Meixner Wavelet Transform: A Tool for Studying Stationary Discrete-Time Stochastic Processes

A general approach to analyzing discrete stochastic processes in the context of spectral analysis in the Laplace domain is considered. It is shown that a multichannel algorithm, which may be used for determining a discrete Laplace transform of the correlation function corresponding to a stationary discrete-time stochastic process, may be designed on the basis of Meixner wavelets.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45795/1/11175_2004_Article_463362.pd

Theory of Laplace Analysis of Non-Gaussian Noise

An algorithm for directly calculating third-order noise operation spectra, which includes no evaluation of the third-order correlation function as a preliminary stage, is found. For the Ershler–Randles circuit, an expression is found, which links bispectra of the equilibrium electrode potential fluctuation determined in the imaginary and real axes of the Laplace plane. Advantages of using the Laplace space in studies of the fine non-Gaussian structure of random time series are discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45797/1/11175_2004_Article_491780.pd

Strongly nonlinear dynamics of electrolytes in large ac voltages

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.Comment: 30 pages, 17 eps-figures, RevTe

Diffuse-Charge Dynamics in Electrochemical Systems

The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate, blocking electrodes which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The ``weakly nonlinear'' limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter $\epsilon = \lambda_D/L$, where $\lambda_D$ is the screening length and $L$ the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of $\lambda_D L / D$ (not $\lambda_D^2/D$), where $D$ is the ionic diffusivity, but nonlinearity violates this common picture and introduce multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, $L^2/D$. In the ``strongly nonlinear'' regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multi-component electrolytes, and Faradaic processes.Comment: 10 figs, 26 pages (double-column), 141 reference

Search for the Radiative Capture d+d->^4He+\gamma Reaction from the dd\mu Muonic Molecule State

A search for the muon catalyzed fusion reaction dd --> ^4He +\gamma in the dd\mu muonic molecule was performed using the experimental \mu CF installation TRITON and NaI(Tl) detectors for \gamma-quanta. The high pressure target filled with deuterium at temperatures from 85 K to 800 K was exposed to the negative muon beam of the JINR phasotron to detect \gamma-quanta with energy 23.8 MeV. The first experimental estimation for the yield of the radiative deuteron capture from the dd\mu state J=1 was obtained at the level n_{\gamma}\leq 2\times 10^{-5} per one fusion.Comment: 9 pages, 3 Postscript figures, submitted to Phys. At. Nuc