A preliminary study on sea wave packet equations on slowly varying topography

There is a common hypothesis for the presently popular mild-slope equations that wave particle motion is irrotational. In this paper, an attempt is made to abandon the irrotational assumption and to set up new sea wave packet equations on slowly varying topography by use of the WKBJ method. To simplify the deduction, the two-dimensional shallow water equations are used to describe the sea wave particle motion in the very shallow nearshore area. The established equations can give some characteristics of wave propagation near shore.     

A WAVE-OPTICS EFFECT WHICH ENHANCES LIGHT ABSORPTION BY CHLOROPHYLL IN VIVO

Abstract Light is widely thought to move through cells and tissues as rays. Actually light is inherently wave-like; ray motion is a special simple case of wave motion. To determine how well rays simulate light propagation and gradients within cells, absorption and scattering by particles were calculated with two sets of equations: one based on wave propagation within the particle and the other based on ray propagation. The ray model is found to substantially describe absorption at all particle size levels; however, it does not correctly describe scattering. Furthermore, for biological cells and structures larger than λ, the wave equations predict absorption cross sections which are 8–10% larger than expected on the basis of ray optics and extraction data: i.e. absorption is increased by a peculiar wave optics effect. This effect must enhance the efficiency with which the plants collect light energy for photosynthesis. The effect should be accounted for in corrections for the sieve effect.     

3-D transient electrophoretic motion of a spherical particle in a T-shaped rectangular microchannel

This paper considers the electrophoretic motion of a spherical particle in an aqueous electrolyte solution in a T-shaped rectangular microchannel, where the size of the channel is close to that of the particle. This is a complicated transient process where the electric field, the flow field, and the particle motion are coupled together. A theoretical model was developed to investigate the influences of the applied electric potentials, the zeta potentials of the channel and the particle, and the size of the particle on the particle motion. A direct numerical simulation method using the finite element method is employed. This method employs a generalized Galerkin finite element formulation that incorporates both equations of the fluid flow and equations of the particle motion into a single variational equation where the hydrodynamic interactions are eliminated. The ALE method is used to track the surface of the particle at each time step. The numerical results show that the electric field in the T-shaped microchannel is influenced by the presence of the particle, and that the particle motion is influenced by the applied electric potentials and the zeta potentials of the channel and the particle. The path of the particle motion is dominated by the local electric field and the ratio of the zeta potential of the channel to that of the particle. The particle's velocity is also dependent on its size in a small channel.     

Influence of particle-particle interactions and particles rotational motion in traveling wave dielectrophoresis

Traveling wave dielectrophoresis provides an interesting method for the controlled movement of microsized particles in suspended mixtures, and as such is a promising tool in microfluidic technology. In this case, the electrostatic force acting on the particles has two components: one due to the spatially varying magnitude of the electric field and the other due to the spatially varying phase. The actual movement of the particle is determined by the combined effect of these two forces and corresponding torques, the viscous drag exerted by the fluid on the particle, and the electrostatic and hydrodynamic particle-particle interactions. This paper presents the first numerical simulations of the motion of particles subjected to all previous forces and torques. Our technique is based on a finite-element scheme in which the particles are moved using a direct simulation scheme respecting the fundamental equations of motion for both the fluid and the solid particles. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the electrostatic forces are computed using the point-dipole approximation. Our simulations show that the particle behavior strongly depends on the mismatch of the dielectric properties between the particles and the fluid, and that the particle-particle interaction force as well as particles rotation speeds play crucial roles in the various regimes.     

Ultrasonic Scattering by a Spheroidal Suspension Including Dissipative Effects

This study treats the axisymmetric interaction of a plane compressional sound wave with a viscoelastic (viscous) prolate spheroidal particle (droplet) suspended in a boundless viscous fluid medium. The method of eigen‐function expansion along with the novel features of Havriliak‐Negami model for viscoelastic material behavior and the linearized equations of Navier‐Stokes for wave motion in a viscous non‐heat‐conducting compressible fluid are employed to develop a closed form series solution involving Spheroidal harmonics of complex argument. The complications arising due to the non‐orthogonality of angular Spheroidal functions corresponding to different wave numbers as well as problems associated with the appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Spheroidal functions in terms of Lengedre functions which are themselves expanded in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of unknown scattering and transmission coefficients. The presented solution demonstrates that the acoustic characteristics of particulate suspensions are strongly influenced by spheroidicity of particle cross‐section. Limiting case involving an elastic (ideal) spheroidal particle (droplet) in an ideal fluid is considered and fair agreement with available solution is established.     

Non-Born-Oppenheimer treatment of the H2 Hookean molecule

We show that the exact non-Born-Oppenheimer Schrodinger equation for the Hookean diatomic molecule H2 (a two-proton, two-electron system where the electron-proton interaction is harmonic while the proton-proton and electron-electron interactions are Coulombic) can be decoupled into equations describing the relative motion of the electrons, the relative motion of nuclei, the motion of a collective mode representing a three-dimensional harmonic oscillator, and the motion of a free particle expressed as a linear combination of the individual center-of-mass coordinates of the nuclei and electrons. Analytic solutions to the relative motion of electrons can be readily obtained for the given values of the harmonic coupling constant. However, exact analytic solutions to the equation for the relative motion of the nuclei cannot be obtained simultaneously due to the fact that the harmonic constants in these two equations are coupled. For this reason, we present for the relative nuclear motion approximate analytic wave functions, one of them obtained variationally and the other by a series solution where the coefficients are determined recursively. We also explore a variational solution to the Taylor-series expansion of the nuclear interaction potential. Properties of the electronic and nuclear intracule densities are examined at different values of the coupling constant. An interesting result of the present non-Born-Oppenheimer treatment of this harmonic model is the fact that the relative nuclear motion occurs in a highly correlated regime. This leads in a natural way to a spatial localization of the nuclei akin to Wigner electronic crystallization.     

Time-dependent quantum Monte Carlo and the stochastic quantization

We examine the relation between the recently proposed time-dependent quantum Monte Carlo (TDQMC) method and the principles of stochastic quantization. In both TDQMC and stochastic quantization, particle motion obeys stochastic guidance equations to preserve quantum equilibrium. In this way the probability density of the Monte Carlo particles corresponds to the modulus square of the many-body wave function at all times. However, in TDQMC, the motion of particles and guide waves occurs in physical space unlike in stochastic quantization where it occurs in configuration space. Hence, the practical calculation of time evolution of many-body fully correlated quantum systems becomes feasible within the TDQMC methodology. We illustrate the TDQMC technique by calculating the symmetric and antisymmetric ground state of a model one-dimensional helium atom, and the time evolution of the dipole moment when the atom is irradiated by a strong ultrashort laser pulse.     

Motion of a colloidal sphere with interfacial self-electrochemical reactions induced by a magnetic field

The motion of a spherical colloidal particle with spontaneous electrochemical reactions occurring on its surface in an ionic solution subjected to an applied magnetic field is analyzed for an arbitrary zeta potential distribution. The thickness of the electric double layer adjacent to the particle surface is assumed to be much less than the particle radius. The solutions of the Laplace equations governing the magnetic scalar potential and electric potential, respectively, lead to the magnetic flux and electric current density distributions in the particle and fluid phases of arbitrary magnetic permeabilities and electric conductivities. The Stokes equations modified with the Lorentz force contribution for the fluid motion are dealt by using a generalized reciprocal theorem, and closed-form formulas for the translational and angular velocities of the colloidal sphere induced by the magnetohydrodynamic effect are obtained. The dipole and quadrupole moments of the zeta potential distribution over the particle surface cause the particle translation and rotation, respectively. The induced velocities of the particle are unexpectedly significant, and their dependence on the characteristics of the particle-fluid system is physically different from that for electromagnetophoretic particles or phoretic swimmers.     

A simple, direct derivation and proof of the validity of the SLLOD equations of motion for generalized homogeneous flows

We present a simple and direct derivation of the SLLOD equations of motion for molecular simulations of general homogeneous flows. We show that these equations of motion (1) generate the correct particle trajectories, (2) conserve the total thermal momentum without requiring the center of mass to be located at the origin, and (3) exactly generate the required energy dissipation. These equations of motion are compared with the g-SLLOD and p-SLLOD equations of motion, which are found to be deficient. Claims that the SLLOD equations of motion are incorrect for elongational flows are critically examined and found to be invalid. It is confirmed that the SLLOD equations are, in general, non-Hamiltonian. We derive a Hamiltonian from which they can be obtained in the special case of a symmetric velocity gradient tensor. In this case, it is possible to perform a canonical transformation that results in the well-known DOLLS tensor Hamiltonian.     

ON THE Benjamin-Ono EQUATION AND ITS GENERALIZATION IN THE ATMOSPHERE

This paper deals with the nonlinear problems of the two-layer shallow water wave modelin the atmosphere by the multiple scale method and points out that a nonlinear Benjamin-Ono equation may be obtained if the meridional disturbance wind is weak. Furthermore, thealgebraic solitary waves and nonlinear periodic waves are also calculated and the breakup ofan algebraic solitary wave at the initial time into two is discussed. It is found that the waveform steepens in this process, which is similar to the triggering process of squall lines inthe atmosphere. On the other hand, we also point out that when the meridional disturbancewind is strong, we may obtain a modified Benjamin-Ono equation, i. e. the Benjamin-Ono-KDV equation.     

Unified view on multiconfigurational time propagation for systems consisting of identical particles

We show that the successful and formally exact multiconfigurational time-dependent Hartree method (MCTDH) takes on a unified and compact form when specified for systems of identical particles (MCTDHF for fermions MCTDHB for bosons). In particular the equations of motion for the orbitals depend explicitly and solely on the reduced one- and two-body density matrices of the system's many-particle wave function. We point out that this appealing representation of the equations of motion opens up further possibilities for approximate propagation schemes.     

Effect of growth conditions on the structure of two-dimensional latex crystals: modeling

Essential experimental features of the nucleation and growth of a 2D colloidal crystal on a solid substrate are modeled. The crystal, composed of sub-micron-sized latex spheres, is grown by the evaporation of water from the particle suspension in a circular cell. The calculation of the meniscus profile in the cell allows the prediction of the particle volume fraction in the suspension surrounding the crystal as a function of time. This quantity enters into a convective-diffusion model for the crystal growth which calculates the crystal radius as a function of time. Comparison with experimental data for 2D latex particle crystals shows predominant convective growth over a wide range of evaporation rates set by varying the humidity of the air. Microscopic parameters of the particle assembly can also be estimated such as the particle velocity, diffusivity, characteristic time constants, Peclet number, etc. The nucleation is simulated by simultaneously solving the equations of motion for the ensemble of particles trapped in a thin liquid film using the discrete-element method. These equations account for the forces which are physically important in the system: contact particle–particle friction, increased viscous resistance during the particle motion in a wetting film, long-range capillary attraction between two particles screened by the rest of particles. The final result of the simulation is a particle cluster of hexagonal packing, whose structure resembles very much the monolayer nucleus of latex particles observed experimentally. The models proposed by us could also be implemented for the aggregation of species in a variety of practical processes such as coating, texturing, crystal growth from a melt or liquid solution, or a biological array. Received: 10 May 1999 Accepted in revised form: 6 July 1999     

Diffusiophoresis of an Elongated Cylindrical Nanoparticle along the Axis of a Nanopore

The translation of a charged, elongated cylindrical nanoparticle along the axis of a nanopore driven by an imposed axial salt concentration gradient is investigated using a continuum theory, which consists of the ionic mass conservation equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the modified Stokes equations for the hydrodynamic field. The diffusiophoretic motion is driven by the induced electrophoresis and chemiphoresis. The former is driven by the generated overall electric field arising from the difference in the ionic diffusivities and the double layer polarization, while the latter is generated by the induced osmotic pressure gradient around the charged particle. The induced diffusiophoretic motion is investigated as functions of the imposed salt concentration gradient, the ratio of the particle’s radius to the double layer thickness, the cylinder’s aspect ratio (length/radius), the ratio of the nanopore size to the particle size, the surface charge densities of the nanoparticle and the nanopore, and the type of the salt used. The induced diffusiophoretic motion of a nanorod in an uncharged nanopore is mainly governed by the induced electrophoresis, driven by the induced electric field arising from the double layer polarization. The induced particle motion is driven by the induced electroosmotic flow, if the charges of the nanorod and nanopore wall have the same sign.     

THEORETICAL AND COMPUTATIONAL INVESTIGATIONS OF NONLINEAR WAVE PROPAGATIONS IN ARTERIES (Ⅰ)——A THEORETICAL MODEL OF NONLINEAR PULSE WAVE PROPAGATIONS

In this paper, a new theoretical model of nonlinear wave propagations in arteries with surrounding tissues was put forward. The equations of motion for the blood vessels and their peripheral tissues as a system have been derived. These equations were expressed in terms of the stresses of the vessel wall and fluid, and the geometry of the blood vessel. They can be used to solve numerically the problems for the propagations of nonlinear pulse waves in arteries together with the momentum and continuity equations of incompressible-viscous flow, as well as the constitutive equations of fluid and vessel wall. The numerical solutions can involve pressure, velocities and flowrate of the blood flow, as well as displacements, velocities and stresses of the vessel wall. These physical variables of propagations of pulse waves in arteries are all of significance physiologically and clinically.     

Effect of surface tension and surface elasticity of a fluid-fluid interface on the motion of a particle immersed near the interface

The motion of a particle immersed in a fluid near a fluid-fluid interface is studied on the basis of the linearized Navier-Stokes equations. The motion is influenced by surface tension, dilatational surface elasticity modulus, and surface shear modulus, as well as by gravity. The backflow at the location of the particle after a sudden impulse has some universal features that are the same as for a rigid wall with stick boundary conditions. At short times the flow depends only on the mass densities of the two fluids. The nature of the short-time flow is calculated from potential flow theory. At a somewhat later time the particle shows a pronounced rebound. The maximum value of the rebound and the time at which the maximum occurs depend on the elastic properties of the interface.     

A new method for solving the quantum hydrodynamic equations of motion: application to two-dimensional reactive scattering

The de Broglie-Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian-Eulerian frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method.     

Time propagation of constrained coupled Gaussian wave packets

The dynamics of quantum systems can be approximated by the time propagation of Gaussian wave packets. Applying a time dependent variational principle, the time evolution of the parameters of the coupled Gaussian wave packets can be calculated from a set of ordinary differential equations. Unfortunately, the set of equations is ill behaved in most practical applications, depending on the number of propagated Gaussian wave packets, and methods for regularization are needed. We present a general method for regularization based on applying adequate nonholonomic inequality constraints to the evolution of the parameters, keeping the equations of motion well behaved. The power of the method is demonstrated for a nonintegrable system with two degrees of freedom.     

Brownian diffusion close to a polymer brush

In an effort to control particle diffusion near surfaces, we have studied the dynamics of colloidal hard spheres and soft compliant star copolymers on surfaces coated with polymer brushes using evanescent wave dynamic light scattering. The same experiments provide information on the brush structure and confined particle motion. The penetration into dense polydisperse brushes is size- and solvent-dependent.