scholarly journals The structure of the reaction zone in a flame

1949 ◽  
Vol 197 (1048) ◽  
pp. 90-106 ◽  
Keyword(s):  
Heat Conductivity ◽  
Mathematical Problem ◽  
Reaction Rates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Unimolecular Reaction ◽  
Homogeneous Reaction ◽  
One Dimensional ◽  
Mathematical Approximation ◽  
Low Pressures

The structure of one-dimensional flames is shown to be completely determined by constants such as those of heat conductivity, of diffusion, and of the homogeneous reaction rates. The mathematical problem in the most general case is intractable, but three simple cases are solved fully by a mathematical method of successive approximations. The three cases are those in which diffusion is neglected compared with heat conductivity and in which reaction velocities of the following types are considered: unimolecular, bimolecular, and the quasibimolecular form of a unimolecular reaction at low pressures. The method of mathematical approximation is shown to involve errors of the order of only 10 % in some actual cases, an error which is negligible compared with other uncertainties of the problem. In these simple cases it is possible to solve all details of the structure such as the variation of composition and temperature through the flame.

On the Connection of Cascade-Probability Function on the Formation of Primary-Knocked on Atoms for Ions Taking into Account Energy Losses with a Boltzman Equation

2020 ◽  
Vol 992 ◽  
pp. 929-933
Author(s):  
Nataliya A. Voronova ◽  
Anatoliy I. Kupchishin
Keyword(s):  
Probability Function ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Cascade Process ◽  
One Dimensional ◽  
Boltzman Equation ◽  
Detection Depth ◽  
The Laplace Transform ◽  
The Right ◽  
Integral Differential Equation

The integral-differential equation of the cascade process for ions was solved using the Laplace transform and the method of successive approximations, taking into account the energy loss during the formation of primary-knocked-on atoms (PKA) in a one-dimensional model of an elementary atom. It is shown that the solution includes a cascade-probability function (CPF) for these particles. The main properties of CPF are considered and its graphical dependencies on the depth of registration are presented. It is shown that with the specific ionization loss coefficient k = 0, the FQM turns into the simplest cascade-probability function. When λ0→ 0, λ0→∞ and n→∞, the KV-function is equal to 0. The sum of the probabilities for all possible collisions from 0 to ∞ is 1. As the detection depth h increases, for all values of n, the CRF increases, reaches a maximum and then decreases . With increasing n, the curves shift to the right.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

scholarly journals Electrolyte-Assisted Hydrogen Cycling in Lithium and Sodium Alanates at Low Pressures and Temperatures

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5868
Author(s):  
Jason Graetz ◽  
John J. Vajo
Keyword(s):  
Growth Parameters ◽  
Reaction Times ◽  
Hydrogen Uptake ◽  
Hydrogen Desorption ◽  
Reaction Rates ◽  
Rate Coefficients ◽  
Aluminum Hydrides ◽  
Dehydrogenation Reactions ◽  
Low Pressures ◽  
Sodium Alanates

An investigation of electrolyte-assisted hydrogen storage reactions in complex aluminum hydrides (LiAlH4 and NaAlH4) reveals significantly reduced reaction times for hydrogen desorption and uptake in the presence of an electrolyte. LiAlH4 evolves ~7.8 wt% H2 over ~3 h in the presence of a Li-KBH4 eutectic at 130 °C compared to ~25 h for the same material without the electrolyte. Similarly, NaAlH4 exhibits 4.8 wt% H2 evolution over ~4 h in the presence of a diglyme electrolyte at 150 °C compared to 4.4 wt% in ~15 h for the same material without the electrolyte. These reduced reaction times are composed of two effects, an increase in reaction rates and a change in the reaction kinetics. While typical solid state dehydrogenation reactions exhibit kinetics with rates that continuously decrease with the extent of reaction, we find that the addition of an electrolyte results in rates that are relatively constant over the full desorption window. Fitting the kinetics to an Avrami-Erofe’ev model supports these observations. The desorption rate coefficients increase in the presence of an electrolyte, suggesting an increase in the velocities of the reactant-product interfaces. In addition, including an electrolyte increases the growth parameters, primarily for the second desorption steps, resulting in the observed relatively constant reaction rates. Similar effects occur upon hydrogen uptake in NaH/Al where the presence of an electrolyte enables hydrogenation under more practical low temperature (75 °C) and pressure (50 bar H2) conditions.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Universality of one-dimensional heat conductivity

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
Trieu Mai ◽  
Onuttom Narayan
Keyword(s):  
Heat Conductivity ◽  
One Dimensional

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

scholarly journals DISTRIBUTION OF MAXIMA OF THE ANTISYMMETRIZED WAVE FUNCTION FOR THE NUCLEONS OF A CLOSED-SHELL AND FOR THE NUCLEONS OF ALL CLOSED-SHELLS IN A NUCLEUS.

2020 ◽  
Vol 15 ◽  
pp. 57
Author(s):  
G. S. Anagnostatos
Keyword(s):  
Wave Function ◽  
Mathematical Problem ◽  
Closed Shell ◽  
Wave Functions ◽  
Pictorial Representation ◽  
One Dimensional ◽  
Regular Polyhedra ◽  
Closed Shell Nuclei ◽  
Simple Systems ◽  
Closed Shells

The significant features of exchange symmetry are displayed by simple systems such as two identical, spinless fermions in a one-dimensional well with infinite walls. The conclusion is that the maxima of probability of the antisymmetrized wave function of these two fermions lie at the same positions as if a repulsive force (of unknown nature) was applied between these two fermions. This conclusion is combined with the solution of a mathematical problem dealing with the equilibrium of identical repulsive particles (of one or two kinds) on one or more spheres like neutrons and protons on nuclear shells. Such particles are at equilibrium only for specific numbers of particles and, in addition, if these particles lie on the vertices of regular polyhedra or their derivative polyhedra. Finally, this result leads to a pictorial representation of the structure of all closed shell nuclei. This representation could be used as a laboratory for determining nuclear properties and corresponding wave functions.

scholarly journals A new method of successive approximations when calculating elements of electromechanical machines

2020 ◽  
Vol 5 (2) ◽  
pp. 168-172
Author(s):  
K. Ismayilov ◽  
◽  
S.T. Suleymanov ◽  
S.T. Ruziev ◽  
M.B. Aripjanova ◽  
...  
Keyword(s):  
New Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations
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