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31.
We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series. 相似文献
32.
Large eddy simulations of two basic configurations (decay of isotropic turbulence, and the academic plane channel flow) with heat transfer have been performed comparing several convection numerical schemes, in order to discuss their ability to evaluate temperature fluctuations properly. Results are compared with the available incompressible heat transfer direct numerical simulation data. It is shown that the use of regularizing schemes (such as high order upwind type schemes) for the temperature transport equation in combination with centered schemes for momentum transport equation gives better results than the use of centred schemes for both equations. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
33.
The reversible nonlinear conduction (RNC) in of high‐density polyethylene/acetylene carbon black composites with different degrees of crosslinking was studied above room temperature and below the melting point of high‐density polyethylene (HDPE). The experimental current density‐electric field strength curves can be overlapped onto a master curve, suggesting that the microscopic mechanisms for the appearance of RNC exist regardless of the ambient temperature and the crosslinking degree of the HDPE matrix. The relationship between the crossover current density and the linear conductivity can be explained in the framework of the dynamic random‐resistor‐network model. According to these results, two electron‐tunneling models are suggested to interpret the microscopic conduction behavior. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1212–1217, 2004 相似文献
34.
Becky Lavi Abraham Marmur 《Colloids and surfaces. A, Physicochemical and engineering aspects》2004,250(1-3):409-414
An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating. 相似文献
35.
36.
Kinetic parameters of amino acid cations in an MK-40 ion-exchange membrane are calculated from the conductivity data. A theoretical quantum-chemical analysis of experimental activation energies for conduction suggests a mechanism of elementary act of transport of amino acid cations in the membrane. 相似文献
37.
A. Bourgeat O. Gipouloux E. Marui‐Paloka 《Mathematical Methods in the Applied Sciences》2004,27(4):381-403
In this paper, we study the global behaviour of an underground waste disposal in order to have an accurate upscaled model suitable for the computations involved in safety assessment processes. We start from a detailed model describing the transport of pollutant leaking from a high number of units. Using the method of homogenization, going to the limit, we obtain first a macroscopic model where the sources are now appearing globally. Then we compute a first‐order matched asymptotic expansion and we give the error estimates for this approximation. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
38.
M. A. Efendiev J. Fuhrmann S. V. Zelik 《Mathematical Methods in the Applied Sciences》2004,27(8):907-930
For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
39.
The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines. 相似文献
40.
R. Norvaisa 《Lithuanian Mathematical Journal》2005,45(4):447-457
We give a characterization of Gaussian chaos laws on Banach function spaces which do not contain ℓ
∞
n
's uniformly. The result is applied to describe the convergence in law of U-processes with sample paths in certain Banach function spaces.
__________
Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 553–566, October–December, 2005. 相似文献