Paolo Sibani - Academia.edu (original) (raw)

Papers by Paolo Sibani

Cornell University - arXiv, Nov 28, 2000

We study the noisy dynamics of a close relative to the sand pile model. Depending on the type of ... more We study the noisy dynamics of a close relative to 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, evolution models and vibrated granular media.

SSRN Electronic Journal

Eight centuries of yearly GDP data from three regions of Western Europe, corresponding to present... more Eight centuries of yearly GDP data from three regions of Western Europe, corresponding to present days UK, France and Sweden, gauge economic interactions that reflect the societal structures in which they unfold. In short, they provide an insight on human wealth evolution. Our data analysis is carried out in two steps. First, a Monte Carlo algorithm is used to fit the time series to a piecewise continuous function comprising a sequence of exponentials with different exponents. These arguably correspond to different social and technological stages of societal organization. As a function of time, human wealth evolution features an accelerating trend and is thus an evolutionary expansion process [1]. The intensity of human interactions driving the evolutionary process has increased manyfold over the centuries. This motivates our second analysis step, where 'wall clock time' as independent variable is replaced with a measure of human interactions intensity τ as introduced in a previous work [2]. In terms of this interaction variable τ , human wealth evolution displays two different logarithmic regimes, both decelerating, and connected by a rapid cross-over. The latter occurs around the outbreak of World War I and coincides with the transition in Western Europe from a mainly agricultural to a mainly industrial and urbanized society. Finally, wealth evolution in terms of τ shows the hallmarks of record dynamics optimization.

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temp... more Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below T_ c and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures T can be collapsed by scaling them with T^1.75, a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the c...

Bulletin of the American Physical Society, 2010

ABSTRACT The dynamics of complex systems collectively known as glassy share important phenomenolo... more ABSTRACT The dynamics of complex systems collectively known as glassy share important phenomenological traits. Whether structural or quenched, either in low-T magnets or in dense colloids, physical changes occur in an intermittent fashion and, on average, at a decreasing rate. Despite their microscopic differences, generally, a transition is observed from a time-homogeneous regime to one which is likewise homogeneous, but in terms of the logarithm of time: A global change of the independent variable trivializes the dynamics. Focusing here on experimental data from dense colloidsfootnotetextCourtland & Weeks, J. Phys.: Condens. Matter 15, S359 (2003)., the crucial importance of record-size fluctuation for the aging dynamics is revealed. A model with a generic stochastic dynamics is introducedfootnotetextsee also: Boettcher & Sibani, http://arxiv.org/pdf/0910.5470. which relies on the growth and collapse of strongly correlated clusters (``dynamic heterogeneities''). In the limit where large clusters dominate the dynamics, intermittency in terms of record-size events occurs with rate 1/t, implying a homogeneous, -Poissonian process that qualitatively reproduces the experimental results for colloidal dynamics.footnotetextSee also http://www.physics.emory.edu/faculty/boettcher/.

Physica A: Statistical Mechanics and its Applications, 2021

Cooperative events requiring anomalously large fluctuations, are a defining characteristic for th... more Cooperative events requiring anomalously large fluctuations, are a defining characteristic for the onset of glassy relaxation across many materials. The importance of such intermittent events has been noted in systems as diverse as superconductors, metallic glasses, gels, colloids, and granular piles. Here, we show that prohibiting the attainment of new record-high energy fluctuations-by explicitly imposing a "lid" on the fluctuation spectrum-impedes further relaxation in the glassy phase. This lid allows us to directly measure the impact of record events on the evolving system in extensive simulations of aging in such vastly distinct glass formers as spin glasses and tapped granular piles. Interpreting our results in terms of a dynamics of records succeeds in explaining the ubiquity of both, the logarithmic decay of the energy and the memory effects encoded in the scaling of two-time correlation functions of aging systems.

The European Physical Journal B, 2021

Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages.... more Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as “physical aging”, but from the vantage point of RD, the evolution of a class of systems of physical, biological, and cultural origin is rooted in a hierarchically structured configuration space and can, therefore, be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self-Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time-series, and connects it to the sta...

Physica A: Statistical Mechanics and its Applications, 2020

Is a causal description of human wealth history conceivable? To investigate the matter we introdu... more Is a causal description of human wealth history conceivable? To investigate the matter we introduce a simple causal albeit strongly aggregated model, assuming that the observed wealth growth is mainly driven by human collaborative efforts whose intensity itself increases with increasing wealth. As an empirical reference we use time series describing eight centuries of per capita annual gross domestic products (GDP) of three European countries, the UK, France and Sweden. The model requires a population large enough for disruptive events, e.g. famine, epidemics and wars, not to destroy the fundamental workings of society. Cultural interchanges between different geographical areas are not explicitly taken into account. The wealth evolution trend can then be described by an ordinary differential equation with three free parameters: one producing a short term exponential growth rate, one defining an additional minute constant growth rate and finally one that specifies the time scale below which human collaboration intensity can be treated as constant. Beyond that scale, wealth enhances the fundamental collaborative infrastructure of society. The solution features a finite time singularity, which implies infinite GDP per capita in finite time and thus suggests a lack of long term sustainability. The year at which the singularity occurs has a slight variation near 2020 AD from one country to another. GDP time series curtailed after 1900 AD produce similar values for the occurrence of the singularity, which thus could be predicted more than hundred years ago. Curtailing the GDP series from the early years up to 1700 AD also produces stable and consistent predictions for the singularity time. Power spectra are obtained for de-trended data spanning eight centuries, as well as for the first and last four centuries of the same period. All spectra have an overall signature where the power decays as the inverse frequency squared. The embedded peaks are reminiscent of the cycles described in the economic literature, but are also present in time series far predating industrialization. The background fluctuations in the GDP series is tentatively interpreted as societal response to disruptive stochastic events. e.g. new economic activities following epochal discoveries, as well as wars and epidemics.

Physical Review B, 2018

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temp... more Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below Tc and, in analogy with a recent model of dense colloidal suspensions, interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures T can be collapsed by scaling them with T −1.75 , a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the cluster, as recently assumed in a coarse grained model of dense colloidal dynamics. The evolving structure of clusters in real space is finally ssociated to the decay of the thermo-remanent magnetization. Our analysis provides an unconventional coarse-grained description of spin glass aging as statistically subordinated to a Poisson quaking process and highlights record dynamics as a viable common theoretical framework for aging in different systems.

Artificial Life, 2019

We document and discuss two different modes of evolution across multiple systems, optimization an... more We document and discuss two different modes of evolution across multiple systems, optimization and expansion. The former suffices in systems whose size and interactions do not change substantially over time, while the latter is a key property of open-ended evolution, where new players and interaction types enter the game. We first investigate systems from physics, biology, and engineering and argue that their evolutionary optimization dynamics is the cumulative effect of multiple independent events, or quakes, which are uniformly distributed on a logarithmic time scale and produce a decelerating fitness improvement when using the appropriate independent variable. The appropriate independent variable can be physical time for a disordered magnetic system, the number of generations for a bacterial system, or the number of produced units for a particular technological product. We then derive and discuss a simple microscopic theory that explains the nature of the involved optimization pr...

Physical Review E, 2018

Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench ... more Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a non-equilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process like CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations ("quakes"). We show that such a record dynamics (RD) provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.

Physica A: Statistical Mechanics and its Applications, 2017

We discuss fitness landscapes and how they can be modified to account for co-evolution. We are in... more We discuss fitness landscapes and how they can be modified to account for co-evolution. We are interested in using the landscape as a way to model rational decision making in a toy economic system. We develop a model very similar to the Tangled Nature Model of Christensen et. al. that we call the Tangled Decision Model. This is a natural setting for our discussion of co-evolutionary fitness landscapes. We use a Monte Carlo step to simulate decision making and investigate two different decision making procedures.

EPL (Europhysics Letters), 2016

In a broad class of complex materials a quench leads to a multi-scaled relaxation process known a... more In a broad class of complex materials a quench leads to a multi-scaled relaxation process known as aging. To explain its commonality and the astounding insensitivity to most microscopic details, record dynamics (RD) posits that a small set of increasingly rare and irreversible events, so called quakes, controls the dynamics. While key predictions of RD are known to concur with a number of experimental and simulational results, its basic assumption on the nature of quake statistics has proven extremely difficult to verify experimentally. The careful distinction of rare ("record") cage-breaking events from in-cage rattle accomplished in previous experiments on jammed colloids, enables us to extract the first direct experimental evidence for the fundamental hypothesis of RD that the rate of quakes decelerates with the inverse of the system age. The resulting description shows the predicted growth of the particle mean square displacement and of a mesoscopic lengthscale with the logarithm of time.

Physical review. E, 2016

Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tang... more Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer K. We first show that the interactions generated by our rule are nearly independent of K. Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing K strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time t_{w} also survives at t>t_{...

Physical review. E, 2016

We present an analytical and numerical study of the parking lot model (PLM) of granular relaxatio... more We present an analytical and numerical study of the parking lot model (PLM) of granular relaxation and make a connection to the aging dynamics of dense colloids. As we argue, the PLM is a Kinetically Constrained Model which features astronomically large equilibration times and displays a characteristic aging behavior on all observable time scales. The density of parked cars displays quasi-equilibrium Gaussian fluctuations interspersed by increasingly rare intermittent events, quakes, which can lead to an increase of the density to new record values. Defining active clusters as the shortest domains of parked cars which must be rearranged to allow further insertions, we find that their typical length grows logarithmically with time for low enough temperatures and show how the number of active clusters on average gradually decreases as the system approaches equilibrium. We further characterize the aging process in terms of the statistics of the record-sized fluctuations in the intersti...

International Journal of Modern Physics B, 1998

After an introductory section summarizing the paleontological data and some of their theoretical ... more After an introductory section summarizing the paleontological data and some of their theoretical descriptions, we describe the "reset" model and its (in part analytically soluble) mean field version, which have been briefly introduced in Letters.1,2 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 non-stationary dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also consider the effect of externally added "mass" extinctions. The predictions for various quantities of paleontological interest (life-time distribution, distribution of event sizes and behavior of the rate of e...

Physical Review B, 1994

We study the phase-space geometry and the low-temperature relaxation of short range Gaussian Isin... more We study the phase-space geometry and the low-temperature relaxation of short range Gaussian Ising spin glasses, by finding all the configurations and their interconnection within a "pocket" of states surrounding a low-lying energy minimum. Thermalization within the pocket is modeled by a master equation, which is solved numerically, yielding the time-dependent propagator. The findings show that the relaxation proceeds by a series of local equilibrations in nested "valleys, " and support the dynamical predictions of hierarchical relaxation models.

SSRN Electronic Journal, 2015

The Tangled Nature Model-a biologically inspired model of evolutionary ecology-is described, simu... more The Tangled Nature Model-a biologically inspired model of evolutionary ecology-is described, simulated, and analyzed to show its applicability in organization science and organizational ecology. It serves as a conceptual framework for understanding the dynamics in populations of organizations. A salient dynamical feature of this model is the spontaneous generation of a symbiotic group of core organizations. This core, consisting of several dominating species, introduces a mesoscopic level between that of the individual and the whole system. Despite prolonged periods of stability, this core is disrupted at random by parasitic interactions causing sudden core rearrangements. The size distribution of the core organizations is log-normal as predicted by theory and supported by empirical findings. As a simple application of the model, we study the adaptation of organizations to changes in resource availability in terms of population size, population diversity, and ecological efficiency. We find evidence that a temporary reduction in resources forces a consolidation resulting in a sustained increase in overall efficiency, suggesting that such reductions can be applied strategically to drive incremental improvements.

Physics Procedia, 2014

A model of dense hard sphere colloids building on simple notions of particle mobility and spatial... more A model of dense hard sphere colloids building on simple notions of particle mobility and spatial coherence is presented and shown to reproduce results of experiments and simulations for key quantities such as the intermediate scattering function, the particle mean-square displacement and the χ 4 mobility correlation function. All results are explained by two emerging and interrelated dynamical properties: i) a rate of intermittent events, quakes, which decreases as the inverse of the system age t, leading to μ q (t w , t) ∝ log(t/t w) as the average number of quakes occurring between the 'waiting time' t w and the current time t; ii) a length scale characterizing correlated domains, which increases linearly in log t.

Cornell University - arXiv, Nov 28, 2000

We study the noisy dynamics of a close relative to the sand pile model. Depending on the type of ... more We study the noisy dynamics of a close relative to 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, evolution models and vibrated granular media.

SSRN Electronic Journal

Eight centuries of yearly GDP data from three regions of Western Europe, corresponding to present... more Eight centuries of yearly GDP data from three regions of Western Europe, corresponding to present days UK, France and Sweden, gauge economic interactions that reflect the societal structures in which they unfold. In short, they provide an insight on human wealth evolution. Our data analysis is carried out in two steps. First, a Monte Carlo algorithm is used to fit the time series to a piecewise continuous function comprising a sequence of exponentials with different exponents. These arguably correspond to different social and technological stages of societal organization. As a function of time, human wealth evolution features an accelerating trend and is thus an evolutionary expansion process [1]. The intensity of human interactions driving the evolutionary process has increased manyfold over the centuries. This motivates our second analysis step, where 'wall clock time' as independent variable is replaced with a measure of human interactions intensity τ as introduced in a previous work [2]. In terms of this interaction variable τ , human wealth evolution displays two different logarithmic regimes, both decelerating, and connected by a rapid cross-over. The latter occurs around the outbreak of World War I and coincides with the transition in Western Europe from a mainly agricultural to a mainly industrial and urbanized society. Finally, wealth evolution in terms of τ shows the hallmarks of record dynamics optimization.

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temp... more Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below T_ c and, in analogy with a recent model of dense colloidal suspensions,interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures T can be collapsed by scaling them with T^1.75, a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the c...

Bulletin of the American Physical Society, 2010

ABSTRACT The dynamics of complex systems collectively known as glassy share important phenomenolo... more ABSTRACT The dynamics of complex systems collectively known as glassy share important phenomenological traits. Whether structural or quenched, either in low-T magnets or in dense colloids, physical changes occur in an intermittent fashion and, on average, at a decreasing rate. Despite their microscopic differences, generally, a transition is observed from a time-homogeneous regime to one which is likewise homogeneous, but in terms of the logarithm of time: A global change of the independent variable trivializes the dynamics. Focusing here on experimental data from dense colloidsfootnotetextCourtland & Weeks, J. Phys.: Condens. Matter 15, S359 (2003)., the crucial importance of record-size fluctuation for the aging dynamics is revealed. A model with a generic stochastic dynamics is introducedfootnotetextsee also: Boettcher & Sibani, http://arxiv.org/pdf/0910.5470. which relies on the growth and collapse of strongly correlated clusters (``dynamic heterogeneities''). In the limit where large clusters dominate the dynamics, intermittency in terms of record-size events occurs with rate 1/t, implying a homogeneous, -Poissonian process that qualitatively reproduces the experimental results for colloidal dynamics.footnotetextSee also http://www.physics.emory.edu/faculty/boettcher/.

Physica A: Statistical Mechanics and its Applications, 2021

Cooperative events requiring anomalously large fluctuations, are a defining characteristic for th... more Cooperative events requiring anomalously large fluctuations, are a defining characteristic for the onset of glassy relaxation across many materials. The importance of such intermittent events has been noted in systems as diverse as superconductors, metallic glasses, gels, colloids, and granular piles. Here, we show that prohibiting the attainment of new record-high energy fluctuations-by explicitly imposing a "lid" on the fluctuation spectrum-impedes further relaxation in the glassy phase. This lid allows us to directly measure the impact of record events on the evolving system in extensive simulations of aging in such vastly distinct glass formers as spin glasses and tapped granular piles. Interpreting our results in terms of a dynamics of records succeeds in explaining the ubiquity of both, the logarithmic decay of the energy and the memory effects encoded in the scaling of two-time correlation functions of aging systems.

The European Physical Journal B, 2021

Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages.... more Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as “physical aging”, but from the vantage point of RD, the evolution of a class of systems of physical, biological, and cultural origin is rooted in a hierarchically structured configuration space and can, therefore, be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self-Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time-series, and connects it to the sta...

Physica A: Statistical Mechanics and its Applications, 2020

Is a causal description of human wealth history conceivable? To investigate the matter we introdu... more Is a causal description of human wealth history conceivable? To investigate the matter we introduce a simple causal albeit strongly aggregated model, assuming that the observed wealth growth is mainly driven by human collaborative efforts whose intensity itself increases with increasing wealth. As an empirical reference we use time series describing eight centuries of per capita annual gross domestic products (GDP) of three European countries, the UK, France and Sweden. The model requires a population large enough for disruptive events, e.g. famine, epidemics and wars, not to destroy the fundamental workings of society. Cultural interchanges between different geographical areas are not explicitly taken into account. The wealth evolution trend can then be described by an ordinary differential equation with three free parameters: one producing a short term exponential growth rate, one defining an additional minute constant growth rate and finally one that specifies the time scale below which human collaboration intensity can be treated as constant. Beyond that scale, wealth enhances the fundamental collaborative infrastructure of society. The solution features a finite time singularity, which implies infinite GDP per capita in finite time and thus suggests a lack of long term sustainability. The year at which the singularity occurs has a slight variation near 2020 AD from one country to another. GDP time series curtailed after 1900 AD produce similar values for the occurrence of the singularity, which thus could be predicted more than hundred years ago. Curtailing the GDP series from the early years up to 1700 AD also produces stable and consistent predictions for the singularity time. Power spectra are obtained for de-trended data spanning eight centuries, as well as for the first and last four centuries of the same period. All spectra have an overall signature where the power decays as the inverse frequency squared. The embedded peaks are reminiscent of the cycles described in the economic literature, but are also present in time series far predating industrialization. The background fluctuations in the GDP series is tentatively interpreted as societal response to disruptive stochastic events. e.g. new economic activities following epochal discoveries, as well as wars and epidemics.

Physical Review B, 2018

Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temp... more Isothermal simulational data for the 3D Edwards-Anderson spin glass are collected at several temperatures below Tc and, in analogy with a recent model of dense colloidal suspensions, interpreted in terms of clusters of contiguous spins overturned by quakes, non-equilibrium events linked to record sized energy fluctuations. We show numerically that, to a good approximation, these quakes are statistically independent and constitute a Poisson process whose average grows logarithmically in time. The overturned clusters are local projections on one of the two ground states of the model, and grow likewise logarithmically in time. Data collected at different temperatures T can be collapsed by scaling them with T −1.75 , a hitherto unnoticed feature of the E-A model, which we relate on the one hand to the geometry of configuration space and on the other to experimental memory and rejuvenation effects. The rate at which a cluster flips is shown to decrease exponentially with the size of the cluster, as recently assumed in a coarse grained model of dense colloidal dynamics. The evolving structure of clusters in real space is finally ssociated to the decay of the thermo-remanent magnetization. Our analysis provides an unconventional coarse-grained description of spin glass aging as statistically subordinated to a Poisson quaking process and highlights record dynamics as a viable common theoretical framework for aging in different systems.

Artificial Life, 2019

We document and discuss two different modes of evolution across multiple systems, optimization an... more We document and discuss two different modes of evolution across multiple systems, optimization and expansion. The former suffices in systems whose size and interactions do not change substantially over time, while the latter is a key property of open-ended evolution, where new players and interaction types enter the game. We first investigate systems from physics, biology, and engineering and argue that their evolutionary optimization dynamics is the cumulative effect of multiple independent events, or quakes, which are uniformly distributed on a logarithmic time scale and produce a decelerating fitness improvement when using the appropriate independent variable. The appropriate independent variable can be physical time for a disordered magnetic system, the number of generations for a bacterial system, or the number of produced units for a particular technological product. We then derive and discuss a simple microscopic theory that explains the nature of the involved optimization pr...

Physical Review E, 2018

Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench ... more Aging is a ubiquitous relaxation dynamic in disordered materials. It ensues after a rapid quench from an equilibrium "fluid" state into a non-equilibrium, history-dependent jammed state. We propose a physically motivated description that contrasts sharply with a continuous-time random walk (CTRW) with broadly distributed trapping times commonly used to fit aging data. A renewal process like CTRW proves irreconcilable with the log-Poisson statistic exhibited, for example, by jammed colloids as well as by disordered magnets. A log-Poisson process is characteristic of the intermittent and decelerating dynamics of jammed matter usually activated by record-breaking fluctuations ("quakes"). We show that such a record dynamics (RD) provides a universal model for aging, physically grounded in generic features of free-energy landscapes of disordered systems.

Physica A: Statistical Mechanics and its Applications, 2017

We discuss fitness landscapes and how they can be modified to account for co-evolution. We are in... more We discuss fitness landscapes and how they can be modified to account for co-evolution. We are interested in using the landscape as a way to model rational decision making in a toy economic system. We develop a model very similar to the Tangled Nature Model of Christensen et. al. that we call the Tangled Decision Model. This is a natural setting for our discussion of co-evolutionary fitness landscapes. We use a Monte Carlo step to simulate decision making and investigate two different decision making procedures.

EPL (Europhysics Letters), 2016

In a broad class of complex materials a quench leads to a multi-scaled relaxation process known a... more In a broad class of complex materials a quench leads to a multi-scaled relaxation process known as aging. To explain its commonality and the astounding insensitivity to most microscopic details, record dynamics (RD) posits that a small set of increasingly rare and irreversible events, so called quakes, controls the dynamics. While key predictions of RD are known to concur with a number of experimental and simulational results, its basic assumption on the nature of quake statistics has proven extremely difficult to verify experimentally. The careful distinction of rare ("record") cage-breaking events from in-cage rattle accomplished in previous experiments on jammed colloids, enables us to extract the first direct experimental evidence for the fundamental hypothesis of RD that the rate of quakes decelerates with the inverse of the system age. The resulting description shows the predicted growth of the particle mean square displacement and of a mesoscopic lengthscale with the logarithm of time.

Physical review. E, 2016

Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tang... more Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer K. We first show that the interactions generated by our rule are nearly independent of K. Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing K strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time t_{w} also survives at t>t_{...

Physical review. E, 2016

We present an analytical and numerical study of the parking lot model (PLM) of granular relaxatio... more We present an analytical and numerical study of the parking lot model (PLM) of granular relaxation and make a connection to the aging dynamics of dense colloids. As we argue, the PLM is a Kinetically Constrained Model which features astronomically large equilibration times and displays a characteristic aging behavior on all observable time scales. The density of parked cars displays quasi-equilibrium Gaussian fluctuations interspersed by increasingly rare intermittent events, quakes, which can lead to an increase of the density to new record values. Defining active clusters as the shortest domains of parked cars which must be rearranged to allow further insertions, we find that their typical length grows logarithmically with time for low enough temperatures and show how the number of active clusters on average gradually decreases as the system approaches equilibrium. We further characterize the aging process in terms of the statistics of the record-sized fluctuations in the intersti...

International Journal of Modern Physics B, 1998

After an introductory section summarizing the paleontological data and some of their theoretical ... more After an introductory section summarizing the paleontological data and some of their theoretical descriptions, we describe the "reset" model and its (in part analytically soluble) mean field version, which have been briefly introduced in Letters.1,2 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 non-stationary dynamics is studied by numerical simulations and, in a simpler mean field version, analytically. We also consider the effect of externally added "mass" extinctions. The predictions for various quantities of paleontological interest (life-time distribution, distribution of event sizes and behavior of the rate of e...

Physical Review B, 1994

We study the phase-space geometry and the low-temperature relaxation of short range Gaussian Isin... more We study the phase-space geometry and the low-temperature relaxation of short range Gaussian Ising spin glasses, by finding all the configurations and their interconnection within a "pocket" of states surrounding a low-lying energy minimum. Thermalization within the pocket is modeled by a master equation, which is solved numerically, yielding the time-dependent propagator. The findings show that the relaxation proceeds by a series of local equilibrations in nested "valleys, " and support the dynamical predictions of hierarchical relaxation models.

SSRN Electronic Journal, 2015

The Tangled Nature Model-a biologically inspired model of evolutionary ecology-is described, simu... more The Tangled Nature Model-a biologically inspired model of evolutionary ecology-is described, simulated, and analyzed to show its applicability in organization science and organizational ecology. It serves as a conceptual framework for understanding the dynamics in populations of organizations. A salient dynamical feature of this model is the spontaneous generation of a symbiotic group of core organizations. This core, consisting of several dominating species, introduces a mesoscopic level between that of the individual and the whole system. Despite prolonged periods of stability, this core is disrupted at random by parasitic interactions causing sudden core rearrangements. The size distribution of the core organizations is log-normal as predicted by theory and supported by empirical findings. As a simple application of the model, we study the adaptation of organizations to changes in resource availability in terms of population size, population diversity, and ecological efficiency. We find evidence that a temporary reduction in resources forces a consolidation resulting in a sustained increase in overall efficiency, suggesting that such reductions can be applied strategically to drive incremental improvements.

Physics Procedia, 2014

A model of dense hard sphere colloids building on simple notions of particle mobility and spatial... more A model of dense hard sphere colloids building on simple notions of particle mobility and spatial coherence is presented and shown to reproduce results of experiments and simulations for key quantities such as the intermediate scattering function, the particle mean-square displacement and the χ 4 mobility correlation function. All results are explained by two emerging and interrelated dynamical properties: i) a rate of intermittent events, quakes, which decreases as the inverse of the system age t, leading to μ q (t w , t) ∝ log(t/t w) as the average number of quakes occurring between the 'waiting time' t w and the current time t; ii) a length scale characterizing correlated domains, which increases linearly in log t.