Francisco Salva's Electric Telegraph

This article takes a look at the life and accomplishments of Francisco Salva of Spain, including his work with an electric telegraph system. The author states that information herein is based on the original report and some practical demonstrations that Salva presented to the Barcelona Academy of Sciences in 1804

Survival probability and order statistics of diffusion on disordered media

We investigate the first passage time t_{j,N} to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered medium. To solve this order-statistics problem we assume that, for short times, the survival probability (the probability that a single random walker is not absorbed by a hyperspherical surface during some time interval) decays for disordered media in the same way as for Euclidean and some class of deterministic fractal lattices. This conjecture is checked by simulation on the incipient percolation aggregate embedded in two dimensions. Arbitrary moments of t_{j,N} are expressed in terms of an asymptotic series in powers of 1/ln N which is formally identical to those found for Euclidean and (some class of) deterministic fractal lattices. The agreement of the asymptotic expressions with simulation results for the two-dimensional percolation aggregate is good when the boundary is defined in terms of the chemical distance. The agreement worsens slightly when the Euclidean distance is used.Comment: 8 pages including 9 figure

Number of distinct sites visited by N random walkers on a Euclidean lattice

The evaluation of the average number S_N(t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is the volume of a hypersphere of radius (4Dt \ln N)^{1/2}, \Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N, d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the dimension and time. The first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1, 2, and 3. Some implications of these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.

Properties of the reaction front in a reaction-subdiffusion process

We study the reaction front for the process $A+B\to C$ in which the reagents move subdiffusively. We propose a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. Scaling solutions to these equations are presented and compared with those of a direct numerical integration of the equations. We find that for reactants whose mean square displacement varies sublinearly with time as $\sim t^\gamma$, the scaling behaviors of the reaction front can be recovered from those of the corresponding diffusive problem with the substitution $t\to t^\gamma$Comment: Errata corrected, one reference update

Some exact results for the trapping of subdiffusive particles in one dimension

We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided random distribution of static absorbing traps with concentration c. The survival probability Phi(t) that the random walker is not trapped by time t is obtained exactly in both versions of the problem through a fractional diffusion approach. Comparison with simulation results is madeComment: 15 pages, 2 figure

Fast, Accurate and Robust Adaptive Finite Difference Methods for Fractional Diffusion Equations: The Size of the Timesteps does Matter

The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of the number of timesteps. Besides, the solutions of these problems usually involve markedly different time scales, which leads to quite inhomogeneous numerical errors. A natural way to address these difficulties is by resorting to adaptive numerical methods where the size of the timesteps is chosen according to the behaviour of the solution. A key feature of these methods is then the efficiency of the adaptive algorithm employed to dynamically set the size of every timestep. Here we discuss two adaptive methods based on the step-doubling technique. These methods are, in many cases, immensely faster than the corresponding standard method with fixed timesteps and they allow a tolerance level to be set for the numerical errors that turns out to be a good indicator of the actual errors

A formal analysis of the notion of preference between deductive arguments

In the last two decades, justification logic has addressed the problem of including justifications into the field of epistemic logic. Nevertheless, there is something that has not received enough attention yet: how epistemic agents might prefer certain justifications to others, in order to have better pieces of evidence to support a particular belief. In this work, we study the notion of preference between a particular kind of justifications: deductive arguments. For doing so, we have built a logic using tools from epistemic logic, justification logic and logics for belief dependence. According to our solution, the preferences of an epistemic agent between different deductive arguments can be reduced to other notions

From preferences between arguments to preferences between explanations

In this ongoing work we present a new approach to the problem of argument evaluation. According to our view the notion of preference between deductive arguments is reducible to simpler notions. Departuring from this analysis we intend to apply it to the problem of hypothesis selection in explanatory practices.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech