Hyperspherical theory of anisotropic exciton

A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the perturbation theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obtained numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributed between optically active and formerly inactive states, making the latter optically active. An approximate analytical solution of the anisotropic exciton problem taking into account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good accuracy and provides a useful qualitative description of the energy level evolution.Comment: 23 pages, 8 figure

Kinetic Path Summation, Multi--Sheeted Extension of Master Equation, and Evaluation of Ergodicity Coefficient

We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.Comment: The final journal versio

Experimental and Numerical Study of Low Temperature Methane Steam Reforming for Hydrogen Production

Low temperature methane steam reforming for hydrogen production, using experimental developed Ni/Al2O3 catalysts is studied both experimentally and numerically. The catalytic activity measurements were performed at a temperature range of 500–700 °C with steam to carbon ratio (S/C) of 2 and 3 under atmospheric pressure conditions. A mathematical analysis to evaluate the reaction feasibility at all different conditions that have been applied by using chemical equilibrium with applications (CEA) software and in addition, a mathematical model focused on the kinetics and the thermodynamics of the reforming reaction is introduced and applied using a commercial finite element analysis software (COMSOL Multiphysics 5.0). The experimental results were employed to validate the extracted simulation data based on the yields of the produced H2, CO2 and CO at different temperatures. A maximum hydrogen yield of 2.7 mol/mol-CH4 is achieved at 700 °C and S/C of 2 and 3. The stability of the 10%Ni/Al2O3 catalyst shows that the catalyst is prone to deactivation as supported by Thermogravimetric Analysis TGA results

Whisker's Directional Selectivity: Orientation Columns in the Barrel Field?

Using voltage-sensitive dye optical imaging methods, we visualized neural activity in the rat barrel cortex in response to the deflection of a single whisker in different directions. Obtained data indicates that fast movements of single whiskers in varying directions correlate with different patterns of activation in the somatosensory cortex. A functional map was created based on the voltage-sensitive dye optical signal. This supports prior research that vibrissae deflections cause responses in different cortical neurons within the barrel field according to the direction of the deflection. By analogy with the orientation columns in the visual cortex, directionally-biased single whisker responses to different directions of deflection could be a possible mechanism for the directional selectivity of this important sensory response

Voting and Catalytic Processes with Inhomogeneities

We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many ``competing'' inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a nontrivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particles) in the presence of an arbitrary number $n$ of inhomogeneities (``zealots'' in the voter language) and formal similarities with {\it suitable electrostatic systems} are pointed out. In the nontrivial cases $n=1, 2$, we explicitly compute the static and long-time properties of the order parameters and therefore capture the generic features of the systems. When $n>2$, the problems are studied through numerical simulations. In one spatial dimension, we also compute the expressions of the stationary order parameters in the completely disordered case, where $n$ is arbitrary large. Particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics.Comment: 17 pages, 6 figures, revtex4 2-column format. Original title ("Are Voting and Catalytic Processes Electrostatic Problems ?") changed upon editorial request. Minor typos corrected. Published in Physical Review

Entropy: The Markov Ordering Approach

The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the {\em Markov order}). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally "most random" distributions.Comment: 50 pages, 4 figures, Postprint version. More detailed discussion of the various entropy additivity properties and separation of variables for independent subsystems in MaxEnt problem is added in Section 4.2. Bibliography is extende

Automated control system for a mashing process

The goal of this paper is to describe a system for a mashing process, which is the first part of brewing beer. The mashing is a procedure where the fermentable (and some non-fermentable) sugars are extracted from malts. The program part based on LabVIEW, which is used to control NI CompactRIO. The main target of the project is to reach a predefined levels of the temperatures and maintain it during the pauses. When the necessary break time is ended the system is ready to go to the new value. The precise control of the temperatures during the breaks is one of the critical factors that define the texture and alcohol content of the beer. The system has two tanks with resistors PT100 in both of them, heat exchanger (coil), heater and pump. The first tank has heating element in order to rise the temperature in the other one. This project has practical solution with all explanations and graphs which are proven working ability of this control system

Reciprocal Relations Between Kinetic Curves

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, $\dot{x}=Kx$, the kinetic operator $K$ is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, $\exp (Kt)$, is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the $i$th pure state and measure the probability $p_j(t)$ of the $j$th state ($j\neq i$), and, similarly, measure $p_i(t)$ for the process, which starts at the $j$th pure state, then the ratio of these two probabilities $p_j(t)/p_i(t)$ is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.Comment: 6 pages, 1 figure, the final versio