arXiv subjects

Andrea Giansanti

Publications and source records attributed to Andrea Giansanti.

27 records · Page 2Linked to original sources

arXiv2005

Dynamics and thermodynamics of rotators interacting with both long and short range couplings

The effect of nearest-neighbor coupling on the thermodynamic and dynamical properties of the ferromagnetic Hamiltonian Mean Field model (HMF) is studied. For a range of antiferromagnetic nearest-neighbor coupling, a canonical first order transition is observed, and the canonical and microcanonical ensembles are non-equivalent. In studying the relaxation time of non-equilibrium states it is found that as in the HMF model, a class of non-magnetic states is quasi-stationary, with an algebraic divergence of their lifetime with the number of degrees of freedom $N$. The lifetime of metastable states is found to increase exponentially with $N$ as expected.

cond-mat.stat-mech↗

arXiv2004

Co-expression of statistically over-represented peptides in proteomes: a key to phylogeny ?

It is proposed that the co-expression of statistically significant motifs among the sequences of a proteome is a phylogenetic trait. From the co-expression matrix of such motifs in a group of prokaryotic proteomes a suitable definition of a phylogenetic distance is introduced and the corresponding distance matrix between proteomes is constructed. From the distance matrix a phylogenetic tree is inferred, following a standard procedure. It compares well with a reference tree deduced from a distance matrix obtained from the alignment of ribosomal RNA sequences. Our results are consistent with the hypothesis that biological evolution manifests itself with a modulation of basic correlations between shared peptides of short length, present in protein sequences. Moreover, the simple procedure we propose reconfirms that it is possible, sampling entire proteomes, to average the effects of lateral gene transfer and infer reasonable phylogenies.

q-bio.MN↗

arXiv2001

Metastable states in a class of long-range Hamiltonian systems

We numerically show that metastable states, similar to the Quasi Stationary States found in the so called Hamiltonian Mean Field Model, are also present in a generalized model in which $N$ classical spins (rotators) interact through ferromagnetic couplings decaying as $r^{-α}$, where $r$ is their distance over a regular lattice. Scaling laws with $N$ are briefly discussed.

cond-mat.stat-mech↗

arXiv2000

Universal behavior in the static and dynamic properties of the $α$-XY model

The $α$-XY model generalizes, through the introduction of a power-law decaying potential, a well studied mean-field hamiltonian model with attractive long-range interactions. In the $α$-model, the interaction between classical rotators on a lattice is gauged by the exponent $α$ in the couplings decaying as $r^α$, where $r$ are distances between sites. We review and comment here a few recent results on the static and dynamic properties of the $α$-model. We discuss the appropriate $α$ dependent rescalings that map the canonical thermodynamics of the $α$-model into that of the mean field model. We also show that the chaotic properties of the model, studied as a function of $α$ display an universal behaviour.

cond-mat.stat-mech↗

arXiv2000

Long-range interacting classical systems: universality in mixing weakening

Through molecular dynamics, we study the $d=2,3$ classical model of $N$ coupled rotators (inertial XY model) assuming a coupling constant which decays with distance as $r_{ij}^{-α}$ ($α\ge 0$). The total energy $ $ is asymptotically $\propto N {\tilde N}$ with ${\tilde N} \equiv [N^{1-α/d}-(α/d)]/[1-α/d]$, hence the model is thermodynamically extensive if $α/d>1$ and nonextensive otherwise. We numerically show that, for energies above some threshold, the (appropriately scaled) maximum Lyapunov exponent is $\propto N^{-κ}$ where $κ$ is an {\it universal} (one and the same for $d=1,2$ and 3, and all energies) function of $α/d$, which monotonically decreases from 1/3 to zero when $α/d$ increases from 0 to 1, and identically vanishes above 1. These features are consistent with the nonextensive statistical mechanics scenario, where thermodynamic extensivity is associated with {\it exponential} mixing in phase space, whereas {\it weaker} (possibly {\it power-law} in the present case) mixing emerges at the $N \to \infty$ limit whenever nonextensivity is observed.

cond-mat.stat-mech↗

arXiv2000

Canonical solution of a system of long-range interacting rotators on a lattice

The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a rescaling function that allows to reduce the model, for any d-dimensional lattice and for any alpha<d, to the mean field (alpha=0) model.

cond-mat.stat-mech↗

arXiv1998

Percolation and lack of self-averaging in a frustrated evolutionary model

We present a stochastic evolutionary model obtained through a perturbation of Kauffman's maximally rugged model, which is recovered as a special case. Our main results are: (i) existence of a percolation-like phase transition in the finite phase space case; (ii) existence of non self-averaging effects in the thermodynamic limit. Lack of self-averaging emerges from a fragmentation of the space of all possible evolutions, analogous to that of a geometrically broken object. Thus the model turns out to be exactly solvable in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv1998

Critical percolation and lack of self-averaging in disordered models

Lack of self-averaging originates in many disordered models from a fragmentation of the phase space where the sizes of the fragments remain sample-dependent in the thermodynamic limit. On the basis of new results in percolation theory, we give here an argument in favour of the conjecture that critical two dimensional percolation on the square lattice lacks of self-averaging.

cond-mat.stat-mech↗

arXiv1998

First experimental tests of the Peyrard-Bishop model applied to the melting of very short DNAs

The melting curves of short heterogeneous DNA chains in solution are calculated on the basis of statistical thermodynamics and compared to experiments. The computation of the partition function is based on the Peyrard-Bishop hamiltonian, which has already been adopted in the theoretical description of the melting of long DNA chains. In the case of short chains it is necessary to consider not only the breaking of the hydrogen bonds between single base pairs, but also the complete dissociation of the two strands forming the double helix.

physics.bio-ph↗