In this paper we propose a generalized model for the motion of a two-species self-driven objects ... more In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called σmax. Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac like distribution, considering a parameter α that controls the system randomness. We show that for a certain α = αc the system abruptly transits from a mobile scenario to a clogged state which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement.
In this work, we propose a simple stochastic agent-based model to describe the revenue dynamics o... more In this work, we propose a simple stochastic agent-based model to describe the revenue dynamics of a nightclub venue based on the relationship between profit and spatial occupation. The system consists of an underlying square lattice (nightclub's dance floor) where every attendee (agent) is allowed to move to its first neighboring cells. Each guess has a characteristic delayed time between drinks, denoted as τ, after which it will show an urge to drink. At this moment, the attendee will tend to move towards the bar where a drink will be bought. After it has left the bar zone, τ time steps should pass so it shows once again the need to drink. Our model among other points show that it is no use filling the bar to obtain profit, and optimization should be analyzed. This can be done in a more secure way taking into consideration the ratio between income and ticket cost.
Social dilemmas concern a natural conflict between cooperation and self interests among individua... more Social dilemmas concern a natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the evolution of species. In order to understand the mechanisms involved in this framework, here we study the Optional Public Good Games with focus on the effects of diffusive aspects in the emergent patterns of cyclic dominance between the strategies. Differently from other works, we showed that rock-paper-scissors (RPS) patterns occur by introducing a simple kind of random mobility in a lattice sparsely occupied. Such pattern has been revealed to be very important in the conservation of the species in ecological and social environments. The goal of this paper is to show that we do not need more elaborated schemes for construction of the neighbourhood in the game to observe RPS patterns as suggested in the literature. As an interesting additional resul...
In this work we study a stochastic dynamic of particles of two types based on cells. Basically we... more In this work we study a stochastic dynamic of particles of two types based on cells. Basically we incorporate some innovations on a one-dimensional model proposed and solved by R. da Silva et al. (Physica A, 2015) which considers that in the absence of particles of the opposite species in the cell a particle goes toward the next cell with probability p and returns to the previous cell with probability q = 1− p. However this motion probability linearly decreases with the relative density of the contrary species. Our work not only expands the problem for two dimensions but also includes collision aspects by adding scattering to the neighbouring cells. Our results are divided into two different categories: a) One of the species remain fixed in their places which means that such particles will work as obstacles; b) Both species can move in the environment. In the first situation we can observe, by monitoring the kurtosis, that an interesting transition of the crossing time distribution ...
Journal of Statistical Mechanics: Theory and Experiment, 2019
The collective motion of self-driven particles shows interesting novel phenomena such as swarming... more The collective motion of self-driven particles shows interesting novel phenomena such as swarming and the emergence of patterns. We have recently proposed a model for counterflowing particles that captures this idea and exhibits clogging transitions. This model is based on a generalization of the Fermi-Dirac statistics wherein the maximal occupation of a cell is used. Here we present a detailed study comparing synchronous and asynchronous stochastic dynamics within this model. We show that an asynchronous updating scheme supports the mobile-clogging transition and eliminates some mobility anomalies that are present in synchronous Monte Carlo simulations. Moreover, we show that this transition is dependent upon its initial conditions. Although the Gini coefficient was originally used to model wealth inequalities, we show that it is also efficient for studying the mobile-clogging transition. Finally, we compare our stochastic simulation with direct numerical integration of partial differential equations used to describe this model.
In this paper we propose a generalized model for the motion of a two-species self-driven objects ... more In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called σmax. Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac like distribution, considering a parameter α that controls the system randomness. We show that for a certain α = αc the system abruptly transits from a mobile scenario to a clogged state which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement.
In this paper, we proposed a stochastic model which describes two species of particles moving in ... more In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile obstacles, whereas particles of one species move in opposite direction to the particles of the other species, or they can work as fixed obstacles remaining in their places during the time evolution. We conducted a detailed study about the statistics concerning the crossing time of particles, as well as the effects of the lateral transitions on the time required to the system reaches a state of complete geographic separation of species. The spatial effects of jamming were also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observed in our study the formation of patterns of lanes which reach the steady state regardless the initial conditions used for the evolution. A similar result is also observed in real experiments involving charged colloids motion and simulations of pedestrian dynamics based on Langevin equations, when periodic boundary conditions are considered (particles counterflow in a ring symmetry). The results obtained through Monte Carlo numerical simulations and numerical integrations are in good agreement with each other. However, differently from previous studies, the dynamics considered in this work is not Newton-based, and therefore, even artificial situations of self-propelled objects should be studied in this first-principle modeling.
Physica A: Statistical Mechanics and its Applications, 2017
h i g h l i g h t s • We studied spatial diffusion in optional public goods game; • We quantify t... more h i g h l i g h t s • We studied spatial diffusion in optional public goods game; • We quantify the global oscillations (RPS cycles) by proposing a new amount; • High mobility and low occupation enlarge the occurrence of global oscillations;
The equation of the magnetization dynamics proposed by Landau and Lifshitz is widely-used and is ... more The equation of the magnetization dynamics proposed by Landau and Lifshitz is widely-used and is the base for numerous studies on simulations of magnetic systems. In this work we confer a theoretical review of the basic concepts of micromagnetism. First, the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations are presented. After that, the construction of the numerical model used here is described, where the magnetic dynamics is based on the Landau-Lifshitz-Gilbert equation. A presentation of the algorithm on which the code used in our simulation is based is then performed. A brief description of the programming language on which the code is written is made as well. At the end of the study, some simulation results are shown and proposals for future development are presented.
Physica A: Statistical Mechanics and its Applications
In this work, we extended a stochastic model for football leagues based on the team's potential [... more In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. 184 661-670 (2013)] for making predictions instead of only performing a successful characterization of the statistics on the punctuation of the real leagues. Our adaptation considers the advantage of playing at home when considering the potential of the home and away teams. The algorithm predicts the tournament's outcome by using the market value or/and the ongoing team's performance as initial conditions in the context of Monte Carlo simulations. We present and compare our results to the worldwide known SPI predictions performed by the "FiveThirtyEight" project. The results show that the algorithm can deliver good predictions even with a few ingredients and in more complicated seasons like the 2020 editions where the matches were played without fans in the stadiums.
In this work, we propose a two-dimensional extension of a previously defined one-dimensional vers... more In this work, we propose a two-dimensional extension of a previously defined one-dimensional version of a model of particles in counterflowing streams, which considers an adapted Fermi-Dirac distribution to describe the transition probabilities. In this modified and extended version of the model, we consider that only particles of different species can interact, and they hop through the cells of a two-dimensional rectangular lattice with probabilities taking into account diffusive and scattering aspects. We show that for a sufficiently low level of randomness (α 10), the system can relax to a mobile self-organized steady state of counterflow (lane formation) or to an immobile state (clogging) if the system has an average density near a certain crossover value (ρ c). We also show that in the case of imbalance between the species, we can simultaneously have three different situations for the same density value set: (i) an immobile phase, (ii) a mobile pattern organized by lanes, and (iii) a profile with mobility but without lane formation, which essentially is the coexistence of situations (i) and (ii). All of our results were obtained by performing Monte Carlo simulations.
In this paper we propose a generalized model for the motion of a two-species self-driven objects ... more In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called σmax. Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac like distribution, considering a parameter α that controls the system randomness. We show that for a certain α = αc the system abruptly transits from a mobile scenario to a clogged state which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement.
In this work, we propose a simple stochastic agent-based model to describe the revenue dynamics o... more In this work, we propose a simple stochastic agent-based model to describe the revenue dynamics of a nightclub venue based on the relationship between profit and spatial occupation. The system consists of an underlying square lattice (nightclub's dance floor) where every attendee (agent) is allowed to move to its first neighboring cells. Each guess has a characteristic delayed time between drinks, denoted as τ, after which it will show an urge to drink. At this moment, the attendee will tend to move towards the bar where a drink will be bought. After it has left the bar zone, τ time steps should pass so it shows once again the need to drink. Our model among other points show that it is no use filling the bar to obtain profit, and optimization should be analyzed. This can be done in a more secure way taking into consideration the ratio between income and ticket cost.
Social dilemmas concern a natural conflict between cooperation and self interests among individua... more Social dilemmas concern a natural conflict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the evolution of species. In order to understand the mechanisms involved in this framework, here we study the Optional Public Good Games with focus on the effects of diffusive aspects in the emergent patterns of cyclic dominance between the strategies. Differently from other works, we showed that rock-paper-scissors (RPS) patterns occur by introducing a simple kind of random mobility in a lattice sparsely occupied. Such pattern has been revealed to be very important in the conservation of the species in ecological and social environments. The goal of this paper is to show that we do not need more elaborated schemes for construction of the neighbourhood in the game to observe RPS patterns as suggested in the literature. As an interesting additional resul...
In this work we study a stochastic dynamic of particles of two types based on cells. Basically we... more In this work we study a stochastic dynamic of particles of two types based on cells. Basically we incorporate some innovations on a one-dimensional model proposed and solved by R. da Silva et al. (Physica A, 2015) which considers that in the absence of particles of the opposite species in the cell a particle goes toward the next cell with probability p and returns to the previous cell with probability q = 1− p. However this motion probability linearly decreases with the relative density of the contrary species. Our work not only expands the problem for two dimensions but also includes collision aspects by adding scattering to the neighbouring cells. Our results are divided into two different categories: a) One of the species remain fixed in their places which means that such particles will work as obstacles; b) Both species can move in the environment. In the first situation we can observe, by monitoring the kurtosis, that an interesting transition of the crossing time distribution ...
Journal of Statistical Mechanics: Theory and Experiment, 2019
The collective motion of self-driven particles shows interesting novel phenomena such as swarming... more The collective motion of self-driven particles shows interesting novel phenomena such as swarming and the emergence of patterns. We have recently proposed a model for counterflowing particles that captures this idea and exhibits clogging transitions. This model is based on a generalization of the Fermi-Dirac statistics wherein the maximal occupation of a cell is used. Here we present a detailed study comparing synchronous and asynchronous stochastic dynamics within this model. We show that an asynchronous updating scheme supports the mobile-clogging transition and eliminates some mobility anomalies that are present in synchronous Monte Carlo simulations. Moreover, we show that this transition is dependent upon its initial conditions. Although the Gini coefficient was originally used to model wealth inequalities, we show that it is also efficient for studying the mobile-clogging transition. Finally, we compare our stochastic simulation with direct numerical integration of partial differential equations used to describe this model.
In this paper we propose a generalized model for the motion of a two-species self-driven objects ... more In this paper we propose a generalized model for the motion of a two-species self-driven objects ranging from a scenario of a completely random environment of particles of negligible excluded volume to a more deterministic regime of rigid objects in an environment. Each cell of the system has a maximum occupation level called σmax. Both species move in opposite directions. The probability of any given particle to move to a neighboring cell depends on the occupation of this cell according to a Fermi-Dirac like distribution, considering a parameter α that controls the system randomness. We show that for a certain α = αc the system abruptly transits from a mobile scenario to a clogged state which is characterized by condensates. We numerically describe the details of this transition by coupled partial differential equations (PDE) and Monte Carlo (MC) simulations that are in good agreement.
In this paper, we proposed a stochastic model which describes two species of particles moving in ... more In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile obstacles, whereas particles of one species move in opposite direction to the particles of the other species, or they can work as fixed obstacles remaining in their places during the time evolution. We conducted a detailed study about the statistics concerning the crossing time of particles, as well as the effects of the lateral transitions on the time required to the system reaches a state of complete geographic separation of species. The spatial effects of jamming were also studied by looking into the deformation of the concentration of particles in the two-dimensional corridor. Finally, we observed in our study the formation of patterns of lanes which reach the steady state regardless the initial conditions used for the evolution. A similar result is also observed in real experiments involving charged colloids motion and simulations of pedestrian dynamics based on Langevin equations, when periodic boundary conditions are considered (particles counterflow in a ring symmetry). The results obtained through Monte Carlo numerical simulations and numerical integrations are in good agreement with each other. However, differently from previous studies, the dynamics considered in this work is not Newton-based, and therefore, even artificial situations of self-propelled objects should be studied in this first-principle modeling.
Physica A: Statistical Mechanics and its Applications, 2017
h i g h l i g h t s • We studied spatial diffusion in optional public goods game; • We quantify t... more h i g h l i g h t s • We studied spatial diffusion in optional public goods game; • We quantify the global oscillations (RPS cycles) by proposing a new amount; • High mobility and low occupation enlarge the occurrence of global oscillations;
The equation of the magnetization dynamics proposed by Landau and Lifshitz is widely-used and is ... more The equation of the magnetization dynamics proposed by Landau and Lifshitz is widely-used and is the base for numerous studies on simulations of magnetic systems. In this work we confer a theoretical review of the basic concepts of micromagnetism. First, the Landau-Lifshitz and Landau-Lifshitz-Gilbert equations are presented. After that, the construction of the numerical model used here is described, where the magnetic dynamics is based on the Landau-Lifshitz-Gilbert equation. A presentation of the algorithm on which the code used in our simulation is based is then performed. A brief description of the programming language on which the code is written is made as well. At the end of the study, some simulation results are shown and proposals for future development are presented.
Physica A: Statistical Mechanics and its Applications
In this work, we extended a stochastic model for football leagues based on the team's potential [... more In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. 184 661-670 (2013)] for making predictions instead of only performing a successful characterization of the statistics on the punctuation of the real leagues. Our adaptation considers the advantage of playing at home when considering the potential of the home and away teams. The algorithm predicts the tournament's outcome by using the market value or/and the ongoing team's performance as initial conditions in the context of Monte Carlo simulations. We present and compare our results to the worldwide known SPI predictions performed by the "FiveThirtyEight" project. The results show that the algorithm can deliver good predictions even with a few ingredients and in more complicated seasons like the 2020 editions where the matches were played without fans in the stadiums.
In this work, we propose a two-dimensional extension of a previously defined one-dimensional vers... more In this work, we propose a two-dimensional extension of a previously defined one-dimensional version of a model of particles in counterflowing streams, which considers an adapted Fermi-Dirac distribution to describe the transition probabilities. In this modified and extended version of the model, we consider that only particles of different species can interact, and they hop through the cells of a two-dimensional rectangular lattice with probabilities taking into account diffusive and scattering aspects. We show that for a sufficiently low level of randomness (α 10), the system can relax to a mobile self-organized steady state of counterflow (lane formation) or to an immobile state (clogging) if the system has an average density near a certain crossover value (ρ c). We also show that in the case of imbalance between the species, we can simultaneously have three different situations for the same density value set: (i) an immobile phase, (ii) a mobile pattern organized by lanes, and (iii) a profile with mobility but without lane formation, which essentially is the coexistence of situations (i) and (ii). All of our results were obtained by performing Monte Carlo simulations.
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