scholarly journals Numerical estimation of thermal ignition conditions for reactive medium with Gaussian distribution of activation energy

2021 ◽  
Vol 2119 (1) ◽  
pp. 012102
Author(s):  
I G Donskoy
Keyword(s):  
Activation Energy ◽  
Gaussian Distribution ◽  
Critical Conditions ◽  
Differential Heat ◽  
Reactive Medium ◽  
One Dimensional ◽  
Analytical Approximations ◽  
Gaussian Distribution Function ◽  
The One ◽  
Thermal Explosion Theory

Abstract The article investigates the solutions of the one-dimensional stationary integro-differential heat equation. The source of heat release is determined through the Gaussian distribution function of the activation energy. In such a statement, the critical conditions for the existence of a bounded solution depend on the distribution variance. With the help of numerical methods, such dependences are obtained; for their explanation, the analytical approximations of the thermal explosion theory are used.

Theory of thermal explosions with simultaneous parallel reactions I. Foundations and the one-dimensional case

1984 ◽  
Vol 393 (1804) ◽  
pp. 85-100 ◽  
Keyword(s):  
Activation Energy ◽  
Dimensionless Parameter ◽  
Exothermic Reactions ◽  
One Dimensional ◽  
Temperature Excess ◽  
Parallel Reactions ◽  
The One ◽  
Definition Of ◽  
Thermal Explosions ◽  
Thermal Explosion Theory

Many real, exothermic systems involve more than one simultaneous reaction. Even when they are chemically independent, interactions must arise through their several responses to the collective generation of heat. A simple and unifying approach is possible to the behaviour of such systems below and up to criticality. It introduces a communal activation energy E as the basis for dimensionless quantities ( θ, δ, ϵ and so on) but otherwise involves only familiar ideas from basic thermal explosion theory. The definition of E is E = RT 2 d (In Z )/d T , where Z = Ʃ Z i . Here, Z is the rate of energy release per unit volume (the power density) by the whole system and Z i is the contribution of the constituent i . This enables us to define and use the conventional dimensionless parameter δ for the whole system and for its constituent reactions. We illustrate affairs by considering a pair of concurrent, exothermic reactions; heat is transferred solely by conduction towards the faces (temperature T a ) of an infinite slab of thickness 2 a and conductivity k . For a constituent reaction ( i = 1, 2 here) δ i = ( Ea 2 / k RT 2 a ) Z i ( T a ) and for the whole system δ = δ 1 + δ 2 (+...) for two (or more) reactions. We find that the condition δ > δ cr guarantees instability, where δ cr is always less than 0.878. The bounds 0.65 < δ cr < 0.878 are good enough for a substantial range of relative sizes of activation energy 0.2 < E 1 / E 2 < 5. We also pursue the problem numerically and present solutions for critical δ and critical central temperature excess over the whole composition range for a pair of simultaneous exothermic reactions.

scholarly journals Hydraulic Control of a Highly Stratified Estuarine Front*

2005 ◽  
Vol 35 (3) ◽  
pp. 374-387 ◽  
Author(s):  
Daniel G. MacDonald ◽  
W. Rockwell Geyer
Keyword(s):  
Froude Number ◽  
Flow Direction ◽  
Vertical Direction ◽  
Critical Conditions ◽  
Hydraulic Control ◽  
Dimensional Theory ◽  
One Dimensional ◽  
River Outflow ◽  
Natural Break ◽  
The One

Abstract Observations at the mouth of the Fraser River (British Columbia, Canada) indicate an abrupt frontal transition between unstratified river outflow and a highly stratified river plume with differences in salinity greater than 25 psu across a few meters in the vertical direction and several hundred meters in the horizontal direction. The front roughly follows a natural break in the bathymetry, crossing the channel at an angle of approximately 45°, and is essentially stationary for a period of approximately 3.5 h centered on the low tide following the larger of two daily ebbs. The location of the front is coincident with observations of significantly supercritical internal Froude numbers at the front, based on velocities in the along-flow direction. This observation contradicts the one-dimensional theory, which indicates that the Froude number should be 1. However, because the front is oriented obliquely to the outflow, a coordinate system can be selected that is normal to the front and for which a critical Froude number of 1 is obtained. This indicates that a Froude angle, similar in application to a Mach angle for transonic flows, can be used to determine critical conditions when the front is oblique to the principal flow direction.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

Sign in / Sign up

Export Citation Format

Share Document