arXiv subjects

Simone Pigolotti

Publications and source records attributed to Simone Pigolotti.

62 records · Page 4Linked to original sources

arXiv2008

Coarse graining of master equations with fast and slow states

We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can be analytically carried out and is consistent with other analytical approaches, like in the problem of the random walk in a double-well potential. We discuss the application of our method to nontrivial examples: diffusion in a lattice with defects and a model of an enzymatic reaction outside the steady state regime.

cond-mat.soft↗

arXiv2007

Macroscopic equations for the adiabatic piston

A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on the left and right chambers of the piston are always in equilibrium (that is the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution) after any collision with the piston. Then by using kinetic theory we derive the collision statistics from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables (namely the piston average velocity and position, the velocity variance and the temperatures of the two compartments). The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).

nlin.CD↗

arXiv2007

Species clustering in competitive Lotka-Volterra models

We study the properties of Lotka-Volterra competitive models in which the intensity of the interaction among species depends on their position along an abstract niche space through a competition kernel. We show analytically and numerically that the properties of these models change dramatically when the Fourier transform of this kernel is not positive definite, due to a pattern forming instability. We estimate properties of the species distributions, such as the steady number of species and their spacings, for different types of kernels.

q-bio.PE↗

arXiv2006

Oscillation patterns in negative feedback loops

Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein concentrations or gene expression levels are related to the presence of at least one negative feedback loop in the regulatory network. Here we study the dynamics of a very general class of negative feedback loops. Our main result is that in these systems the sequence of maxima and minima of the concentrations is uniquely determined by the topology of the loop and the activating/repressing nature of the interaction between pairs of variables. This allows us to devise an algorithm to reconstruct the topology of oscillating negative feedback loops from their time series; this method applies even when some variables are missing from the data set, or if the time series shows transients, like damped oscillations. We illustrate the relevance and the limits of validity of our method with three examples: p53-Mdm2 oscillations, circadian gene expression in cyanobacteria, and cyclic binding of cofactors at the estrogen-sensitive pS2 promoter.

q-bio.MN↗

arXiv2006

Absorbing processes in Richardson diffusion: analytical results

We consider the recently addressed problem of a passive particle (a predator), being the center of a ``sphere of interception'' of radius $R$ and able to absorb other passive particles (the preys) entering into the sphere. Assuming that all the particles are advected by a turbulent flow and that, in particular, the Richardson equation properly describes the relative dispersion, we calculate an analytical expression for the flux into the sphere as a function of time, assuming an initial constant density of preys outside the sphere. In the same framework, we show that the distribution of times of first passage into the sphere has a $t^{-5/2}$ power law tail, seen in contrast to the $t^{-3/2}$ appearing in standard 3D diffusion. We also discuss the correction due to the integral length scale on the results in the stationary case.

nlin.CD↗

arXiv2005

Properties making a chaotic system a good Pseudo Random Number Generator

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generators are performed.

nlin.CD↗

arXiv2005

Boltzmann entropy and chaos in a large assembly of weakly interacting systems

We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in thermodynamic systems. We study the growth with time of the Boltzmann entropy, S_B, in this system as a function of the coarse graining resolution. We show that a characteristic scale emerges, and that the behavior of S_B vs t, at variance with the Gibbs entropy, does not depend on the coarse graining resolution, as far as it is finer than this scale. The interaction among particles is crucial to achieve this result, while the rate of entropy growth depends essentially on the single-particle chaotic dynamics (for t not too small). It is possible to interpret the basic features of the dynamics in terms of a suitable Markov approximation.

nlin.CD↗

arXiv2004

A Stochastic Model for the Species Abundance Problem in an Ecological Community

We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical expression for the marginalized stationary distribution. Our solution is found in excellent agreement with numerical simulations and compares rather well with observational data from tropical forests.

q-bio.PE↗