ON STABILITY OF STATIONARY STATES OF REVERSIBLE REACTIONS OF THE FIRST ORDER

The article discusses reversible first-order reactions. A system of differential equations is written. First integral and stationary state found. Using Lyapunov's direct method, stationary stability was investigated

Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion

Physical processes occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are often modeled using systems of nonlinear equations. Solving such a system is sometimes impossible in an analytical manner. The iterative methods, such as Newton’s method, are not always sufficiently effective in such cases. In this article, a combination of the homotopy method and the parametric continuation method was proposed to solve the system of nonlinear differential equations. These methods are symmetrical, i.e., the calculations can be made by increasing or decreasing the value of the parameters. Thanks to this approach, the determination of all roots of the system does not require any iterative method. Moreover, when the solutions of the system are close to each other, the proposed method easily determines all of them. As an example of the method use a mathematical model of a non-adiabatic catalytic pseudohomogeneous tubular chemical reactor with longitudinal dispersion was chosen.

Mathematical modeling nonstationarity of biotechnological production of lactic acid: stability

The article presents the calculated ratios of indicators determining the stationary states of the lactic acid production process. Three technologies that are most often mentioned in scientific publications are identified: the technology of using strains of microorganisms to produce biomass is a technology that is extremely rarely used; the fairly common technology of using strains of microorganisms to produce lactic acid with the consumption of the main substrate (most often glucose); the promising technology of obtaining lactic acid using, in addition to the main substrate, a component that reproduces the main substrate in the synthesis process. For each technology, the equations of material balance for stationary and non-stationary conditions, a generalized differential equation for non-stationary conditions, and a characteristic equation are given. The formulas for estimating the coefficients of differential equations and the coefficients of the characteristic equation are also given. The equations for non-stationary conditions according to the last two technologies are based on the use of the Taylor series expansion of functions with the preservation of only the first terms of the expansion, i. e. deviations from stationarity in small. The characteristic equation is formed using the eigenvalues . The methodology for all three technologies is given, which allows us to assess the stability of the considered stationary state – the Hurwitz method. For all three technologies, numerical results are obtained for estimating the coefficients of the characteristic equations Pi. Tabular values of the coefficients are given, according to which stability estimates for the dilution rate of 0.1 h–1, 0.2 h–1, 0.3 h–1 are obtained using determinants according to the Hurwitz matrix. The results of numerical estimates for the stability of stationary states for all three technologies are presented. The estimates were based on the indicators of constants published in scientific studies.

Comment on “Linear and bent triatomic molecules are not qualitatively different!”

Jensen (Can. J. Phys. 98, 506 (2020). doi: 10.1139/cjp-2019-0395 ) presents theoretical justification for the claim that linear triatomic molecules are necessarily observed to be bent. The basis of the assertion is that the expectation value of the supplement of the bending angle, [Formula: see text] used in Jensen’s paper, is calculated to be positive. In this comment, we examine the interpretation of the expectation values of [Formula: see text] in stationary states, and indicate that Jensen’s claim contradicts a basic principle of quantum mechanics that the energy and geometrical variables cannot have definite values at the same time.

Midisuperspace foam and the cosmological constant

Wheeler's conjectured "spacetime foam" -- large quantum fluctuations of spacetime at the Planck scale -- could have important implications for quantum gravity, perhaps even explaining why the cosmological constant seems so small. Here I explore this problem in a midisuperspace model consisting of metrics with local spherical symmetry. Classically, an infinite class of ``foamy'' initial data can be constructed, in which cancellations between expanding and contracting regions lead to a small average expansion even if Λ is large. Quantum mechanically, the model admits corresponding stationary states, for which the probability current is also nearly zero. These states appear to describe a self-reproducing spacetime foam with very small average expansion, effectively hiding the cosmological constant.

The Relationship between Mourning and Society in their Diversity of Concepts My Love to Tricky Mourning

The mourning in its instances, references, connections and ties among individuals, the title of this song indicates lack of our foundations, who loves us also rejects and abandon us (Nirvana - Jesus Doesn't Want Me For Sunbeam [1], with these customs we acquire the notion of love and mourning, and it is where the mirror of illusions and reality collide, where human omnipotence, omniscience, and omnivision meet death; It's long been known that in general the brain in its psychic processes does not recognize death, with the psychic structure not to recognize death, and how to understand how these external factors affect our psyche, our psychic structure and the ways one can possibly deal with such feeling within a Freudian psychoanalytic approach, that is, in simple words, the mourning in this intense period, as initially we do not recognize it as reality and have to accept and recognize it in the face of real impotence. Through a psychoanalytic approach this work seeks to face mourning to reduce suffering and remove the patient from possible stationary states within the state of mourning. "We need to love not to get sick.” Sigmund Freud.

About Chemical Modifications of Finite Dimensional QED Models

Suggestion of modifications of finite-dimensional quantum-electrodynamic (QED) models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due to quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.