Effect of reactant consumption on the induction period and critical condition for a thermal explosion

1961 ◽  
Vol 262 (1309) ◽  
pp. 192-206 ◽  
Keyword(s):  
Theoretical Model ◽  
Theoretical Analysis ◽  
Induction Period ◽  
Thermal Explosion ◽  
Numerical Solutions ◽  
Critical Value ◽  
Maximum Temperature ◽  
Analytic Expressions ◽  
Effective Transfer ◽  
Explosion Parameter

An approximate theoretical analysis is given of a thermal explosion or ignition. The treat­ment leads to analytic expressions for the effect of reactant consumption on the critical explosion parameter and the induction period for a theoretical model, where spatial varia­tion of temperature is treated by considering only the maximum temperature at the centre of the reacting material and an effective transfer coefficient between the centre and the environment. The results are found to agree satisfactorily with detailed numerical solutions by Rice, Allen & Campbell (1935) and Todes & Melentiev (1939, 1940) where these are applicable. The effect of reactant consumption on the critical value of the explosion para­meter is shown to be more than twice that calculated by Frank-Kamenetskii (1946).

scholarly journals A Framework for Modelling Economic Regional Location Processes Under Uncertainty

2021 ◽  
Author(s):  
Roy Cerqueti ◽  
Eleonora Cutrini
Keyword(s):  
Theoretical Model ◽  
Theoretical Analysis ◽  
Site Selection ◽  
Decision Problem ◽  
Stochastic Theory ◽  
Spatial Location ◽  
Probabilistic Framework ◽  
Location Patterns ◽  
Regional Location ◽  
Quantitative Tool

AbstractThis paper deals with the theoretical analysis of the spatial concentration and localization of firms and employees over a set of regions. In particular, it provides a simple site-selection theoretical model to describe the probabilistic framework of the location patterns. The adopted quantitative tool is the stochastic theory of urns. The model moves from the empirical evidence of the deviation of the spatial location of companies from the uniform distribution and of employees from the distribution of firms. Factors leading to such deviations are taken into consideration. Specifically, we formalize a decision problem grounded on the economic attributes of the regions and also on the distribution of the existing firms and employees in the territory. To our purpose, the site-selection model is presented as a stepwise process.

scholarly journals Nonlinear feedback in a six-dimensional Lorenz Model: impact of an additional heating term

2015 ◽  
Vol 2 (2) ◽  
pp. 475-512
Author(s):  
B.-W. Shen
Keyword(s):  
Rayleigh Number ◽  
Numerical Solutions ◽  
Critical Rayleigh Number ◽  
Critical Value ◽  
Small Scale ◽  
Solution Stability ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Additional Heating ◽  
The Impact

Abstract. In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred to as a secondary streamfunction mode, while the two additional modes, that appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado. The implications of this and previous work, as well as future work, are also discussed.

scholarly journals Theoretical analysis of legislative definition of the regime in correctional institutions: problems and ways to solve them

2021 ◽  
Vol 7 (1) ◽  
pp. 70-75
Author(s):  
V. E. Juzhanin ◽  
D. V. Gorban'
Keyword(s):  
Theoretical Model ◽  
Theoretical Analysis ◽  
Russian Federation ◽  
Criminal Code ◽  
Penal System ◽  
Correctional Institutions ◽  
Scientific Thought ◽  
General Part ◽  
The Russian Federation ◽  
Definition Of

The article provides a theoretical analysis of Part 1 of Article 82 of the Criminal Code of the Russian Federation, which defines the regime in correctional institutions of the Russian penal system. It is noted that this definition does not correspond to the achievements of modern penitentiary scientific thought about the regime. In particular, it is emphasized that the regime cannot provide conditions for serving a sentence, since it includes these conditions. Also, the regime cannot ensure the protection of convicts, supervision over them and separate maintenance of different categories of convicts, since, on the contrary, the latter are the means of ensuring the regime. According to the authors of the article, the legislator incorrectly uses the phrase regime of detention of convicts, meaning regime of serving a sentence, since they are different legal phenomena. It is noted that the most optimal definition of the regime is presented in the theoretical model of the general part of the new Criminal Code of the Russian Federation, prepared by a group of authors, but the authors also subjected this definition to some adjustments.

Theoretical and Methodological Model of the Influence of Mindfulness Practices on the Teacher’s Personality

2020 ◽  
Vol 6 (2) ◽  
pp. 67-73
Author(s):  
Olha P. Shevchuk ◽  
Natalia P. Yaroshchuk
Keyword(s):  
Academic Success ◽  
Theoretical Model ◽  
Theoretical Analysis ◽  
Well Being ◽  
Educational Process ◽  
The Body ◽  
Subjective Feeling ◽  
Emotional States ◽  
Mindfulness Practices

The relevance of the study lies in covering the potential of meditative practices in the educational process. The purpose of the study is to carry out a theoretical analysis and outline the probable forms of integration of mindfulness practices into the educational process on the example of teachers, as well as to create a theoretical model of the influence of mindfulness practices on the teacher’s personality with professional destruction. The study highlights the main theoretical models of understanding mindfulness practices. The most effective and most frequently used techniques of awareness practice are analysed. The main educational centres of mindfulness in Ukraine are highlighted. Theoretical analysis of empirical research of foreign colleagues in the field of positive influence of mindfulness practices on the personality is carried out. The causes of professional destruction of teachers are analysed. The expediency and efficiency of this integration are argued. Among the positive changes due to the use of awareness practices by teachers are: improving the level of concentration and recollection; increasing attention to the needs and emotional states of students; creating emotional balance and preventing burnout; increasing the level of stress resistance; improving the quality of relationships at work and at home; increasing productivity and as a result of academic success; forming openness and readiness for selfdevelopment; development of the level of reflection and skills to regulate one’s emotions; improving the psychological climate in the classroom and maintaining overall psychological well-being; improving the quality of life and increasing the subjective feeling of happiness. The scientific novelty lies in the creation and operationalisation of a theoretical model of the influence of mindfulness practices on the teacher’s personality with professional destruction through the lens of cognitive, emotional, physiological, and behavioural levels. It is established that the practice of awareness is the main skill of presence in everything that happens to us, around and inside, in the body, feelings and thoughts

Interactions of cell volume, membrane potential, and membrane transport parameters

1980 ◽  
Vol 238 (5) ◽  
pp. C196-C206 ◽  
Author(s):  
E. Jakobsson
Keyword(s):  
Membrane Potential ◽  
Cell Volume ◽  
Membrane Transport ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Time Varying ◽  
Transport Parameters ◽  
Animal Cells ◽  
Analytic Expressions ◽  
Solute Species

Equations have been written and solved that describe for animal cells the relationships among membrane transport, cell volume, membrane potential, and distribution of permeant solute. The essential system consists of n + 2 equations, where n is the number of permeant solute species. The n of the equations are the n transport equations for the permeant species, one for each species. The other two equations are statements of 1) the condition for bulk electroneutrality inside the cell and 2) the condition for isotonicity between the interior and exterior of the cell. Numerical solutions have been obtained in both the steady-state and time-varying cases for transport equations that are physically and phenomenologically reasonable. In addition to numerical solutions analytic expressions are presented that show the ranges of membrane parameters essential for volume regulation; for values of membrane parameters beyond explicitly defined bounds, the equations do not have real, positive solutions for cell volume.

Theoretical Analysis of an Internally-Braced, Two-Dimensional Air Strut which is Partially Buckled

1968 ◽  
Vol 19 (1) ◽  
pp. 71-79 ◽  
Author(s):  
B. G. Newman ◽  
D. Jones
Keyword(s):  
Theoretical Analysis ◽  
Numerical Solutions ◽  
Resultant Force ◽  
Two Dimensional ◽  
End Plate ◽  
Thin Membranes

SummaryA theoretical analysis is presented for a two-dimensional air strut with walls consisting of thin membranes which are joined by many inextensible strings. The strut is deflected through large angles so than an appreciable portion of each membrane is buckled and lies along the solid plates which form the ends of the strut. Numerical solutions are obtained for two cases and, in particular, the resultant force on each end plate is determined.

Computational analysis of the steady state performance of an adjustable/controllable multi-pad bearing profile under LBP orientations

2020 ◽  
pp. 095440622095770
Author(s):  
Girish Hariharan ◽  
Raghuvir Pai
Keyword(s):  
Steady State ◽  
Theoretical Model ◽  
Theoretical Analysis ◽  
Film Thickness ◽  
Computational Analysis ◽  
Fluid Film ◽  
Adjustable Mechanism ◽  
State Behaviour ◽  
Steady State Behaviour ◽  
Steady State Performance

A theoretical model of a four-pad bearing profile with unique adjustable or controllable features is simulated in the present study by considering load directed between the pads. Radial and tilt adjustable mechanism of the four bearing pads can effectively control and modify the rotor operating behaviour. Inward and outward motions of the bearing pads result in the generation of narrow and broader convergent regions, which directly influences the fluid film pressures. In the theoretical analysis, load-between-pad (LBP) orientations and pad adjustment configurations are taken account of by employing a modified film thickness equation. The effect of load position in influencing the steady state behaviour of the four-pad adjustable bearing under varied pad displaced conditions is analysed in this study. The outcome of the analysis highlighted the effectiveness of four-pad adjustable bearing in improving the steady state performance by operating under negative adjustment conditions and with load acting on the bearing pads.

Theoretical Analysis of Porosity in an Ordered Porous Copper Fabricated by Continuous Unidirectional Solidification

2018 ◽  
Vol 933 ◽  
pp. 136-141
Author(s):  
Rong Cao ◽  
Qing Lin Jin
Keyword(s):  
High Pressure ◽  
Theoretical Model ◽  
Theoretical Analysis ◽  
Processing Parameters ◽  
Unidirectional Solidification ◽  
Hydrogen Gas ◽  
Porous Copper ◽  
Gas Atmosphere ◽  
Ordered Porous ◽  
Good Agreement

Ordered porous copper with elongated pores has been fabricated by a continuous unidirectional solidification method in a hydrogen gas atmosphere with high pressure. The porosity of the ordered porous copper is significantly affected by the pressure of hydrogen. A theoretical model is developed to get the relation between the porosity and the processing parameters. The calculated values are in good agreement with the experimental results. Key words: Unidirectional solidification; Ordered porous copper; Porosity; Modeling.

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