Statistical Thermodynamic Properties of Linear Protein Solutions

利用统计力学理论结合格点模型,讨论了链状蛋白质分子溶液的热力学性质. 结果表明,对于稀溶液来说,溶液的吉布斯函数随蛋白质浓度的增加而降低,蛋白质分子化学势随其浓度增加而升高. 还分析了蛋白质分子链长及温度对溶液吉布斯函数和蛋白质分子化学势的影响. 并且计算讨论了几种第一类抗冻蛋白的化学势.     

A Chebyshev–Lagrangian method for acoustic analysis of a rectangular cavity with arbitrary impedance walls

A general Chebyshev–Lagrangian method is proposed to obtain the analytical solution for a rectangular acoustic cavity with arbitrary impedance boundary conditions. The originality of the present paper is the successful attempt of applying orthogonal polynomials, such as Chebyshev polynomials of the first kind, to the analysis of a rectangular sound field with general wall impedance. The sound pressure is uniformly expressed as triplicate Chebyshev polynomial series which is independent in each direction. The Chebyshev polynomial series solution is obtained using the Rayleigh–Ritz procedure after considering the influence of boundary impedance on the cavity as the work done by the impedance surfaces in the Lagrangian function. The accuracy and reliability of the proposed method are validated against the analytical solutions and some numerical results available in the literature. Excellent orthogonality and complete properties of the Chebyshev polynomials ensure the rapid convergence, numerical stability, high accuracy of the current solution. The simplicity and low computational cost of the present approach make it preferable to obtain the results of complex models even in the relative high frequency range by choosing enough truncated terms in the sound pressure expression. Numerous cases with various uniform or non-uniform impedance boundary conditions are analyzed numerically and some of the results can be used as benchmark. It is shown that the impedance boundary condition can effectively influence or modify the acoustic characteristics and response of a cavity.     

Dimers and the Critical Ising Model on lattices of genus >1

We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency matrices have a dependence on the boundary conditions that, for large lattice size, can be expressed in terms of genus two theta functions. The period matrix characterizing the continuum limit of the lattice is computed using a discrete holomorphic structure. These results relate in a direct way the lattice combinatorics with conformal field theory, providing new insight to the lattice regularization of conformal field theories on higher genus Riemann surfaces.     

Dipole soliton formation in a nematic liquid crystal in the nonlocal limit

The interaction of two symmetric solitary waves, termed nematicons, in a liquid crystal is considered in the limit of nonlocal response of the liquid crystal. This nonlocal limit is the applicable limit for most experimentally available liquid crystals. In this nonlocal limit, two separate cases for the initial separation of the nematicons are considered, these being large and small separation. Both spinning and nonspinning nematicons are considered. It is found that in the case of large initial separation, the nematicons can form a spinning or nonspinning bound state with a finite steady separation, this being called a nematicon dipole, when they are π out of phase. On the other hand, well separated, nonspinning, in-phase nematicons attract and merge, while well separated, spinning, in-phase nematicons can either form a bound state or merge into a single nematicon. In the limit of small initial separation, the nematicons rapidly merge when they are in phase. Modulation equations describing the nematicon interaction are derived via suitable trial functions in an averaged Lagrangian. These modulation equations are further modified to include the effect of the diffractive radiation shed as the nematicons evolve. Finally the modulation equations are approximated in order to investigate the various interaction regimes. Good to excellent agreement is found between their solutions and full numerical solutions of the nematicon equations.     

A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows

A momentum exchange-based immersed boundary-lattice Boltzmann method is presented in this Letter for simulating incompressible viscous flows. This method combines the good features of the lattice Boltzmann method (LBM) and the immersed boundary method (IBM) by using two unrelated computational meshes, an Eulerian mesh for the flow domain and a Lagrangian mesh for the solid boundaries in the flow. In this method, the non-slip boundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation (LBE). Unlike the conventional IBM using the penalty method with a user-defined parameter or the direct forcing scheme based on the Navier–Stokes (NS) equations, the forcing term is simply calculated by the momentum exchange of the boundary particle density distribution functions, which are interpolated by the Lagrangian polynomials from the underlying Eulerian mesh. Numerical examples show that the present method can provide very accurate numerical results.     

Spontaneous symmetry breaking for zero mass

We investigate spontaneous symmetry breaking of a zero mass free Lagrangian within a functional formalism. We find that the boundary conditions of field solutions are responsible for the spontaneous symmetry breaking and this can be incorporated naturally in a functional method.     

Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect

In this paper, a set of 3D general solutions to static problems of 1D hexagonal piezoelectric quasicrystals is obtained by introducing two displacement functions and utilizing the rigorous operator theory. All the physical quantities are expressed by five quasi-harmonic functions. Based on the general solutions and with the help of the superposition principle, fundamental solutions for infinite/half-infinite spaces are presented by trial-and-error technique. The general solutions can be conveniently used to solve the boundary value problems regarding dislocations, cracks and inhomogeneities. The fundamental solutions are of primary significance to development of numerical codes such as boundary element method.     

Efficient numerical techniques for perturbative lattice gauge theory computations

We discuss a set of methods and numerical tools, which are useful for a computer based approach to perturbative calculations in lattice gauge theory. The topics considered include the automatic generation of gluon vertex programs, a derivation of the Faddeev-Popov determinant on lattices with boundary, the use of a partially finite lattice with twisted boundary conditions as an infrared cutoff without zero modes, and finally the numerical extrapolation of lattice Feynman diagrams to the continuum limit. As an illustration of the methods we describe their implementation in the computation of the on-shell improved lattice action at weak coupling.     

Spectroscopy for cold atom gases in periodically phase-modulated optical lattices

The response of cold atom gases to small periodic phase modulation of an optical lattice is discussed. For bosonic gases, the energy absorption rate is given, within linear response theory, by the imaginary part of the current autocorrelation function. For fermionic gases in a strong lattice potential, the same correlation function can be probed via the production rate of double occupancy. The phase modulation gives thus direct access to the conductivity of the system, as a function of the modulation frequency. We give an example of application in the case of bosonic systems at zero temperature and discuss the link between the phase and amplitude modulation.     

纳米线减反层的解析设计法

本文通过分析比较给出了常用二维等效介质理论解析解的适用条件并 且将有效介质理论的适用范围推广至零级衍射边界处, 并通过FDTD模拟验证了该解析方法的准确性. 这不仅解决了长期以来没有精确二维有效介质理论(2D-EMT)解析解的困境, 而且使得直接用解析公式设计和定量解释减反微结构的减反效果变得可能, 有着广泛的应用前景. 关键词： 零级衍射光栅 有效介质理论 太阳能电池减反 纳米线阵列     

Random lattice field theory: General formulation

A new type of lattice field theory is formulated in which the sites are chosen randomly in space. An algorithm is given for linking nearby sites; these links form the edges of non-overlapping simplices which fill the entire volume. All physical quantities averaged over such a lattice can therefore be translationally and rotationally symmetric.     

The shallow water equations in Lagrangian coordinates

Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. We apply numerical methods traditionally used to solve differential equations in Eulerian coordinates, to solve the shallow water equations in Lagrangian coordinates. The difficulty with solving in Lagrangian coordinates is that the transformation from Eulerian coordinates results in solving a highly nonlinear partial differential equation. The non-linearity is mainly due to the Jacobian of the coordinate transformation, which is a precise record of how the particles are rotated and stretched. The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes. For linear (spatial) flows we give an explicit formula for the Jacobian and describe the two situations where the Lagrangian shallow water equations cannot be used because either the Jacobian vanishes or the shallow water assumption is violated. We also prove that linear (in space) steady state solutions of the Lagrangian shallow water equations have Jacobian equal to one. In the situations where the shallow water equations can be solved in Lagrangian coordinates, accurate numerical solutions are found with finite differences, the Chebyshev pseudospectral method, and the fourth order Runge–Kutta method. The numerical results shown here emphasize the need for high order temporal approximations for long time integrations.     

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations.     

An approximate analytic solution of the steady state Brillouin scattering in single mode optical fiber without neglecting the attenuation coefficient

The analysis of steady state Brillouin scattering in a long single mode optical fiber is presented. Meanwhile, an approximate analytical functions of distributed Brillouin scattering and pump wave along the fiber with the fiber attenuation coefficient are obtained for the first time. A comparison is made among the analytical solutions with the attenuation coefficient, the analytical solutions without the attenuation coefficient and the exact numerical solutions. The results show that the analytical solutions with fiber attenuation coefficient are more close to the numerical solutions, which can be used to describe the power distribution of the pump wave and the Stokes wave along the long distance single mode optical fiber accurately.     

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two-dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plane Poiseuille flow and the plane Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time , and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation. Using the analytical solution, it is shown that in Poiseuille flow the bounce-back boundary condition introduces an error of first order in the lattice spacing. The boundary condition used by Kadanoffet al. in lattice gas automata to simulate Poiseuille flow is also considered for the triangular lattice Boltzmann BGK model. An analytical solution is obtained and used to show that the boundary condition introduces an error of second order in the lattice spacing.     

Non—equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method

In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527).     

Asymptotics for kink propagation in the discrete Sine-Gordon equation

The evolution of a propagating kink in a Sine-Gordon lattice is studied asymptotically using an averaged Lagrangian formulation appropriately coupled to the effect of the radiation. We find that unlike the continuum case the interaction with the Goldstone mode is important to explain the acceleration of the kink as it hops along the lattice. We develop a discrete WKB type solution to study the interaction of the kink and the radiation. In particular using this solution we show how to calculate the effect of the Peyrard and Kruskal resonant radiation in the energy loss of the kink. We obtain a set of modulation equation which explains qualitatively the evolution of the kink with remarkable quantitative agreement.     

Lagrangian approach for dark soliton in nonlocal nonlinear media

We theoretically investigate the dynamics of dark solitons as well as their interaction in nonlocal media. Approximate equations describing the evolution of the beams are obtained via suitable trial functions of amplitude u and refractive index n in an averaged Lagrangian. Our results reveal that out-of-phase dark solitons can evolve into stable bound states in nonlocal materials. Moreover, it is found that the separations in the bound state monotonically increase with the degree of nonlocality in nonlocal limit. These results are in excellent agreement with the numerical simulations.     

位势系统的界面估计

本文讨论了如何由边界数据对一个位势系统的界面进行估计的技术,它可以化为一个泛函的约束极小化问题,解法采用了增广Lagrange乘子法,数值计算采用了有限元离散化技术。