Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles

Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and reactions between heterogenous particles is less well known. In this paper we develop a novel framework for modeling reaction-diffusion processes which directly incorporates volume exclusion. From an off-lattice microscopic individual based model we use the Fokker--Planck equation and the method of matched asymptotic expansions to derive a low-dimensional macroscopic system of nonlinear partial differential equations describing the evolution of the particles. A biologically motivated, hybrid model of chemotaxis with volume exclusion is explored, where reactions occur at rates dependent upon the chemotactic environment. Further, we show that for reactions due to contact interactions the appropriate reaction term in the macroscopic model is of lower order in the asymptotic expansion than the nonlinear diffusion term. However, we find that the next reaction term in the expansion is needed to ensure good agreement with simulations of the microscopic model. Our macroscopic model allows for more direct parameterization to experimental data than the models available to date.Comment: 13 pages, 4 figure

Fundamental Principles and Rights At Work: Value, Viability, Incidence and Importance as Elements For Economic Progress and Social Justice

Working Paper prepared for the ILO by Maria Luz Vega Ruiz and Daniel Martinez, focusing on the rights at work in Latin America and the Caribbean

Influence of the nonlocal parameter on the transverse vibration of double-walled carbon nanotubes

A high-order nonlocal continuum beam model is proposed, which can be applied to study the transverse vibrations of double-walled carbon nanotubes (DWCNTs), including those that could have initial deformations due to defects or external actions. A beam element is developed adopting Hermite cubic polynomials as shape functions, and mass and elastic stiffness matrix are presented. The influence of the nonlocal parameter on the vibrational properties of DWCNTs is studied. Using the proposed model, it was found that the nonlocal parameter has a strong influence on the natural frequencies.Fil: de Borbon, Fernanda Maria. Universidad Nacional de Cuyo. Facultad de Ingeniería. Instituto de Mecánica Estructural y Riesgo Sísmico. Maestría en Ingeniería Estructural; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Ambrosini, Ricardo Daniel. Universidad Nacional de Cuyo. Facultad de Ingeniería. Instituto de Mecánica Estructural y Riesgo Sísmico. Maestría en Ingeniería Estructural; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentin

Dynamic transition in Landau-Zener-St\"uckelberg interferometry of dissipative systems: the case of the flux qubit

We study Landau-Zener-Stuckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from a LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to 10 energy levels.Comment: One new figure added. Final version to be published in PR