Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

Simple bimolecular reactions $A_1+A_2\rightleftharpoons A_3+A_4$ are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction $H_2+Cl\rightleftharpoons HCl+H$, and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.Comment: 11 pages, 5 figures, to appear in vol.42 of the Brazilian Journal of Physic

A unified approach for the solution of the Fokker-Planck equation

This paper explores the use of a discrete singular convolution algorithm as a unified approach for numerical integration of the Fokker-Planck equation. The unified features of the discrete singular convolution algorithm are discussed. It is demonstrated that different implementations of the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. Three benchmark stochastic systems, the repulsive Wong process, the Black-Scholes equation and a genuine nonlinear model, are employed to illustrate the robustness and to test accuracy of the present approach for the solution of the Fokker-Planck equation via a time-dependent method. An additional example, the incompressible Euler equation, is used to further validate the present approach for more difficult problems. Numerical results indicate that the present unified approach is robust and accurate for solving the Fokker-Planck equation.Comment: 19 page

Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

On the kinetic systems for simple reacting spheres : modeling and linearized equations

Series: Springer Proceedings in Mathematics & Statistics, Vol. 75In this work we present some results on the kinetic theory of chemically reacting gases, concerning the model of simple reacting spheres (SRS) for a gaseous mixture undergoing a chemical reaction of type A1 +A2 A3 +A4. Starting from the approach developed in paper [11], we provide properties of the SRS system needed in the mathematical and physical analysis of the model. Our main result in this proceedings provides basic properties of the SRS system linearized around the equilibrium, including the explicit representations of the kernels of the linearized SRS operators.Fundação para a Ciência e a Tecnologia (FCT), PEst-C/MAT/UI0013/2011, SFRH/BD/28795/200

Agency, qualia and life: connecting mind and body biologically

Many believe that a suitably programmed computer could act for its own goals and experience feelings. I challenge this view and argue that agency, mental causation and qualia are all founded in the unique, homeostatic nature of living matter. The theory was formulated for coherence with the concept of an agent, neuroscientific data and laws of physics. By this method, I infer that a successful action is homeostatic for its agent and can be caused by a feeling - which does not motivate as a force, but as a control signal. From brain research and the locality principle of physics, I surmise that qualia are a fundamental, biological form of energy generated in specialized neurons. Subjectivity is explained as thermodynamically necessary on the supposition that, by converting action potentials to feelings, the neural cells avert damage from the electrochemical pulses. In exchange for this entropic benefit, phenomenal energy is spent as and where it is produced - which precludes the objective observation of qualia

At What Stage of Neural Processing Does Cocaine Act to Boost Pursuit of Rewards?

Dopamine-containing neurons have been implicated in reward and decision making. One element of the supporting evidence is that cocaine, like other drugs that increase dopaminergic neurotransmission, powerfully potentiates reward seeking. We analyze this phenomenon from a novel perspective, introducing a new conceptual framework and new methodology for determining the stage(s) of neural processing at which drugs, lesions and physiological manipulations act to influence reward-seeking behavior. Cocaine strongly boosts the proclivity of rats to work for rewarding electrical brain stimulation. We show that the conventional conceptual framework and methods do not distinguish between three conflicting accounts of how the drug produces this effect: increased sensitivity of brain reward circuitry, increased gain, or decreased subjective reward costs. Sensitivity determines the stimulation strength required to produce a reward of a given intensity (a measure analogous to the KM of an enzyme) whereas gain determines the maximum intensity attainable (a measure analogous to the vmax of an enzyme-catalyzed reaction). To distinguish sensitivity changes from the other determinants, we measured and modeled reward seeking as a function of both stimulation strength and opportunity cost. The principal effect of cocaine was a two-fourfold increase in willingness to pay for the electrical reward, an effect consistent with increased gain or decreased subjective cost. This finding challenges the long-standing view that cocaine increases the sensitivity of brain reward circuitry. We discuss the implications of the results and the analytic approach for theories of how dopaminergic neurons and other diffuse modulatory brain systems contribute to reward pursuit, and we explore the implications of the conceptual framework for the study of natural rewards, drug reward, and mood

On modified simple reacting spheres kinetic model for chemically reactive gases

Versão dos autores para esta publicação.We consider the modiffed simple reacting spheres (MSRS) kinetic model that, in addition to the conservation of energy and momentum, also preserves the angular momentum in the collisional processes. In contrast to the line-of-center models or chemical reactive models considered in [1], in the MSRS (SRS) kinetic models, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justi ed. In the MSRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard spheres-like. We consider a four component mixture A, B, A*, B*, in which the chemical reactions are of the type A + B = A* + B*, with A* and B* being distinct species from A and B. We provide fundamental physical and mathematical properties of the MSRS model, concerning the consistency of the model, the entropy inequality for the reactive system, the characterization of the equilibrium solutions, the macroscopic setting of the model and the spatially homogeneous evolution. Moreover, we show that the MSRS kinetic model reduces to the previously considered SRS model (e.g., [2], [3]) if the reduced masses of the reacting pairs are the same before and after collisions, and state in the Appendix the more important properties of the SRS system.Fundação para a Ciência e a Tecnologi