Natural Bifurcation Coordinates for Three‐Dimensional Chemical Reactions

1972 ◽  
Vol 57 (7) ◽  
pp. 2722-2727 ◽  
Author(s):  
Susan H. Harms ◽  
Robert E. Wyatt
Keyword(s):  
Chemical Reactions ◽  
Three Dimensional

scholarly journals Augmented Reality Chemical Reaction with User-Centered Design

2018 ◽  
Vol 218 ◽  
pp. 04012
Author(s):  
Finsa Nurpandi ◽  
Agung Gumelar
Keyword(s):  
Augmented Reality ◽  
Chemical Reactions ◽  
Periodic Table ◽  
Three Dimensional ◽  
User Centered Design ◽  
Structure Of Molecules ◽  
Level Of Activity ◽  
Chemistry Learning ◽  
Chemical Concepts ◽  
User Centered

One of chemistry is the chemical element that is represented by the symbol on the periodic table. The low level of activity, interest, and the result of chemistry learning in school is caused by the students generally having difficulty in solving problems related to chemical reactions. In addition, most of the chemical concepts are abstract so it is difficult to imagine the structure of molecules clearly. Augmented Reality can integrate digital elements with the real world in real time and follow the circumstances surrounding environment. Augmented Reality can provide a new more interactive concept in the learning process because users can directly interact naturally. By using Augmented Reality, the atoms in the periodic table will be scanned using a camera from an Android-based smartphone that has installed this app. The scan results are then compared with existing data and will show the molecular structure in three-dimensional form. Users can also observe reactions between atoms by combining multiple markers simultaneously. Augmented Reality application is built using the concept of user-centered design and Unity with personal license as development tools. By using this app, studying chemical reactions no longer requires a variety of chemicals that could be harmful to users.

scholarly journals Non-Equilibrium Liouville and Wigner Equations: Classical Statistical Mechanics and Chemical Reactions for Long Times

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 179 ◽  
Author(s):  
Ramon Álvarez-Estrada
Keyword(s):  
Orthogonal Polynomials ◽  
Chemical Reactions ◽  
Thermal Equilibrium ◽  
Three Dimensional ◽  
Liapunov Function ◽  
Heat Bath ◽  
Wigner Functions ◽  
Statistical Systems ◽  
Non Equilibrium

We review and improve previous work on non-equilibrium classical and quantum statistical systems, subject to potentials, without ab initio dissipation. We treat classical closed three-dimensional many-particle interacting systems without any “heat bath” ( h b ), evolving through the Liouville equation for the non-equilibrium classical distribution W c , with initial states describing thermal equilibrium at large distances but non-equilibrium at finite distances. We use Boltzmann’s Gaussian classical equilibrium distribution W c , e q , as weight function to generate orthogonal polynomials ( H n ’s) in momenta. The moments of W c , implied by the H n ’s, fulfill a non-equilibrium hierarchy. Under long-term approximations, the lowest moment dominates the evolution towards thermal equilibrium. A non-increasing Liapunov function characterizes the long-term evolution towards equilibrium. Non-equilibrium chemical reactions involving two and three particles in a h b are studied classically and quantum-mechanically (by using Wigner functions W). Difficulties related to the non-positivity of W are bypassed. Equilibrium Wigner functions W e q generate orthogonal polynomials, which yield non-equilibrium moments of W and hierarchies. In regimes typical of chemical reactions (short thermal wavelength and long times), non-equilibrium hierarchies yield approximate Smoluchowski-like equations displaying dissipation and quantum effects. The study of three-particle chemical reactions is new.

Vortices in Motionless Media

1990 ◽  
Vol 43 (12) ◽  
pp. 297-309 ◽  
Author(s):  
A. T. Winfree
Keyword(s):  
Mathematical Models ◽  
Chemical Reactions ◽  
Heart Muscle ◽  
Local Reaction ◽  
Three Dimensional ◽  
Vortex Filament ◽  
Local Geometry ◽  
Lateral Motion ◽  
Local Activation ◽  
Vortex Lines

Three-dimensional continua capable of recurrent local activation are observed—both in the laboratory and in mathematical models—to support persistent self-organizing patterns of activity most conveniently described in terms of vortex lines. These lines generally close in rings, which may be linked and knotted. In some cases they adopt stable configurations resembling tiny dynamos of millimeter dimensions. The dynamics of these “organizing centers” has been investigated in certain chemical reactions, in heart muscle, and numerically in digital computers. The pertinent mathematical principles appear to entail consequences of local reaction and neighborhood diffusion, in the form of a dependency of the vortex filament’s lateral motion upon its local geometry and, when too closely approached by another segment of vortex filament, upon the distance and orientation involved.

scholarly journals Asymptotic Limit-cycle Analysis of Oscillating Chemical Reactions

2021 ◽  
Author(s):  
Alain Brizard ◽  
Samuel Berry
Keyword(s):  
Limit Cycle ◽  
Chemical Reactions ◽  
Relaxation Oscillation ◽  
Three Dimensional ◽  
Van Der Pol Oscillator ◽  
Asymptotic Limit ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Parameter Values ◽  
Analytical Expressions

Abstract The asymptotic limit-cycle analysis of mathematical models for oscillating chemical reactions is presented. In this work, after a brief presentation of mathematical preliminaries applied to the biased Van der Pol oscillator, we consider a two-dimensional model of the Chlorine dioxide Iodine Malonic-Acid (CIMA) reactions and the three-dimensional and two-dimensional Oregonator models of the Belousov-Zhabotinsky (BZ) reactions. Explicit analytical expressions are given for the relaxation-oscillation periods of these chemical reactions that are accurate within 5% of their numerical values. In the two-dimensional CIMA and Oregonator models, we also derive critical parameter values leading to canard explosions and implosions in their associated limit cycles.

scholarly journals On the Regularity of the Electron Configuration of Atoms in the Periodic Table

2021 ◽  
Author(s):  
Toshihiro Konishi ◽  
Ryosuke Miura
Keyword(s):  
Energy Level ◽  
Chemical Reactions ◽  
Basic Principle ◽  
Periodic Table ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Electron Configuration ◽  
Transition Elements ◽  
Complex Chemical ◽  
Complex Chemical Reactions

Abstract The current periodic table does not necessarily have a clear position for transition elements. Therefore, the purpose of this paper is to use the basic principle discovered by Mendeleev as it is and to create a periodic ta ble with consistency for transition elements. By setting some hypotheses, it was found that transition elements also have regular periodicity, so we succeeded in clarifying the energy level of electrons in each orbit. In addition, by utilizing its periodic ity, the electron configuration for each orbit was predicted for unknown elements. In this paper, we did not take the conventional idea of electron orbitals, that is, the idea of forming a hybrid orbital, but assumed a new orbital.Since the state in which electrons fit in orbits and stabilize is defined as an octet, this idea was used as the basic principle in this paper, but the hypothesis that "there are only three orbits in each shell" was established and verified.The calculatio n of the energy level of the electrons on the orbit became extremely easy, and the order of each orbit could be clarified. It was also found that the three dimensional structure of the molecule may be visualizedby paying attention to the valence electrons of the outermost shell of the element and the octet of the stability condition. Therefore, in this paper, by slightly expanding the structural formula of Kekulé, it became possible to easily determine whether or not the molecule synthesized by the became possible to easily determine whether or not the molecule synthesized by the bond bebond between elements is stable.tween elements is stable. In addition, it has become possible to predict the three In addition, it has become possible to predict the three--dimensional structure of the dimensional structure of the molecule as well.molecule as well. Furthermore, not only will it be easier for students studying chemistry to understand Furthermore, not only will it be easier for students studying chemistry to understand complex chemical reactions, but it will complex chemical reactions, but it will also be useful for researchers in the development also be useful for researchers in the development and research of new drugs.and research of new drugs.

Three-Dimensional Modeling of Solar Thermochemical Splitting of CO2 in a CR5

2011 ◽  
Author(s):  
Ken S. Chen ◽  
Roy E. Hogan
Keyword(s):  
Chemical Reactions ◽  
Gas Injection ◽  
Three Dimensional ◽  
Generation Model ◽  
Three Dimensional Modeling ◽  
Neutral Gas ◽  
Solar Thermochemical ◽  
Multiple Species ◽  
Carbon Dioxide Co2 ◽  
Efficiency Effects

A three-dimensional (3-D) numerical model for simulating the process of solar thermochemical splitting of carbon dioxide (CO2) into carbon monoxide (CO) in a counter-rotating-ring receiver/reactor/recuperator or CR5 are developed in order to account for three-dimensional effects such as edge effect of side walls. The present 3-D model, which is based on our previous two-dimensional first-generation model, takes into account heat transfer, gas-phase flow, multiple-species transport in open channels and through pores of the porous reactant layer, and redox chemical reactions at the gas/solid interfaces. Sample computed results (e.g., temperature distribution, species concentration contours) are presented to illustrate model utility. The model is employed to examine the effects of rates of CO2 and argon neutral gas injection and the redox chemical reactions on thermochemical solar conversion efficiency. Effects of the CR5 width and argon neutral gas injection on O2 crossover are also explored.

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