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Potential Theory (potential + theory)
Selected AbstractsComplex-distance potential theory, wave equations, and physical waveletsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002Gerald Kaiser Potential theory in ,n is extended to ,n by analytically continuing the Euclidean distance function. The extended Newtonian potential ,(z) is generated by a (non-holomorphic) source distribution ,,(z) extending the usual point source ,(x). With Minkowski space ,n, 1 embedded in ,n+1, the Laplacian ,n+1 restricts to the wave operator ,n,1 in ,n, 1. We show that ,,(z) acts as a propagator generating solutions of the wave equation from their initial values, where the Cauchy data need not be assumed analytic. This generalizes an old result by Garabedian, who established a connection between solutions of the boundary-value problem for ,n+1 and the initial-value problem for ,n,1 provided the boundary data extends holomorphically to the initial data. We relate these results to the physical avelets introduced previously. In the context of Clifford analysis, our methods can be used to extend the Borel,Pompeiu formula from ,n+1 to ,n+1, where its riction to Minkowski space ,n, 1 provides solutions for time-dependent Maxwell and Dirac equations. Copyright © 2002 John Wiley & Sons, Ltd. [source] A Screening Model for Injection-Extraction Treatment Well Recirculation System DesignGROUND WATER MONITORING & REMEDIATION, Issue 4 2008Monica Y. Wu Implementation of injection-extraction treatment well pairs for in situ, in-well, or on-site remediation may be facilitated by development and application of modeling tools to aid in hydraulic design and remediation technology selection. In this study, complex potential theory was employed to derive a simple one-step design equation and related type curves that permit the calculation of the extraction well capture zone and the hydraulic recirculation between an injection and extraction well pair oriented perpendicular to regional flow. This equation may be used to aid in the design of traditional fully screened injection-extraction wells as well as innovative tandem recirculating wells when an adequate geologic barrier to vertical ground water flow exists. Simplified models describing in situ bioremediation, in-well vapor stripping, and in-well metal reactor treatment efficiency were adapted from the literature and coupled with the hydraulic design equation presented here. Equations and type curves that combine the remediation treatment efficiency with the hydraulic design equation are presented to simulate overall system treatment efficiency under various conditions. The combined model is applied to predict performance of in situ bioremediation and in-well palladium reactor designs that were previously described in the literature. This model is expected to aid practitioners in treatment system screening and evaluation. [source] A viscoelastic model for the dynamic response of soils to periodical surface water disturbanceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006P. C. Hsieh Abstract In many instances soils can be assumed to behave like viscoelastic materials during loading/unloading cycles, and this study is aimed at setting up a viscoelastic model to investigate the dynamic response of a porous soil layer of finite thickness under the effect of periodically linear water waves. The waves and homogeneous water are described by potential theory and the porous material is described by a viscoelastic model, which is modified from Biot's poroelastic theory (1956). The distributions of pore water pressures and effective stresses of various soils such as silt, sand, and gravel are demonstrated by employing the proposed viscoelastic model. The discrepancies of the dynamic response between the simulations of viscoelastic model and elastic model are found to be strongly dependent on the wave frequency. Copyright © 2006 John Wiley & Sons, Ltd. [source] Dynamic response of a soft soil layer to flow and periodical disturbanceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2003Ping-Cheng Hsieh Abstract The dynamic response of a soft soil layer of finite thickness under the mutual effects of flow and periodical disturbance at the free surface is discussed in this work. The homogeneous water is governed by potential theory and the soil layer obeys Biot's theory of poroelasticity. The boundary-value problem is solved by an analytical algorithm, in which the wave number is found first. Secondly, the closed form solutions are found by a two-parameter perturbation method with the boundary-layer correction. The results are also compared with those of the poroelastic soil layer of infinite thickness to show the impermeable rigid boundary effect. Copyright © 2003 John Wiley & Sons, Ltd. [source] A mixed finite element solver for liquid,liquid impactsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004Enrico Bertolazzi Abstract The impact of a liquid column on a liquid surface initially at rest is numerically modelled to describe air entrapment and bubble formation processes. The global quantities of interest are evaluated in the framework of the potential theory. The numerical method couples a potential flow solver based on a Mixed Finite Element Method with an Ordinary Differential Equation solver discretized by the Crank,Nicholson scheme. The capability of the method in solving liquid,liquid impacts is illustrated in two numerical experiments taken from literature and a good agreement with the literature data is obtained. Copyright © 2004 John Wiley & Sons, Ltd. [source] Explicit expressions for 3D boundary integrals in potential theory,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2009S. Nintcheu Fata Abstract On employing isoparametric, piecewise linear shape functions over a flat triangular domain, exact expressions are derived for all surface potentials involved in the numerical solution of three-dimensional singular and hyper-singular boundary integral equations of potential theory. These formulae, which are valid for an arbitrary source point in space, are represented as analytic expressions over the edges of the integration triangle. They can be used to solve integral equations defined on polygonal boundaries via the collocation method or may be utilized as analytic expressions for the inner integrals in the Galerkin technique. In addition, the constant element approximation can be directly obtained with no extra effort. Sample problems solved by the collocation boundary element method for the Laplace equation are included to validate the proposed formulae. Published in 2008 by John Wiley & Sons, Ltd. [source] A new approach to describe high-pressure adsorption isotherms in subcritical and supercritical conditionsAICHE JOURNAL, Issue 7 2009Ch. Chilev Abstract In this article, we present a new approach to describe adsorption equilibrium of pure gases in a wide range of pressure. This approach is based on a simple statistical mechanics treatment combining the potential theory and lattice fluid models. The obtained equation for the calculation of the excess adsorption can predict the curve progression of isotherms defined by the IUPAC I classification, and for those at supercritical conditions. Notwithstanding that the basic idea of the developed equation is to adapt to the adsorption equilibrium in supercritical conditions at high pressure, the model correlates very well experimental data at low pressure in subcritical conditions. It is applicable to a wide range of pressures and fits satisfactorily the experimental data in a broad range of pressures and temperatures. In particular, the model predicts the maximum of excess adsorption and its minimum. A comparison between this approach and two others is given. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] On the spectra of some integral operators related to the potential theory in the planeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2010Oleg F. Gerus Abstract We study point spectra of the two integral operators that are generated by the boundary values of the simple-layer potential and of the integral tightly related to the double-layer potential; the operators act on the Hölder space Hµ(,), µ,(0,1), and on the Lebesgue space Lp(,), p>2, where , is a closed Lyapunov curve. Copyright © 2010 John Wiley & Sons, Ltd. [source] Complex-distance potential theory, wave equations, and physical waveletsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16-18 2002Gerald Kaiser Potential theory in ,n is extended to ,n by analytically continuing the Euclidean distance function. The extended Newtonian potential ,(z) is generated by a (non-holomorphic) source distribution ,,(z) extending the usual point source ,(x). With Minkowski space ,n, 1 embedded in ,n+1, the Laplacian ,n+1 restricts to the wave operator ,n,1 in ,n, 1. We show that ,,(z) acts as a propagator generating solutions of the wave equation from their initial values, where the Cauchy data need not be assumed analytic. This generalizes an old result by Garabedian, who established a connection between solutions of the boundary-value problem for ,n+1 and the initial-value problem for ,n,1 provided the boundary data extends holomorphically to the initial data. We relate these results to the physical avelets introduced previously. In the context of Clifford analysis, our methods can be used to extend the Borel,Pompeiu formula from ,n+1 to ,n+1, where its riction to Minkowski space ,n, 1 provides solutions for time-dependent Maxwell and Dirac equations. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||