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Marco Pettini

Publications and source records attributed to Marco Pettini.

At least 37 records · Page 2Linked to original sources
arXiv2017

Detection of long-range electrostatic interactions between charged molecules by means of Fluorescence Correlation Spectroscopy

The present paper deals with an experimental feasibility study concerning the detection of long- range intermolecular interactions through molecular diffusion behavior in solution. This follows previous analyses, theoretical and numerical, where it was found that inter-biomolecular long-range force fields of electrodynamic origin could be detected through deviations from Brownian diffusion. The suggested experimental technique was Fluorescence Correlation Spectroscopy (FCS). By con- sidering two oppositely charged molecular species in watery solution, that is, Lysozyme protein and a fluorescent dye molecule (Alexa488), the diffusion coefficient of the dye has been measured by means of the FCS technique at different values of the concentration of Lysozyme molecules, that is, at different average distances between the oppositely charged molecules. For the model consid- ered long-range interactions are built-in as electrostatic forces, the action radius of which can be varied by changing the ionic strength of the solution. The experimental outcomes clearly prove the detectability of long-range intermolecular interactions by means of the FCS technique. Molecular Dynamics simulations provide a clear and unambiguous interpretation of the experimental results.

physics.bio-ph↗
arXiv2016

On the apparent failure of the topological theory of phase transitions

The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It has been recently argued that the $2D$ lattice $ϕ^4$-model provides a counterexample that falsifies this theory. It is here shown that this is not the case: the phase transition of this model stems from an asymptotic ($N\to\infty$) change of topology of the energy level sets, in spite of the absence of critical points of the potential in correspondence of the transition energy.

cond-mat.stat-mech↗
arXiv2016

Random walk of passive tracers among randomly moving obstacles

Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. Method: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle in a crowded environment made of randomly moving and interacting obstacles. Results: The relevant physical quantity which is worked out is the diffusion cofficient of the passive tracer which is computed as a function of the average inter-obstacles distance. Coclusions: The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down. Hence, if such a slowing down could compromise the efficiency of the task to be performed by the test molecule, some accelerating factor would be required. Intermolecular electrodynamic forces are good candidates as accelerating factors because they can act at a long distance in a medium like the cytosol despite its ionic strength.

physics.bio-ph↗
arXiv2016

Persistent Homology analysis of Phase Transitions

Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called XY-mean field model and by the phi^4 lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a-priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.

cond-mat.stat-mech↗
arXiv2015

A geometric entropy detecting the Erdös-Rényi phase transition

We propose a method to associate a differentiable Riemannian manifold to a generic many degrees of freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical Statistical Mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the `giant component' according to the Erdös-Rényi theorem.

math-ph↗
arXiv2014

On the role of electrodynamic interactions in long-distance biomolecular recognition

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to calculate the frequencies of the normal modes, which are then used to estimate the interaction potential. The main results thus found are in perfect agreement with several results obtained from quantum computations. Moreover, when applied in a biophysical context, our findings shed new light on Frohlich's theory of selective long-range interactions between biomolecules. In particular, at variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.

physics.bio-ph↗
arXiv2014

Quantifying Networks Complexity from Information Geometry Viewpoint

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension.

math-ph↗
arXiv2014

Experimental detection of long-distance interactions between biomolecules through their diffusion behavior: Numerical study

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coefficient is always lowered by the considered interparticle interactions, irrespective of their attractive or repulsive character. This fact is also confirmed by a simple model to compute the correction to the Brownian diffusion coefficient due to the interactions among the particles. These interactions are also responsible for the onset of dynamical chaos and an associated chaotic diffusion which still follows an Einstein-Fick like law for the mean square displacement as a function of time. Transitional phenomena are observed for Coulomb-electrostatic (repulsive) and dipole-electrodynamic (attractive) interactions considered both separately and in competition. The outcomes reported in this paper clearly indicate a feasible experimental method to probe the activation of resonant electrodynamic interactions among biomolecules.

physics.bio-ph↗
arXiv2014

Beam-Plasma Instability and Fast Particles: the Lynden-Bell Approach

The beam-plasma instability, i.e. the response of the plasma bulk to the injection of supra thermal charged-particle beams, results to be appropriately characterized by a long-range interaction system. This physical system hosts a number of very interesting phenomena and, in particular, the emergence of long-lived quasi-stationary states. We characterize the self-consistent distribution functions of such out-of-equilibrium states by means of the Lynden-Bell's theory. The prediction of this theory, based on the statistical mechanics of the Vlasov equation, are checked against the outcomes of numerical simulations of the discrete system. Moreover, a phenomenological study of the effective resonance band for the system response is also addressed. A threshold value has been found in the initial spread of beam-particle momenta. This threshold allows to discriminate between the resonant and non-resonant regimes. The analysis of the thermalization of a few percents of the beam population characterized by large initial momenta (with respect to the main part of the beam itself) is also performed and it confirms and deepens the understanding of the physical meaning of the mentioned threshold.

physics.plasm-ph↗
arXiv2012

Long-range resonant interactions in biological systems

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to work out the frequencies of the normal modes, which are then used to estimate the interaction potential. The main results thus found are in perfect agreement with several outcomes obtained from quantum computations. Moreover, when applied to a biophysical context, our findings shed new light on Fröhlich's theory of selective long-range interactions between biomolecules. In particular, at variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.

physics.bio-ph↗
arXiv2012

Experimental assessment of the contribution of electrodynamic interactions to long-distance recruitment of biomolecular partners: Theoretical basis

Highly specific spatiotemporal interactions between cognate molecular partners essentially sustain all biochemical transactions in the living matter. That such an exquisite level of accuracy may result from encountering forces solely driven by thermal diffusive processes is unlikely. Here we propose a yet unexplored strategy to experimentally tackle the long-standing question of a possibly active recruitment at a distance of cognate partners of biomolecular reactions via the action of resonant electrodynamic interactions. We considered two simplified models for a preliminary feasibility investigation of the devised methodology. By taking advantage of advanced experimental techniques nowadays available, we propose to measure the characteristic encounter time scales of dually-interacting biopartners and to compare them with theoretical predictions worked out both in the presence or absence of putative long-range electromagnetic forces.

physics.bio-ph↗
arXiv2007

Control of test particle transport in a turbulent electrostatic model of the Scrape Off Layer

The ${\bm E}\times{\bm B}$ drift motion of charged test particle dynamics in the Scrape Off Layer (SOL)is analyzed to investigate a transport control strategy based on Hamiltonian dynamics. We model SOL turbulence using a 2D non-linear fluid code based on interchange instability which was found to exhibit intermittent dynamics of the particle flux. The effect of a small and appropriate modification of the turbulent electric potential is studied with respect to the chaotic diffusion of test particle dynamics. Over a significant range in the magnitude of the turbulent electrostatic field, a three-fold reduction of the test particle diffusion coefficient is achieved.

physics.plasm-ph↗
arXiv2006

Hamiltonian dynamics of homopolymer chain models

The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of observables numerically computed along dynamical trajectories are found to reproduce results given by the statistical mechanics of homopolymer models. The dynamical treatment, however, indicates a nontrivial transition between regimes of slow and fast phase space mixing. Such a transition is inaccessible to a statistical mechanical treatment and reflects a bimodality in the relaxation of time averages to corresponding ensemble averages. It is also found that a change in the energy dependence of the largest Lyapunov exponent indicates the theta-transition between filamentary and globular polymer configurations, clearly detecting the transition even for a finite number of particles.

cond-mat.stat-mech↗
arXiv2006

Topology and Phase Transitions I. Preliminary Results

In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase transitions: we prove that the topology of certain submanifolds of configuration space must necessarily change at the phase transition point. The theorem applies to smooth, finite-range and confining potentials V bounded below, describing systems confined in finite regions of space with continuously varying coordinates. The relevant configuration space submanifolds are both the level sets {Σ_v := V_N^{-1} (v)}_{v \in R} of the potential function V_N and the configuration space submanifolds enclosed by the Σ_{v} defined by {M_v := V_N^{-1} ((-\infty,v])}_{v \in R}, which are labeled by the potential energy value v, and where N is the number of degrees of freedom. The proof of the theorem proceeds by showing that, under the assumption of diffeomorphicity of the equipotential hypersurfaces {Σ_v}_{v \in R}, as well as of the ${M_v}_{v \in R}, in an arbitrary interval of values for \vb=v/N, the Helmoltz free energy is uniformly convergent in N to its thermodynamic limit, at least within the class of twice differentiable functions, in the corresponding interval of temperature. This preliminary theorem is essential to prove another theorem - in paper II - which makes a stronger statement about the relevance of topology for phase transitions.

math-ph↗
arXiv2005

Topology and Phase Transitions: Theorem on a necessary relation

An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601, (2004). Moreover, in order to prove the relevance of topology for phase transition phenomena in a broad domain of physically interesting cases, we have proved another theorem which is reported in math-ph/0505058 and which is crucially based on the result of the paper archived in math-ph/0505057.

math-ph↗
arXiv2004

Weak and strong chaos in FPU models and beyond

We briefly review some of the most relevant results that our group obtained in the past, while investigating the dynamics of the Fermi-Pasta-Ulam (FPU) models. A first result is the numerical evidence of the existence of two different kinds of transitions in the dynamics of the FPU models: i) a Stochasticity Threshold (ST), characterized by a value of the energy per degree of freedom below which the overwhelming majority of the phase space trajectories are regular (vanishing Lyapunov exponents). It tends to vanish as the number N of degrees of freedom is increased. ii) a Strong Stochasticity Threshold (SST), characterized by a value of the energy per degree of freedom at which a crossover appears between two different power laws of the energy dependence of the largest Lyapunov exponent, which phenomenologically corresponds to the transition between weakly and strongly chaotic regimes. It is stable with N. A second result is the development of a Riemannian geometric theory to explain the origin of Hamiltonian chaos. The starting of this theory has been motivated by the inadequacy of the approach based on homoclinic intersections to explain the origin of chaos in systems of arbitrarily large N, or arbitrarily far from quasi-integrability, or displaying a transition between weak and strong chaos. Finally, a third result stems from the search for the transition between weak and strong chaos in systems other than FPU. Actually, we found that a very sharp SST appears as the dynamical counterpart of a thermodynamic phase transition, which in turn has led, in the light of the Riemannian theory of chaos, to the development of a topological theory of phase transitions.

cond-mat.stat-mech↗