Conductance increases produced by bath application of cholinergic agonists to Electrophorus electroplaques

When solutions containing agonists are applied to the innervated face of an Electrophorus electroplaque, the membrane's conductance increases. The agonist-induced conductance is increased at more negative membrane potentials. The "instantaneous" current-voltage curve for agonist-induced currents is linear and shows a reversal potential near zero mV; chord conductances, calculated on the basis of this reversal potential, change epsilon-fold for every 62-mV change in potential when the conductance is small. Conductance depends non- linearly on small agonist concentrations; at all potentials, the dose-response curve has a Hill coefficient of 1.45 for decamethonium (Deca) and 1.90 for carbamylcholine (Carb). With agonist concentrations greater than 10^(-4) M Carb or 10^(-5) M Deca, the conductance rises to a peak 0.5-1.5 min after introduction of agonist, then declines with time; this effect resembles the "desensitization" reported for myoneural junctions. Elapid alpha-toxin, tubocurarine, and desensitization reduce the conductance without changing the effects of potential; the apparent dissociation constant for tubocurarine is 2 X 10^(-7) M. By contrast, procaine effects a greater fractional inhibition of the conductance at high negative potentials

Whitney coverings and the tent spaces T1,q(γ)T^{1,q}(\gamma) for the Gaussian measure

We introduce a technique for handling Whitney decompositions in Gaussian harmonic analysis and apply it to the study of Gaussian analogues of the classical tent spaces $T^{1,q}$ of Coifman, Meyer and Stein.Comment: 13 pages, 1 figure. Revised version incorporating referee's comments. To appear in Arkiv for Matemati

Propagation and organization in lattice random media

We show that a signal can propagate in a particular direction through a model random medium regardless of the precise state of the medium. As a prototype, we consider a point particle moving on a one-dimensional lattice whose sites are occupied by scatterers with the following properties: (i) the state of each site is defined by its spin (up or down); (ii) the particle arriving at a site is scattered forward (backward) if the spin is up (down); (iii) the state of the site is modified by the passage of the particle, i.e. the spin of the site where a scattering has taken place, flips ($\uparrow \Leftrightarrow \downarrow$). We consider one dimensional and triangular lattices, for which we give a microscopic description of the dynamics, prove the propagation of a particle through the scatterers, and compute analytically its statistical properties. In particular we prove that, in one dimension, the average propagation velocity is $= 1/(3-2q)$, with $q$ the probability that a site has a spin $\uparrow$, and, in the triangular lattice, the average propagation velocity is independent of the scatterers distribution: $= 1/8$. In both cases, the origin of the propagation is a blocking mechanism, restricting the motion of the particle in the direction opposite to the ultimate propagation direction, and there is a specific re-organization of the spins after the passage of the particle. A detailed mathematical analysis of this phenomenon is, to the best of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat. Phy

Evolving localizations in reaction-diffusion cellular automata

We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in each one state. We employ evolutionary algorithms to breed local transition functions that support mobile localizations (gliders), and characterize sets of the functions selected in terms of quasi-chemical systems. Analysis of the set of functions evolved allows to speculate that mobile localizations are likely to emerge in the quasi-chemical systems with limited diffusion of one reagent, a small number of molecules is required for amplification of travelling localizations, and reactions leading to stationary localizations involve relatively equal amount of quasi-chemical species. Techniques developed can be applied in cascading signals in nature-inspired spatially extended computing devices, and phenomenological studies and classification of non-linear discrete systems.Comment: Accepted for publication in Int. J. Modern Physics

Numerical Analysis of a New Mixed Formulation for Eigenvalue Convection-Diffusion Problems

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization

The Generalized Graetz Problem in Finite Domains

We consider the generalized Graetz problem associated with stationary convection-diffusion inside a domain having any regular three-dimensional translationally invariant section and finite or semi-infinite extent. Our framework encompasses any previous “extended” and “conjugated” Graetz generalizations and provides theoretical bases for computing the orthogonal set of generalized two-dimensional Graetz modes. The theoretical framework includes both heterogeneous and possibly anisotropic diffusion tensors. In the case of semi-infinite domains, the existence of a bounded solution is shown from the analysis of two-dimensional operator eigenvectors which form a basis of L2 . In the case of finite domains a similar basis can be exhibited, and the mode’s amplitudes can be obtained from the inversion of newly defined finite domain operator. Our analysis includes both the theoretical and practical issues associated with this finite domain operator inversion as well as its interpretation as a multireflection image method. Error estimates are provided when numerically truncating the spectrum to a finite number of modes. Numerical examples are validated for reference configurations and provided in nontrivial cases. Our methodology shows how to map the solution of stationary convection-diffusion problems in finite three-dimensional domains into a two-dimensional operator spectrum, which leads to a drastic reduction in computational cost

Detailed design of a resonantly-enhanced axion-photon regeneration experiment

A resonantly-enhanced photon-regeneration experiment to search for the axion or axion-like particles is described. This experiment is a shining light through walls study, where photons travelling through a strong magnetic field are (in part) converted to axions; the axions can pass through an opaque wall and convert (in part) back to photons in a second region of strong magnetic field. The photon regeneration is enhanced by employing matched Fabry-Perot optical cavities, with one cavity within the axion generation magnet and the second within the photon regeneration magnet. Compared to simple single-pass photon regeneration, this technique would result in a gain of (F/pi)^2, where F is the finesse of each cavity. This gain could feasibly be as high as 10^(10), corresponding to an improvement in the sensitivity to the axion-photon coupling, g_(agg), of order (F/pi)^(1/2) ~ 300. This improvement would enable, for the first time, a purely laboratory experiment to probe axion-photon couplings at a level competitive with, or superior to, limits from stellar evolution or solar axion searches. This report gives a detailed discussion of the scheme for actively controlling the two Fabry-Perot cavities and the laser frequencies, and describes the heterodyne signal detection system, with limits ultimately imposed by shot noise.Comment: 10 pages, 5 figure