arXiv subjects

Attilio L. Stella

Publications and source records attributed to Attilio L. Stella.

At least 37 records · Page 2Linked to original sources

arXiv2010

The entropic cost to tie a knot

We estimate by Monte Carlo simulations the configurational entropy of $N$-steps polygons in the cubic lattice with fixed knot type. By collecting a rich statistics of configurations with very large values of $N$ we are able to analyse the asymptotic behaviour of the partition function of the problem for different knot types. Our results confirm that, in the large $N$ limit, each prime knot is localized in a small region of the polygon, regardless of the possible presence of other knots. Each prime knot component may slide along the unknotted region contributing to the overall configurational entropy with a term proportional to $\ln N$. Furthermore, we discover that the mere existence of a knot requires a well defined entropic cost that scales exponentially with its minimal length. In the case of polygons with composite knots it turns out that the partition function can be simply factorized in terms that depend only on prime components with an additional combinatorial factor that takes into account the statistical property that by interchanging two identical prime knot components in the polygon the corresponding set of overall configuration remains unaltered. Finally, the above results allow to conjecture a sequence of inequalities for the connective constants of polygons whose topology varies within a given family of composite knot types.

cond-mat.stat-mech↗

arXiv2009

Anomalous scaling due to correlations: Limit theorems and self-similar processes

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.

cond-mat.stat-mech↗

arXiv2008

Scaling and efficiency determine the irreversible evolution of a market

In setting up a stochastic description of the time evolution of a financial index, the challenge consists in devising a model compatible with all stylized facts emerging from the analysis of financial time series and providing a reliable basis for simulating such series. Based on constraints imposed by market efficiency and on an inhomogeneous-time generalization of standard simple scaling, we propose an analytical model which accounts simultaneously for empirical results like the linear decorrelation of successive returns, the power law dependence on time of the volatility autocorrelation function, and the multiscaling associated to this dependence. In addition, our approach gives a justification and a quantitative assessment of the irreversible character of the index dynamics. This irreversibility enters as a key ingredient in a novel simulation strategy of index evolution which demonstrates the predictive potential of the model.

q-fin.ST↗

arXiv2008

Role of scaling in the statistical modeling of finance

Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return probability density function sampled from the historical series suggests a successful model. The resulting stochastic process is a heteroskedastic, non-Markovian martingale, which can be used to simulate index evolution on the basis of an auto-regressive strategy. Results are fully consistent with volatility clustering and with the multi-scaling properties of the return distribution. The idea of basing the process construction on scaling, and the construction itself, are closely inspired by the probabilistic renormalization group approach of statistical mechanics and by a recent formulation of the central limit theorem for sums of strongly correlated random variables.

q-fin.ST↗

arXiv2007

Self-reptation and slow topological time scale of knotted polymers

We investigate the Rouse dynamics of a flexible ring polymer with a prime knot. Within a Monte Carlo approach, we locate the knot, follow its diffusion, and observe the fluctuations of its length. We characterise a topological time scale, and show that it is related to a self-reptation of the knotted region. The associated dynamical exponent, $z_T=2.32\pm.1$, can be related to that of the equilibrium knot length distribution and determines the behaviour of several dynamical quantities.

cond-mat.stat-mech↗

arXiv2007

Central limit theorem for anomalous scaling due to correlations

We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling and is based on a correspondence with the Lévy-Gnedenko uncorrelated case. In particular, correlated anomalous diffusion is mapped onto Lévy diffusion. Under suitable assumptions, the nonstandard multiplicative structure used for constructing the characteristic function of the total sum allows us to determine correlations of partial sums exclusively on the basis of the global anomalous scaling.

cond-mat.stat-mech↗

arXiv2005

Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares

Introducing thresholds to analyze time series of emission from the Sun enables a new and simple definition of solar flare events, and their interoccurrence times. Rescaling time by the rate of events, the waiting and quiet time distributions both conform to scaling functions that are independent of the intensity threshold over a wide range. The scaling functions are well described by a two parameter function, with parameters that depend on the phase of the solar cycle. For flares identified according to the current, standard definition, similar behavior is found.

cond-mat.stat-mech↗

arXiv2005

Scaling of a collapsed polymer globule in 2D

Extensive Monte Carlo data analysis gives clear evidence that collapsed linear polymers in two dimensions fall in the universality class of athermal, dense self-avoiding walks, as conjectured by B.Duplantier [Phys.Rev.Lett. 71, 4274 (1993)]. However, the boundary of the globule has self affine roughness and does not determine the anticipated nonzero topological boundary contribution to entropic exponents. Scaling corrections are due to subleading contributions to the partition function corresponding to polymer configurations with one end located on the globule-solvent interface.

cond-mat.stat-mech↗

arXiv2002

A simple model of DNA denaturation and mutually avoiding walks statistics

Recently Garel, Monthus and Orland (Europhys. Lett. v 55, 132 (2001)) considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition.

cond-mat.stat-mech↗

arXiv2002

Roles of stiffness and excluded volume in DNA denaturation

The nature and the universal properties of DNA thermal denaturation are investigated by Monte Carlo simulations. For suitable lattice models we determine the exponent c describing the decay of the probability distribution of denaturated loops of length l, $P \sim l^{-c}$. If excluded volume effects are fully taken into account, c= 2.10(4) is consistent with a first order transition. The stiffness of the double stranded chain has the effect of sharpening the transition, if it is continuous, but not of changing its order and the value of the exponent c, which is also robust with respect to inclusion of specific base-pair sequence heterogeneities.

cond-mat.stat-mech↗

arXiv2001

Turbulent self-organized criticality

In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and global simple scaling regimes analogous to those holding for velocity structure functions in fluid turbulence. The correspondence involves identity of a basic scaling relation and of the form of relevant probability distributions. The sandpile provides a qualitative analog of many features of turbulent phenomena.

cond-mat.stat-mech↗

arXiv2001

Directed polymers with tilted columnar disorder and Burgers-like turbulence

The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey a multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario is analogous to that of structure functions in bifractal Burgers' turbulence. Some scaling properties are predicted from extreme value statistics. The multiscaling disappears for zero tilt.

cond-mat.stat-mech↗

arXiv2001

Peculiar scaling of self-avoiding walk contacts

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N going to infinity they are strictly finite in number but their radius of gyration Rc is power law distributed, ~ Rc^{-τ}, where τ>1 is a novel exponent characterizing universal behavior. A continuum of diverging lengths scales is associated to the Rc distribution. A possibly super-universal τ=2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.

cond-mat.stat-mech↗

arXiv2000

Zipping and collapse of diblock copolymers

Using exact enumeration methods and Monte Carlo simulations we study the phase diagram relative to the conformational transitions of a two dimensional diblock copolymer. The polymer is made of two homogeneous strands of monomers of different species which are joined to each other at one end. We find that depending on the values of the energy parameters in the model, there is either a first order collapse from a swollen to a compact phase of spiral type, or a continuous transition to an intermediate zipped phase followed by a first order collapse at lower temperatures. Critical exponents of the zipping transition are computed and their exact values are conjectured on the basis of a mapping onto percolation geometry, thanks to recent results on path-crossing probabilities.

cond-mat.stat-mech↗

arXiv2000

From waves to avalanches: two different mechanisms of sandpile dynamics

Time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld model, long range correlations determine a modification of the wave size distribution under coarse graining in time, and multifractal scaling for avalanches. In the Manna model, the distribution of avalanches coincides with that of waves, which are uncorrelated and obey finite size scaling, a result expected also for the d=3 Bak et al. model.

cond-mat.stat-mech↗

arXiv1999

Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events

An analysis of moments and spectra shows that, while the distribution of avalanche areas obeys finite size scaling, that of toppling numbers is universally characterized by a full, nonlinear multifractal spectrum. Rare, large avalanches dissipating at the border influence the statistics very sensibly. Only once they are excluded from the sample, the conditional toppling distribution for given area simplifies enough to show also a well defined, multifractal scaling. The resulting picture brings to light unsuspected, novel physics in the model.

cond-mat.stat-mech↗

arXiv1999

Sequence randomness and polymer collapse transitions

Contrary to expectations based on Harris' criterion, chain disorder with frustration can modify the universality class of scaling at the theta transition of heteropolymers. This is shown for a model with random two-body potentials in 2D on the basis of exact enumeration and accurate Monte Carlo results. When frustration grows beyond a certain finite threshold, the temperature below which disorder becomes relevant coincides with the theta one and scaling exponents definitely start deviating from those valid for homopolymers.

cond-mat.soft↗

arXiv1998

First order wetting of rough substrates and quantum unbinding

Replica and functional renormalization group methods show that, with short range substrate forces or in strong fluctuation regimes, wetting of a self-affine rough wall in 2D turns first-order as soon as the wall roughness exponent exceeds the anisotropy index of bulk interface fluctuations. Different thresholds apply with long range forces in mean field regimes. For bond-disordered bulk, fixed point stability suggests similar results, which ultimately rely on basic properties of quantum bound states with asymptotically power-law repulsive potentials.

cond-mat.stat-mech↗