Biomedical subjects

H Larralde

Publications and source records attributed to H Larralde.

At least 19 recordsLinked to original sources

PubMed2005

Static pairwise annihilation in complex networks.

We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e., Poisson), and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the "hubs" have been annihilated, the network disintegrates and only isolated sites are left.

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PubMed2003

Fluctuation-dissipation theorem for metastable systems.

We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.

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PubMed2003

Translocation properties of primitive molecular machines and their relevance to the structure of the genetic code.

We address the question, related with the origin of the genetic code, of why are there three bases per codon in the translation to protein process. As a follow-up to our previous work (Aldana et al., 1998, Martínez-Mekler et al., 1999a,b), we approach this problem by considering the translocation properties of primitive molecular machines, which capture basic features of ribosomal/messenger RNA interactions, while operating under prebiotic conditions. Our model consists of a short one-dimensional chain of charged particles (rRNA antecedent) interacting with a polymer (mRNA antecedent) via electrostatic forces. The chain is subject to external forcing that causes it to move along the polymer which is fixed in a quasi-one-dimensional geometry. Our numerical and analytic studies of statistical properties of random chain/polymer potentials suggest that, under very general conditions, a dynamics is attained in which the chain moves along the polymer in steps of three monomers. By adjusting the model in order to consider present-day genetic sequences, we show that the above property is enhanced for coding regions. Intergenic sequences display a behavior closer to the random situation. We argue that this dynamical property could be one of the underlying causes for the three-base codon structure of the genetic code

Animals↗

PubMed2001

Region visited by a spherical Brownian particle in the presence of an absorbing boundary.

We calculate the time dependence of the average volume of a Wiener sausage in the presence of an absorbing boundary in one and three dimensions. In one dimension it is shown that the presence of an absorbing point reduces the time dependence of the average span from being proportional to sqrt[t] in an unbounded space, to being proportional to ln(t) at long times. In three dimensions the average volume increases as sqrt[t] at long times rather than being proportional to t as in free space.

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PubMed2001

Transport properties of the diluted Lorentz slab.

We study the behavior of a point particle incident on a slab of a randomly diluted triangular array of circular scatterers. Various scattering properties, such as the reflection and transmission probabilities and the scattering time are studied as a function of thickness and dilution. We show that a diffusion model satisfactorily describes the mentioned scattering properties. We also show how some of these quantities can be evaluated exactly and their agreement with numerical experiments. Our results exhibit the dependence of these scattering data on the mean free path. This dependence again shows excellent agreement with the predictions of a Brownian motion model.

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PubMed2001

Coupled normal heat and matter transport in a simple model system.

We introduce the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system is a Lorentz gas with fixed freely rotating circular scatterers which scatter point particles via perfectly rough collisions. Upon imposing either a temperature gradient and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds. Transport in this system is normal in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are nontrivially coupled, satisfying Onsager's reciprocity relations.

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PubMed2001

Simple model of a random walk with arbitrarily long memory.

We present a generalization of the persistent random-walk model in which the step at time n depends on the state of the step at time n-T, for arbitrary T. This gives rise to arbitrarily long memory effects, yet by an appropriate transformation the model is tractable by essentially the same techniques applicable to the usual persistent random-walk problem. We apply our results to the specific case of delayed "step" persistence, and analyze its asymptotic statistical properties.

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PubMed2000

Dynamical weight functions for a planar crack

The stress intensity factors are evaluated for a moving planar crack for loadings which vary arbitrarily in time and three dimensions of space. We exploit the adjoint elasticity equation obeyed by the corresponding weight functions, and a new and more universal Wiener-Hopf factorization of the Rayleigh function, this being the central difficulty in such calculations. For the mode II weight function we give further asymptotic results crucial to a subsequent calculation of crack stability with respect to out-of-plane perturbations.

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PubMed2000

Statistical characterization of random electrostatic potentials

In this work we study statistical properties of random electrostatic potentials generated by one dimensional lattices with random charges. We show that the resulting random potentials are correlated Gaussian processes, satisfying the Lindeberg version of the central limit theorem, if certain restrictions are imposed on the individual potentials generated by the particles on the lattice. Since most of the point-particle electrostatic potentials occurring in nature satisfy the Lindeberg condition, the correlation properties of the random potentials are not arbitrary and must comply with the central limit theorem. Based on this theorem we can obtain explicit expressions for these correlations. We thus are able to give a characterization of a broad class of potentials yielding feasible physical scenarios. We illustrate some consequences of our findings by considering dynamical properties of a test particle interacting with the lattice. We show how the long range correlations generate statistical features in these properties, which are best exhibited when considering different length scales.

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PubMed1999

Deterministic transport in ratchets.

We present the deterministic transport properties of driven overdamped particles in a simple piecewise-linear ratchet potential. We consider the effects on the stationary current due to local spatial asymmetry, time asymmetry in the driving force, and we include the possibility of a global spatial asymmetry. We present an extremely simple scheme for evaluating the current that is established on the ratchet within an "adiabatic" approximation, and compare the results with exact numerical integration of the process.

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PubMed1996