Infinite Boundary Conditions Research Articles

Solution for wave propagation through a circular cylinder mounted on different topography ripple-bed profile shoals using DRBEM

In this paper, the dual reciprocity boundary element method wave model that is governed by a modified mild-slope equation is developed. Instead of addressing the infinite boundary condition, the model automatically satisfies the Sommerfeld radiation condition. This work examines the effects of both the bottom curvature and the slope-squared terms. The conducted numerical experiments have a topography that is composed of a cylinder mounted on two kinds of basic shoal: types 1 and 2 cubic. In addition, numerical experiments that combine two cubic type islands with ripple-beds are performed. The results show that the curvature term dominates the calculation of the sinusoidal-varying topography; even a disturbance in the topography is insignificant. In contrast to smooth topographies, the bottom curvature and the slope-squared terms are not dominant. Thus, the extended terms can be neglected if the seabed is smooth and gentle. When the topographies are combined with ripple-beds, the difference in the dimensionless wave amplitudes along the sidewall of the types 1 and 2 cubic islands is found to be 2.9 and 3.02, respectively. According to our study of cubic islands that are combined with ripple-beds, we can conclude with certainty that even though the variation of the seabed is very slight, the curvature and the slope-squared terms cannot be neglected for an uneven bottom.

Dynamical Behavior of Two-Soliton Solution Exhibited by Perturbed Sine-Gordon Equation

We use perturbation methods based on inverse scattering transform to study the dynamical behavior of the kink-antikink solitons exhibited by a driven-damped sine-Gordon equation with infinite boundary condition. It is shown that such solitons may be forced by damping and external forces to remain in a finite region instead of approaching infinity.

Dependence of Optical Matrix Elements on the Boundary Conditions of the Continuum States in Quantum Wells

Unlike for the bound states, several different boundary conditions are used for the continuum states above the barrier in semiconductor quantum wells. We employed three boundary conditions, infinite potential barrier boundary condition, periodic boundary condition and scattering boundary condition, and calculated the local number of states, wavefunctions and optical matrix elements for the symmetric and asymmetric quantum wells. We discussed how these quantities are related in the three boundary conditions. We argue that the scattering boundary condition has several advantages over the other two cases. These results would be useful in understanding quantum well lasers and detectors involving continuum states.

Description of Specifications by Means of Probability Distributions in Small Volumes Under Condition of Very Weak Positivity

The problem of description of s by means of probability distributions in small volumes with infinite boundary conditions is considered. The description of s by means of s (consistent systems of probability distributions in volumes of cardinality bounded by n with infinite boundary conditions) is established under the condition of very weak positivity. Particular attention is paid to the most important case n = 1 which requires special considerations.

TESTING BOUNDARY CONDITIONS EFFICIENCY IN SIMULATIONS OF LONG-RANGE INTERACTING MAGNETIC MODELS

Periodic boundary conditions have no unique implementation in magnetic systems where all spins interact with each other through a power law decaying interaction of the form 1/rα, r being the distance between spins. In this work we present a comparative study of the finite size effects oberved in numerical simulations by using first image and infinite image periodic boundary conditions in one- and two-dimensional spin systems with those interactions, including the ferromagnetic, anti-ferromagnetic and competitive interaction cases. Our results show no significative differences between the finite size effects produced by both boundary conditions when the low temperature phase has zero global magnetization, and it depends on the ratio α/d for systems with a low temperature ferromagnetic phase. In the last case the first image convention gives more stronger finite size effects than the other when the system enters into the classical regime α/d≤3/2.

An Evaluation of Geometric Factors Used in the Two-Stage Borehole Test (ASTM D6391-99) Using the Finite Element Method

Abstract Geometric or shape factors are constants used in the interpretation of in-situ hydraulic conductivity tests, such as the Two-Stage Borehole (TSB) test in ASTM D6391-99. The finite boundary condition shape factors used with the TSB test are an extension of those derived by Hvorslev (1951) for infinite boundary conditions. The accuracy of this extrapolation is investigated here, using the finite element method (FEM) as a tool for deriving shape factors for finite boundary conditions. The utilized FEM has been validated against closed-form solutions for other test geometries. The resulting errors from the incorrect use of shape factors with the TSB test are discussed, and new shape factors derived from the FEM are presented in the form of a chart.

A Finite Difference Domain Decomposition Method Using Local Corrections for the Solution of Poisson's Equation

We present a domain decomposition method for computing finite difference solutions to the Poisson equation with infinite domain boundary conditions. Our method is a finite difference analogue of Anderson's Method of Local Corrections. The solution is computed in three steps. First, fine-grid solutions are computed in parallel using infinite domain boundary conditions on each subdomain. Second, information is transferred globally through a coarse-grid representation of the charge, and a global coarse-grid solution is found. Third, a fine-grid solution is computed on each subdomain using boundary conditions set with the global coarse solution, corrected locally with fine-grid information from nearby subdomains. There are three important features of our algorithm. First, our method requires only a single iteration between the local fine-grid solutions and the global coarse representation. Second, the error introduced by the domain decomposition is small relative to the solution error obtained in a single-grid calculation. Third, the computed solution is second-order accurate and only weakly dependent on the coarse-grid spacing and the number of subdomains. As a result of these features, we are able to compute accurate solutions in parallel with a much smaller ratio of communication to computation than more traditional domain decomposition methods. We present results to verify the overall accuracy, confirm the small communication costs, and demonstrate the parallel scalability of the method.

Use of tile overlays to reduce the radiation efficiency of radiating surfaces

An intriguing possibility for reducing the radiation efficiency of a structure is to overlay its radiating surfaces with a contiguous set of low mass tiles. Experimental results show that significant reductions in sound power are possible depending on number of tiles, their geometry, attachment methods, mass, stiffness, and the amount of shear damping used to connect their edges to one another. This paper presents results of a combined theoretical and experimental study performed on a clamped, flat plate driven at its center and with nearly infinite baffle boundary conditions. Tiles are overlayed on the surface of the plate and lightly attached with a polymer material. A scanning laser vibrometer is used to examine the vibration patterns of the plate and the corresponding tiles for several different tile configurations over a frequency range 20–1000 Hz. Results indicate that sound power reductions occur when the independent response of each tile combines to produce an overall volume velocity that is lower than that of the plate by itself over the frequency range of interest.

Long Distance Photoinduced Electron Transfer in Solutions: A Mechanism for Producing Large Yields of Free Ions by Electron Transfer Quenching

Free ion and fluorescence quantum yields from the geminate ion pairs formed by electron-transfer quenching of the excited acceptor 9,10-dicyanoanthracene by aromatic electron-donors are measured in different solvents. Theeffects of solvent polarity, energetic driving force, and steric substitution on free ion yields are studied. From the comparison of the effect of driving force on free ion yields and fluorescence quantum yields in different solvents, especially those of moderate polarity, it is concluded that free ion yields are controlled by both recombination rate constants and the separation distance distribution of the initially formed geminate radical ion pairs. In dichloromethane (DCM), the recombination and free ion formation processes are directly observed by fluorescence lifetime and transient photocurrent measurements. The time-resolved results indicate that free ion formation is faster than the recombination process. This means that the geminate radical ion pairs that form free ions and those that are neutralized by electron-transfer recombination have different histories with different separation distances. From studies of steric effects on free ion yields in different solvents, it is concluded that, in polar solvents such as acetonitrile and butyronitrile, the main effect of steric hindrance is to decrease the recombination rate constant and increase the escape probability, whereas in moderately polar solvents such as tetrahydrofuran, DCM and 1,2-dichlorobenzene, the main effect of steric bulk is to change the initial separation distance distribution of the geminate radical ion pairs formed by electron-transfer quenching. As an example, we compare donors such as durene (DUR) with those of greater steric bulk like 1,2,4,5-tetra-iso-propylbenzene (TIPB), for which the driving force for electron transfer is similar. The free radical ion yield for TIPB is more than 40 times greater than it is for DUR in DCM. This is the first example from our work in which the infinite rate boundary condition for ion recombination used by Onsager is not adequate, because there is no perfect sink at the origin. The free ion yield data are analyzed by the theory of Hong and Noolandi under the Collins and Kimball boundary condition.

AN ANALYTICAL AND EXPERIMENTAL INVESTIGATION ON ACTIVE CONTROL OF THE FLEXURAL WAVE TRANSMISSION IN A SIMPLY SUPPORTED RIBBED PLATE

The feedforward active control of the plate flexural wave transmission along a semi-infinite simply supported ribbed plate has been analytically and experimentally investigated. The ribbed plate was modelled as a continuous system using equations of motion to describe the plate in flexure and the beam in both flexure and torsion. Due to the simply supported and infinite boundary conditions, the structural response is described by a combination of a modal and a travelling wave solution. The primary and secondary sources are modelled as single point forces, with the primary force located on the plate and the secondary control force applied to the reinforcing beam. This force configuration is to demonstrate the feasibility of attenuating the plate response by actively modifying the beam response. Results show that using a single, properly located control actuator and a single error sensor, global attenuation of the transmitted plate vibration through the reinforcing beam is achieved.

Boundary condition applicable to free-standing quantum films

An alternative to the usual infinite boundary condition is obtained for free-standing quantum films in the framework of effective-mass approximation. This alternative is applied to silicon quantum film to arrive at the confinement conditions in terms of envelope functions. The confinement conditions contain surface effects as well. The present boundary condition yields the energy gap of the film that is comparable to that by ab initio calculation. The approach is also applicable to quantum films embedded by high-energy barriers.

Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures

In this paper, a closed-form solution is presented for the stress and displacement distributions throughout a hollow cylinder subjected to uniform pressures acting on its internal and external boundary surfaces under plane strain conditions. The material is assumed to be elastoplastic, obeying a Mohr–Coulomb failure criterion, and exhibiting dilatant plastic deformation according to a non-associated flow rule. The newly developed analytical solution is verified through comparison with the solutions obtained from an infinite boundary problem (for which a closed-form solution exists), and numerical analyses using the program FLAC. The solution is also compared with the results of a borehole collapse test on a thick-walled hollow cylinder of synthetic shale. The analytical solution can be used to calculate the stress and displacement distributions around boreholes and other cylindrical cavities under both infinite and finite boundary conditions under both drained and undrained conditions. Copyright © 1999 John Wiley & Sons, Ltd.

Pointwise Growth and Uniqueness of Positive Solutions for a Class of Sublinear Elliptic Problems where Bifurcation from Infinity Occurs

In this paper we analyze the uniqueness and the pointwise growth of the positive solutions of a nonlinear elliptic boundary-value problem of general sublinear type with a weight function multiplying the nonlinearity. When this function vanishes on some subdomain, the problem exhibits a bifurcation from infinity. In this case almost nothing is known about the pointwise growth of the positive solutions as the parameter approaches the critical value where the bifurcation from infinity occurs. In this work we show that the positive solutions grow to infinity in the region where the weight function vanishes and that on its support they stabilize to the minimal positive solution of the original equation subject to infinite Dirichlet boundary conditions. This behavior provides us with the uniqueness of the positive solution near the value of the parameter where the bifurcation from infinity occurs. Also, we solve the problem using spectral collocation methods coupled with path-following techniques to show how the main uniqueness result is optimal. Throughout the paper the mathematical analysis aids the numerical study, and the numerical study confirms and illuminates the analysis.

Microwave heating of an infinite solid slab and its thermal stability analysis using steady state bifurcation theory

This paper presents an analytical solution of the steady state temperature profiles in a microwave heated slab. The analytical solution has been obtained by taking advantages of the well known Frank-Kamenetskii thermal ignition theory. Both the finite Biot number and infinite Biot number boundary conditions have been considered and their effects upon the critical parameters for the onset of thermal instability evaluated.

Expression of optical diffusion coefficient in high-absorption turbid media

The optical diffusion coefficient in a homogeneous turbid medium with high absorption was determined by steady-state measurements of the light transmission under the infinite-boundary condition. The intensity of the transmission was well described by the solution of the optical diffusion equation. Moreover, the optical diffusion coefficient D was given by a constant, , where is the reduced scattering coefficient, up to the absorption coefficient of about . These results mean that attenuation by absorption only contributes to exponential attenuation along the optical path defined by the scattering coefficient and geometry of the system even in high-absorption turbid media such as the pathological living tissues of bleeding or haematoma.

Thermodynamics of strongly-coupled Yukawa systems near the one-component-plasma limit. II. Molecular dynamics simulations

Molecular dynamics simulations are employed to study the equilibrium thermodynamics of strongly-coupled systems of particles interacting through the Yukawa potential. Such systems serve, under the Debye–Hückel approximation, as a model for the physical behavior of plasma or colloidal suspensions of charged particulates. The thermodynamics may be characterized in terms of two dimensionless parameters—the ratio κ of the mean interparticle distance to the Debye length, and an approximate measure Γ of the interparticle potential energy in units of the thermal kinetic energy. Employing an accurate representation of infinite periodic boundary conditions, we focus on the regime of weak Debye screening (κ ≲ 1) and strong coupling (Γ≫1). Excess internal energies measured at many points (κ,Γ) are fitted to simple functional forms for the fluid and solid phases, representing extrapolations of the classical one-component plasma (OCP) limit, κ=0. Quantitative expressions for the Helmholtz free energy and the ‘‘equation of state’’ of the Yukawa system— giving the pressure p in terms of κ and Γ—are thus derived, and the freezing/melting curve in the (κ,Γ) plane is traced as the intersection of the fluid and solid free-energy surfaces.

Mathematical modeling of drug release from hydrogel matrices via a diffusion coupled with desorption mechanism

Model calculations have been performed to account for the kinetics of drug release from polymeric matrices where both diffusion and desorption mechanisms control the overall release rate. The model incorporates both a desorption term, based on Langmuir kinetics, and a transient Fickian diffusion term and is solved for infinite sink boundary conditions. Solutions by both finite difference and finite element techniques indicate the effects of binding interaction strength, binding capacity, amount of drug loaded and rate of desorption on the release kinetics of drugs adsorbed to polymer matrices. Simulation results indicate that it is possible to modulate the net release rates of drugs over a wide range by altering the binding parameters enumerated above as well as drug diffusivities in the matrix.

A simplified finite element model for ultrasonic cleaning

Simplified models for ultrasonic cleaning are presented which require significantly less computational effort than the transient finite element analysis previously employed for this fluid—structure interaction problem. The analysis is simplified three ways: (1) by solving for the steady state frequency solution; (2) by assuming that the solid is rigid to scattered waves; and (3) by using an infinite boundary condition approximation in the finite element solution. When the wave is incident from the solid, estimating the force on contaminant particles using these techniques requires only one-thousandth the computational effort of a full transient analysis. When the wave is incident from the fluid, treating the solid as completely rigid gives essentially the same results at 0·1 and 1 GHz as treating the solid as rigid to scattered waves only. However, this analysis indicates that the force on the contaminant particle produced by a wave originating in the solid is less than one-seventh the force produced by a wave originating in the fluid.

Effects of the nonlinear gradient term on the transient pressure solution for a radial flow system

This study presents new analytical pressure solutions for high pressure-gradient flow of a single-phase, slightly compressible fluid under transient conditions. A nonlinear partial differential equation is generally used to describe the pressure behavior during such flows through porous media. The nonlinearity of this equation arises from the presence of the quadratic pressure-gradient term in the diffusion equation. In order to obtain a standard linear diffusion equation so that closed-form analytical solutions can be developed, the original nonlinear equation has traditionally been linearized by assuming the pressure gradient to be small throughout the reservoir at all times. However, during certain operations such as hydraulic-fracturing, high-drawdown flows, slug testing, large-pressure pulse testing, etc., the assumpution of a small pressure gradient may not be justified and the nonlinear pressure-gradient term must be taken into account. Moreover, in an age of increased sophistication of reservoir flow analysis and prediction methods and improved resolution of pressure-measurement devices, the effects of the quadratic pressure-gradient term on the transient pressure behavior must be understood quantitatively. In this paper, analytical dimensionless pressure solutions of the nonlinear diffusion equation are derived by using the Laplace transform. Constant-rate and constant-pressure inner boundary conditions and infinite, closed and constant-pressure outer boundary conditions have been considered. For the constant-rate inner boundary condition, solutions are presented for both injection and production problems by taking into account the presence of wellbore storage. Deviations from existing linear solutions are identified and are related to a dimensionless group, α, which is proportional to the fluid compressibility. It is shown that for constant-rate inner boundary condition, and infinite or constant-pressure outer boundary conditions, the linear pressure solutions are within 5% of the corresponding nonlinear solutions for magnitudes of α less than 0.01 (within the dimensionless time range considered). However, for a closed outer boundary, the wellbore pressure predicted by the linear solution may be significantly smaller than that predicted by the nonlinear solution at large times. Analytical steady- and pseudosteady-state solutions are also presented and compared with the corresponding linear solutions. It has been shown, with examples, that significant errors may be incurred by using the linear pressure solutions in some cases.

Dynamic fracture mechanics under electromagnetic force

This paper is concerned with two topics on dynamic fracture phenomena related to electromagnetic force. An edge-cracked specimen which carries a transient electric current I is simply supported in a steady magnetic field B. As a result of their interaction, the dynamic electromagnetic force occurs in the whole body of the specimen, which is then deformed to fracture in the opening mode of cracking. The first half of the paper describes three-dimensional finite element analyses of the transient electric current flowing around a crack. The magnetic vector potential method (i.e. A-Φ method) is employed to formulate the three-dimensional electromagnetic field problem. In order to deal with infinite boundary conditions in the FE analyses, an infinite element technique is utilized. The skin effects on the electric current distribution around the crack are discussed in detail. The second half describes high-strain-rate effects on fracture toughness under the dynamic electromagnetic force. To obtain the fracture toughness values, we use the electric potential and the J-R curve methods to determine the dynamic crack initiation point in the experiment, together with the finite element method to calculate the dynamic fracture parameter with high-strain-rate plasticity effects. Then, the dynamic fracture toughness values of a ferritic steel are evaluated over a wide temperature range from lower shelf to upper shelf.