arXiv subjects

Duccio Fanelli

Publications and source records attributed to Duccio Fanelli.

At least 127 records · Page 7Linked to original sources

arXiv2011

Non-Gaussian fluctuations in stochastic models with absorbing barriers

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for {\it all times} and arbitrarily {\it close} to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.

cond-mat.stat-mech↗

arXiv2011

Efficiency of cyclic devices working with non-Boltzmannian fluids: challenging the second principle of thermodynamics

According to classical Boltzmannian thermodynamics, the efficiency of a cyclic machine is strictly lower than one. Such a result is a straightforward consequence of the second principle of thermodynamics. Recent advances in the study of the thermodynamics of long-range interacting system report however on a rather intricate zoology of peculiar behaviors, which are occasionally in contrast with customarily accepted scenarios, dueling with intuition and common sense. In this paper, a thermodynamical cycle is assembled for an ideal device working with non-Boltzmaniann long-range fluid and operating in contact with two thermal reservoirs. The system is analytically shown to violate the second principle of thermodynamics, a phenomenon that ultimately relates to the existence of regions with negative kinetic specific heat, in the canonical ensemble for the system under scrutiny. We argue that the validity of the second principle of thermodynamics can be possibly restored, by revisiting the definition of canonical ensemble, as well as the Fourier law of heat transport, and consequently relaxing the constraint on the maximal efficiency as imposed by the Carnot theorem.

cond-mat.stat-mech↗

arXiv2010

Deterministic and stochastic aspects of VEGF-A production and the cooperative behavior of tumoral cell colony

A model is proposed to study the process of hypoxia-induced angiogenesis in cancer cells. The model accounts for the role played by the vascular endothelial growth factor (VEGF)-A in regulating the oxygen intake. VEGF-A is dynamically controlled by the HIF-1alpha concentration. If not degraded, HIF-1alpha can bind to the subunit termed HIF-1beta and so experience translocation to the nucleus, to exert its proper transcriptional activity. The delicate balance between these opposing tendencies translates into the emergence of distinct macroscopic behaviors in terms of the associated molecular concentrations that we here trace back to normoxia, hypoxia and death regimes. These aspects are firstly analyzed with reference to the ideal mean-field scenario. Stochastic fluctuations are also briefly discussed and shown to seed a cooperative interaction among cellular units, competing for the same oxygen reservoir.

q-bio.CB↗

arXiv2010

Dynamical description of vesicle growth and shape change

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.

cond-mat.soft↗

arXiv2010

Out of equilibrium statistical ensemble inequivalence

We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the system behaviour, driving the emergence of ensemble inequivalence in the out-of-equilibrium phase, as signalled by a negative (microcanonical) magnetic susceptibility. The thermodynamic of the system is analytically discussed, building on a maximum entropy scheme justified from first principles. Simulations confirm the adequacy of the theoretical picture. Ensemble inequivalence is shown to rely on a peculiar phenomenon, different from the one observed in previous works. As a result, the existence of a convex intruder in the micro-canonical energy is found to be a necessary but not sufficient condition for inequivalence to be (macroscopically) observed. Negative temperature states are also found to occur. These intriguing phenomena reflect the non-Boltzmanian nature of the scrutinized problem and, as such, bear traits of universality that embraces equilibrium as well out-of-equilibrium regimes.

cond-mat.stat-mech↗

arXiv2010

Existence of Quasi-stationary states at the Long Range threshold

In this paper the lifetime of quasi-stationary states (QSS) in the $α-$HMF model are investigated at the long range threshold ($α=1$). It is found that QSS exist and have a diverging lifetime $τ(N)$ with system size which scales as $\mbox{\ensuremathτ(N)\ensuremath{\sim}}\log N$, which contrast to the exhibited power law for $α<1$ and the observed finite lifetime for $α>1$. Another feature of the long range nature of the system beyond the threshold ($α>1$) namely a phase transition is displayed for $α=1.5$. The definition of a long range system is as well discussed.

cond-mat.stat-mech↗

arXiv2010

Experimental perspectives for systems based on long-range interactions

The possibility of observing phenomena peculiar to long-range interactions, and more specifically in the so-called Quasi-Stationary State (QSS) regime is investigated within the framework of two devices, namely the Free-Electron Laser (FEL) and the Collective Atomic Recoil Laser (CARL). The QSS dynamics has been mostly studied using the Hamiltonian Mean-Field (HMF) toy model, demonstrating in particular the presence of first versus second order phase transitions from magnetized to unmagnetized regimes in the case of HMF. Here, we give evidence of the strong connections between the HMF model and the dynamics of the two mentioned devices, and we discuss the perspectives to observe some specific QSS features experimentally. In particular, a dynamical analog of the phase transition is present in the FEL and in the CARL in its conservative regime. Regarding the dissipative CARL, a formal link is established with the HMF model. For both FEL and CARL, calculations are performed with reference to existing experimental devices, namely the FERMI@Elettra FEL under construction at Sincrotrone Trieste (Italy) and the CARL system at LENS in Florence (Italy).

nlin.CD↗

arXiv2010

Diffusion in a crowded environment

We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the depletion of resources on which the particles rely. The macroscopic equations are studied both analytically and numerically, and are shown to yield anomalous diffusion which does not follow a power law with time, as is frequently assumed when fitting data for such phenomena. These anomalies are here understood within a consistent dynamical picture which applies to a wide range of physical and biological systems, underlining the need for clearly defined mechanisms which are systematically analyzed to give definite predictions.

cond-mat.stat-mech↗

arXiv2010

Stationary states and fractional dynamics in systems with long range interactions

Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $α-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the $α-$HMF model for which the spatial organization satisfies a fractional equation. At variance, the microscopic dynamics turns out to be regular and explicitly known. As a consequence, dynamical regularity is achieved at the price of strong spatial complexity, namely a microscopic inhomogeneity which locally displays scale invariance.

cond-mat.stat-mech↗

arXiv2010

Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction

The out-of-equilibrium mean-field dynamics of a model for wave-particle interaction is investigated. Such a model can be regarded as a general formulation for all those applications where the complex interplay between particles and fields is known to be central, e.g., electrostatic instabilities in plasma physics, particle acceleration and free-electron lasers (FELs). The latter case is here assumed as a paradigmatic example. A transition separating different macroscopic regimes is numerically identified and interpreted by making use of the so-called violent relaxation theory. In the context of free-electron lasers, such a theory is showed to be effective in predicting the saturated regime for energies below the transition. The transition is explained as a dynamical switch between two metastable regimes, and is related to the properties of a stationary point of an entropic functional.

physics.plasm-ph↗

arXiv2010

Universal fluctuations in tropospheric radar measurements

Radar data collected at an experimental facility arranged on purpose suggest that the footprint of atmospheric turbulence might be encoded in the radar signal statistics. Radar data probability distributions are calculated and nicely fitted by a one parameter family of generalized Gumbel (GG) distributions, G(a). A relation between the wind strength and the measured shape parameter "a" is obtained. Strong wind fluctuations return pronounced asymmetric leptokurtic profiles, while Gaussian profiles are eventually recovered as the wind fluctuations decrease. Besides stressing the crucial impact of air turbulence for radar applications, we also confirm the adequacy of G(a) statistics for highly correlated complex systems.

cond-mat.stat-mech↗

arXiv2010

Stochastic Turing patterns in the Brusselator model

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross diffusive terms, often neglected in the heuristic derivation of reaction diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

cond-mat.stat-mech↗

arXiv2010

A spatial model of autocatalytic reactions

Biological cells with all of their surface structure and complex interior stripped away are essentially vesicles - membranes composed of lipid bilayers which form closed sacs. Vesicles are thought to be relevant as models of primitive protocells, and they could have provided the ideal environment for pre-biotic reactions to occur. In this paper, we investigate the stochastic dynamics of a set of autocatalytic reactions, within a spatially bounded domain, so as to mimic a primordial cell. The discreteness of the constituents of the autocatalytic reactions gives rise to large sustained oscillations, even when the number of constituents is quite large. These oscillations are spatio-temporal in nature, unlike those found in previous studies, which consisted only of temporal oscillations. We speculate that these oscillations may have a role in seeding membrane instabilities which lead to vesicle division. In this way synchronization could be achieved between protocell growth and the reproduction rate of the constituents (the protogenetic material) in simple protocells.

cond-mat.stat-mech↗

arXiv2009

Out of Equilibrium Solutions in the $XY$-Hamiltonian Mean Field model

Out of equilibrium magnetised solutions of the $XY$-Hamiltonian Mean Field ($XY$-HMF) model are build using an ensemble of integrable uncoupled pendula. Using these solutions we display an out-of equilibrium phase transition using a specific reduced set of the magnetised solutions.

cond-mat.stat-mech↗

arXiv2009

Analytical results on the magnetization of the Hamiltonian Mean Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high and low energy limits are investigated and the analytical predictions are compared with direct $N$-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.

nlin.CD↗

arXiv2009

Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with $N$ nodes and $N^γ$ edges, with $1 < γ\leq 2$. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of $γ$ at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter $γ$, using two different approaches: a replica-based finite $N$ expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics.

cond-mat.stat-mech↗

arXiv2009

Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems

We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian Mean Field model as a case study. We show that an abundance of regular trajectories, associated with invariant tori of the single-particle dynamics, exists. The presence of such tori provides a dynamical interpretation of the emergence of long-lasting out-of-equilibrium regimes observed generically in long-range systems. This is alternative to a previous statistical mechanics approach to such phenomena which was based on a maximum entropy principle. Previously detected out-of-equilibrium phase transitions are also reinterpreted within this framework.

cond-mat.stat-mech↗

arXiv2008

Collective observables in repeated experiments of population dynamics

We here discuss the outcome of an hypothetic experiments of populations dynamics, where a set of independent realizations is made available. The importance of ensemble average is clarified with reference to the registered time evolution of key collective indicators. The problem is here tackled for the logistic case study. Theoretical prediction are compared to numerical simulations.

cond-mat.stat-mech↗