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Papers by Rafael Mynssem Brum

Research paper thumbnail of Dynamics of tax evasion through an epidemic-like model

International Journal of Modern Physics C, 2017

In this work, we study a model of tax evasion. We considered a fixed population divided in three ... more In this work, we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call susceptibles to become evaders. The transitions among those compartments are ruled by probabilities, similarly to a model of epidemic spreading. These probabilities model social interactions among the individuals, as well as the government’s fiscalization. We simulate the model on fully-connected graphs, as well as on scale-free and random complex networks. For the fully-connected and random graph cases, we observe that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium phase transition, that is absent in scale-free networks.

Research paper thumbnail of Pressure exerted by a grafted polymer: Bethe lattice solution

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a s... more We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walks on regular lattices and gaussian walks. The adsorption transition, which is discontinuous, and its influence on the pressure are also studied.

Research paper thumbnail of Reversible limit of processes of heat transfer

Research paper thumbnail of Pressure exerted by a grafted polymer: Bethe lattice solution

Journal of Physics A: Mathematical and Theoretical, 2014

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a s... more We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walk on regular lattices and gaussian walks. The adsorptions transition, which is discontinuous, and its influence on the pressure are also studied.

Research paper thumbnail of Reversible limit of processes of heat transfer

Revista Brasileira de Ensino de Física, 2013

We study a process of heat transfer between a body of heat capacity C(T) and a sequence of N heat... more We study a process of heat transfer between a body of heat capacity C(T) and a sequence of N heat reservoirs, with temperatures equally spaced between an initial temperature T0 and a final temperature T N. The body and the heat reservoirs are isolated from the rest of the universe, and the body is brought in thermal contact successively with reservoirs of increasing temperature. We determine the change of entropy of the composite thermodynamic system in the total process in which the temperature of the body changes from T0 to T N. We find that for large values of N the total change of entropy of the composite process is proportional to (T N - T0) / N, but eventually a non-monotonic behavior is found at small values of N.

Research paper thumbnail of Pressure exerted by a grafted polymer: Bethe lattice solution

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a s... more We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point.
The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walk on regular lattices and gaussian walks. The adsorptions transition, which is discontinuous, and its influence on the pressure are also studied.

Research paper thumbnail of Reversible limit of processes of heat transfer

We study a process of heat transfer between a body of heat capacity C(T ) and a sequence of N hea... more We study a process of heat transfer between a body of heat capacity C(T ) and a sequence of N heat reservoirs, with temperatures equally spaced between an initial temperature T0 and a final temperature TN . The body and the heat reservoirs are isolated from the rest of the universe, and the body is brought in thermal contact successively with reservoirs of increasing temperature. We determine the change of entropy of the composite thermodynamic system in the total process in which the temperature of the body changes from T0 to TN . We find that for large values of N the total change of entropy of the composite process is proportional to (TN − T0)/N , but eventually a non-monotonic behavior is found at small values of N . Keywords: second law of thermodynamics, entropy, reversible and irreversible processes, heat exchange.

Research paper thumbnail of Dynamics of tax evasion through an epidemic-like model

International Journal of Modern Physics C, 2017

In this work, we study a model of tax evasion. We considered a fixed population divided in three ... more In this work, we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call susceptibles to become evaders. The transitions among those compartments are ruled by probabilities, similarly to a model of epidemic spreading. These probabilities model social interactions among the individuals, as well as the government’s fiscalization. We simulate the model on fully-connected graphs, as well as on scale-free and random complex networks. For the fully-connected and random graph cases, we observe that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium phase transition, that is absent in scale-free networks.

Research paper thumbnail of Pressure exerted by a grafted polymer: Bethe lattice solution

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a s... more We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walks on regular lattices and gaussian walks. The adsorption transition, which is discontinuous, and its influence on the pressure are also studied.

Research paper thumbnail of Reversible limit of processes of heat transfer

Research paper thumbnail of Pressure exerted by a grafted polymer: Bethe lattice solution

Journal of Physics A: Mathematical and Theoretical, 2014

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a s... more We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point. The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walk on regular lattices and gaussian walks. The adsorptions transition, which is discontinuous, and its influence on the pressure are also studied.

Research paper thumbnail of Reversible limit of processes of heat transfer

Revista Brasileira de Ensino de Física, 2013

We study a process of heat transfer between a body of heat capacity C(T) and a sequence of N heat... more We study a process of heat transfer between a body of heat capacity C(T) and a sequence of N heat reservoirs, with temperatures equally spaced between an initial temperature T0 and a final temperature T N. The body and the heat reservoirs are isolated from the rest of the universe, and the body is brought in thermal contact successively with reservoirs of increasing temperature. We determine the change of entropy of the composite thermodynamic system in the total process in which the temperature of the body changes from T0 to T N. We find that for large values of N the total change of entropy of the composite process is proportional to (T N - T0) / N, but eventually a non-monotonic behavior is found at small values of N.

Research paper thumbnail of Pressure exerted by a grafted polymer: Bethe lattice solution

We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a s... more We solve the problem of a chain, modeled as a self-avoiding walk, grafted o the wall limiting a semi-infinite Bethe lattice of arbitrary coordination number q. In particular, we determine the pressure exerted by the polymer on the wall, as a function of the distance to the grafting point.
The pressure, in general, decays exponentially with the distance, at variance with what is found for SAWs and directed walk on regular lattices and gaussian walks. The adsorptions transition, which is discontinuous, and its influence on the pressure are also studied.

Research paper thumbnail of Reversible limit of processes of heat transfer

We study a process of heat transfer between a body of heat capacity C(T ) and a sequence of N hea... more We study a process of heat transfer between a body of heat capacity C(T ) and a sequence of N heat reservoirs, with temperatures equally spaced between an initial temperature T0 and a final temperature TN . The body and the heat reservoirs are isolated from the rest of the universe, and the body is brought in thermal contact successively with reservoirs of increasing temperature. We determine the change of entropy of the composite thermodynamic system in the total process in which the temperature of the body changes from T0 to TN . We find that for large values of N the total change of entropy of the composite process is proportional to (TN − T0)/N , but eventually a non-monotonic behavior is found at small values of N . Keywords: second law of thermodynamics, entropy, reversible and irreversible processes, heat exchange.