Phase field modeling of electrochemistry I: Equilibrium

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories. We calculate the surface energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4, SIUnits.sty. Precedes cond-mat/030817

Modeling diffusion of intracellular metabolites in the mouse brain up to very high diffusion-weighting: Diffusion in long fibers (almost) accounts for non-monoexponential attenuation

Purpose: To investigate how intracellular metabolites diffusion measured in vivo up to very high q/b in the mouse brain can be explained in terms of simple geometries. / Methods: 10 mice were scanned using our new STE‐LASER sequence, at 11.7 Tesla (T), up to qmax = 1 μm−1 at diffusion time td = 63.2 ms, corresponding to bmax = 60 ms/µm². We model cell fibers as randomly oriented cylinders, with radius a and intracellular diffusivity urn:x-wiley:07403194:media:mrm26548:mrm26548-math-0004, and fit experimental data as a function of q to estimate urn:x-wiley:07403194:media:mrm26548:mrm26548-math-0005 and a. / Results: Randomly oriented cylinders account well for measured attenuation, giving fiber radii and urn:x-wiley:07403194:media:mrm26548:mrm26548-math-0006 in the expected ranges (0.5–1.5 µm and 0.30–0.45 µm2/ms, respectively). The only exception is N‐acetyl‐aspartate (NAA) (extracted a∼0), which we show to be compatible with a small fraction of the NAA pool being confined in highly restricted compartments (with short T2). / Conclusion: The non‐monoexponential signal attenuation of intracellular metabolites in the mouse brain can be described by diffusion in long and thin cylinders, yielding realistic Dintra and fiber diameters. However, this simple model may require small “corrections” for NAA, in the form of a small fraction of the NAA signal originating from a highly restricted compartment

Seiberg duality, quiver gauge theories, and Ihara's zeta function

We study Ihara’s zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara’s zeta function to be the generating function for the generic superpotential of the gauge theory

Property (RD) for Hecke pairs

As the first step towards developing noncommutative geometry over Hecke C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H) has (RD) if and only if G has (RD). This provides us with a family of examples of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989 to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has property (RD), the algebra of rapidly decreasing functions on the set of double cosets is closed under holomorphic functional calculus of the associated (reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the subalgebra of rapidly decreasing functions is smooth. This is the final version as published. The published version is available at: springer.co

On twisted Fourier analysis and convergence of Fourier series on discrete groups

We study norm convergence and summability of Fourier series in the setting of reduced twisted group $C^*$-algebras of discrete groups. For amenable groups, F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson summation holds for a large class of groups, including e.g. all Coxeter groups and all Gromov hyperbolic groups. As a tool in our presentation, we introduce notions of polynomial and subexponential H-growth for countable groups w.r.t. proper scale functions, usually chosen as length functions. These coincide with the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update

Isometric group actions on Banach spaces and representations vanishing at infinity

Our main result is that the simple Lie group $G=Sp(n,1)$ acts properly isometrically on $L^p(G)$ if $p>4n+2$. To prove this, we introduce property ({\BP}_0^V), for $V$ be a Banach space: a locally compact group $G$ has property ({\BP}_0^V) if every affine isometric action of $G$ on $V$, such that the linear part is a $C_0$-representation of $G$, either has a fixed point or is metrically proper. We prove that solvable groups, connected Lie groups, and linear algebraic groups over a local field of characteristic zero, have property ({\BP}_0^V). As a consequence for unitary representations, we characterize those groups in the latter classes for which the first cohomology with respect to the left regular representation on $L^2(G)$ is non-zero; and we characterize uniform lattices in those groups for which the first $L^2$-Betti number is non-zero.Comment: 28 page

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA

Impact of the 26-30 May 2003 solar events on the earth ionosphere and thermosphere.

During the last week of May 2003, the solar active region AR 10365 produced a large number of flares, several of which were accompanied by Coronal Mass Ejections (CME). Specifically on 27 and 28 May three halo CMEs were observed which had a significant impact on geospace. On 29 May, upon their arrival at the L1 point, in front of the Earth's magnetosphere, two interplanetary shocks and two additional solar wind pressure pulses were recorded by the ACE spacecraft. The interplanetary magnetic field data showed the clear signature of a magnetic cloud passing ACE. In the wake of the successive increases in solar wind pressure, the magnetosphere became strongly compressed and the sub-solar magnetopause moved inside five Earth radii. At low altitudes the increased energy input to the magnetosphere was responsible for a substantial enhancement of Region-1 field-aligned currents. The ionospheric Hall currents also intensified and the entire high-latitude current system moved equatorward by about 10°. Several substorms occurred during this period, some of them - but not all - apparently triggered by the solar wind pressure pulses. The storm's most notable consequences on geospace, including space weather effects, were (1) the expansion of the auroral oval, and aurorae seen at mid latitudes, (2) the significant modification of the total electron content in the sunlight high-latitude ionosphere, (3) the perturbation of radio-wave propagation manifested by HF blackouts and increased GPS signal scintillation, and (4) the heating of the thermosphere, causing increased satellite drag. We discuss the reasons why the May 2003 storm is less intense than the October-November 2003 storms, although several indicators reach similar intensities