Home About us Contact
|
Home About us Contact | ||
|
|
||
One-dimensional Case (one-dimensional + case)
Selected AbstractsMathematical modeling of boundary conditions for laser-molecule time-dependent Schrödinger equations and some aspects of their numerical computation,One-dimensional caseNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Emmanuel Lorin Abstract This article deals with boundary conditions for time-dependent Schrödinger equations for molecules excited by intense and ultrashort electric fields. On the basis of Volkov wavefunctions, we propose an original boundary condition design that allows to reduce spurious reflections at the domain boundary and allows to take at least partially, plasma effects into account. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Modelling of cement suspension flow in granular porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2005Z. Saada Abstract A theoretical model of cement suspensions flow in granular porous media considering particle filtration is presented in this paper. Two phenomenological laws have been retained for the filtration rate and the intrinsic permeability evolution. A linear evolution with respect to the volume fraction of cement in the grout has been retained for the filtration rate. The intrinsic permeability of the porous medium is looked for in the form of a hyperbolic function of the porosity change. The model depends on two phenomenological parameters only. The equations of this model are solved analytically in the one-dimensional case. Besides, a numerical resolution based on the finite element method is also presented. It could be implemented easily in situations where no analytical solution is available. Finally, the predictions of the model are compared to the results of a grout injection test on a long column of sand. Copyright © 2005 John Wiley & Sons, Ltd. [source] A visco-plastic constitutive model for granular soils modified according to non-local and gradient approachesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002C. di Prisco Abstract An already available non-associated elastic,viscoplastic constitutive model with anisotropic strain hardening is modified in order to describe both the constitutive parameter dependency on relative density and the spatio-temporal evolution of strain localization. To achieve this latter goal, two distinct but similar approaches are introduced: one inspired by the gradient theory and one by the non-local theory. A one-dimensional case concerning a simple shear test for a non-homogeneous infinitely long dense sand specimen is numerically discussed and a finite difference scheme is employed for this purpose. The results obtained by following the two different approaches are critically analysed and compared. Copyright © 2001 John Wiley & Sons, Ltd. [source] Non-local dispersive model for wave propagation in heterogeneous media: one-dimensional caseINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Jacob Fish Abstract Non-local dispersive model for wave propagation in heterogeneous media is derived from the higher-order mathematical homogenization theory with multiple spatial and temporal scales. In addition to the usual space,time co-ordinates, a fast spatial scale and a slow temporal scale are introduced to account for rapid spatial fluctuations of material properties as well as to capture the long-term behaviour of the homogenized solution. By combining various order homogenized equations of motion the slow time dependence is eliminated giving rise to the fourth-order differential equation, also known as a ,bad' Boussinesq problem. Regularization procedures are then introduced to construct the so-called ,good' Boussinesq problem, where the need for C1 continuity is eliminated. Numerical examples are presented to validate the present formulation. Copyright © 2002 John Wiley & Sons, Ltd. [source] Two-dimensional psychophysics in chickens and humans: Comparative aspects of perceptual relativityJAPANESE PSYCHOLOGICAL RESEARCH, Issue 4 2008PETRA HAUF Abstract:, Whereas the contextual basis of psychophysical responding is well founded, the compound influence of sensory and perceptual frames of reference constitutes a challenging issue in comparative one- and multidimensional psychophysics (e.g., Sarris, 2004, 2006). We refer to previous investigations, which tested the assumption that the chicken's relational choice in the one-dimensional case is systematically altered by context conditions similar to the findings stemming from human participants. In this paper mainly the context-dependent stimulus coding was investigated for the important, but largely neglected, two-dimensional case in humans and chickens. Three strategies were predicted for the generalization of size discriminations, which had been learned in a different color context. In two experiments, which varied in the testing procedure, both species demonstrated profound contextual effects in psychophysics; they differed, however, in the way the information from either dimension was used: Chickens throughout used color as a cue to separate the respective size discriminations and generalizations. Whereas humans predominantly generalized according to size information only or according to absolute stimulus properties, the chickens showed some important species-specific differences. Common and heterogeneous findings of this line of comparative research in multidimensional psychophysics are presented and discussed in various ways. [source] On a generalized Appell system and monogenic power seriesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2010S. Bock Abstract Recently Appell systems of monogenic polynomials in ,3 were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion-valued functions. A new Taylor-type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one-dimensional case. These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space. Copyright © 2009 John Wiley & Sons, Ltd. [source] An approximation result for free discontinuity functionals by means of non-local energiesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2008Luca Lussardi Abstract We approximate, in the sense of ,-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722,744), where there is the proof of the general one-dimensional case, and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135,162), where the n -dimensional case with ,=Id is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies. Copyright © 2008 John Wiley & Sons, Ltd. [source] Two-dimensional failure modeling with minimal repairNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2004J. Baik In this paper, we discuss two-dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one-dimensional case to the two-dimensional case and characterize the failures over a two-dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two-dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004. [source] Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winnerCOMPLEXITY, Issue 4 2003Jens Christian Claussen Abstract The magnification behavior of a generalized family of self-organizing feature maps, the winner relaxing and winner enhancing Kohonen algorithms is analyzed by the magnification law in the one-dimensional case, which can be obtained analytically. The winner-enhancing case allows to achieve a magnification exponent of one and therefore provides optimal mapping in the sense of information theory. A numerical verification of the magnification law is included, and the ordering behavior is analyzed. Compared to the original self-organizing map and some other approaches, the generalized winner enforcing algorithm requires minimal extra computations per learning step and is conveniently easy to implement. © 2003 Wiley Periodicals, Inc. [source] | |||||||||||||