Stefano Ruffo | Università degli Studi di Firenze (University of Florence) (original) (raw)

Papers by Stefano Ruffo

Physica A-statistical Mechanics and Its Applications, 1997

Computer Programs in Biomedicine, 1985

Physics Letters A, 1992

Using the concept of the Boolean derivative we study damage spreading for one dimensional element... more Using the concept of the Boolean derivative we study damage spreading for one dimensional elementary cellular automata and define their maximal Lyapunov exponent. A random matrix approximation describes quite well the behavior of ``chaotic'' rules and predicts a directed percolation-type phase transition. After the introduction of a small noise elementary cellular automata reveal the same type of transition.

European Physical Journal B, 2000

It is well known that long-range interactions pose serious problems for the formulation of statis... more It is well known that long-range interactions pose serious problems for the formulation of statistical mechanics. We show in this paper that ensemble equivalence is violated in a simple mean-field model of N fully coupled classical rotators with repulsive interaction (antiferromagnetic XY model). While in the canonical ensemble the rotators are randomly dispersed over all angles, in the microcanonical ensemble a bi-cluster of rotators separated by angle pi\pipi, forms in the low energy limit. We attribute this behavior to the extreme degeneracy of the ground state: only one harmonic mode is present, together with N-1 zero modes. We obtain empirically an analytical formula for the probability density function for the angle made by the rotator, which compares extremely well with numerical data and should become exact in the zero energy limit. At low energy, in the presence of the bi-cluster, an extensive amount of energy is located in the single harmonic mode, with the result that the energy temperature relation is modified. Although still linear, T=alphaUT = \alpha UT=alphaU, it has the slope alphaapprox1.3\alpha \approx 1.3alphaapprox1.3, instead of the canonical value alpha=2\alpha =2alpha=2.

Physica D-nonlinear Phenomena, 1998

Physical Review Letters, 1999

Mean-field models, while they can be cast into an extensive thermodynamic formalism, are inherent... more Mean-field models, while they can be cast into an extensive thermodynamic formalism, are inherently non additive. This is the basic feature which leads to ensemble inequivalence in these models. In this paper we study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The microcanonical solution is obtained both by direct state counting and by the application of large deviation theory. The canonical phase diagram has first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These two features are discussed in a general context and the appropriate Maxwell constructions are introduced. Some preliminary extensions of these results to weakly decaying nonintegrable interactions are presented.

Journal of Statistical Physics, 2005

We discuss a method to solve models with long-range interactions in the microcanonical and canoni... more We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.

Physica A-statistical Mechanics and Its Applications, 2004

Physical Review Letters, 1998

We study the largest Lyapunov exponent lambda\lambdalambda and the finite size effects of a system of N ful... more We study the largest Lyapunov exponent lambda\lambdalambda and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density UcU_cUc, lambda\lambdalambda shows a peak which persists for very large N-values (N=20000). We show, both numerically and analytically, that chaoticity is strongly related to kinetic energy fluctuations. In the limit of small energy, lambda\lambdalambda goes to zero with a N-independent power law: lambdasimsqrtU\lambda \sim \sqrt{U}lambdasimsqrtU. In the continuum limit the system is integrable in the whole high temperature phase. More precisely, the behavior lambdasimN−1/3\lambda \sim N^{-1/3}lambdasimN−1/3 is found numerically for U>UcU > U_cU>Uc and justified on the basis of a random matrix approximation.

Physical Review A, 1983

The Fermi-Pasta-Ulam model has been studied following the time evolution of the space Fourier spe... more The Fermi-Pasta-Ulam model has been studied following the time evolution of the space Fourier spectrum through the numerical integration of the equations of motion for a system of 128 non-linearly coupled oscillators. One-mode and multimode excitations have been ...

Journal of Statistical Physics, 1994

We perform a detailed numerical study of the transition to equipartition in the Fermi-Pasta-Ulam ... more We perform a detailed numerical study of the transition to equipartition in the Fermi-Pasta-Ulam quartic model and in a class of potentials of given symmetry using the normalized spectral entropy as a probe. We show that the typical time scale for the equipartition of energy among Fourier modes grows linearly with system size: this is the time scale associated with the smallest frequency present in the system. We obtain two different scaling behaviors, either with energy or with energy density, depending on the scaling of the initial condition with system size. These different scaling behaviors can be understood by a simple argument, based on the Chirikov overlap criterion. Some aspects of the universality of this result are investigated: symmetric potentials show a similar transition, regulated by the same time scale.

Physica D-nonlinear Phenomena, 1990

A coupled map lattice model is studied which presents transient and asymptotic chaotic states dep... more A coupled map lattice model is studied which presents transient and asymptotic chaotic states depending on the value of the control parameters. A first-order approximation detects the presence of asymptotic periodic attractors. The statistics of transient times as well as their dependence on lattice size are investigated.

Journal of Theoretical Biology, 1996

We have used an improved block-entropy measure in order to gain some further insights into the sh... more We have used an improved block-entropy measure in order to gain some further insights into the short-range correlations present in whole chromosomes of S. cerevisiae, viruses and organelles and very large genomic regions of E. coli. Although DNA sequences are largely inhomogeneous and word frequencies are unevenly distributed, the comparison of entire chromosomes and large genomic regions show a "bulk" composition homogeneity. This property suggests that biases in selection, directional mutational pressure and recombination processes act in homogenizing the base composition of the DNA molecules within a genome but their mode of action, relative impact and direction may vary in different organisms. The most interesting results appear to be the differences between the SW (C,G/A,T) and RY (A,G/C,T) two-letter alphabet entropies. Deviations from randomness in E. coli and S. cerevisiae sequences particularly concern SW dinucleotide frequencies and RY tetranucleotide frequencies.

Journal of Biological Physics, 1999

The real mechanisms of several biological processes involving DNA are not yet understood. We disc... more The real mechanisms of several biological processes involving DNA are not yet understood. We discuss here some aspects of the initiation of transcription, in particular the formation of the open complex and the activation mechanism associated to enhancer binding proteins. Transcription activation seems to be governed by underlying dynamical mechanisms related to several distortions of the double chain structure: a dynamical approach on a mesoscopic description level could then allow a deeper understanding of this complex process. Starting from the Peyrard Bishop (PB) model, that considers only the hydrogen bond stretching of each base pair, we describe here an extended DNA model, proposed in [1], that allows a rather good representation of the double helix geometry and of its structural features by the introduction of angular variables related to the twist angle. Using a generalized multiple scale expansion for the case of vectorial lattices derived elsewhere [2], we derive analytically small amplitude approximate solutions of the model which are movable and spatially localized: we present here the results of this calculation and show how the special shape of the solutions is in good agreement with what can be expected for coupled angular radial distortions in the real molecule.

Physical Review E, 1995

We study the dynamics of a fully coupled network of N classical rotators, which can also be viewe... more We study the dynamics of a fully coupled network of N classical rotators, which can also be viewed as a mean-field XY Heisenberg (HMF) model, in the attractive (ferromagnetic) and repulsive (antiferromagnetic) cases. The exact free energy and the spectral properties of a Vlasov-...

Physical Review Letters, 2001

We study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the c... more We study the global phase diagram of the infinite range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram is known to exhibit first order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying nonintegrable interactions.

Journal of Clinical Pharmacy and Therapeutics, 1984

The usefulness of a calculator programme that enables individualization of the dosage of Factor V... more The usefulness of a calculator programme that enables individualization of the dosage of Factor VIII, based on the concentration-time data measured after a test-dose, was assessed. The programme was tested in 12 haemophiliacs who required multiple-dose treatment with Factor VIII.Individual kinetic parameters were estimated in each patient from the plasma level data following the test-dose. Then, each patient received the multiple dose treatment with Factor VIII according to the dosage regimen suggested by the calculator programme.The time-curve of Factor VIII plasma levels at steady state was predicted by using the kinetic variables previously estimated. The plasma levels of Factor VIII were measured in all patients at steady state. As a result, good agreement between predicted and measured steady state concentrations was observed (r2= 0.9797; P < 0.001).The calculator programme tested in the present study appears to be a useful tool for individualizing the dosage regimen of Factor VIII in haemophiliacs.

After a brief comprehensive review of old and new results on the well known Fermi-Pasta-Ulam (FPU... more After a brief comprehensive review of old and new results on the well known Fermi-Pasta-Ulam (FPU) conservative system of NNN nonlinearly coupled oscillators, we present a compact linear mode representation of the Hamiltonian of the FPU system with quartic nonlinearity and periodic boundary conditions, with explicitly computed mode coupling coefficients. The core of the paper is the proof of the existence of one-mode and two-mode exact solutions, physically representing nonlinear standing and travelling waves of small wavelength whose explicit lattice representations are obtained, and which are valid also as NrightarrowinftyN \rightarrow \inftyNrightarrowinfty. Moreover, and more generally, we show the presence of multi-mode invariant submanifolds. Destabilization of these solutions by a parametric perturbation mechanism leads to the establishment of chaotic in time mode interaction channels, corresponding to the formation in phase space of bounded stochastic layers on submanifolds. The full mode-space stability problem of the N/2N/2N/2 zone-boundary mode is solved, showing that this mode becomes unstable through a mechanism of the modulational Benjamin-Feir type. In the thermodynamic limit the mode is always unstable but with instability growth rate linearly vanishing with energy density. The physical significance of these solutions and of their stability properties, with respect to the previously much more studied equipartition problem for long wavelength initial excitations, is briefly discussed.