Weak Gradients and the Diffusion Equation
No diffusion in solid, no concentration gradients in liquid
... Not only mole fractions of the second component in the solid and liquid phases can be used, but weight fractions and concentrations as well. Needless to clarify that the value of distribution coefficient depends on units ...
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1 The Diffusion Equation
... 4.1.1 Wells Controlled by Bottom Hole Pressure If a reservoir contains two wells with specified bottom hole pressures p 1 and p 2 a pressure solution can be obtained by summing two solutions for a sin- gle well at ...
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Convection-Diffusion Equation
... In particular, we propose a systematic technique in the selection of the grid expansion factor based on its logarithmic relationship with low Peclet number. Such linear mathematical connection between the two ...
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On a Fractional Master Equation and a Fractional Diffusion Equation
... *Corresponding Author: [email protected] Copyright © 2013 Horizon Research Publishing All rights reserved. Abstract In this paper , we derive the solutions of fractional master equation defined by (2.1) and ...
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identification in a convection-diffusion equation
... (Received 8 August 2003; revised 30 January 2004) Abstract We use a recently developed Sinc-Galerkin method for the solu- tion of non-self-adjoint equations to solve a parameter identification problem arising from the ...
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The effect of different number of diffusion gradients on SNR of diffusion tensor derived measurement maps
... the diffusion tensor, result- ing in more accurate tensor estimation but much longer imaging ...6-diffusion gradients is used, and the other 12-diffusion gradients, in the former, more ...
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The weakness of weak ties for novel information diffusion
... p weak = .4. In contrast to the addition of weak ties in ...improves diffusion Just how constrained a person’s opportunities to share information are– the true value of x– surely depends on the ...
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Numerical solution of the advective-diffusion equation
... Numerical Laplace inversion techniques are required to solve the system of simultaneous equations that result from the application of the Laplace time finite analytic space method. Two well known methods were examined, ...
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Solution of a modified fractional diffusion equation
... fractional diffusion equations [14]. The fractional diffusion equation is characterised by the presence of either a fractional tem- poral derivative or fractional spatial derivative or both ...
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The boundary degeneracy of a singular diffusion equation
... diffusion equation with boundary degeneracy: ∂ u ∂ t = div(d α · |∇u| p–2 ∇u), (x, t) ∈ Q T = × (0,T), where ⊂ R N is a bounded domain with appropriately smooth boundary, p > 1, α > 0, and d = d(x) = dist(x, ∂ ...
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Discrete model of a nonlocal diffusion equation
... Palabras y frases clave . Difusi´ on no local, condiciones de Neumann, discretiza- ci´ on, convergencia. 2010 Mathematics Subject Classification. 35K57, 35B40. Abstract . In this work we prove the existence and ...
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The Mathematical Modeling of the Atmospheric Diffusion Equation
... Abstract : The advection diffusion equation (ADE) is solved in two directions to obtain the crosswind integrated concentration. The solution is solved using separation variables technique and considering ...
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Numerical simulation of Feller’s diffusion equation
... https://github.com/dutykh/Feller/ 5.2. Perspectives All the numerical schemes and results presented in this paper were in one ‘spatial’ dimension. The F ELLER equation considered here is 1 − D as well. However, it ...
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Impulsive Diffusion Equation on Time Scales
... impulsive diffusion equation with boundary conditions on T ...classical diffusion equation into T ...impulsive diffusion eigenvalue problem are established on T ...
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5.4 The Heat Equation and Convection-Diffusion
... Heat Equation and Convection-Diffusion The wave equation conserves ...heat equation u t = u xx dissipates ...wave equation can be recovered by going backward in ...heat equation ...
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A parsimonious diffusion equation for electricity demand
... The expression simplifies to the result by exploiting the fact that expectations of the diffusion terms are zero. ♠ 3.3 Demand regression model To perform the calibration of the sde, a key element in our method ...
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Infinitely many weak solutions for a fractional Schrödinger equation
... Schrödinger equation (– ) α u + V(x)u = f (x,u), x ∈ R N , where 0 < α < 1, N > 2 α , (– ) α stands for the fractional Laplacian of order α , V is a positive continuous potential, and f is a continuous subcritical ...
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An Introductory View of the Weak Solution of the p Laplacian Equation
... a weak solution as requiring only u ∈ C ∞ or even u ∈ C 1 is too narrow for the treatment of such problem and clearly the less smoothness we assume of u to start with, more theory can be developed, hence a notion ...
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The local strong and weak solutions to a generalized Novikov equation
... proved the local well-posedness for the periodic Cauchy problem of the Novikov equation in Sobolev space H s (R) with s > . The orbit invariants are used to show the existence of a periodic global strong ...
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Existence of nontrivial weak solutions for a quasilinear Choquard equation
... of weak solutions for the problem above via the mountain pass theorem and the fountain ...of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term f ...
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