High-Accurate Transparent Boundary Conditions for Time-Dependent Quantum Wave Packet Method

Complex absorbing potential is usually required in a time-dependent wave packet method to accomplish the calculation in a truncated region. Usually it works effectively but becomes inefficient when the wave function involves translational energy of broad range, particularly involving ultra-low energy. In this work, a new transparent boundary condition (TBC) is proposed for the time-dependent wave packet method. It in principle is of spectral accuracy when typical discrete variable representations are applied. The prominent merit of the new TBC is that its accuracy is insensitive to the translational energy distribution of the wave function, in contrast with the complex absorbing potential. Application of the new TBC is given to one-dimensional particle wave packet scatterings from a barrier with a potential well, which supports resonances states.     

Time-dependent wave packet propagation using quantum hydrodynamics

A new approach for propagating time-dependent quantum wave packets is presented based on the direct numerical solution of the quantum hydrodynamic equations of motion associated with the de Broglie–Bohm formulation of quantum mechanics. A generalized iterative finite difference method (IFDM) is used to solve the resulting set of non-linear coupled equations. The IFDM is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a “smart” Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is generalized to treat higher-dimensional problems and anharmonic potentials. The method is applied to a one-dimensional Gaussian wave packet scattering from an Eckart barrier, a one-dimensional Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. The 2D scattering results represent the first successful application of an accurate direct numerical solution of the quantum hydrodynamic equations to an anharmonic potential energy surface.     

不同边界条件下导电高分子电子结构的研究

用一维复式晶格作为反式聚乙炔的模型 ,在周期与非周期边界条件下 ,考虑链端效应并计及电子的非近邻跳跃 ,数值计算了格点数分别等于N =10、5 0、10 0和 2 0 0时聚乙炔的能谱和态密度 .讨论了不同格点数和结构参数对态密度及带宽的影响 ,并对两种边界条件下的计算结果进行了比较 .计算结果表明 ,当格点数N <5 0时 ,两者相差较大 ,这表明系统的边界将起很大作用 ;当格点数N≥ 5 0时 ,两者相差甚微 ,这时可利用周期性边界条件来研究有限系统问题 .     

Elastic bag model for molecular dynamics simulations of solvated systems: application to liquid water and solvated peptides

The fluctuating elastic boundary (FEB) model for molecular dynamics has recently been developed and validated through simulations of liquid argon. In the FEB model, a flexible boundary which consists of particles connected by springs is used to confine the solvated system, thereby eliminating the need for periodic boundary conditions. In this study, we extend this model to the simulation of bulk water and solvated alanine dipeptide. Both the confining potential and boundary particle interaction functions are modified to preserve the structural integrity of the boundary and prevent the leakage of the solute-solvent system through the boundary. A broad spectrum of structural and dynamic properties of liquid water are computed and compared with those obtained from conventional periodic boundary condition simulations. The applicability of the model to biomolecular simulations is investigated through the analysis of conformational population distribution of solvated alanine dipeptide. In most cases we find remarkable agreement between the two simulation approaches.     

Stability conditions of an electrified miscible viscous fluid sheet

The Kelvin-Helmholtz problem of viscous fluids under the influence of a normal periodic electric field in the absence of surface charges is studied. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming finite dielectric fluids. The interfaces permit mass and heat transfer. Because of the complexity of the considered system, a mathematical simplification is adopted. The weak viscous effects are taken into account so that their contributions are incorporated into the boundary conditions. Therefore, the equations of motion are solved in the absence of viscous effects. The boundary value problem leads to two simultaneous Mathieu equations of damped terms having complex coefficients. The symmetric and antisymmetric deformations reduced the coupled Mathieu equations to a single Mathieu equation. The classical stability criterion is found to be substantially modified due to the effect of mass and heat transfer. The analytical results are numerically confirmed. It is found that the sheet thickness and mass and heat transfer parameters have a dual influence on the stability criteria. It is also found that the field frequency has a stabilizing influence especially at small values of the wave number. In contrast to the case of a pure inviscid fluid, it is found that the uniform normal electric field plays a dual role in the stability criteria. This role depends on the choice of the numerical values of the physical parameters of the system under consideration.     

Chiral exciton wave functions in cylindrical J aggregates

We study the exciton wave functions and the optical properties of cylindrical molecular aggregates. The cylindrical symmetry allows for a decomposition of the exciton Hamiltonian into a set of effective one-dimensional Hamiltonians, characterized by a transverse wave number k2. These effective Hamiltonians have interactions that are complex if the cylinder exhibits chirality. We propose analytical ansatze for the eigenfunctions of these one-dimensional problems that account for a finite cylinder length, and present a general study of their validity. A profound difference is found between the Hamiltonian for the transverse wave number k2=0 and those with k2 not equal 0. The complex nature of the latter leads to chiral wave functions, which we characterize in detail. We apply our general formalism to the chlorosomes of green bacteria and compare the wave functions as well as linear optical spectra (absorption and dichroism) obtained through our ans?tze with those obtained by numerical diagonalization as well as those obtained by imposing periodic boundary conditions in the cylinder's axis direction. It is found that our ans?tze, in particular, capture the finite-length effect in the circular dichroism spectrum much better than the solution with periodic boundary conditions. Our ans?tze also show that in finite-length cylinders seven superradiant states dominate the linear optical response.     

Analysis of droplet behavior in a de-oiling hydrocyclone

A mechanical separation process in a de-oiling hydrocyclone is described in which disperse oil droplets are separated from a continuous water phase. This separation process is influenced by droplet breakage and coalescence. Based on experimental data and simulation results in a stirred tank, a modified breakage model, which can be applied to droplet breakage in the de-oiling hydrocyclone, is developed. Then, a simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics (CFD) with population balances. The homogenous discrete method and the inhomogeneous discrete method are applied for solving the population balance model (PBM). The investigations show that the numerical results obtained by the simulation model coupled with the modified PBM using the inhomogeneous discrete method are in good accordance with experimental data under a high flow rate. According to this simulation model, the effect of three different inlet designs on the separation efficiency of the de-oiling hydrocyclone has been discussed. The results indicate that the separation efficiency of the de-oiling hydrocyclone can be improved with an appropriate inlet design.     

Band structure of one-dimensional polymers via an SCF-Xα scattered-wave method: I. General formalism

A model of the multiple-scattering type is presented to study the band structure of periodic one-dimensional conductors. The potential is of a modified muffin-tin form: spherically averaged inside the atomic spheres, cylindrically averaged outside a cylinder enclosing the polymer and spatially averaged in between. Taking advantage of the periodicity of the system and using the Born—Kármán periodic boundary conditions the occurring infinite hypermatrix of the problem can be brought into a block-diagonal form. Thus the formalism includes only matrices of the order of the unit cell. The necessary steps for carrying out self-consistent calculations are discussed. In this connection a theorem is proved which allows the normalization of a scattered wave orbital function for an arbitrary outer surface.     

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain

A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.     

Scattered wave packet formalism for the energy-resolved reaction probability

The scattered wave packet formalism developed for a quantum subsystem interacting with reservoirs through open boundaries is utilized to calculate the energy-resolved transmission probability. The total wave function is split into incident and scattered components. Markovian outgoing wave boundary conditions are imposed on the scattered or total wave function by the polynomial method. The wave packet correlation function approach is employed to compute the energy-resolved transmission probability for a one-dimensional potential barrier and a one-dimensional model chemical reaction exhibiting a quantum resonance. Accurate results demonstrate that this formalism can significantly reduce the number of grid points required in a dynamical calculation for the reaction probability.     

A vibronic approach to the band-filling and temperature-dependent metal-insulator transition

A model of vibronic origin is used to investigate the important issue of metal-insulator transition in low-dimensional materials. For zero temperature, the stability of the single-band model chain is controlled by the competition between the internal electron-phonon coupling and the nearest-neighbor hopping integral. Assuming one particular deformation mode, one can analytically derive an instability criterion in which the band filling is explicitly included. The carrier doping directly controls the stability of a one-dimensional chain. For a half-filled band, the Peierls instability is recovered. For finite temperatures, a similar criterion is derived and can be used to investigate the metal-insulator transition temperatures.     

Nonlinear surface wave instability for electrified Kelvin fluids

A weakly nonlinear approach is utilized here to discuss surface wave instability for two superposed electrified fluids of Kelvin type. The influence of a vertical electric field is discussed. The linear form for equations of motion is solved in the light of nonlinear boundary conditions. The method of multiple scales is used for the purpose of nonlinear perturbation. The surface wave response is governed by the well-known nonlinear Ginzburg-Landau equation rather than the transcendental dispersion relation in the linear scope. Although linear stability conditions are not available for arbitrary viscosity, the nonlinear analysis allowed deriving necessary and sufficient stability conditions. Moreover, at the marginal state, the nonlinear scope for stability is discussed through its dependence on the wavetrain frequency, in which short-wave disturbance is assumed to relax the linear transcendental terms. Besides the linear stability constraint, the nonlinear scope gives an additional constraint on the wavetrain frequency. Nonlinear stability criteria are derived and are performed in view of a nondimensional form. Furthermore, the nonlinear analysis is repeated for an arbitrary wave disturbance. A suitable choice for dimensionless form made it possible to relax transcendental terms included in stability conditions. Numerical calculations at the marginal state show that both the vertical electric field and the stratified fluid density play a dual role in the stability criteria. This dual role is the opposite to the dual role that the stratified viscosity plays in the stability profile. For the marginal state representation, numerical examination shows that elasticity plays a dual role in the stability criteria in a manner similar to that of the viscosity behavior.     

非等温单分子化学反应体系中温度场的时空对称破缺及温度波

从线性稳定性分析和计算机数值模拟两个方面研究了小尺度空间展布、伴有扩散和热传导的Lindemann单分子化学反应体系的温度场时空对称破缺. 研究结果表明, 在一定参数值和固定边界条件下, 反应体系经由时间-空间对称破缺分支能够产生温度波.     

Radiation: Waves or particles? A quantized approach to time

A fundamental difficulty in theoretical physics is the dual and apparently incompatible interpretations of radiation as showing both continuous and extensive wave properties but also those of discrete atomic or smaller individual particles. Some of these contradictions are outlined. The explanation offered is of a quantized nature of time; units t_o=h/m_oc² for a particle at rest, and of similar interval unit s_o when in relative motion, with conventional relativistic corrections.

For many purposes this form of quantization replaces the need for a wave concept which then appears as a mathematical approach, chosen to avoid the physical concept of an intrinsicc time for any particle, just as we have for its intrinsic mass, spin and electrical charge. t_o and s_o are directly related to its frequency, energy and mass. The uncertainty principle and interference relations follow directly from this model, without any physical wave concept.     

The influence of drift gas composition on the separation mechanism in traveling wave ion mobility spectrometry: insight from electrodynamic simulations

The influence of three different drift gases (helium, nitrogen, and argon) on the separation mechanism in traveling wave ion mobility spectrometry is explored through ion trajectory simulations which include considerations for ion diffusion based on kinetic theory and the electrodynamic traveling wave potential. The model developed for this work is an accurate depiction of a second-generation commercial traveling wave instrument. Three ion systems (cocaine, MDMA, and amphetamine) whose reduced mobility values have previously been measured in different drift gases are represented in the simulation model. The simulation results presented here provide a fundamental understanding of the separation mechanism in traveling wave, which is characterized by three regions of ion motion: (1) ions surfing on a single wave, (2) ions exhibiting intermittent roll-over onto subsequent waves, and (3) ions experiencing a steady state roll-over which repeats every few wave cycles. These regions of ion motion are accessed through changes in the gas pressure, wave amplitude, and wave velocity. Resolving power values extracted from simulated arrival times suggest that momentum transfer in helium gas is generally insufficient to access regions (2) and (3) where ion mobility separations occur. Ion mobility separations by traveling wave are predicted to be effectual for both nitrogen and argon, with slightly lower resolving power values observed for argon as a result of band-broadening due to collisional scattering. For the simulation conditions studied here, the resolving power in traveling wave plateaus between regions (2) and (3), with further increases in wave velocity contributing only minor improvements in separations.     

On the self-consistent-field linear combination of atomic orbitals for bounded crystal orbitals (SCF-LCAO-BCO) method

The self-consistent-field linear combination of atomic orbitais for bounded crystal orbitais (SCF-LCAO-BCO) method can be used to study the electronic structure of bounded polymers and crystals if they have a significant amount of internal translational symmetry, at the ab initio Hartree-Fock level. The direct recursion (transfer matrix) method (DRM) is applied to its derivation, here only for certain simpler models. It is shown that the application of the free boundary condition instead of the periodic (Born-von Kármán) one halves the conventional one-dimensional Brillouin zone and resolves the double degeneracy of the Bloch states. A longitudinal bulk-state distortion (LBSD) is demonstrated for a linear bounded polymer model possessing perfect translational symmetry and symmetrical intercell interaction matrices. The block diagonalizability is discussed when free boundary conditions are applied. The non-existence of limit wave functions in the overlapping regions of bands is shown for the infinite size limit. The use of certain averaged wave functions is proposed for the calculation of the charge-bond order matrices in order to resolve the above difficulty.     

Finite difference method of simulation of non-steady-state ion transfer in electrochemical systems with allowance for migration

Finite difference methods of the second order of accuracy are elaborated for numerical calculation of non-steady-state ion transfer, which is caused by diffusion, migration, and convection in the unidimensional electrochemical systems. The methods of decoupling a set of coupled continuity equations of the electrolyte species are proposed, which ensures that the discrete equations are consistent with the initial differential equations and the electroneutrality condition is rigorously met. The methods of approximation of the boundary conditions of the second order temporal and spatial accuracy and the method of decoupling the transfer equations in the boundary nodes are elaborated. The explicit, fully implicit, and semi-implicit finite difference schemes are elaborated. For semi-implicit schemes, two versions of difference equation closure are proposed, which assure the unambiguity of determination of the distribution of electrical potential. Comparison analysis of the accuracy of elaborated finite difference methods of calculation of non-steady-state ion transfer is performed.     

光驱动一维活性凝胶自发定向运动

许多生物都具备一种自发响应环境刺激进行自动运动的本能。光照是一种强有力的外部刺激,且对生物系统具有正负驱动的双重效应;本实验设计了一个一维活性BZ凝胶体系,利用钌催化BZ反应的光敏性,控制凝胶振荡频率,驱动凝胶进行定向自发运动。同时,我们修正了V. V. Yashin 提出的BZ响应胶模型活性凝胶光强频率曲线进行模拟,揭示光驱动活性凝胶运动的本质。这有助于研发新型仿生智能机器人来对生物系统响应外部刺激的自发运动进行研究。     

Density functional study on the structural and thermodynamic properties of aqueous DNA-electrolyte solution in the framework of cell model

A density functional theory (DFT) in the framework of cell model is proposed to calculate the structural and thermodynamic properties of aqueous DNA-electrolyte solution with finite DNA concentrations. The hard-sphere contribution to the excess Helmholtz energy functional is derived from the modified fundamental measure theory, and the electrostatic interaction is evaluated through a quadratic functional Taylor expansion around a uniform fluid. The electroneutrality in the cell leads to a variational equation with a constraint. Since the reference fluid is selected to be a bulk phase, the Lagrange multiplier proves to be the potential drop across the cell boundary (Donnan potential). The ion profiles and electrostatic potential profiles in the cell are calculated from the present DFT-cell model. Our DFT-cell model gives better prediction of ion profiles than the Poisson-Boltzmann (PB)- or modified PB-cell models when compared to the molecular simulation data. The effects of polyelectrolyte concentration, ion size, and added-salt concentration on the electrostatic potential difference between the DNA surface and the cell boundary are investigated. The expression of osmotic coefficient is derived from the general formula of grand potential. The osmotic coefficients predicted by the DFT are lower than the PB results and are closer to the simulation results and experimental data.     

Hückel and möbius boundary conditions for solids and orbital symmmetry correlation in the rotational phase transition of molecular crystals

A new cyclic boundary condition which corresponds to a Möbius strip representation of a one-dimensional crystal is introduced. It is compared with the usual Bloch and Born—von Karman boundary condition which is shown to be a Hückel condition in the sense of LCAO MO treatment of a ring structure. The potential relevance of this Möbius condition to one-dimensional molecular and liquid crystals in which the relative molecular orientation changes during phase transition is alluded to. A comparison of the energies for the twisted and non-twisted form of the linear crystal is derived in the LCAO approximation. The orbital symmetry correlation in the concerted twist of the atomic or molecular orbitals atom! the linear backbone during a rotational polymorphic structural transition is also derived.