André L. A. Penna

Pattern formation and coexistence domains for a nonlocal population dynamics.

In this Rapid Communication we propose a most general equation to study pattern formation for one-species populations and their limit domains in systems of length L. To accomplish this, we include nonlocality in the growth and competition terms, where the integral kernels now depend on characteristic length parameters α and β. Therefore, we derived a parameter space (α,β) where it is possible to analyze a coexistence curve α^{*}=α^{*}(β) that delimits domains for the existence (or absence) of pattern formation in population dynamics systems. We show that this curve is analogous to the coexistence curve in classical thermodynamics and critical phenomena physics. We have successfully compared this model with experimental data for diffusion of Escherichia coli populations.

Thermodynamics aspects of noise-induced phase synchronization.

In this article, we present an approach for the thermodynamics of phase oscillators induced by an internal multiplicative noise. We analytically derive the free energy, entropy, internal energy, and specific heat. In this framework, the formulation of the first law of thermodynamics requires the definition of a synchronization field acting on the phase oscillators. By introducing the synchronization field, we have consistently obtained the susceptibility and analyzed its behavior. This allows us to characterize distinct phases in the system, which we have denoted as synchronized and parasynchronized phases, in analogy with magnetism. The system also shows a rich complex behavior, exhibiting ideal gas characteristics for low temperatures and susceptibility anomalies that are similar to those present in complex fluids such as water.

Charge degeneracy removal in the screened hydrogen atom

We derive an analytical model for the states of the screened hydrogen atom by using a new charge degeneracy removal approach. Starting from the nonzero Thomas?Fermi parameter q, we show that screening effect is due to breaks of the charge degeneracy in each quantum level of the hydrogen atom. The charge degeneracy removal reparametrizes the atomic system through the effective nuclear charge ?n,l and the appearance of a dual charge ?n,l for each quantum level. In this approach, we show that the screening of a quantum state depends hierarchically on the screening from all previous quantum states with the same angular quantum numbers. The excited state energies En,l(q) are analytically found taking into account the contribution of this new charge degeneracy for each quantum level. Finally, we also have estimated accurate critical screening parameters q*n,l for the bound?unbound transition.

Critical behavior of noise-induced phase synchronization

In this article, we present a systematic study of the critical behavior of phase oscillators with multiplicative noise from a thermodynamic equilibrium approach. We have already presented the thermodynamics of phase noise oscillators and mapped out in detail the behavior of free energy, entropy, and specific heat in a previous work [P. D. Pinto, F.A. Oliveira, A.L.A. Penna, Phys. Rev. E 93, 052220 (2016)], in which we also introduced the concept of synchronization field. This proved to be important in order to understand the effect of multiplicative noise in the synchronization of the system. Using this approach, our aim is now to study analytically the critical behavior of this system from which we derive a fluctuation-dissipation relation as well as the critical exponents associated with the order parameter, specific heat, and susceptibility. We show that the exponents obey the Rushbrooke and Widom scaling laws.

Auto-organização e formação de padrão em sistemas físicos e biológicos

In this work we present a brief discussion of the mathematical description of pattern formation phenomena in biological systems through the mathematical models of population dynamics. We present some examples of physical, chemical and biological systems which exhibit this phenomena. For each system we show the main parameters that describe the patterns. We show that in the case of population, patterns can be described when we modify the Fisher-Kolmogorov equation, considering a non-local interaction for the competition term. We present an analytical and numerical study of the Fisher-Kolmogorov equation with diffusion and we analyze the role of growth, diffusion and competition term in the pattern formation.

Leis de escala e a dinâmica do crescimento em estruturas biológicas

In this article we will briefly present an interdisciplinary relationship between scaling laws in physics and growth dynamics in biological structures. First, will be discussed the preliminary concepts of the scaling laws applied in biology. By using the West similarity hypothesis, we formulate, in a deductive and didactic way, a generalized differential equation to study the growth of organisms in general.