Applying Periodic Boundary Conditions to Predict Open Water Propeller Performance

Mathematical models of propellers were created that investigate the influence of periodic boundary conditions on predictions of a propeller's performance.Thrust and torque coefficients corresponding to different advance coefficients of DTMB 4119, 4382, and 4384 propellers were calculated.The pressure coefficient distribution of the DTMB 4119 propeller at different sections was also physically tested.Comparisons indicated good agreement between the results of experiments and the simulation.It showed that the periodic boundary condition can be used to rationally predict the open water performance of a propeller.By analyzing the three established modes for the computation, it was shown that using the spline curve method to divide the grids can meet the calculation's demands for precision better than using the rake cutting method.

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.

Heteroclinic Breather-Wave Solutions for Davey-Stewartson Equation

Exact heteroclinic breather-wave solutions for Davey-Stewartson （DSI, DSII） system with periodic boundary condition are constructed using Hirota＇s bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.

Laser-Manipulating Macroscopic Quantum States of a Bose-Einstein Condensate Held in a Kronig-Penny Potential

We investigate the boundary vaJue problem （BVP） of a quasi-one-dimensional Gross-Pitaevskii equation with the Kronig-Penney potential （KPP） of period d, which governs a repulsive Bose-Einstein condensate. Under the zero and periodic boundary conditions, we show how to determine n exact stationary eigenstates {Rn} corresponding to different chemical potentials {μn} from the known solutions of the system. The n-th eigenstate P~ is the Jacobian elliptic function with period 2din for n = 1,2,…, and with zero points containing the potential barrier positions. So Rn is differentiable at any spatial point and R2 describes n complete wave-packets in each period of the KPP. It is revealed that one can use a laser pulse modeled by a 5 potential at site xi to manipulate the transitions from the states of {Rn} with zero Point x≠xi to the states of {Rn＇} with zero Point x= Xi. The results suggest an experimental scheme for applying BEC to test the BVP and to observe the macroscopic quantum transitions.

Multiple templates-based homology modeling and docking analysis of angiotensin Ⅱ type 1 receptor

Using the latest reported homologous Chemokine receptors （PDB ID： 3ODU, 3OE0 and 3OE6） as templates, twenty models of angiotensin II （Ang II） type 1 （AT1） receptor （known as p30556） were generated by multiple templates homology modeling. According to the results of the initial validation of these twenty models, the model 0020 was finally chosen as the best one for further studies. Then, a 2 ns molecular dynamic （MD） simulation for model 0020 was conducted in normal saline （0.9%, w/F） under periodical boundary conditions, which was followed by docking studies of model 0020 with several existing AT1 receptor blockers （ARBs）. The docking results reveal that model 0020 possesses good affinities with these docked ARBs which are in accordance with both the IC50 inhibitor values and their curative effects. The results also show more potent interactions between the model 0020 and its ARBs than those of ever reported results, such as hydrogen bonds, hydrophobic interactions, and especially cation-n interactions and π-π interactions which have never been reported before. This may reveal that the structure of the model 0020 is quite close to its real crystal structure and the model 0020 may have the potential to be used for structure based drug design：

Numerical Solution of Some Diffusion Problems in 3-Layered 3D Domain

In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in a multilayered domain. We consider the metal concentration in the 3 layered peat blocks. Using experimental data the mathematical model for calculating the concentration of metal at different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for the partial differential equations （PDEs） of the elliptic type of second order with piece-wise diffusion coefficients in the three layer domain. We develop here a finite-difference method for solving a problem of the above type with the periodical boundary condition in x direction. This procedure allows reducing the 3-D problem to a system of 2-D problems by using a circulant matrix.

有限晶体中的电子态

传统的固体物理中的电子态的理论实质上是无限晶体中的电子态的理论 .但是任何真实晶体的尺寸都是有限的 .文章简单介绍了作者最近提出的有限晶体中的电子态的理论的一些背景材料和主要的新结果 .

Thermodynamic properties and constitutive relations of crystals at finite temperature

The dynamics equation for each individual atom is established directly around the equilibrium state of the system of N atoms based on the inter-atomic potential energy of EAM model.Using the theory of lattice dynamics and periodical boundary condition,the 3N×3N stiffness matrix in eigen equations of vibration frequencies for a parallelepiped crystal is reduced to a 3n×3n matrix of eigen equations of vibration frequencies for a unit lattice.The constitutive relation of the crystal at finite temperature is extracted based on the quantum-mechanical principle.The thermodynamic properties and the stress-strain relationships of crystal Cu with large plastic deformation at different temperatures are calculated,the calculation results agree well with experimental data.

Solutions of second order degenerate integro-differential equations in vector-valued function spaces

We study the well-posedness of the second order degenerate integro-differential equations （P2）： （Mu）t＇（t） ＋ a（Mu）＇（t） = Au（t） ＋ ft_c~ a（t - s）Au（s）ds ＋ f（t）, 0 ≤ t ≤ 27r, with periodic boundary conditions Mu（O） = Mu（27r）, （Mu）＇（O） = （Mu）＇（2π）, in periodic Lebesgue-Bochner spaces LP（T,X）, periodic Besov spaces BBp,q（T, X） and periodic Triebel-Lizorkin spaces F~,q（＇F, X）, where A and M are closed linear operators on a Banach space X satisfying D（A） C D（M）, a C LI（R＋） and a is a scalar number. Using known operator- valued Fourier multiplier theorems, we completely characterize the well-posedness of （P2） in the above three function spaces.

RRS-PBC: a molecular approach for periodic systems

Technically, when dealing with a perfect crystal, methods （PBC） in conjunction with plane-wave basis sets are widely in k-（reciprocal） space that impose periodic boundary conditions used. Chemists, however, tend to think of a solid as a giant mole- cule, which offers a molecular way to describe a solid by using a finite cluster model （FCM）. However, FCM may fail to sim- ulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space infor- mation of a perfect crystalline solid out of a reduced real space （RRS） of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.

Global existence for slightly compressible hydrodynamic flow of liquid crystals in two dimensions

In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by Ding et al. （2013）, when the parameter λ→∞ oo, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, Ding et al. （2013） proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that is sufficiently large and the initial data are almost incompressible.

Optimized Ewald sum for electrostatics in molecular self-assembly systems at interfaces

We extend the recent formulation of the Ewald sum for electrostatics in a two-dimensionally periodic three-dimensional multi- atom layer or two-dimensional single-atom layer system with a rectangular periodic boundary condition （J Chem Theory, Comput, 2014, 10： 534-542） to that with a parallelogrammic periodic boundary condition in general. Following the discussion of an efficient implementation of the formula, we suggest a simple setup of parameters using a relatively smaller screening factor and the associated larger real space cutoff distance to reach an optimized algorithm of an order N computational cost. The connection between the previous application of the Ewald sum to ionic crystal systems and the future application to mo- lecular self-assembly or disassembly systems on solid surfaces or at liquid-liquid interfaces ate illustrated to demonstrate the applicability of the present work to simulate the self-assembly process and to produce dynamical, structural and thermody- namic properties of experimental self-assembly systems of interest.

Boundary element method for calculation of elastic wave transmission in two-dimensional phononic crystals

A boundary element method(BEM) is presented to compute the transmission spectra of two-dimensional(2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction.The cross sections of the scatterers may be circular or square.For a periodic cell,the boundary integral equations of the matrix and the scatterers are formulated.Substituting the periodic boundary conditions and the interface continuity conditions,a linear equation set is formed,from which the elastic wave transmission can be obtained.From the transmission spectra,the band gaps can be identified,which are compared with the band structures of the corresponding infinite systems.It is shown that generally the transmission spectra completely correspond to the band structures.In addition,the accuracy and the efficiency of the boundary element method are analyzed and discussed.

Automatic modeling together with numerical simulation of the different-scale microstructures of human tooth enamels

The present paper aims to develop an automatical strategy for generating accurate different-scale microstructures of human tooth enamels(HTEs),and to elaborate a numerical scheme for simulating their elastic responses.At first,the strong governing formulation of these microstructures is briefly constructed,and the relevant weak formulation is then deduced based on the virtual work theorem.Afterwards,a subdividing approach,which cuts the elements intercepted by the interfaces between distinct phases automatically,is established with the aid of the level set method(LSM),and the discrete counterpart of the governing formula is obtained by combining the weak formulation derived and a discretized model.To be noted,two silent merits are found when the elaborated strategy is applied:(1) the continents constituting the microstructures of different scales can be arbitrarily-shaped and conveniently reproduced;(2) the periodic boundary condition commonly employed can be enforced on the external surfaces of representative unit cells(RUCs) with no difficulty.Besides,a boundary value problem(BVP) involving a simplified HTE nanostructure is designed,analytically solved,and hereafter applied to verify the correctness of the proposed strategy.It is observed that both the displacement and stress predictions by the computational approach are in good agreement with the relevant analytical results irrespective of the material combinations applied.Eventually,discussions are made on the influence of material organizations of both the 2D and 3D HTE microstructures at the ultrastructural and repeated rod levels,and some concluding remarks are drawn.

Quasi-periodic Solutions for the Derivative Nonlinear Schrdinger Equation with Finitely Differentiable Nonlinearities

The authors are concerned with a class of derivative nonlinear Schr¨odinger equation iu_t + u_(xx) + i?f(u, ū, ωt)u_x=0,(t, x) ∈ R × [0, π],subject to Dirichlet boundary condition, where the nonlinearity f(z1, z2, ?) is merely finitely differentiable with respect to all variables rather than analytic and quasi-periodically forced in time. By developing a smoothing and approximation theory, the existence of many quasi-periodic solutions of the above equation is proved.

Markov selection and W-strong Feller for 3D stochastic primitive equations

This paper studies some analytical properties of weak solutions of 3D stochastic primitive equations with periodic boundary conditions. The martingale problem associated to this model is shown to have a family of solutions satisfying the Markov property, which is achieved by means of an abstract selection principle. The Markov property is crucial to extend the regularity of the transition semigroup from small times to arbitrary times. Thus, under a regular additive noise, every Markov solution is shown to have a property of continuous dependence on initial conditions, which follows from employing the weak-strong uniqueness principle and the Bismut-Elworthy-Li formula.