Field Approximation Research Articles

TAYLOR-ARIS DISPERSION DURING LUBRICATION FLOW IN A PERIODIC CHANNEL

Generalized Taylor-Aris dispersion (macrotransport) theory for spatially periodic media is used to study the dispersion of a point-sized particle during pressure-driven flow between two plates whose separation slowly varies in a spatially periodic manner.Invoking a lubrication approximation for the flow field, the macrotransport equations are solved in the long-wavelength asymptotic limit. Remarkably, the leading-order dispersivity during pressure-driven flow is identical to prior studies of electrophoretic and electroosmotic transport in such systems, provided that the O(1) Péclet number is defined in terms of the mean velocity of the particle. Particle velocity fluctuations induced by longitudinal variations in the mean velocity, rather than transverse diffusion in the local parabolic flow, are thus the dominant contribution to dispersion during this lubrication flow.

Green's function of a parallel plate waveguide with multiple abrupt changes of interwall distances

The Green's function of a parallel plate waveguide with cascaded step discontinuities is computed by using analytical methods. The expression is written as a sum of two terms, the first of which corresponds to the effect of the horizontal plates on the primary source's field taking into account the symmetric images with respect to the metallic boundaries. The second term is related to the reflections from the vertical discontinuity edges, which are treated by applying successively a mode‐matching technique. The solution of the posed boundary value problem is obtained through a well‐conditioned linear system. The behavior of the guided waves far from the discontinuity region is determined with the help of far field approximations. Numerical computations for specific cases are presented and examined and many general purpose procedures of educational and tutorial interest are extensively described.

Kaon condensation in neutron stars in relativistic mean field theory with isovector-scalar channel interaction

We study the properties of neutron stars involving antikaon condensation with three different models in the framework of relativistic mean field (RMF) approximation theory: the Glendenning-Moszkowski (GM) model, the Zimanyi-Moszkowski (ZM) model, and the hybrid derivative coupling (HD) model. We take the isovector-scalar (\ensuremath{\delta}-meson) channel interaction into account in our calculations and find that large mass neutron stars with kaon condensation can exist if the kaon optical potential is appropriately weak. The \ensuremath{\delta}-meson channel interaction has a significant influence on the property of neutron stars and the effects are a little different for the three models.

Modelling the Heat and Fluid Flow in the Welded Pool from High Power Arc Sources

The paper proposes a numerical method for analyzing the complex phenomena’s that appear in the case of keyholes welded pool geometry. Present model consist in a succession of analyses steps, needed to solve the interaction between the liquid/solid, liquid/protection gaze and liquid/MHD welded arc for arc welding, or electrons, or electromagnetic waves. The liquid/solid geometry result by dissipation of the welding power source in a matrix of many point sources. This process gives a first approximation of temperature fields and a good approximation of the digit 3D position, and information about the vaporization area.

Acoustic methods in extremely shallow water: validity of the far field approximation

In this paper we present some experimental results concerning the possibility of using traditional echosounder in extremely shallow water environments. In the framework of the Echos Project, a collaboration between ISMAR and IA, a wide area of the Venice Lagoon has been explored with a traditional echosounder. Since the explored area was extremely shallow (up to 50 cm), it became necessary to check experimentally whether the far field approximation was still valid in such conditions. In this work the acoustic field of the echosounder ELAC LAZ72 used for the sub bottom investigation is experimentally characterized and the validity of the far field approximation is verified.

Spatially resolved piezo-spectroscopic characterizations for the validation of theoretical models of notch-root stress fields in ceramic materials

The main aim of this work is a precise experimental assessment of the local stress fields developed at the notch-root in a ruby crystal, selected as a paradigm brittle material, by means of photo- and electron-stimulated luminescence techniques. Our approach takes advantage of the piezo-spectroscopic (PS) effect, which consists of a spectral shift of the luminescence emitted by the material due to lattice strain. Highly spatially resolved stress maps were extensively collected at the notch-root and spectral shifts monitored for the chromophoric (R-lines) fluorescence observed in a single-crystalline ruby sample. Experimental data were analyzed and compared to the theoretical solutions of notch-root stress fields given by Filippi and by Creager-Paris. Due to its inherent simplifications, the Creager–Paris solution was found leading to underestimation of the maximum stress value piled up in the material, while the Filippi’s solution represented a more suitable approximation for the stress field developed at the notch-root.

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.

A variational formulation in fracture mechanics

A variational approach to linear elasticity problems is considered. The family of variational principles is proposed based on the linear theory of elasticity and the method of integrodifferential relations. The idea of this approach is that the constitutive relation is specified by an integral equality instead of the local Hooke’s law and the modified boundary value problem is reduced to the minimization of a nonnegative functional over all admissible displacements and equilibrium stresses. The conditions of decomposition on two separated problems with respect to displacements and stresses are found for the variational problems formulated and the relation between the approach under consideration and the minimum principles for potential and complementary energies is shown. The effective local and integral criteria of solution quality are proposed. A numerical algorithm based on the piecewise polynomial approximations of displacement and stress fields over an arbitrary domain triangulation are worked out to obtained numerical solutions and estimate their convergence rates. Numerical results for 2D linear elasticity problems with cracks are presented and discussed.

Pseudo-polyharmonic vectorial approximation for div-curl and elastic semi-norms

Vector field reconstruction is a problem arising in many scientific applications. In this paper, we study a div-curl approximation of vector fields by pseudo-polyharmonic splines. This leads to the variational smoothing and interpolating spline problems with minimization of an energy involving the curl and the divergence of the vector field. The relationship between the div-curl energy and elastic energy is established. Some examples are given to illustrate the effectiveness of our approach for a vector field reconstruction.

Application of multiple-scale wavelet analysis to analytical approximations of geopotential fields

Application of multiple-scale wavelet analysis to analytical approximations of geopotential fields

Stark effect of electrons in semiconducting rectangular quantum boxes

The Stark shift of the electronic energy levels in semiconducting rectangular quantum boxes with different sizes is investigated by the use of variational solutions to the effective-mass approximation for electric fields of various orientations with respect to the center axis of the box. The asymptotic expansions of the Stark shift are given in the limits of low and high fields, respectively; they clearly indicate that the Stark shift is a quadratic function of the electric field for low electric fields and is an approximate linear function of the electric field for high electric fields. Likewise, our results also show that the largest Stark shift is obtained for the field directed along the diagonal in a cubic box, and is found for the low field directed along a side of the box and for the high field along the diagonal in a rectangular one. The large Stark shift of the electron and hole trapped in a quantum box leads to an obvious reduction of the interband recombination.

Remarks concerning kaon condensation in neutron stars

We reanalyze the existence of antikaon condensation phase in neutron stars with large mass and high gravitational redshift with not only the Glendenning-Moszkowski (GM) model but also the Zimanyi-Moszkowski (ZM) model in the framework of relativistic mean field (RMF) approximation theory. We find that even in the large mass and high redshift neutron stars, there are still some stiff enough equations of state of neutron star matter so that the pure antikaon condensation phase and the mixed phase of normal baryons and antikaon condensation can exist. By comparing the result given in the GM model and that in the ZM model, we notice that the existence of antikaon condensation phase does not depend on the details of the models.

Molecules in intense xuv pulses: Beyond the dipole approximation in linearly and circularly polarized fields

The ionization dynamics of $\mathrm{H}_{2}{}^{+}$ in an intense xuv laser pulse is studied beyond the dipole approximation in fields of linear and circular polarization. Our theoretical work shows distinct signatures of new ionization mechanisms and subsequent dynamics. Both low- and high-energy electrons emerge from the interaction to yield a characteristic and universal multilobe structure in the angular distributions which is uniquely linked to the initial molecular orientation. Each lobe is associated with its own characteristic electron dynamics. The emission spectra reveal processes that can be associated with single-center scattering, but show also clear evidence of two-center interference dynamics that can be explained by a simple two-center interference-diffraction model capturing the symmetry differences between $1{\ensuremath{\sigma}}_{g}$ and $1{\ensuremath{\sigma}}_{u}$ initial states.

Lattice of microtraps for ultracold atoms based on patterned magnetic films

We have realized a two-dimensional permanent magnetic lattice of Ioffe-Pritchard microtraps for ultracold atoms. The lattice is formed by a single $300\text{\ensuremath{-}}\mathrm{nm}$ magnetized layer of FePt, patterned using optical lithography. Our magnetic lattice consists of more than 15 000 tightly confining microtraps with a density of $1250\phantom{\rule{0.3em}{0ex}}\text{traps}∕{\mathrm{mm}}^{2}$. Simple analytical approximations for the magnetic fields produced by the lattice are used to derive relevant trap parameters. We load ultracold atoms into at least 30 lattice sites at a distance of approximately $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the film surface. The present result is an important first step toward quantum information processing with neutral atoms in magnetic lattice potentials.

Self-consistent dipole coherent oscillations of a coasting ion beam with strong space charge

For non-resonant collective interactions we discuss effects of the space charge fields of an intense coasting ion beam on Landau damping of its dipole coherent oscillations and fluctuations. Within the framework of a special simplifying model we use self-consistent expressions for the space charge fields of the ion beam to calculate the stability diagrams for coherent oscillations and the spectra of the transverse Schottky noise of the ion beam. We trace the deviations of the predictions of this model from that assuming the rigid beam approximation for the space charge fields. Since the dipole oscillations of the beam can be measured directly such a comparison enables to figure out more reliable predictions for such measurements.

Theory of Liquid‐crystalline Ordering in Polymer Brushes

AbstractSummary: We present a review of the works devoted to investigation of LC ordering in polymer brushes. This series has been carried out by the group of T. M. Birshtein and covers the following aspects of the problem: thermotropic LC phase transition in LCP brushes, microphase segregation, homeotropic and planar LC phases, LC polymer in LC solvent, lyotropic LCP brushes, LC transitions under normal or lateral force (shear flow). Analytical theory is developed for simplified model of polymer brush with accounting for thermotropic attraction in Mayer‐Saupe approximation and lyotropic repulsion in DiMarzio formalism; numerical calculations are fulfilled in self‐consistent field approximation (method of Scheutjens and Fleer). Brownian dynamics simulations are applied for modeling polymer brush in a shear flow.

Light Scattering from Filaments

Photo realistic visualization of a huge number of individual filaments like in the case of hair, fur, or knitwear is a challenging task: Explicit rendering approaches for simulating radiance transfer at a filament get totally impracticable with respect to rendering performance and it is also not obvious how to derive efficient scattering functions for different levels of (geometric) abstraction or how to deal with very complex scattering mechanisms. We present a novel uniform formalism for light scattering from filaments in terms of radiance, which we call the Bidirectional Fiber Scattering Distribution Function (BFSDF). We show that previous specialized approaches, which have been developed in the context of hair rendering, can be seen as instances of the BFSDF. Similar to the role of the BSSRDF for surface scattering functions, the BFSDF can be seen as a general approach for light scattering from filaments, which is suitable for deriving approximations in a canonic and systematic way. For the frequent cases of distant light sources and observers, we deduce an efficient far field approximation (Bidirectional Curve Scattering Distribution Function, BCSDF). We show that on the basis of the BFSDF, parameters for common rendering techniques can be estimated in a non-ad-hoc, but physically-based way.

Benchmark 3D solution and assessment of a zigzag theory for free vibration of hybrid plates under initial electrothermomechanical stresses

A benchmark three-dimensional (3D) exact piezothermoelasticity solution is presented for free vibration of simply supported cross-ply symmetrically laminated hybrid rectangular plates under initial in-plane electrothermomechanical stresses. The solution, based on second Piola stress tensor and nonlinear Lagrangian strains, accounts for the effect of initial transverse normal strain and the two-way electromechanical coupling. Benchmark results are presented for the natural frequencies under initial stresses and the modal distributions of displacements and stresses across the thickness, against which the accuracy of various 2D plate theories for hybrid plates can be assessed. A recently developed coupled 2D zigzag theory for hybrid plates is extended for the vibration under initial stresses. The theory uses a piecewise linear approximation for the thermal and potential fields across sublayers, and combines a global third-order variation with a piecewise linear (zigzag) variation across the layers for the inplane displacements. Using the conditions of continuity of transverse shear stresses at the layer interfaces and the shear traction-free conditions at the top and bottom, the number of primary displacement variables is reduced to five, as in the corresponding smeared third-order theory (TOT). The zigzag theory and the smeared TOT are assessed in comparison with the exact 3D solution for the natural frequencies and mode shapes of simply-supported rectangular plates under initial stresses. The zigzag theory results show excellent agreement with the 3D results when the initial thermal transverse normal strain is neglected, whereas the TOT may yield very inaccurate results depending upon the plate layup.

Effects of Fresnel Corrections in the Scattered Field of General Ellipsoids

The study of the scattered field of non-spherical scatterers is becoming an important field, especially in the remote sensing of vegetation. In this study, the scattered field of general ellipsoidal scatterers is formulated based on the generalized Rayleigh-Gans approximation, in which at least one of the dimensions of the ellipsoid is comparably smaller than the wavelength. The scattered field is formulated for the case in which far field approximations are used, as well as for the case in which the Fresnel zone effects are included. Results show that when the Fresnel corrections axe considered, the calculated backscattering cross section gives a better match with measurement data compared to when far field approximations are used.

Construction of analytical approximations of geopotential fields with the consideration of their fractal structure

Principal trends in the development of mathematical geophysics at the modern stage include the comprehensive development of the approximation approach [1]. Researchers widely use approximations of external elements of gravitational and magnetic fields by equivalent source assemblages ( source-like approximations [2]) and numerical field simulations [3]. We propose a new method for the approximation of geopotential fields by grid distribution of sources. This method takes into account the fractal structure of the fields and is based on the quadrotree technique used for the compression of digital graphic images [4]. The essence of the considered approximation transformations is as follows: all information related to the observed geophysical field U ( x , y , z ) is stored as a certain number k of vectors of parameter P = { p 1 , p 2 , …, p n } of sources creating the simulation field U mod ( x , y , z ) , which is practically equivalent to the field U ( x , y , z ) . The unknown parameters of sources are found by solving an inverse problem (IP) usually consisting in minimization of the functional within the ensemble µ of the field specification points. In the process of minimization, we solve a system of linear algebraic equations (SLAE) for the linear IP formulation and a sequence of SLAE for the nonlinear IP formulation. At F ( k , P ) ≤ e , where e is a sufficiently Fk P