Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Density functional calculations for polymers and clusters - progress and limitations

The applicability of density functional (DF) methods has progressed greatly since the first workshop of this series ten years ago. Applications that show both the successes and the limitations can be found in the fields of: (a) the structures of the isomers of atomic clusters. and (b) the structure of organic molecules and polymers, and their reactions with additional molecules. We shall review some of the results and the lessons to be learned from them. (C) 2001 Elsevier Science B.V. All rights reserved.

Fixed-node diffusion Monte Carlo computations for closed-shell jellium spheres

Fixed-node diffusion Monte Carlo computations are used to determine the ground state energy and electron density for jellium spheres with up to N = 106 electrons and background densities corresponding to the electron gas parameter 1 less than or equal to r(s)less than or equal to5.62. We analyze the density and size dependence of the surface energy, and we extrapolate our data to the thermodynamic limit. The results agree well with the predictions of density functional computations using the local density approximation. In the case of N = 20, we extend our computation to higher densities and identify a transition between atomic- and jelliumlike nodal structures occurring at the background density corresponding to r(s)=0.13. In this case the local density approximation is unable to reproduce the changes in the correlation energy due to the discontinuous transition in the ground state nodal structure. We discuss the relevance of our results for nonlocal approximations to density functional theory.

Thin Ta films: growth, stability, and diffusion studied by molecular-dynamics simulations

We report results of classical molecular-dynamics simulations of bcc and beta-Ta thin films. Thermal PVD film growth, surface roughness, argon ion bombardment, phase stability and transformation, vacancy and adatom diffusion, and thermal relaxation kinetics are discussed. Distinct differences between the two structures are observed, including a complex vacancy diffusion mechanism in beta-Ta. Embedded atom method potentials, which were fitted to bcc properties, have been used to model the Ta-Ta interactions. In order to verify the application of these potentials to the more complex beta-Ta structure, we have also performed density functional theory calculations. Results and implications of these calculations are discussed.

Exploring Technology Related Design-Space Limitations of High Performance Network Processing

This paper summarizes numerous research activities in high-performance networks and network security processing, and explores technology related performance constraints such as critical performance limitations of circuit architectures, which are set by the semiconductor technologies.

Limitations in using peptide drugs to characterize calcitonin gene-related peptide receptors

Calcitonin gene-related peptide (CGRP) is an endogenous vasodilator peptide that produces its effects by activation of CGRP(1) and CGRP(2) receptor subtypes, These receptor subtypes are characterized in functional studies using the agonist Cys(Acm)(2,7)-human-alpha-calcitonin gene-related peptide (Cys(ACM)(2,7)-h-alpha-CGRP), which activates CGRP(2) receptors, and the antagonist h-alpha CGRP(8-37) which has a high affinity for CGRP, receptors and a low affinity for CGRP(2) receptors. Our aim was to identify factors that may limit the use of these drugs to characterize CGRP receptor subtypes. We studied CGRP receptors using isolated ring segments of pig coronary and basilar arteries studied in vitro. The affinity of the antagonist h-alpha CGRP(8-37) for inhibiting h-alpha CGRP-induced relaxation of coronary arteries (log(10) of the antagonist equilibrium dissociation constant = -5.33) was determined from Schild plots that had steep slopes. Therefore, we used capsaicin to investigate the role of endogenous CGRP in confounding affinity measurements for h-alpha CGRP(8-37). After capsaicin treatment, the slopes of the Schild plots were not different from one, and a higher affinity of h-CGRP(8-37) in blocking relaxation was obtained (log(10) of the antagonist equilibrium dissociation constant = -6.01). We also investigated the agonist activity of the putative CGRP, receptor selective agonist Cys(Acm)(2,7)-h-alpha-CGRP. We found that maximal relaxation of coronary arteries caused by Cys(Acm)(2,7)-h-alpha CGRP was dependent upon the level of contractile tone induced by KCI. We also determined the K-A for Cys(Acm)(2,7)-h-alpha CGRP and found that the K-A (817 nM) was not significantly different from the EC50 (503 nM) for this drug in causing relaxation, indicating that Cys(Acm)(2,7)-h-alpha CGRP is a partial agonist. Because experimental conditions affect the actions of h-CGRP(8-37) and Cys(Acm)(2,7)-h-alpha CGRP, the conditions must be carefully controlled to reliably identify CGRP receptor subtypes.

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

Extraction of electrode kinetic parameters from microdisc voltammetric data measured under transport conditions intermediate between steady-state convergent and transient linear diffusion as typically applies to room temperature ionic liquids

The extraction of electrode kinetic parameters for electrochemical couples in room-temperature ionic liquids (RTILs) is currently an area of considerable interest. Electrochemists typically measure electrode kinetics in the limits of either transient planar or steady-state convergent diffusion for which the voltammetic response is well understood. In this paper we develop a general method allowing the extraction of this kinetic data in the region where the diffusion is intermediate between the planar and convergent limits, such as is often encountered in RTILs using microelectrode voltammetry. A general working surface is derived, allowing the inference of Butler-Volmer standard electrochemical rate constants for the peak-to-peak potential separation in a cyclic voltammogram as a function of voltage scan rate. The method is applied to the case of the ferrocene/ferrocenium couple in [C(2)mim][N(Tf)(2)] and [C(4)mim][N(Tf)(2)].

A comparative electrochemical study of diffusion in room temperature ionic liquid solvents versus acetonitrile

Measurements on the diffusion coefficient of the neutral molecule N,N,N',N'-tetramethyl-para-phenylenediamine and the radical cation and dication generated by its one- and two-electron oxidation, respectively, are reported over the range 298-348 K in both acetonitrile and four room temperature ionic liquids (RTILs). Data were collected using single and double potential step chronamperometry at a gold disk electrode of micrometer dimension, and analysed via fitting to the appropriate analytical expression or, where necessary, to simulation. The variation of diffusion coefficient with temperature was found to occur in an Arrhenius-type manner for all combinations of solute and solvent. For a given ionic liquid, the diffusional activation energies of each species were not only closely equivalent to each other, but also to the RTIL's activation energy of viscous flow. In acetonitrile supported with 0.1 M tetrabutylammonium perchlorate, the ratio in diffusion coefficients of the radial cation and dication tot he neutral molecule were calculated as 0.89 +/- 0.05 and 0.51 +/- 0.03, respectively. In contrast, amongst the ionic liquids the same ratios were determined to be on average 0.53 +/- 0.04 and 0.33 +/- 0.03. The consequences of this dissimilarity are considered in terms of the modelling of voltammetric data gathered within ionic liquid solvents.