Doubly Asymptotic Approximations for Submerged Structures With Internal Fluid Volumes: Formulation

1994 ◽  
Vol 61 (4) ◽  
pp. 893-899 ◽  
Author(s):  
T. L. Geers ◽  
Peizhen Zhang
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Complex Geometry ◽  
Spherical Geometry ◽  
Companion Paper ◽  
Boundary Integral ◽  
Asymptotic Approximations ◽  
Flexible Body ◽  
Structural Acoustics ◽  
Internal Fluid

Doubly asymptotic approximations (DAAs) are approximate temporal impedance relations for a medium in contact with a flexible body. In this paper, the method of operator matching previously used for external acoustic domains is used to develop first- and second-order boundary integral DAAs for internal acoustic domains. Corresponding boundary element forms permit the numerical solution of transient structural acoustics problems with complex geometry. The accuracy of the DAAs is assessed in the following companion paper by comparing DAA and exact solutions for a canonical problem with spherical geometry.

Doubly Asymptotic Approximations for Submerged Structures With Internal Fluid Volumes: Evaluation

1994 ◽  
Vol 61 (4) ◽  
pp. 900-906 ◽  
Author(s):  
T. G. Geers ◽  
Peizhen Zhang
Keyword(s):  
Spherical Shell ◽  
Transient Response ◽  
Companion Paper ◽  
Second Order ◽  
Numerical Results ◽  
Asymptotic Approximations ◽  
Incident Plane ◽  
Internal Fluid ◽  
Plane Step

The accuracy of the doubly asymptotic approximations formulated in the previous companion paper is examined through the comparison of DAA and exact transient response histories for a fluid-filled, submerged spherical shell excited by an incident plane step-wave. The numerical results indicate that second-order DAAs are satisfactory for problems of this type.

FEW-PARTICLE ANYON EXCITON: EXACT SOLUTIONS

2003 ◽  
Vol 02 (06) ◽  
pp. 461-468
Author(s):  
D. G. W. PARFITT ◽  
M. E. PORTNOI
Keyword(s):  
Exact Solutions ◽  
Finite Size ◽  
Spherical Geometry ◽  
Planar Geometry ◽  
Quantum Liquid ◽  
Dimensional Electron ◽  
Adequate Description ◽  
Exciton Model ◽  
Finite Size Effects ◽  
Dimensional Electron Gas

The anyon exciton model, which describes an exciton against the background of an incompressible quantum liquid, is generalized to the case of an arbitrary number of anyons. Some mathematical aspects of this quantum-mechanical few-particle problem are considered and several exact solutions are obtained. The four-particle case is also considered in the classical limit in both planar and spherical geometries. Such a classical approach gives an adequate description of an anyon exciton at large separation between the valence hole and the two-dimensional electron gas. It is shown that in this limit in a planar geometry the anyon exciton is always energetically more favorable than a charged anyon ion. This indicates that the appearance of fractionally-charged anyon ions reported in recent numerical calculations is an artefact apparently caused by finite-size effects in a spherical geometry.

Viscous Flows Involving a Liquid-Vapor Compound Droplet

2001 ◽  
Author(s):  
D. Palaniappan
Keyword(s):  
Exact Solutions ◽  
Viscosity Ratio ◽  
Numerical Algorithms ◽  
Flow Fields ◽  
Continuous Phase ◽  
Boundary Integral ◽  
Liquid Volume ◽  
Drag Forces ◽  
Compound Droplet ◽  
Fluid Interactions

Abstract Exact analytical solutions for steady-state axisymmetric creeping flows in and around a compound multiphase droplet are presented. The solutions given here explain the droplet fluid interactions in uniform and nonuniform flow fields. The compound droplet has a two-sphere geometry with the two spherical surfaces (of unequal radii) intersecting orthogonally. The surface tension forces are assumed to be sufficiently large so that the interfaces have uniform curvature. The singularity solutions for the uniform and paraboloidal flows in the presence of a compound droplet are derived using the method of reflections. The exact solutions for the velocity and pressure fields in the continuous and dispersed phases are given in terms of the fundamental singularities (Green’s functions) and their derivatives. It is found that flow fields and the drag forces depend on two parameters namely, the viscosity ratio and the radii ratio. In the case of paraboloidal flows, a single or a pair of eddies is noticed in the continuous phase for various values of these parameters. The eddies changes their size and shape if the size of the droplet is altered. These observations may be useful in the study of hydrodynamic interactions of compound droplets in complex situations. It is found that the Stokes resistance is greater when the liquid volume is large compared to the vapor volume in uniform flow. It is also noticed that the maximum value of the drag in paraboloidal flow depends on the viscosity ratio and significantly on the liquid volume in the dispersed phase. The exact solutions presented here may be useful for boundary integral formulations that are based on special kernels and also in validating numerical algorithms and codes on multiphase flow and droplet-fluid interactions.

scholarly journals Preconditioners for hierarchical matrices based on their extended sparse form

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Darya A. Sushnikova ◽  
Ivan V. Oseledets
Keyword(s):  
Numerical Solution ◽  
Linear Systems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Hierarchical Matrices ◽  
Dense Matrices

AbstractIn this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with ℋ

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