Soft Boundary Conditions Research Articles

The effects of varying tympanic-membrane material properties on human middle-ear sound transmission in a three-dimensional finite-element model.

An anatomically based three-dimensional finite-element human middle-ear (ME) model is used to test the sensitivity of ME sound transmission to tympanic-membrane (TM) material properties. The baseline properties produce responses comparable to published measurements of ear-canal input impedance and power reflectance, stapes velocity normalized by ear-canal pressure (PEC), and middle-ear pressure gain (MEG), i.e., cochlear-vestibule pressure (PV) normalized by PEC. The mass, Young's modulus (ETM), and shear modulus (GTM) of the TM are varied, independently and in combination, over a wide range of values, with soft and bony TM-annulus boundary conditions. MEG is recomputed and plotted for each case, along with summaries of the magnitude and group-delay deviations from the baseline over low (below 0.75 kHz), mid (0.75-5 kHz), and high (above 5 kHz) frequencies. The MEG magnitude varies inversely with increasing TM mass at high frequencies. Increasing ETM boosts high frequencies and attenuates low and mid frequencies, especially with a bony TM annulus and when GTM varies in proportion to ETM, as for an isotropic material. Increasing GTM on its own attenuates low and mid frequencies and boosts high frequencies. The sensitivity of MEG to TM material properties has implications for model development and the interpretation of experimental observations.

Log corrections to entropy of three dimensional black holes with soft hair

We calculate log corrections to the entropy of three-dimensional black holes with “soft hairy” boundary conditions. Their thermodynamics possesses some special features that preclude a naive direct evaluation of these corrections, so we follow two different approaches. The first one exploits that the BTZ black hole belongs to the spectrum of Brown-Henneaux as well as soft hairy boundary conditions, so that the respective log corrections are related through a suitable change of the thermodynamic ensemble. In the second approach the analogue of modular invariance is considered for dual theories with anisotropic scaling of Lifshitz type with dynamical exponent z at the boundary. On the gravity side such scalings arise for KdV-type boundary conditions, which provide a specific 1-parameter family of multi-trace deformations of the usual AdS3/CFT2 setup, with Brown-Henneaux corresponding to z = 1 and soft hairy boundary conditions to the limiting case z → 0+. Both approaches agree in the case of BTZ black holes for any non-negative z. Finally, for soft hairy boundary conditions we show that not only the leading term, but also the log corrections to the entropy of black flowers endowed with affine û (1) soft hair charges exclusively depend on the zero modes and hence coincide with the ones for BTZ black holes.

Some Factors Affecting Structure, Transition Phase and Crystallized of CuNi Nanoparticles

This paper studies the influence of atomic number at temperature of 300 K, temperature at 5324 atoms, phase transition & crystallization at different temperatures of 300 K, 500 K, 600 K, 700 K, 1100 K after 2×10 5 move steps number by increasing temperature of 4×10 12 K/s on microstructure, phase transition temperature, phase transition & crystallization of CuNi nanoparticle by molecular dynamics (MD) with embedded interaction Sutton-Chen and soft boundary conditions. Microstructure characteristics are analyzed through radial distribution function (RDF), energy, size, phase transition temperature (via relationship between energy and temperature), phase transition & crystallization (via radial distribution function, E tot , move step number and common neighbor analysis (CNA)). Results show that first peak position of the radial distribution function is dominant; lengths of Cu-Cu, Ni-Ni with the results of Ni-Ni consistent with simulation. At 300 K temperature, nanoparticle appears in four phases namely FCC, HCP, ICO and Amorphous, presenting the effect of atomic number, temperature and move step number on microstructure, phase transition temperature and phase transition & crystallization of CuNi nanoparticle.

An induced real quaternion spherical ensemble of random matrices

We study the induced spherical ensemble of non-Hermitian matrices with real quaternion entries (considering each quaternion as a [Formula: see text] complex matrix). We define the ensemble by the matrix probability distribution function that is proportional to [Formula: see text] These matrices can also be constructed via a procedure called ‘inducing’, using a product of a Wishart matrix (with parameters [Formula: see text]) and a rectangular Ginibre matrix of size [Formula: see text]. The inducing procedure imposes a repulsion of eigenvalues from [Formula: see text] and [Formula: see text] in the complex plane with the effect that in the limit of large matrix dimension, they lie in an annulus whose inner and outer radii depend on the relative size of [Formula: see text], [Formula: see text] and [Formula: see text]. By using functional differentiation of a generalized partition function, we make use of skew-orthogonal polynomials to find expressions for the eigenvalue [Formula: see text]-point correlation functions, and in particular the eigenvalue density (given by [Formula: see text]). We find the scaled limits of the density in the bulk (away from the real line) as well as near the inner and outer annular radii, in the four regimes corresponding to large or small values of [Formula: see text] and [Formula: see text]. After a stereographic projection, the density is uniform on a spherical annulus, except for a depletion of eigenvalues on a great circle corresponding to the real axis (as expected for a real quaternion ensemble). We also form a conjecture for the behavior of the density near the real line based on analogous results in the [Formula: see text] and [Formula: see text] ensembles; we support our conjecture with data from Monte Carlo simulations of a large number of matrices drawn from the [Formula: see text] induced spherical ensemble. This ensemble is a quaternionic analog of a model of a one-component charged plasma on a sphere, with soft wall boundary conditions.

The Bending–Gradient theory for the linear buckling of thick plates: Application to Cross Laminated Timber panels

In this paper, the linear buckling of a heterogeneous thick plate is studied using the Bending–Gradient theory which is an extension of the Reissner–Mindlin plate theory to the case of heterogeneous plates. Reference results are taken from a 3D numerical analysis using finite-elements and applied to Cross Laminated Timber panels which are thick and highly anisotropic laminates. First, it is shown that critical buckling loads are close to the material failure load which proves the necessity of a design model for the buckling of Cross Laminated Timber panels. Second, the soft simple support boundary condition is introduced as an opposition to the conventional hard simple support condition. It is shown that this distinction could be taken into account for designing timber structures depending on the accuracy needed. Third, it is observed that for varying plate geometries and arrangements, the Bending–Gradient theory predicts more precisely the critical load of CLT panels than classical lamination and first-order shear deformation theories. Finally, it is demonstrated that one of the suggested projections of the Bending–Gradient on a Reissner–Mindlin model gives very accurate results and could favorably allow the development of engineering recommendations for estimating properly transverse shear effects.

Scattering of Waves by a Perfectly Conducting Wedge Residing at the Interface Between Two Isorefractive Media

Scattered field by a wedge that is surrounded by isorefractive media is analyzed. A series-based method is introduced and applied to the wedge problem with soft boundary condition. The fields are examined numerically. The numerical results show that the proposed method is suitable for analysis of these kinds of problems.

Electromagnetic interaction with uniaxial metamaterials

AbstractIn this paper, the reflection behavior of a particular class of metamaterials, strongly connected with the realization of the DB boundary conditions (so called due to the vanishing of the normal components of the D and B fluxes) and the soft and hard (SH) boundary conditions, is presented. The metamaterial under study is modeled as an anisotropic, uniaxial, material with both permittivity and permeability dyadics. We consider several characteristics of such medium: presenting the critical angle of total transmission for the SH/DB material, analyzing its behavior as a function of the longitudinal permittivity and permeability, for both positive and negative values, and presenting its applications to the electromagnetic absorbers and to the polarization inverters.

A Study of Three-Dimensional Acoustic Scattering by Arbitrary Distribution Multibodies Using Extended Immersed Boundary Method

A three-dimensional computational model for acoustic scattering with complex geometries is presented, which employs the immersed boundary technique to deal with the effect of both hard and soft wall boundary conditions on the acoustic fields. In this numerical model, the acoustic field is solved on uniform Cartesian grids, together with simple triangle meshes to partition the immersed body surface. A direct force at the Lagrangian points is calculated from an influence matrix system, and then spreads to the neighboring Cartesian grid points to make the acoustic field satisfy the required boundary condition. This method applies a uniform stencil on the whole domain except at the computational boundary, which has the benefit of low dispersion and dissipation errors of the used scheme. The method has been used to simulate two benchmark problems to validate its effectiveness and good agreements with the analytical solutions are achieved. No matter how complex the geometries are, single body or multibodies, complex geometries do not pose any difficulty in this model. Furthermore, a simple implementation of time-domain impedance boundary condition is reported and demonstrates the versatility of the computational model.

Approximate Solutions to Nonlinear Optimal Control Problems in Astrodynamics

A method to solve nonlinear optimal control problems is proposed in this work. The method implements an approximating sequence of time-varying linear quadratic regulators that converge to the solution of the original, nonlinear problem. Each subproblem is solved by manipulating the state transition matrix of the state-costate dynamics. Hard, soft, and mixed boundary conditions are handled. The presented method is a modified version of an algorithm known as “approximating sequence of Riccati equations.” Sample problems in astrodynamics are treated to show the effectiveness of the method, whose limitations are also discussed.

Reverse time migration for extended obstacles: acoustic waves

We consider the resolution of the single-frequency reverse time migration method for extended targets without the assumption of the validation of the geometric optics approximation. The resolution analysis, which applies in both penetrable and non-penetrable obstacles with sound soft or impedance boundary condition on the boundary of the obstacle, implies that the imaginary part of the cross-correlation imaging functional is always positive and thus may have better stability properties. Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.

A fast BIE iteration method for an arbitrary body in a flow of incompressible inviscid fluid

The paper is concerned with the new iteration algorithm to solve boundary integral equations arising in boundary value problems of mathematical physics. The stability of the algorithm is demonstrated on the problem of a flow around bodies placed in the incompressible inviscid fluid. With a discrete numerical treatment, we approximate the exact matrix by a certain Töeplitz one and then apply a fast algorithm for this matrix, on each iteration step. We illustrate the convergence of this iteration scheme by a number of numerical examples, both for hard and soft boundary conditions. It appears that the method is highly efficient for hard boundaries, being much less efficient for soft boundaries.

One-component plasma on a spherical annulus and a random matrix ensemble

The two-dimensional one-component plasma at the special couplingβ = 2 is known to be exactly solvable, for its free energy and all of its correlations,on a variety of surfaces and with various boundary conditions. Here we studythis system confined to a spherical annulus with soft wall boundary conditions,paying special attention to the resulting asymptotic forms from the viewpointof expected general properties of the two-dimensional plasma. Our study ismotivated by the realization of the Boltzmann factor for the plasma system withβ = 2, after stereographic projection from the sphere to the complex plane, by a certain randommatrix ensemble constructed out of complex Gaussian and Haar distributed unitarymatrices.

Nonlinear Electromagnetic Waves in a Nematic Slab

We consider a nonlinear system formed by a thin nematic slab immersed in vacuum, submitted to the action of a high-intensity normally-incident plane electromagnetic wave. We solve simultaneously, by using a numerical scheme, the director's orientational configuration and Maxwell's equations for this system using homeotropic soft boundary conditions. For a given field intensity, we find multiple equilibrium director's configurations. In addition, we study the reflectance versus the wavelength and the field intensity.

A finite element model for mechanical deformation of single tomato suspension cells

A finite element model was developed to simulate compression experiments on single tomato cells from suspension cultures. The cell was modelled as a thin-walled liquid-filled sphere with a permeable wall allowing flow of fluid out in response to internal turgor increases due to the compression. The permeability of the cell wall/plasma lemma was considered to be constant throughout compression. The contact between cell and compression probe was modelled using a soft contact boundary condition. The cytoplast was represented as an internal pressure acting on the plasma lemma and cell wall. Assuming linear elastic constitutive behaviour for the cell wall, and using previously determined cell wall material parameters, the model was found to be remarkably capable of reproducing the force–deformation behaviour of a single cell in compression, as well as its deformed shape, even for large strains. The model might be used as a building block to construct more comprehensive tissue deformation models.

Homogenization and two‐scale simulations of granular materials for different microstructural constraints

AbstractThe paper presents a new method for quasi‐static homogenization of granular microstructures and its embedding into two‐scale simulations. On the coarse scale, a homogenized standard continuum is considered where the granular microstructures are locally attached at each point. These representative volumes are defined by aggregates of discrete solid particles, which may come into contact. On the micromechanical side, the interparticle contact mechanisms between particles is governed by a Coulomb‐type frictional contact. In particular, elliptical‐shaped plane particles are investigated. A consistent extension of classical stiff, soft and periodic boundary conditions from continuous to granular microstructures induce new classes of micro‐to‐macro transitions for granular aggregates. These include constraints not only for particle center displacements but also for particle rotations at a driving boundary frame. The stiff and soft constraints at the driving frame of the particle aggregate induce upper and lower bounds of the particle aggregate's stiffness. On the computational side, we outline a unified implementation of the displacement and rotational constraints by penalty methods that proves to be convenient for straightforward integration into discrete element codes. Representative numerical examples with elliptical‐shaped particles are investigated, where the macroscopic stress responses for different boundary constraints are comparatively discussed. Finally, we embed the granular microstructures into a coarse graining discrete‐to‐finite element model, where they govern the micromechanical behavior of a two‐scale simulation. Copyright © 2010 John Wiley & Sons, Ltd.

Nonlinear TM modes in cylindrical liquid crystal waveguide

We consider a nonlinear cylindrical fiber with a nematic liquid crystal (LC) core having initially the escaped configuration and subject to the action of a normal mode propagating electromagnetic field of arbitrary intensity. We derive a set of coupled equations governing the nonlinear dynamics of the electromagnetic field and the confined LC. We solve numerically these coupled equations and find simultaneously the distorted textures of the nematic inside the cylinder and the Transverse Magnetic modes in the guide. We analyze the dependence of these solutions on the electromagnetic field intensity by assuming consistently soft boundary conditions. We have found a dramatic correlation in the spatial distribution of the nematic's configuration and the Transverse Magnetic modes. Thus, the director adopts configurations completely guided by the specific mode involved. We show that the cut-off frequencies and dispersion relations can be tuned by varying the intensity of the electromagnetic propagating field.

Scattered fields of conducting half-plane between two dielectric media

We investigate the scattering process of plane waves by a conducting half-plane between two dielectric media by introducing novel boundary conditions, in terms of soft and hard surfaces. The cases of soft and hard half-planes are studied independently. The scattered waves are examined numerically. The numerical results show that the behavior of the fields is in harmony with the theory. The transition between the two dielectric media is continuous, and the structure of the method enables one also to examine more complex geometries, such as wedges having soft and hard boundary conditions.

Formulation of boundary conditions for vorticity in viscous incompressible flow problems

For the stream function-vorticity formulation of the Navier-Stokes equations, vorticity boundary conditions are required on the body surface and the far-field boundary. A two-parameter approximating formula is derived that relates the velocity and vorticity on the outer boundary of the computational domain. The formula is used to construct an algorithm for correcting the conventional far-field boundary conditions. Specifically, a soft boundary condition is set for the vorticity and a uniform flux is specified for the transversal velocity. A third-order accurate three-parameter formula for the vorticity on the wall is derived. The use of the formula does not degrade the convergence of the iterative process of finding the vorticity as compared with a previously derived and tested two-parameter formula.

Structural transitions of nematics upon interaction of coherent acoustic waves

The features of the structural transition of homeotropically oriented nematic liquid crystal (NLC) upon the interaction of coherent longitudinal and shear waves in a cell with acoustically soft boundary conditions at the ends for the frequency range, where the viscous wavelength is smaller and the elastic wavelength in NLC is larger than the mesophase layer thickness, have been experimentally investigated. The data obtained are analyzed within a model developed for this problem geometry based on a hypothesis postulating the flow mechanism of the orientational effect of ultrasound on NLC.

On the effect that acoustic boundary conditions have on the structural transitions in nematics in the field of ultrasonic compressional waves

The peculiarities of the structural transition in a homeotropic layer of nematic liquid crystal (NLC) affected by compressional waves in a cell with acoustically soft or hard boundary conditions at its ends have been studied for the frequency range where the wavelength of viscous wave is smaller than the layer thickness, while the wavelength of the elastic wave in NLC exceeds the layer thickness. The data obtained are analyzed within the known theoretical models developed for these two geometries based on the unified hypothesis, which postulates the flow mechanism of the orientational effect of ultrasound on NLC.