Search results for "Diffusion"

The Heat Content for Nonlocal Diffusion with Non-singular Kernels

2017

Abstract We study the behavior of the heat content for a nonlocal evolution problem.We obtain an asymptotic expansion for the heat content of a set D, defined as ℍ D J ⁢ ( t ) := ∫ D u ⁢ ( x , t ) ⁢ 𝑑 x ${\mathbb{H}_{D}^{J}(t):=\int_{D}u(x,t)\,dx}$ , with u being the solution to u t = J ∗ u - u ${u_{t}=J\ast u-u}$ withinitial condition u 0 = χ D ${u_{0}=\chi_{D}}$ . This expansion is given in terms of geometric values of D. As a consequence, we obtain that ℍ D J ⁢ ( t ) = | D | - P J ⁢ ( D ) ⁢ t + o ⁢ ( t ) ${\mathbb{H}^{J}_{D}(t)=\lvert D\rvert-P_{J}(D)t+o(t)}$ as t ↓ 0 ${t\downarrow 0}$ .We also recover the usual heat content for the heat equation when we rescale the kernel J in an appro…

Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system

2008

In this work we investigate the possibility of the pattern formation for a reaction-di®usion system with nonlinear di®usion terms. Through a linear sta- bility analysis we ¯nd the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-di®usion e®ects are responsible for the initiation of spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

Diffusion Equations with Finite Speed of Propagation

2007

In this paper we summarize some of our recent results on diffusion equations with finite speed of propagation. These equations have been introduced to correct the infinite speed of propagation predicted by the classical linear diffusion theory.

Hillslope evolution by nonlinear creep and landsliding: An experimental study: Comment and Reply

2002

[Roering et al. (2001)][1] describe very careful and interesting experiments that beautifully illustrate the transition from steady downhill creep at low gradients to highly dynamic transport on steep slopes. They interpret this behavior in terms of a single nonlinear diffusion coefficient,

Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source

1999

Intracrystalline Diffusion of Benzene in Ga-Silicate

1991

Abstract The sorption kinetics of benzene in large Ga-MFI crystals was investigated under constant volume- variable pressure conditions. A complete analysis of the uptake curves has been performed using solution of a nonlinear Volterra equation which describes the interaction of uptake process with the apparatus. Within the time scale of uptake measurements (10 3 -10 4 s) the uptake curves were found to be consistent with the solution of the second Fick's law. Corrected diffusion coefficients were found to be essentially independent of loading within the loading range investigated and in contrast to the system benzene-HNaZSM-5 [1,2] their temperature dependence is much stronger.

Impact of Stock Price Jumps on Option Values

1999

Many empirical papers document the fact that the distribution of stock returns exhibits fatter tails than would be expected from a normal distribution. This might explain some of the pricing biases of the Black/Scholes model, which is] based on a normal return distribution. Given this result, alternative option pricing models should be based on one of the following three classes of return models: (1) a stationary process, such as a paretian stable or a student’s t-distribution, (2) a mixture of stationary distributions, such as two normal distributions with different means or variances, or a mixture of a diflusion and a pure jump process, or (3) a distribution such as a normal distribution …

HEAT FLUX IN SUPERFLUID TRANSITION AND IN TURBULENT HELIUM COUNTERFLOW

Mössbauer investigations on glass-forming organic liquids

1992

Glycerol forms a molecular glass near 180K. Fe2+ dissolved in glycerol allows the study of the dynamics of the system by Mossbauer spectroscopy. Recently it has been shown that the Mossbauer spectra can be understood in a way consistent with the results of dielectric and ultrasonic viscoelastic relaxation measurements. A jump diffusion model of Sinqwi and Sjolander with a jump rate distribution according to Davidson and Cole allowed us to fit the Mossbauer spectra of Fe in glycerol. First attempts to compare mode coupling theory with Mossbauer spectra are reported.

Far-off-resonance averaging of dipolar interactions in solids

1997

Abstract The far-off-resonance performance of several line-narrowing sequences is investigated. Both theoretically and experimentally, it is found that transverse relaxation times, dominated by dipole–dipole interactions, are most effectively prolonged not only on-resonance but also for certain, generally large, resonance offsets. These correspond to a situation when, during the basic pulse separation, the frequency offset rotates the toggling-frame Hamiltonian by multiples of 180°. The implications of these results for the study of macroscopic translational diffusion using static-field-gradient NMR are discussed.