Set Of Rate Parameters Research Articles

A Diffusion-Based Approach for Simulating Forward-in-Time State-Dependent Speciation and Extinction Dynamics.

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios.

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models.

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

Synchronization dynamics of coupled van der Pol systems

We investigate the dynamic processes of synchronizing chaotic van der Pol systems driven by periodic force. For a given set of rate parameters, a driven oscillator could possess two types of chaotic attractor. Different initial condition results in the appearance of two trajectories which have inversion symmetry with respect to each other. Attraction basins of these two degenerate attractors are derived numerically. Possibilities of synchronizing same and different chaotic trajectories are probed. We investigate carefully the transient processes preceding to synchronization. With appropriate criterion, we define and obtain the synchronization domain in the coupling parameter space.

The influence of steps on the desorption kinetics of NO from Pt(111)

A kinetic model is presented which describes thermal desorption of molecules from surfaces and incorporates trapping at steps. The model is applied to desorption of NO from Pt(111). The results of three molecular beam experiments, which differ substantially from each other, are accounted for quantitatively by the model using one set of rate parameters. It is demonstrated that steps, even when present in small concentrations on accurately cut crystals, can play a dominant role in thermal desorption. The magnitude of the effect depends on the difference between the binding energies on the terrace and at steps, which for NO on Pt(111) is large (25±2 kcal/mol and 34±2 kcal/mol, respectively). Furthermore, it is shown that the rate parameters governing terrace desorption, escape from steps, and surface diffusion can all be extracted from modulated molecular beam studies carried out for a suitable range of conditions.

Fundamental harmonic a.c. polarography with disproportionation following the charge transfer step Theory and experimental results with the U(VI)/U(V) couple

A theoretical and experimental study is presented for the small amplitude a.c. polarographic response with systems involving second-order disproportionation following the charge transfer step. The theoretical derivation combines wellestablished analytical procedures for solving the a.c. boundary value problem with various nummerical methods to account for effects of d.c. polarization. The resulting rate law predicts significant influences of the disproportionation step on a.c. polarographic observables, including several novel effects not predicted or observed with first-order coupled chemical reactions. The basis for kinetic assessment of rate parameters associated with the heterogeneous charge transfer step and the homogenous disproportionation mechanism is clearly indicated by the theoretical rate law. The computer programs developed on the basis of the derivation provide the means for calculating predicted responses on the basis of most commonly-used mathematical models for the DME, including the expanding sphere model. The electrode reduction of UO22+ at the mercury-aqueous 6 M HClO4 interface is used as a model for the mechanism in question in an experimental assay of the theory's fidelity. Various predicted trends are verified experimentally. Analysis of the experimental data using the theoretical rate law generated rate parameters for the heterogeneous electrode reaction, the homogeneous disproportionation step and the diffusion process. Agreement between theory and experiment obtained with this set of rate parameters is quite satisfactory for a variety of observables. Finally, the disproportionation rate constant obtained is consistent with previous measurements by a variety of authors using both electrochemical and non-electrochemical methods.

Fundamental harmonic a.c. polarography with disproportionation following the charge transfer step: Theory and experimental results with the U(VI)/U(V) couple

Summary A theoretical and experimental study is presented for the small amplitude a.c. polarographic response with systems involving second-order disproportionation following the charge transfer step. The theoretical derivation combines wellestablished analytical procedures for solving the a.c. boundary value problem with various nummerical methods to account for effects of d.c. polarization. The resulting rate law predicts significant influences of the disproportionation step on a.c. polarographic observables, including several novel effects not predicted or observed with first-order coupled chemical reactions. The basis for kinetic assessment of rate parameters associated with the heterogeneous charge transfer step and the homogenous disproportionation mechanism is clearly indicated by the theoretical rate law. The computer programs developed on the basis of the derivation provide the means for calculating predicted responses on the basis of most commonly-used mathematical models for the DME, including the expanding sphere model. The electrode reduction of UO 2 2+ at the mercury-aqueous 6 M HClO 4 interface is used as a model for the mechanism in question in an experimental assay of the theory's fidelity. Various predicted trends are verified experimentally. Analysis of the experimental data using the theoretical rate law generated rate parameters for the heterogeneous electrode reaction, the homogeneous disproportionation step and the diffusion process. Agreement between theory and experiment obtained with this set of rate parameters is quite satisfactory for a variety of observables. Finally, the disproportionation rate constant obtained is consistent with previous measurements by a variety of authors using both electrochemical and non-electrochemical methods.