Competitive effects between stationary chemical reaction centres: a theory based on off-center monopoles.

The subject of this paper is competitive effects between multiple reaction sinks. A theory based on off-center monopoles is developed for the steady-state diffusion equation and for the convection-diffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convection-diffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an easy-to-use tool for the calibration of other more complicated models in mass and/or heat transfer

Control of Spatially Heterogeneous and Time-Varying Cellular Reaction Networks: A New Summation Law

A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control Analysis (MCA), which quantifies the influence of an individual process on a system variable as the control coefficient, cannot be applied to spatially separated protein networks. The present paper unravels the principles that govern the control over the fluxes and intermediate concentrations in spatially heterogeneous reaction networks. Our main results are two types of the control summation theorems. The first type is a non-trivial generalization of the classical theorems to systems with spatially and temporally varying concentrations. In this generalization, the process of diffusion, which enters as the result of spatial concentration gradients, plays a role similar to other processes such as chemical reactions and membrane transport. The second summation theorem is completely novel. It states that the control by the membrane transport, the diffusion control coefficient multiplied by two, and a newly introduced control coefficient associated with changes in the spatial size of a system (e.g., cell), all add up to one and zero for the control over flux and concentration. Using a simple example of a kinase/phosphatase system in a spherical cell, we speculate that unless active mechanisms of intracellular transport are involved, the threshold cell size is limited by the diffusion control, when it is beginning to exceed the spatial control coefficient significantly.Comment: 19 pages, AMS-LaTeX, 6 eps figures included with geompsfi.st

CIN4: a software tool for simulation of heterogeneous reactions at a reactor scale based on a micro-meso-macro coupling

National audienceUnderstanding the industrial reactors behavior is a difficult task in the case of solid state reactions such as solid-gas reactions. Indeed the solid phase is a granular medium through which circulate gaseous reactants and products. The properties of such a medium are modified in space and time due to reactions occurring at a microscopic scale. The thermodynamic conditions are driven not only by the operating conditions but also by the heat and mass transfers in the reactor. CIN4, a multiphysic software resulting from the collaboration between ASTEK and EMSE, offers the resolution of the thermohydraulic equations combined with kinetic laws which describe the heterogeneous reactions. The heat and mass transfers terms entering in the balance equations at a macroscopic scale depend on the kinetics evaluated at the microscopic scale. These equations give the temperature and partial pressure in the reactor, which in turn influence the microscopic kinetic behavior

Kinetic modeling of solid-gas reactions at reactor scale: A general approach

International audienceUnderstanding the industrial reactors behavior is a difficult task in the case of solid state reactions such as solid-gas reactions. Indeed the solid phase is a granular medium through which circulate gaseous reactants and products. The properties of such a medium are modified in space and time due to reactions occurring at a microscopic scale. The thermodynamic conditions are driven not only by the operating conditions but also by the heat and mass transfers in the reactor. We propose to numerically resolve the thermohydraulic equations combined with kinetic laws which describe the heterogeneous reactions. The major advantage of this approach is due to the large variety of kinetic models of grains transformation (~40) compared to the usual approach, especially in the case of surface nucleation and growth processes which need to quantitatively describe the grain conversion kinetics at a microscopic scale due to nucleation frequency and growth rate laws obtained in separate isothermal and isobaric experiments. The heat and mass transfers terms entering in the balance equations at a macroscopic scale depend on the kinetics evaluated at the microscopic scale. These equations give the temperature and partial pressure in the reactor, which in turn influence the microscopic kinetic behavior

Nuclear burning and mixing in the first stars: entrainment at a convective boundary using the PPB advection scheme

The evolution of the first generations of stars at zero or extremly low metallicity, and especially some crucial properties like the primary N14 production, is charactarized by convective-reactive mixing events that are mostly absent from similar evolution phases at solar-like metallicity. These episodes occur when unprocessed H-rich material is mixed accross a convective boundary into C12 rich He-burning material, as for example in He-shell flashes of extremely-low metallicity AGB stars. In this paper we describe the astrophysical context of such convective-reactive events, including the difficulty of current one-dimensional stellar evolution models to correctly simulate these evolutionary phases. We then describe the requirements and current state of modeling convective-reactive processes in the first stars environment. We demonstrate some of the new concepts that we are applying to this problem, i.e. the highly accurate PPB advection scheme in the framework of PPM hydrodynamic simulations of mixing accross a very stiff convective boundary. We show initial results of such simulations that address the first non-reactive step of this problem, which is the entrainment of H at the top boundary of the He-shell flash convection zone.Comment: Proceedings paper of First Stars III, 2006, Santa Fe, contributions by Falk Herwig and Paul Woodward, to appear in AIP Conf. Ser., ed. T. Abel, A. Heger and B. O'She

Diffusive search for a stochastically-gated target with resetting

In this paper, we analyze the mean first passage time (MFPT) for a single Brownian particle to find a stochastically-gated target under the additional condition that the position of the particle is reset to a fixed position \x_r at a rate $r$. The gate switches between an open and closed state according to a two-state Markov chain and can only be detected by the searcher in the open state. One possible example of such a target is a protein switching between different conformational states. As expected, the MFPT with or without resetting is an increasing function of the fraction of time $\rho_0$ that the gate is closed. However, the interplay between stochastic resetting and stochastic gating has non-trivial effects with regards the optimization of the search process under resetting. First, by considering the diffusive search for a gated target at one end of an interval, we show that the fractional change in the MFPT under resetting exhibits a non-monotonic dependence on $\rho_0$. In particular, the percentage reduction of the MFPT at the optimal resetting rate (when it exists) increases with $\rho_0$ up to some critical value, after which it decreases and eventually vanishes. Second, in the case of a spherical target in $\R^d$, the dependence of the MFPT on the spatial dimension $d$ is significantly amplified in the presence of stochastic gating.Comment: 17 pages, 9 figure