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Differential System (differential + system)
Selected AbstractsDynamic non-planar crack rupture by a finite volume methodGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007M. Benjemaa SUMMARY Modelling dynamic rupture for complex geometrical fault structures is performed through a finite volume method. After transformations for building up the partial differential system following explicit conservative law, we design an unstructured bi-dimensional time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. On these complex surfaces, boundary conditions are set on stress fluxes and not on stress values. Prescribed rupture velocity gives accurate solutions with respect to analytical ones depending on the mesh refinement, while solutions for spontaneous propagation are analysed through numerical means. An example of non-planar spontaneous fault growth in heterogeneous media demonstrates the good behaviour of the proposed algorithm as well as specific difficulties of such numerical modelling. [source] The control-theory-based artificial boundary conditions for time-dependent wave guide problems in unbounded domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2005Tianyun Liu Abstract A method is proposed to obtain the high-performance artificial boundary conditions for solving the time-dependent wave guide problems in an unbounded domain. Using the variable separation method, it is possible to reduce the spatial variables of the wave equation by one. Furthermore, introducing auxiliary functions makes the reduced wave equation a linear first-order ordinary differential system with one control input. Solving the closed-loop control system, a stable and accurate artificial boundary condition is obtained in a rigorous mathematical manner. Numerical examples have demonstrated the effectiveness of the proposed artificial boundary conditions for the time-dependent wave guide problems in unbounded domain. Copyright © 2005 John Wiley & Sons, Ltd. [source] The least-squares meshfree method for elasto-plasticity and its application to metal forming analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005Kie-Chan Kwon Abstract A new meshfree method for the analysis of elasto-plastic deformation is presented. The method is based on the proposed first-order least-squares formulation for elasto-plasticity and the moving least-squares approximation. The least-squares formulation for classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformation are proposed. In the formulation, equilibrium equation and flow rule are enforced in least-squares sense, i.e. their squared residuals are minimized, and hardening law and loading/unloading condition are enforced pointwise at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. The proposed formulation is a mixed-type method since the residuals are represented in a form of first-order differential system using displacement and stress components as nodal unknowns. Also the penalty schemes for the enforcement of boundary and frictional contact conditions are devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near contact interface. The proposed method does not employ structure of extrinsic cells for any purpose. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Development of a class of multiple time-stepping schemes for convection,diffusion equations in two dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006R. K. Lin Abstract In this paper we present a class of semi-discretization finite difference schemes for solving the transient convection,diffusion equation in two dimensions. The distinct feature of these scheme developments is to transform the unsteady convection,diffusion (CD) equation to the inhomogeneous steady convection,diffusion-reaction (CDR) equation after using different time-stepping schemes for the time derivative term. For the sake of saving memory, the alternating direction implicit scheme of Peaceman and Rachford is employed so that all calculations can be carried out within the one-dimensional framework. For the sake of increasing accuracy, the exact solution for the one-dimensional CDR equation is employed in the development of each scheme. Therefore, the numerical error is attributed primarily to the temporal approximation for the one-dimensional problem. Development of the proposed time-stepping schemes is rooted in the Taylor series expansion. All higher-order time derivatives are replaced with spatial derivatives through use of the model differential equation under investigation. Spatial derivatives with orders higher than two are not taken into account for retaining the linear production term in the convection,diffusion-reaction differential system. The proposed schemes with second, third and fourth temporal accuracy orders have been theoretically explored by conducting Fourier and dispersion analyses and numerically validated by solving three test problems with analytic solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source] A general methodology for investigating flow instabilities in complex geometries: application to natural convection in enclosuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2001E. Gadoin Abstract This paper presents a general methodology for studying instabilities of natural convection flows enclosed in cavities of complex geometry. Different tools have been developed, consisting of time integration of the unsteady equations, steady state solving, and computation of the most unstable eigenmodes of the Jacobian and its adjoint. The methodology is validated in the classical differentially heated cavity, where the steady solution branch is followed for vary large values of the Rayleigh number and most unstable eigenmodes are computed at selected Rayleigh values. Its effectiveness for complex geometries is illustrated on a configuration consisting of a cavity with internal heated partitions. We finally propose to reduce the Navier,Stokes equations to a differential system by expanding the unsteady solution as the sum of the steady state solution and of a linear combination of the leading eigenmodes. The principle of the method is exposed and preliminary results are presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] Analysis of OTA-C filters with weakly nonlinear transconductorsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 7 2008Slawomir KozielArticle first published online: 11 OCT 200 Abstract An efficient approach for analysis of nonlinear distortion in OTA-C filters with weakly nonlinear transconductors is presented. The procedure is developed based on an algebraic description of a general OTA-C filter structure and, therefore, the results are valid for any filter architecture within OTA-C class. On the basis of the proposed method, explicit formulas for calculating a gain compression/expansion ratio in an arbitrary OTA-C filter are developed. The formulas are easy to implement and use in computer-aided filter design tools. For illustration purposes, several filter structures are considered. The accuracy of the method is verified by comparing the results with the exact values of gain compression/expansion ratio achieved by integrating the differential system that determines the time response of OTA-C filter. The presented approach can be generalized in order to consider other nonlinear parameters. Copyright © 2007 John Wiley & Sons, Ltd. [source] An analytical and experimental analysis of a very fast thermal transientINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 11 2001C. Aprea Abstract According to some international standards, some products, developed for use under heavy thermal conditions, have to be tested by subjecting them for a short time to a particular heating and cooling thermal stress to allow them an acceptable future operative life. It is possible to obtain these fast thermal gradients in confined environments, called climatic chambers where the air is heated by an electrical resistance and is cooled with a finned evaporator which is linked to a vapour compression system subjected to a particular control system of the refrigerating power. In particular, in this paper the air and object tested thermal transients are studied from an analytical and experimental point of view. The study of the mathematical model is realized assuming simplified hypotheses about the air, the object and the air cooled evaporator temperature. The most complex circumstances are related to a very fast temperature decrease because under this working condition the mathematical model is characterized by a nonlinear differential system. The nonlinear term is represented by the refrigerating power that varies in a definite range with the evaporator temperature according to a sinusoid trend. For this power a suitable analytical expression, derived by the control system performance and by the compressor characteristic, has been found. The analytical,experimental comparison during a cooling thermal stress of typical products subjected to international standard tests as the electronic boards, has been carried out showing acceptable results. The model presented is useful to foresee the climatic chamber performances in the presence of a specific refrigerating power trend; this is the start-point for the design of the vapour compression plant and its control system. Copyright © 2001 John Wiley & Sons, Ltd. [source] The 3-D bifurcation and limit cycles in a food-chain modelMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2009Lemin Zhu Abstract In this paper, by using a corollary to the center manifold theorem, we show that the 3-D food-chain model studied by many authors undergoes a 3-D Hopf bifurcation, and then we obtain the existence of limit cycles for the 3-D differential system. The methods used here can be extended to many other 3-D differential equation models. Copyright © 2008 John Wiley & Sons, Ltd. [source] The transient equations of viscous quantum hydrodynamicsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2008Michael Dreher Abstract We study the viscous model of quantum hydrodynamics in a bounded domain of space dimension 1, 2, or 3, and in the full one-dimensional space. This model is a mixed-order partial differential system with nonlocal and nonlinear terms for the particle density, current density, and electric potential. By a viscous regularization approach, we show existence and uniqueness of local in time solutions. We propose a reformulation as an equation of Schrödinger type, and we prove the inviscid limit. Copyright © 2007 John Wiley & Sons, Ltd. [source] On the hyperbolic system of a mixture of Eulerian fluids: a comparison between single- and multi-temperature modelsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007Tommaso Ruggeri Abstract The first rational model of homogeneous mixtures of fluids was proposed by Truesdell in the context of rational thermodynamics. Afterwards, two different theories were developed: one with a single-temperature (ST) field of the mixture and the other one with several temperatures. The two systems are from the mathematical point of view completely different and the relationship between their solutions was not clarified. In this paper, the hyperbolic multi-temperature (MT) system of a mixture of Eulerian fluids will be explained and it will be shown that the corresponding single-temperature differential system is a principal subsystem of the MT one. As a consequence, the subcharacteristic conditions for characteristic speeds hold and this gives an upper-bound esteem for pulse speeds in an ST model. Global behaviour of smooth solutions for large time for both systems will also be discussed through the application of the Shizuta,Kawashima condition. Finally, as an application, the particular case of a binary mixture is considered. Copyright © 2006 John Wiley & Sons, Ltd. [source] Periodic Orbits near equilibriaCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2010Luis Barreira Lyapunov, Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc. [source] Quadratic Differential Demand Systems and the Retail Demand for Pork in Great BritainJOURNAL OF AGRICULTURAL ECONOMICS, Issue 3 2003Panos Fousekis The primary objective of this paper is to derive a general synthetic quadratic (rank 3) differential demand system which nests within it a range of testable differential demand models including the quadratic AIDS, CBS, Rotterdam and NBR systems. A model selection test procedure is also outlined. These differential systems are then applied and tested to analyse the monthly retail demand for cuts of pork in Great Britain over the period 1989,2000. The empirical results suggest that a quadratic differential AIDS model is most appropriate for the pork demand system studied, but that the need for inclusion of quadratic income/expenditure terms is not universal for every cut within the demand system. Quadratic expenditure effects were appropriate for pork chops and leg roasts, but log linear expenditure effects were adequate for bellies, shoulders and loin roasts. Roasting cuts were expenditure and own price elastic, with pork loins, chops and bellies all expenditure and own price inelastic. [source] Integrable operators and canonical differential systemsMATHEMATISCHE NACHRICHTEN, Issue 1-2 2007Lev Sakhnovich Abstract In this article we consider a class of integrable operators and investigate its connections with the following theories: the spectral theory of the non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems, the random matrices theory and the limit values of the multiplicative integral. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||