Effective field theory of interactions on the lattice

We consider renormalization of effective field theory interactions by discretizing the continuum on a tight-binding lattice. After studying the one-dimensional problem, we address s-wave collisions in three dimensions and relate the bare lattice coupling constants to the continuum coupling constants. Our method constitutes a very simple avenue for the systematic renormalization in effective field theory, and is especially useful as the number of interaction parameters increases.Comment: 7 pages, 0 figure

Recent Developments in Mems-Based Micro Fuel Cells

Micro fuel cells ($\mu$-FC) represent promising power sources for portable applications. Today, one of the technological ways to make $\mu$-FC is to have recourse to standard microfabrication techniques used in the fabrication of micro electromechanical systems (MEMS). This paper shows an overview on the applications of MEMS techniques on miniature FC by presenting several solutions developed throughout the world. It also describes the latest developments of a new porous silicon-based miniature fuel cell. Using a silane grafted on an inorganic porous media as the proton-exchange membrane instead of a common ionomer such as Nafion, the fuel cell achieved a maximum power density of 58 mW cm-2 at room temperature with hydrogen as fuel.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Ancient multiple-layer solutions to the Allen-Cahn equation

We consider the parabolic one-dimensional Allen-Cahn equation $$u_t= u_{xx}+ u(1-u^2)\quad (x,t)\in \mathbb{R}\times (-\infty, 0].$$ The steady state $w(x) =\tanh (x/\sqrt{2})$, connects, as a "transition layer" the stable phases $-1$ and $+1$. We construct a solution $u$ with any given number $k$ of transition layers between $-1$ and $+1$. At main order they consist of $k$ time-traveling copies of $w$ with interfaces diverging one to each other as $t\to -\infty$. More precisely, we find $$u(x,t) \approx \sum_{j=1}^k (-1)^{j-1}w(x-\xi_j(t)) + \frac 12 ((-1)^{k-1}- 1)\quad \hbox{as} t\to -\infty,$$ where the functions $\xi_j(t)$ satisfy a first order Toda-type system. They are given by $$\xi_j(t)=\frac{1}{\sqrt{2}}\left(j-\frac{k+1}{2}\right)\log(-t)+\gamma_{jk},\quad j=1,...,k,$$ for certain explicit constants $\gamma_{jk}.

Ancient shrinking spherical interfaces in the Allen-Cahn flow

We consider the parabolic Allen-Cahn equation in $\mathbb{R}^n$, $n\ge 2$, $$u_t= \Delta u + (1-u^2)u \quad \hbox{ in } \mathbb{R}^n \times (-\infty, 0].$$ We construct an ancient radially symmetric solution $u(x,t)$ with any given number $k$ of transition layers between $-1$ and $+1$. At main order they consist of $k$ time-traveling copies of $w$ with spherical interfaces distant $O(\log |t| )$ one to each other as $t\to -\infty$. These interfaces are resemble at main order copies of the {\em shrinking sphere} ancient solution to mean the flow by mean curvature of surfaces: $|x| = \sqrt{- 2(n-1)t}$. More precisely, if $w(s)$ denotes the heteroclinic 1-dimensional solution of $w'' + (1-w^2)w=0$ $w(\pm \infty)= \pm 1$ given by $w(s) = \tanh \left(\frac s{\sqrt{2}} \right)$ we have $$u(x,t) \approx \sum_{j=1}^k (-1)^{j-1}w(|x|-\rho_j(t)) - \frac 12 (1+ (-1)^{k}) \quad \hbox{ as } t\to -\infty$$ where $$\rho_j(t)=\sqrt{-2(n-1)t}+\frac{1}{\sqrt{2}}\left(j-\frac{k+1}{2}\right)\log\left(\frac {|t|}{\log |t| }\right)+ O(1),\quad j=1,\ldots ,k.$

Heavy-neutrino decays at neutrino telescopes

It has been recently proposed that a sterile neutrino \nu_h of mass m_h=40--80 MeV, mixing |U_{\mu h}|^2=10^{-3}--10^{-2}, lifetime \tau_h \lsim 10^{-9} s, and a dominant decay mode (\nu_h \to \nu_\mu \gamma) could be the origin of the experimental anomalies observed at LSND, KARMEN and MiniBooNE. Such a particle would be abundant inside air showers, as it can be produced in kaon decays (K -> \nu_h \mu, K_L -> \nu_h \pi \mu). We use the Z-moment method to evaluate its atmospheric flux and the frequency of its decays inside neutrino telescopes. We show that the \nu_h would imply around 10^4 contained showers per year inside a 0.03 km^3 telescope like ANTARES or the DeepCore in IceCube. These events would have a characteristic energy and zenith-angle distribution (E_\nu = 0.1--10 TeV and \theta < 90^o), which results from a balance between the reach of the heavy neutrino (that disfavors low energies) and a sizeable production rate and decay probability. The standard background from contained neutrino events (\nu_e N \to e X and neutral-current interactions of high inelasticity) is 100 times smaller. Therefore, although it may be challenging from an experimental point of view, a search at ANTARES and IceCube could confirm this heavy-neutrino possibility.Comment: 10 pages. Comments on constraints from muon capture and cosmology added, minor corrections, references added. Version to appear as a Rapid Communication in PR

Towards a spin foam model description of black hole entropy

We propose a way to describe the origin of black hole entropy in the spin foam models of quantum gravity. This stimulates a new way to study the relation of spin foam models and loop quantum gravity.Comment: 5 pages, 1 figur

Damage Valuation of Indirect Expropriation in Public Services

damage valuation, expropriation, public services, contracting, privatization