arXiv subjects

E. Agliari

Publications and source records attributed to E. Agliari.

13 recordsLinked to original sources

arXiv2012

Exact calculations of first-passage quantities on recursive networks

We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter to characterize transport in complex media. We explicitly perform calculations for different classes of recursive networks (finitely ramified fractals, scale-free (trans)fractals, non-fractals, mixtures between fractals and non-fractals, non-decimable hierarchical graphs) of arbitrary size. Our approach unifies and significantly extends the available results in the field.

cond-mat.stat-mech↗

arXiv2008

Autocatalytic reaction-diffusion processes in restricted geometries

We study the dynamics of a system made up of particles of two different species undergoing irreversible quadratic autocatalytic reactions: $A + B \to 2A$. We especially focus on the reaction velocity and on the average time at which the system achieves its inert state. By means of both analytical and numerical methods, we are also able to highlight the role of topology in the temporal evolution of the system.

cond-mat.stat-mech↗

arXiv2008

Dynamics of continuous-time quantum walks in restricted geometries

We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time. Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms. By means of analytical and numerical investigations, we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum walk performance. We further highlight the interplay between the quantum-walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long time averages.

quant-ph↗

arXiv2008

Fractal geometry of Ising magnetic patterns: signatures of criticality and diffusive dynamics

We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout the sites of the lattice, updating the relevant spins. Since the walker is biased towards borders between clusters, the border-sites are more likely to be updated with respect to a non-diffusive dynamics and therefore, we expect the spin configurations to be affected. In particular, by means of the box-counting technique, we measure the fractal dimension of magnetic patterns emerging on the lattice, as the temperature is varied. Interestingly, our results provide a geometric signature of the phase transition and they also highlight some non-trivial, quantitative differences between the behaviors pertaining to the diffusive and non-diffusive dynamics.

cond-mat.stat-mech↗

arXiv2008

Interacting Random Walkers and Non-Equilibrium Fluctuations

We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on the particle density. A non-equilibrium stationary flux can be induced by suitable boundary conditions, and we show indeed that it is mesoscopically described by a Fourier equation with a density dependent diffusivity. A simple mean-field description predicts a critical diffusivity if the hopping amplitude vanishes for a certain walker density. Actually, we evidence that, even if the density equals this pseudo-critical value, the system does not present any criticality but only a dynamical slowing down. This property is confirmed by the fact that, in spite of interaction, the particle distribution at equilibrium is simply described in terms of a product of Poissonians. For mesoscopic systems with a stationary flux, a very effect of interaction among particles consists in the amplification of fluctuations, which is especially relevant close to the pseudo-critical density. This agrees with analogous results obtained for Ising models, clarifying that larger fluctuations are induced by the dynamical slowing down and not by a genuine criticality. The consistency of this amplification effect with altered coloured noise in time series is also proved.

cond-mat.stat-mech↗

arXiv2008

Diffusive thermal dynamics for the spin-S Ising ferromagnet

We introduce an alternative thermal diffusive dynamics for the spin-S Ising ferromagnet realized by means of a random walker. The latter hops across the sites of the lattice and flips the relevant spins according to a probability depending on both the local magnetic arrangement and the temperature. The random walker, intended to model a diffusing excitation, interacts with the lattice so that it is biased towards those sites where it can achieve an energy gain. In order to adapt our algorithm to systems made up of arbitrary spins, some non trivial generalizations are implied. In particular, we will apply the new dynamics to two-dimensional spin-1/2 and spin-1 systems analyzing their relaxation and critical behavior. Some interesting differences with respect to canonical results are found; moreover, by comparing the outcomes from the examined cases, we will point out their main features, possibly extending the results to spin-S systems.

cond-mat.stat-mech↗

arXiv2008

Random walks interacting with evolving energy landscapes

We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying energetic environment is also made dynamic by properly coupling the walker with the spin lattice. In fact, while the walker hops across nearest-neighbor sites, it can flip the pertaining spins, realizing a diffusive dynamics for the Ising system. As a result, the walk is biased towards high energy regions, namely the boundaries between clusters. Besides, the coupling introduced involves, with respect the ordinary diffusion laws, interesting corrections depending on either the temperature and the spin magnitude. In particular, they provide a further signature of the phase-transition occurring on the magnetic lattice.

cond-mat.stat-mech↗

arXiv2008

Configurations and Observables in an Ising Model with Heat Flow

We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.

cond-mat.stat-mech↗

arXiv2008

Exact mean first-passage time on the T-graph

We consider a simple random walk on the T-fractal and we calculate the exact mean time $τ^g$ to first reach the central node $i_0$. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except $i_0$. By means of analytic techniques based on decimation procedures, we find the explicit expression for $τ^g$ as a function of the generation $g$ and of the volume $V$ of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.

physics.data-an↗

arXiv2007

Random walk on a population of random walkers

We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a stochastic process, where the transition probabilities are a stochastic process themselves. Upon mapping onto two simpler processes, the quantities characterizing $\mathcal{X}(t)$ can be calculated in the limit of long times and low walkers density. The results are compared with numerical simulations. Several different topologies for the substrate underlying diffusion are considered.

cond-mat.stat-mech↗

arXiv2007

Autocatalytic reaction on low-dimensional substrates

We discuss a model for the autocatalytic reaction $A+B\to 2A$ on substrates where the reactants perform a compact exploration of the space, i.e., on lattices whose spectral dimension $\tilde{d}$ is $< 2$. For finite systems, the total time $τ$ for the reaction to end scales according to two different regimes, for high and low concentrations of reactants. The functional dependence of $τ$ on the volume of the substrate and the concentration of reactants is discussed within a mean-field approximation. Possible applications are discussed.

cond-mat.stat-mech↗

arXiv2007

Universal features of information spreading efficiency on $d$-dimensional lattices

A model for information spreading in a population of $N$ mobile agents is extended to $d$-dimensional regular lattices. This model, already studied on two-dimensional lattices, also takes into account the degeneration of information as it passes from one agent to the other. Here, we find that the structure of the underlying lattice strongly affects the time $τ$ at which the whole population has been reached by information. By comparing numerical simulations with mean-field calculations, we show that dimension $d=2$ is marginal for this problem and mean-field calculations become exact for $d > 2$. Nevertheless, the striking nonmonotonic behavior exhibited by the final degree of information with respect to $N$ and the lattice size $L$ appears to be geometry independent.

cond-mat.stat-mech↗

arXiv2006

Efficiency of Information Spreading in a population of diffusing agents

We introduce a model for information spreading among a population of N agents diffusing on a square LxL lattice, starting from an informed agent (Source). Information passing from informed to unaware agents occurs whenever the relative distance is < 1. Numerical simulations show that the time required for the information to reach all agents scales as N^{-alpha}L^{beta}, where alpha and beta are noninteger. A decay factor z takes into account the degeneration of information as it passes from one agent to another; the final average degree of information of the population, I_{av}(z), is thus history-dependent. We find that the behavior of I_{av}(z) is non-monotonic with respect to N and L and displays a set of minima. Part of the results are recovered with analytical approximations.

cond-mat.stat-mech↗