Mendeli Vainstein - Academia.edu (original) (raw)

Papers by Mendeli Vainstein

Lecture Notes in Physics, 2000

Complex systems such as glasses, gels, granular materials, and systems far from equilibrium exhib... more Complex systems such as glasses, gels, granular materials, and systems far from equilibrium exhibit violation of the ergodic hypothesis (EH) and of the fluctuation-dissipation theorem (FDT). Recent investigations in systems with memory [1] have established a hierarchical connection between mixing, the EH and the FDT. They have shown that a failure of the mixing condition (MC) will lead to the subsequent failures of the EH and of the FDT. Another important point is that such violations are not limited to complex systems: simple systems may also display this feature. Results from such systems are analytical and obviously easier to understand than those obtained in complex structures, where a large number of competing phenomena are present. In this work, we review some important requirements for the validity of the FDT and its connection with mixing, the EH and anomalous diffusion in one-dimensional systems. We show that when the FDT fails, an out-ofequilibrium system relaxes to an effective temperature different from that of the heat reservoir. This effective temperature is a signature of metastability found in many complex systems such as spin-glasses and granular materials.

AIP Conference Proceedings, 2007

ABSTRACT Random diffusion is shown to be an important mechanism on fostering cooperative behavior... more ABSTRACT Random diffusion is shown to be an important mechanism on fostering cooperative behavior among simple agents (memoryless, unconditional cooperators or defectors) living on a spatially structured environment. In particular, under the Prisoner’s Dilemma framework, when allowing the agents to move with the simple “always‐move” rule, we find that cooperative behavior is not only possible but may even be enhanced. In addition, for a broad range of densities, mobile cooperators can more easily invade a population of mobile defectors, when compared with the fully viscous, immobile case. Thus, such simple mobility pattern may have played a fundamental role both in the onset and development of cooperative behavior, paving the way to more complex, individual and group, motility rules. © 2007 American Institute of Physics

We propose a novel algorithm that outputs the final standings of a soccer league, based on a simp... more We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a teams' future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileirão). However, other leagues such as the Italian and the Spanish tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: Here several teams were crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserves the gaussian traces during the tournament. On the other hand, in the Italian and Spanish leagues only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the "Brasileirão" cannot be reproduced. Such aspects stress that evolutionary aspects are not superfluous in our modeling. Finally, we analyse the distortions of our model in situations where a large number of teams is considered, showing the existence of a transition from a single to a double peaked histogram of the final classification scores. An interesting scaling is presented for different sized tournaments.

Langmuir, 2015

When a drop of water is placed on a rough surface, there are two possible extreme regimes of wett... more When a drop of water is placed on a rough surface, there are two possible extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets trapped underneath the droplet and the one characterized by the homogeneous wetting of the surface, called the Wenzel (W) state. A way to investigate the transition between these two states is by means of evaporation experiments, in which the droplet starts in a CB state and, as its volume decreases, penetrates the surface's grooves, reaching a W state. Here we present a theoretical model based on the global interfacial energies for CB and W states that allows us to predict the thermodynamic wetting state of the droplet for a given volume and surface texture. We first analyze the influence of the surface geometric parameters on the droplet's final wetting state with constant volume, and show that it depends strongly on the surface texture. We then vary the volume of the droplet keeping fixed the geometric surface parameters to mimic evaporation and show that the drop experiences a transition from the CB to the W state when its volume reduces, as observed in experiments. To investigate the dependency of the wetting state on the initial state of the droplet, we implement a cellular Potts model in three dimensions. Simulations show a very good agreement with theory when the initial state is W, but it disagrees when the droplet is initialized in a CB state, in accordance with previous observations which show that the CB state is metastable in many cases. Both simulations and theoretical model can be modified to study other kinds of surface.

Physics Letters A, 2009

Using both an analytical method and a numerical approach we have investigated pattern formation f... more Using both an analytical method and a numerical approach we have investigated pattern formation for a nonlocal convective Fisher equation with constant and spatial velocity fields. We analyze the limits of the influence function due to nonlocal interaction and we obtain the phase diagram of critical velocities v c as function of the width μ of the influence function, which characterize the self-organization of a finite system.

Recent investigations call attention to the dynamics of anomalous diffusion and its connection wi... more Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.

Physical Review Letters, 2008

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brown... more We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.

Physical Review E, 2014

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playi... more We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius rP that accounts for the population viscosity, and an interaction radius rint that defines the instantaneous contact network for the game dynamics. We show that, differently from the rP = 0 case, the model with finite sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.

Physical Review E, 2001

The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance... more The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that, due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at *, separating a region with spatial chaos from one with localized, stable groups of cooperators.

Physics Letters A, 2005

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a pow... more We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as k −β , using a stochastic description. It establishes a direct connection between the fluctuation in the spin-wave density of states and the noise density of states. For continuous ranges of the exponent β, we find super-diffusive and ballistic spinwave motions. Both diffusion exponents predicted by the stochastic procedure agree with the ones calculated using the Hamiltonian dynamics.

Physical Review Letters, 2008

A recent paper [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact t... more A recent paper [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York) 1949] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a Generalized Langevin Equation the Khinchin theorem holds.

Physical Review E, 2013

Statistics of soccer tournament scores based on the double round robin system of several countrie... more Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva et al., Comput. Phys. Commun. 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

Physica A: Statistical Mechanics and its Applications, 2014

ABSTRACT We present an extensive, systematic study of the Prisoner’s Dilemma and Snowdrift games ... more ABSTRACT We present an extensive, systematic study of the Prisoner’s Dilemma and Snowdrift games on a square lattice under a synchronous, noiseless imitation dynamics. We show that for both the occupancy of the network and the (random) mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear. We analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice. We point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results.

Physica A: Statistical Mechanics and its Applications, 2005

We present here a conjecture about the equivalence between the noise density of states of a syste... more We present here a conjecture about the equivalence between the noise density of states of a system governed by a generalized Langevin equation and the fluctuation in the energy density of states in a Hamiltonian system. We present evidence of this for a disordered Heisenberg system. r

Physica A: Statistical Mechanics and its Applications, 2006

... References. [1] IVL Costa, R. Morgado, MVBT Lima and FA Oliveira, Europhys. Lett. 63 (2003),p... more ... References. [1] IVL Costa, R. Morgado, MVBT Lima and FA Oliveira, Europhys. Lett. 63 (2003),p. 173. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus (32). [2] MH Lee, Phys. Rev. B 26 (1982), p. 2547. MathSciNet | Full Text via CrossRef.

Journal of Theoretical Biology, 2007

We explore the minimal conditions for sustainable cooperation on a spatially distributed populati... more We explore the minimal conditions for sustainable cooperation on a spatially distributed population of memoryless, unconditional strategies (cooperators and defectors) in presence of unbiased, non contingent mobility in the context of the Prisoner's Dilemma game. We find that cooperative behavior is not only possible but may even be enhanced by such an "always-move" rule, when compared with the strongly viscous ("never-move") case. In addition, mobility also increases the capability of cooperation to emerge and invade a population of defectors, what may have a fundamental role in the problem of the onset of cooperation.

Journal of Theoretical Biology, 2009

The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag H... more The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population, sometimes promoting, sometimes inhibiting cooperation. Here we show that random dilution and mobility may suppress the inhibiting factors of the spatial structure in the Snowdrift game, while enhancing the already larger cooperation found in the Prisoner's dilemma and Stag Hunt games.

Lecture Notes in Physics, 2000

Complex systems such as glasses, gels, granular materials, and systems far from equilibrium exhib... more Complex systems such as glasses, gels, granular materials, and systems far from equilibrium exhibit violation of the ergodic hypothesis (EH) and of the fluctuation-dissipation theorem (FDT). Recent investigations in systems with memory [1] have established a hierarchical connection between mixing, the EH and the FDT. They have shown that a failure of the mixing condition (MC) will lead to the subsequent failures of the EH and of the FDT. Another important point is that such violations are not limited to complex systems: simple systems may also display this feature. Results from such systems are analytical and obviously easier to understand than those obtained in complex structures, where a large number of competing phenomena are present. In this work, we review some important requirements for the validity of the FDT and its connection with mixing, the EH and anomalous diffusion in one-dimensional systems. We show that when the FDT fails, an out-ofequilibrium system relaxes to an effective temperature different from that of the heat reservoir. This effective temperature is a signature of metastability found in many complex systems such as spin-glasses and granular materials.

AIP Conference Proceedings, 2007

ABSTRACT Random diffusion is shown to be an important mechanism on fostering cooperative behavior... more ABSTRACT Random diffusion is shown to be an important mechanism on fostering cooperative behavior among simple agents (memoryless, unconditional cooperators or defectors) living on a spatially structured environment. In particular, under the Prisoner’s Dilemma framework, when allowing the agents to move with the simple “always‐move” rule, we find that cooperative behavior is not only possible but may even be enhanced. In addition, for a broad range of densities, mobile cooperators can more easily invade a population of mobile defectors, when compared with the fully viscous, immobile case. Thus, such simple mobility pattern may have played a fundamental role both in the onset and development of cooperative behavior, paving the way to more complex, individual and group, motility rules. © 2007 American Institute of Physics

We propose a novel algorithm that outputs the final standings of a soccer league, based on a simp... more We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the tournament according to the results of previous games. The updated potential modifies a teams' future winning/losing probabilities. We show that this evolutionary game is able to reproduce the statistical properties of final standings of actual editions of the Brazilian tournament (Brasileirão). However, other leagues such as the Italian and the Spanish tournaments have notoriously non-Gaussian traces and cannot be straightforwardly reproduced by this evolutionary non-Markovian model. A complete understanding of these phenomena deserves much more attention, but we suggest a simple explanation based on data collected in Brazil: Here several teams were crowned champion in previous editions corroborating that the champion typically emerges from random fluctuations that partly preserves the gaussian traces during the tournament. On the other hand, in the Italian and Spanish leagues only a few teams in recent history have won their league tournaments. These leagues are based on more robust and hierarchical structures established even before the beginning of the tournament. For the sake of completeness, we also elaborate a totally Gaussian model (which equalizes the winning, drawing, and losing probabilities) and we show that the scores of the "Brasileirão" cannot be reproduced. Such aspects stress that evolutionary aspects are not superfluous in our modeling. Finally, we analyse the distortions of our model in situations where a large number of teams is considered, showing the existence of a transition from a single to a double peaked histogram of the final classification scores. An interesting scaling is presented for different sized tournaments.

Langmuir, 2015

When a drop of water is placed on a rough surface, there are two possible extreme regimes of wett... more When a drop of water is placed on a rough surface, there are two possible extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets trapped underneath the droplet and the one characterized by the homogeneous wetting of the surface, called the Wenzel (W) state. A way to investigate the transition between these two states is by means of evaporation experiments, in which the droplet starts in a CB state and, as its volume decreases, penetrates the surface's grooves, reaching a W state. Here we present a theoretical model based on the global interfacial energies for CB and W states that allows us to predict the thermodynamic wetting state of the droplet for a given volume and surface texture. We first analyze the influence of the surface geometric parameters on the droplet's final wetting state with constant volume, and show that it depends strongly on the surface texture. We then vary the volume of the droplet keeping fixed the geometric surface parameters to mimic evaporation and show that the drop experiences a transition from the CB to the W state when its volume reduces, as observed in experiments. To investigate the dependency of the wetting state on the initial state of the droplet, we implement a cellular Potts model in three dimensions. Simulations show a very good agreement with theory when the initial state is W, but it disagrees when the droplet is initialized in a CB state, in accordance with previous observations which show that the CB state is metastable in many cases. Both simulations and theoretical model can be modified to study other kinds of surface.

Physics Letters A, 2009

Using both an analytical method and a numerical approach we have investigated pattern formation f... more Using both an analytical method and a numerical approach we have investigated pattern formation for a nonlocal convective Fisher equation with constant and spatial velocity fields. We analyze the limits of the influence function due to nonlocal interaction and we obtain the phase diagram of critical velocities v c as function of the width μ of the influence function, which characterize the self-organization of a finite system.

Recent investigations call attention to the dynamics of anomalous diffusion and its connection wi... more Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.

Physical Review Letters, 2008

We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brown... more We present a novel scheme for the appearance of stochastic resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. The entropic stochastic resonance, characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single molecules and nanodevices.

Physical Review E, 2014

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playi... more We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius rP that accounts for the population viscosity, and an interaction radius rint that defines the instantaneous contact network for the game dynamics. We show that, differently from the rP = 0 case, the model with finite sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.

Physical Review E, 2001

The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance... more The Prisoner's dilemma is the main game theoretical framework in which the onset and maintainance of cooperation in biological populations is studied. In the spatial version of the model, we study the robustness of cooperation in heterogeneous ecosystems in spatial evolutionary games by considering site diluted lattices. The main result is that, due to disorder, the fraction of cooperators in the population is enhanced. Moreover, the system presents a dynamical transition at *, separating a region with spatial chaos from one with localized, stable groups of cooperators.

Physics Letters A, 2005

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a pow... more We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as k −β , using a stochastic description. It establishes a direct connection between the fluctuation in the spin-wave density of states and the noise density of states. For continuous ranges of the exponent β, we find super-diffusive and ballistic spinwave motions. Both diffusion exponents predicted by the stochastic procedure agree with the ones calculated using the Hamiltonian dynamics.

Physical Review Letters, 2008

A recent paper [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact t... more A recent paper [M. H. Lee, Phys. Rev. Lett. 98, 190601 (2007)] has called attention to the fact that irreversibility is a broader concept than ergodicity, and that therefore the Khinchin theorem [A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, New York) 1949] may fail in some systems. In this Letter we show that for all ranges of normal and anomalous diffusion described by a Generalized Langevin Equation the Khinchin theorem holds.

Physical Review E, 2013

Statistics of soccer tournament scores based on the double round robin system of several countrie... more Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva et al., Comput. Phys. Commun. 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

Physica A: Statistical Mechanics and its Applications, 2014

ABSTRACT We present an extensive, systematic study of the Prisoner’s Dilemma and Snowdrift games ... more ABSTRACT We present an extensive, systematic study of the Prisoner’s Dilemma and Snowdrift games on a square lattice under a synchronous, noiseless imitation dynamics. We show that for both the occupancy of the network and the (random) mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear. We analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice. We point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results.

Physica A: Statistical Mechanics and its Applications, 2005

We present here a conjecture about the equivalence between the noise density of states of a syste... more We present here a conjecture about the equivalence between the noise density of states of a system governed by a generalized Langevin equation and the fluctuation in the energy density of states in a Hamiltonian system. We present evidence of this for a disordered Heisenberg system. r

Physica A: Statistical Mechanics and its Applications, 2006

... References. [1] IVL Costa, R. Morgado, MVBT Lima and FA Oliveira, Europhys. Lett. 63 (2003),p... more ... References. [1] IVL Costa, R. Morgado, MVBT Lima and FA Oliveira, Europhys. Lett. 63 (2003),p. 173. Full Text via CrossRef | View Record in Scopus | Cited By in Scopus (32). [2] MH Lee, Phys. Rev. B 26 (1982), p. 2547. MathSciNet | Full Text via CrossRef.

Journal of Theoretical Biology, 2007

We explore the minimal conditions for sustainable cooperation on a spatially distributed populati... more We explore the minimal conditions for sustainable cooperation on a spatially distributed population of memoryless, unconditional strategies (cooperators and defectors) in presence of unbiased, non contingent mobility in the context of the Prisoner's Dilemma game. We find that cooperative behavior is not only possible but may even be enhanced by such an "always-move" rule, when compared with the strongly viscous ("never-move") case. In addition, mobility also increases the capability of cooperation to emerge and invade a population of defectors, what may have a fundamental role in the problem of the onset of cooperation.

Journal of Theoretical Biology, 2009

The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag H... more The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population, sometimes promoting, sometimes inhibiting cooperation. Here we show that random dilution and mobility may suppress the inhibiting factors of the spatial structure in the Snowdrift game, while enhancing the already larger cooperation found in the Prisoner's dilemma and Stag Hunt games.