales (rod, planar grid, lamella and tunnels). Besides, the appearance of network in only one system can be regarded as a particular type of intermediate state. Coexistence of several sphere micelles in an amplified dissipative particle dynamics system gives us a better understanding of interactions inside the soft matter. Our simulation results can provide a theoretical guide to further research towards self-assembly behaviours of heterogemini surfactants and practical applications of these matters.     

On the Properties of Accretive-Dissipative Matrices

Let A be a complex n × n matrix, and let A = B + iC, B = B*, C = C* be its Toeplitz decomposition. Then A is said to be (strictly) accretive if B > 0 and (strictly) dissipative if C > 0. We study the properties of matrices that satisfy both these conditions, in other words, of accretive-dissipative matrices. In many respects, these matrices behave as numbers in the first quadrant of the complex plane. Some other properties are natural extensions of the corresponding properties of Hermitian positive-definite matrices.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 832–843.Original Russian Text Copyright ©2005 by A. George, Kh. D. Ikramov.