One, Two and Three-dimensional Spatially Periodic Chemical Reactions

1972 ◽  
Vol 235 (53) ◽  
pp. 15-16 ◽  
Author(s):  
M. T. BECK ◽  
Z. B. VÁRADI
Keyword(s):  
Chemical Reactions ◽  
Three Dimensional ◽  
Spatially Periodic

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.

The development of asymmetry and period doubling for oscillatory flow in baffled channels

1996 ◽  
Vol 328 ◽  
pp. 19-48 ◽  
Author(s):  
E. P. L. Roberts ◽  
M. R. Mackley
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Period Doubling ◽  
Progressive Increase ◽  
Newtonian Flow ◽  
Chaotic Flow ◽  
Spatially Periodic ◽  
Dimensional Simulation ◽  
Time Periodic

We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity. Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow. At modest Reynolds number the observed vortex structure is symmetric and time periodic. At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic. A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number. At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime. A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow.

scholarly journals Triglobal infinite-wing shock-buffet study

2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Base Flow ◽  
Sweep Angle ◽  
Aspect Ratios ◽  
Spatially Periodic ◽  
Time Marching ◽  
High Reynolds ◽  
Limiting Case ◽  
Base Flows

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

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.

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

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 On the Navier-Stokes equations with temperature-dependent transport coefficients

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Eduard Feireisl ◽  
Josef Málek
Keyword(s):  
Stokes Equations ◽  
Transport Coefficients ◽  
Three Dimensional ◽  
Periodic Problem ◽  
Large Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Long Time ◽  
Spatially Periodic ◽  
Dependent Transport

We establish long-time and large-data existence of a weak solution to the problem describing three-dimensional unsteady flows of an incompressible fluid, where the viscosity and heat-conductivity coefficients vary with the temperature. The approach reposes on considering the equation for the total energy rather than the equation for the temperature. We consider the spatially periodic problem.

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.

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