General symmetries in optimal control

In this paper we study general symmetries for optimal control problems making use of the geometric formulation proposed in [7]. This framework allows us to reduce the number of equations associated with optimal control problems with symmetry and compare the solutions of the original system with the solutions of the reduced one. The reconstruction of the optimal controls starting from the reduced problem is also explored.     

On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

Algebraic Formulation of Quantum Decoherence

An algebraic formalism for quantum decoherence in systems with continuous evolution spectrum is introduced. A certain subalgebra, dense in the characteristic algebra of the system, is defined in such a way that Riemann–Lebesgue theorem can be used to explain decoherence in a well defined final pointer basis.     

类铍离子内壳激发态1s2p3 3P0、3D0及2s2p3 3D0 的俄歇宽度和俄歇分支率

采用鞍点变分方法和鞍点复数转动方法并考虑相对论修正和质量极化效应,计算了类铍离子内壳激发态1s2p3 3P0、3D0和内壳双激发态2s2p3 3D0的俄歇宽度、俄歇分支率和俄歇电子能量.同时还对1s22p2 3Pe态到1s2p3 3P0、3D0态(Z=4~10)的振子强度和辐射跃迁率进行了计算,计算结果与其他理论结果以及实验数据符合得很好.     

The fractional variational iteration method using He's polynomials

In this Letter, by introducing He's polynomials in the correct functional, we propose a new fractional variational iteration method to solve nonlinear time-fractional partial differential equations involving Jumarie's modified Riemann-Liouville derivative. Several examples have been solved to illustrate the proposed method is quite effective and convenient for solving kinds of nonlinear fractional order problems.     

凑合反推法──流体力学变分原理建立的一条新途径

凑合反推法是刘商联系统方法[1]的进一步发展，应用这种方法可以方便地构造各种亚广义变分原理及广义变分原理，并可以消除临界变分现象．对于任何二维守恒型流体力学方程，作者推导得到了其广义变分通用公式．几个实例证明这种方法是有效的、简单的，并具有普遍的意义．     

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.     

EQUATION OF STATE OF FLUID He+H2 MIXTURES UNDER HIGH PRESSURE

A statistical mechanical variational theory and an improved van der Waals one-fluid model have been used to compute the equation of state of fluid He+H₂ mixtures with different H₂:He compositions under high pressure. The first-order quantum correction is included. Comparing the present results with Monte Carlo simulations indicates that the quantum corrections for calculating the thermodynamic properties become increasingly important at lower temperatures.     

Deposition pattern of drying droplets

The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.     

Pressure dissociation of dense hydrogen

The self-consistent fluid variational model （SFVM） has been used to describe the pressure dissociation of dense hydrogen at high temperatures. This paper focuses on a mixture of hydrogen atoms and molecules and is devoted to the study of the phenomenon of pressure dissociation at finite temperatures. The equation of state and dissociation degree have been calculated from the free energy functions in the range of temperature 2000-10,000K and density 0.02-1.0g/cm^3, which can be compared with other approaches and experiments. The pressure dissociation is found to occur in higher density range, while temperature dissociation is a more gradual effect.