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Stochastic processes applied to out-of-equilibrium systems


This project is centred on the application of theoretical and computational techniques of stochastic processes to several systems of interest. Stochastic processes is a broad area of knowledge, comprising a large number of tools that are suitable for treating a great variety of problems. The first goal of this project is to optimize and increase the number of tools to which I am acquainted, hence increasing the number of possible applications I may study. The second goal is then to apply these techniques to four specific problems, all related to out- of-equilibrium systems. The first problem is the use of magnetic nanoparticles in a cancer treatment technique known as magnetic-hyperthermia. Computer simulations will be used to optimize the physicochemical parameters of the material in order to improve the application. The second problem deals with Fourier's law of heat conduction. The goal is to develop microscopic stochastic models which lead to this law and also present interesting critical behaviour. The third problem is related to the concept of entropy-production in out-of- equilibrium systems. I will study grids of electrical circuits or chemical reactions with sources in search for non-trivial critical behaviour. Finally, the fourth problem is the use of stochastic techniques to study predator-prey models in population biology. The primary goal is to compare different approaches to the same specific problem, highlighting the advantages and drawbacks of each method. (AU)

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Scientific publications (6)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
RIBEIRO, WELLINGTON L.; LANDI, GABRIEL T.; SEMIAO, FERNANDO L.. Quantum thermodynamics and work fluctuations with applications to magnetic resonance. American Journal of Physics, v. 84, n. 12, p. 948-957, . (14/01218-2)
FIORE, CARLOS E.; LANDI, GABRIEL T.. Effect of diffusion in one-dimensional discontinuous absorbing phase transitions. Physical Review E, v. 90, n. 3, . (14/01218-2)
GUIMARAES, PEDRO H.; LANDI, GABRIEL T.; DE OLIVEIRA, MARIO J.. Nonequilibrium quantum chains under multisite Lindblad baths. Physical Review E, v. 94, n. 3, . (14/01218-2)
RIVALDO-GOMEZ, C. M.; FERREIRA, F. F.; LANDI, G. T.; SOUZA, J. A.. New route for hollow materials. SCIENTIFIC REPORTS, v. 6, . (13/16172-5, 16/09769-3, 15/10900-4, 14/01218-2)
SCHUAB, LUCAS; PEREIRA, EMMANUEL; LANDI, GABRIEL T.. Energy rectification in quantum graded spin chains: Analysis of the XXZ model. Physical Review E, v. 94, n. 4, . (14/01218-2)
BRUNELLI, M.; FUSCO, L.; LANDIG, R.; WIECZOREK, W.; HOELSCHER-OBERMAIER, J.; LANDI, C.; SEMIAO, F. L.; FERRARO, A.; KIESEL, N.; DONNER, T.; et al. Experimental Determination of Irreversible Entropy Production in out-of-Equilibrium Mesoscopic Quantum Systems. Physical Review Letters, v. 121, n. 16, . (14/01218-2)

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