Context Of Chemical Kinetics Research Articles

Effect of acid-temperature-pressure on the damage characteristics of sandstone

The primary objective of this study is to experimentally study the effects of different curing temperatures (25, 50 and 75 °C) and pressures (5, 10 and 15 MPa) on the mechanical properties and damage deterioration mechanism of sandstone samples subjected to pH3 H2SO4. The responses of mass loss, aperture structure based on NMR, deformation behaviour and mechanical parameters of sandstone were compared and analyzed. The microstructure change in sandstone samples was observed and analyzed with SEM-EDS. The deterioration mechanism of sandstone after treatment with acid-temperature-pressure (ATP) was discussed considering pH and ion concentration in acidic solution. The results indicated that mass, uniaxial compressive strength and elastic modulus of the samples decreased and sandstone sample porosity as well as pH and ion concentration of corrosion solution increased after treatment with APT. Under the same conditions, increasing curing temperature had apparent deterioration effect on acid-corroded sandstone, yet increasing pressure had little effect on it, especially the pressure increased from 10 MPa to 15 MPa. The results of SEM and electron spectroscopy showed that the microstructure, defects and mineral content of sandstone changed after treatment with ATP. The secondary pores increased and the surface structures became loose. The chemical reactions between sandstone samples and acidic solutions with different curing temperatures and pressures as well as the damage mechanism underlying the interaction were discussed in the theoretical context of chemical kinetics.

Damage effects and mechanisms in granite treated with acidic chemical solutions

Uniaxial and triaxial compression tests as well as splitting tests were conducted on granite specimens after acidic solution erosion at a variety of different pH values and flow rates. The responses of strength loss, deformation behavior and mechanical parameters of the granite were compared and analyzed. The effects of acidic chemical corrosion on microscopic structures, defect morphology and mineral elements of the granite were observed and analyzed under scanning electron microscopy (SEM) and electron spectroscopy. The aging that resulted from the interactions between the granite and chemical solutions were analyzed based on the mass and elastic wave velocity data of the specimens and pH value of the solutions at different soaking times, along with ion chromatography detection results of the solutions’ chemical constituents and concentrations after soaking. Based on the results of X-ray diffraction for the mineral composition and X-ray fluorescence to determine the chemical elements and compounds in granite, the chemical reactions between granite and acidic solutions as well as the damage mechanism underlying the interaction were discussed in the theoretical context of chemical kinetics.

Thermalization of Lévy Flights: Path-Wise Picture in 2D

We analyze two-dimensional (2D) random systems driven by a symmetric Lévy stable noise which in the presence of confining potentials may asymptotically set down at Boltzmann-type thermal equilibria. In view of the Eliazar-Klafter no-go statement, such dynamical behavior is plainly incompatible with the standard Langevin modeling of Lévy flights. No explicit path-wise description has been so far devised for the thermally equilibrating random motion we address, and its formulation is the principal goal of the present work. To this end we prescribe a priori the target pdf ρ∗ in the Boltzmann form ~exp[] and next select the Lévy noise (e.g., its Lévy measure) of interest. To reconstruct random paths of the underlying stochastic process we resort to numerical methods. We create a suitably modified version of the time honored Gillespie algorithm, originally invented in the chemical kinetics context. A statistical analysis of generated sample trajectories allows us to infer a surrogate pdf dynamics which sets down at a predefined target, in consistency with the associated kinetic (master) equation.

Lévy flights in confining environments: Random paths and their statistics

We analyze a specific class of random systems that, while being driven by a symmetric Lévy stable noise, asymptotically set down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) ρ∗(x)∼exp[−Φ(x)]. This behavior needs to be contrasted with the standard Langevin representation of Lévy jump-type processes. It is known that the choice of the drift function in the Newtonian form ∼−∇Φ excludes the existence of the Boltzmannian pdf ∼exp[−Φ(x)] (Eliazar–Klafter no go theorem). In view of this incompatibility statement, our main goal here is to establish the appropriate path-wise description of the equilibrating jump-type process. A priori given inputs are (i) jump transition rates entering the master equation for ρ(x,t) and (ii) the target (invariant) pdf ρ∗(x) of that equation, in the Boltzmannian form. We resort to numerical methods and construct a suitable modification of the Gillespie algorithm, originally invented in the chemical kinetics context. The generated sample trajectories show up a qualitative typicality, e.g. they display structural features of jumping paths (predominance of small vs large jumps) specific to particular stability indices μ∈(0,2). The obtained random paths statistical data allow us to infer an associated pdf ρ(x,t) dynamics which stands for a validity check of our procedure. The considered exemplary Boltzmannian equilibria ∼exp[−Φ(x)] refer to (i) harmonic potential Φ∼x2, (ii) logarithmic potential Φ∼nln(1+x2) with n=1,2 and (iii) locally periodic confining potential Φ∼sin2(2πx),|x|≤2, Φ∼(x2−4),|x|>2.

Trajectory Statistics of Confined L\'evy Flights and Boltzmann-type Equilibria

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise, where Langevin representation is absent. In view of the L\'{e}vy noise sensitivity to environmental inhomogeneities, the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Here, we infer pdf $\rho (x,t)$ based on numerical path-wise simulation of the underlying jump-type process. A priori given data are jump transition rates entering the master equation for $\rho (x,t)$ and its target pdf $\rho_*(x)$. To simulate the above processes, we construct a suitable modification of the Gillespie algorithm, originally invented in the chemical kinetics context. We exemplified our algorithm simulating different jump-type processes and discuss the dynamics of real physical systems where it can be useful.

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

The Rate-Controlled Constrained-Equilibrium (RCCE) method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system’s internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.