Metric characterization of cluster dynamics on the Sierpinski gasket

We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring on cellular automata defined on an arbitrary structure. As a prototype for such systems we focus on the Ising model on a finite Sierpsinski Gasket, which is known to possess a complex thermodynamic behavior. Our algorithm requires the projection of evolving configurations into an appropriate partition space, where an information-based metrics (Rohlin distance) can be naturally defined and worked out in order to detect the changing and the stable components of clusters. The analysis highlights the existence of different temperature regimes according to the size and the rate of change of clusters. Such regimes are, in turn, related to the correlation length and the emerging "critical" fluctuations, in agreement with previous thermodynamic analysis, hence providing a non-trivial geometric description of the peculiar critical-like behavior exhibited by the system. Moreover, at high temperatures, we highlight the existence of different time scales controlling the evolution towards chaos.Comment: 20 pages, 8 figure

Spin coupling around a carbon atom vacancy in graphene

We investigate the details of the electronic structure in the neighborhoods of a carbon atom vacancy in graphene by employing magnetization-constrained density-functional theory on periodic slabs, and spin-exact, multi-reference, second-order perturbation theory on a finite cluster. The picture that emerges is that of two local magnetic moments (one \pi-like and one \sigma-like) decoupled from the \pi- band and coupled to each other. We find that the ground state is a triplet with a planar equilibrium geometry where an apical C atom opposes a pentagonal ring. This state lies ~0.2 eV lower in energy than the open-shell singlet with one spin flipped, which is a bistable system with two equivalent equilibrium lattice configurations (for the apical C atom above or below the lattice plane) and a barrier ~0.1 eV high separating them. Accordingly, a bare carbon-atom vacancy is predicted to be a spin-one paramagnetic species, but spin-half paramagnetism can be accommodated if binding to foreign species, ripples, coupling to a substrate, or doping are taken into account

Metric Features of a Dipolar Model

The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon entropy, Hamming and Rohlin distances. Previous results based on the two peaks shape of the specific heat, suggested the existence of two possible transitions. By the analysis of the Shannon entropy we are able to prove that the first one is a true phase transition corresponding to a particular melting process of oriented domains, where colored noise is present almost independently of true fractality. The second one is not a real transition and it may be ascribed to a smooth balancing between two geometrical effects: a progressive fragmentation of the big clusters (possibly creating fractals), and the slow onset of a small clusters chaotic phase. Comparison with the nearest neighbor Ising ferromagnetic system points out a substantial difference in the cluster geometrical properties of the two models and in their critical behavior.Comment: 20 pages, 15 figures, submitted to JPhys

Microscopic energy flows in disordered Ising spin systems

An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier dicretized picture. Then, we work out a linearized "mean-field approximation", where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure

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.Comment: 8 pages, 7 figure

Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient

In this paper we present and discuss results of Monte Carlo numerical simulations of the two-dimensional Ising ferromagnet in contact with a heat bath that intrinsically has a thermal gradient. The extremes of the magnet are at temperatures $T_1<T_c<T_2$, where $T_c$ is the Onsager critical temperature. In this way one can observe a phase transition between an ordered phase ($TT_c$) by means of a single simulation. By starting the simulations with fully disordered initial configurations with magnetization $m\equiv 0$ corresponding to $T=\infty$, which are then suddenly annealed to a preset thermal gradient, we study the short-time critical dynamic behavior of the system. Also, by setting a small initial magnetization $m=m_0$, we study the critical initial increase of the order parameter. Furthermore, by starting the simulations from fully ordered configurations, which correspond to the ground state at T=0 and are subsequently quenched to a preset gradient, we study the critical relaxation dynamics of the system. Additionally, we perform stationary measurements ($t\rightarrow\infty$) that are discussed in terms of the standard finite-size scaling theory. We conclude that our numerical simulation results of the Ising magnet in a thermal gradient, which are rationalized in terms of both dynamic and standard scaling arguments, are fully consistent with well established results obtained under equilibrium conditions

Fluctuation-dissipation relationship in chaotic dynamics

We consider a general N-degree-of-freedom dissipative system which admits of chaotic behaviour. Based on a Fokker-Planck description associated with the dynamics we establish that the drift and the diffusion coefficients can be related through a set of stochastic parameters which characterize the steady state of the dynamical system in a way similar to fluctuation-dissipation relation in non-equilibrium statistical mechanics. The proposed relationship is verified by numerical experiments on a driven double well system.Comment: Revtex, 23 pages, 2 figure

A hungry need for knowledge on the black soldier fly digestive system

The interest towards the black soldier fly (BSF), Hermetia illucens, has grown impressively in the last few years, fostered by the legislative changes in the European landscape that have lifted the ban regarding the use of BSF larvae as feedstuff. In addition, bioconversion mediated by the larvae of the BSF is viewed as one of the most promising technologies for organic waste processing and valorisation. Finally, new, alternative applications to exploit various larval products such as lipids, chitin, antimicrobial peptides, and frass are being explored. However, this positive trend, confirmed by the increasing number of companies that deal with BSF mass rearing and processing, is in sharp contrast with the limited information on the biology of this insect, in particular on aspects related to its digestive features. This lack of knowledge needs to be carefully considered and filled in coming years, as a deep characterisation of the morphology, physiology, transcriptomics, and proteomics of the digestive system of the insect, as well a fine dissection of related aspects as gut microbiota and pathogens, is a prerequisite to improve the amazing bioconversion capabilities of this dipteron. So far, the larval stages received the most attention in research, but there might still be a lot to win by focusing more on the adult stage. Further expanding the basic knowledge on both the larval and the adult gut could lead to unexpected findings and open new perspectives to produce value-added bioproducts