arXiv subjects

Paolo Sibani

Publications and source records attributed to Paolo Sibani.

48 records · Page 3Linked to original sources

arXiv2003

Log-Poisson statistics and full aging in glassy systems

We argue that Poisson statistics in logarithmic time provides an idealized description of non-equilibrium configurational rearrangements in aging glassy systems. The description puts stringent requirements on the geometry of the metastable attractors visited at age $t_w$. Analytical implications for the residence time distributions as a function of $t_w$ and the correlation functions are derived. These are verified by extensive numerical studies of short range Ising spin glasses.

cond-mat.stat-mech↗

arXiv2003

Exploring Valleys of Aging Systems: The Spin Glass Case

We present a statistical method for complex energy landscape exploration which provides information on the metastable states--or valleys--actually explored by an unperturbed aging process following a quench. Energy fluctuations of record size are identified as the events which move the system from one valley to the next. This allows for a semi-analytical description in terms of log-Poisson statistics, whose main features are briefly explained. The bulk of the paper is devoted to thorough investigations of Ising spin glasses with Gaussian interactions of both short and long range, a well established paradigm for glassy dynamics. Simple scaling expressions with universal exponents for (a) barrier energies, (b) energy minima, and (c) the Hamming distance as a function of the valley index are found. The distribution of residence time inside valleys entered at age $t_w$ is investigated, along with the distribution of time at which the global minimum inside a valley is hit. Finally, the correlations between the minima of the landscape are presented. The results fit well into the framework of available knowledge about spin glass aging. At the same time they support a novel interpretation of thermal relaxation in complex landscapes with multiple metastable states. The marginal stability of the attractors selected is emphasized and explained in terms of geometrical properties of the landscape.

cond-mat.stat-mech↗

arXiv2003

Extracting the Landscape and Morphology of Aging Glassy Systems

We propose a way to analyze the landscape geometry explored by a glassy system after a quench solely based on time series of energy values recorded during a simulation. Entry and exit times for landscape `valleys' are defined operationally by the occurrence of anomalous energy changes revealed by barrier and energy records. Linking these non-equilibrium events--or `earthquakes'-- to the record statistics of the thermal noise immediately leads to the $\ln t$ relaxation behavior ubiquitous in glassy dynamics. Aging of Ising spin glasses in two and three dimensions is studied as a check for a number of low temperatures and lattice sizes. A simple picture emerges on e.g. 1) the scaling with temperature and system size of the energy barriers as function of the valley index, and 2) the scaling with system size of the lowest energy seen in each valley.

cond-mat.stat-mech↗

arXiv2001

Faster Monte Carlo Simulations at Low Temperatures. The Waiting Time Method

We discuss a rejectionless global optimization technique which, while being technically similar to the recently introduced method of Extremal Optimization, still relies on a physical analogy with a thermalizing system. Our waiting time method (WTM) is mathematically equivalent to the usual Metropolis algorithm, but considerably more efficient at low temperatures. The WTM can be used at constant temperature or it can be combined with annealing techniques. It is especially well suited for studying the low temperature relaxation of complex systems as glasses and spin glasses. In the paper we describe the method and test it on a spin glass example by comparing its performance to Extremal Optimization.

cond-mat.stat-mech↗

arXiv2001

Aging and SOC in driven dissipative systems

We study the noisy dynamics of a close relative of the sand pile model. Depending on the type of noise and the time scale of observation, we find stationary fluctuations (similar to SOC) or an aging dynamics with punctuated equilibria, a decreasing rate of events and reset properties qualitatively similar to those of glassy systems and evolution models.

cond-mat.stat-mech↗

arXiv1999

Evolution dynamics in terraced NK landscapes

We study populations of agents evolving in fitness landscapes constructed according to the rules of a modified NK model with a tunable amount of neutral paths. In the `punctuated equilibrium' regime evolutionary events are identified as jumps in the mean population fitness, and the statistics of these jumps in an ensemble of independently evolving populations is analyzed. We show that, for a wide range of landscapes parameters, the number of events in time t is Poisson distributed, with the time parameter replaced by the logarithm of time. This simple log-Poisson statistics likewise describes the number n of records in any sequence of t independently generated random numbers. The implications of this behavior for evolution dynamics are discussed.

adap-org↗

arXiv1998

Extinction, diversity and survivorship of taxa in the fossil record

Using data drawn from large-scale databases, a number of interesting trends in the fossil record have been observed in recent years. These include the average decline in extinction rates throughout the Phanerozoic, the average increase in standing diversity, correlations between rates of origination and extinction, and simple laws governing the form of survivorship curves and the distribution of the lifetimes of taxa. In this paper we derive mathematically a number of relations between these quantities and show how these different trends are inter-related. We also derive a variety of constraints on the possible forms of these trends, such as limits on the rate at which extinction may decline and limits on the allowed difference between extinction and origination rates at any given time.

adap-org↗

arXiv1998

The lid method for exhaustive exploration of metastable states of complex systems

The `lid' algorithm performs an exhaustive exploration of neighborhoods of local energy minima of energy landscapes. This paper describes an implementation of the algorithm, including issues of parallel performance and scalability. To illustrate the versatility of the approach and to stress the common features present in landscapes of quite different systems, we present selected results for 1) a spin glass, 2) a ferromagnet, 3) a covalent network model for glassy systems, and 4) a polymer. The exponential nature of the local density of states found in these systems and its relation to the ordering transition is briefly commented upon.

physics.comp-ph↗

arXiv1998

Properties of the energy landscape of network models for covalent glasses

We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration space regions enclosing deep-lying energy minima. We extract the local densities of states and of minima, and the number of states and minima accessible below a certain energy barrier, the 'lid'. These quantities show on average a close to exponential growth as a function of their respective arguments. We calculate the configurational entropy for these pockets of states and find that the excess specific heat exhibits a peak at a critical temperature associated with the exponential growth in the local density of states, a feature of the specific heat also observed in real glasses at the glass transition.

cond-mat.stat-mech↗

arXiv1998

Local state space geometry and thermal metastability in complex landscapes: the spin-glass case

A simple geometrical characterization of configuration space neighborhoods of local energy minima in spin glass landscapes is found by exhaustive search. Combined with previous Monte Carlo investigations of thermal domain growth, it allows a discussion of the connection between real and configuration space descriptions of low temperature relaxational dynamics. We argue that the part of state-space corresponding to a single growing domain is adequately modeled by a hierarchically organized set of states and that thermal (meta)stability in spin glasses is related to the nearly exponential local density of states present within each trap.

cond-mat.dis-nn↗

arXiv1997

Evolution and extinction dynamics in rugged fitness landscapes

Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also study the effect of externally added `mass' extinctions. The predictions for various quantities of paleontological interest (life-time distributions, distribution of event sizes and behavior of the rate of extinction) are robust and in good agreement with available data. Brief version of parts of this work have been published as Letters. (PRL 75, 2055, (1995) and PRL, 79, 1413, (1997))

adap-org↗

arXiv1997

A soluble model of evolution and extinction dynamics in a rugged fitness landscape

We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their competitive interactions. We first formulate dynamical equations for the fitness distribution and the survival probability. Secondly we analytically derive the $t^{-2}$ law which characterizes the life time distribution of biological genera. Thirdly we discuss other dynamical properties of the model such as the rate of extinction and conclude with a brief discussion.

physics.bio-ph↗