Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Stochastic Model of Isothermal Continuous Flow Chemical Reactor

1994 ◽  
Vol 59 (8) ◽  
pp. 1772-1787
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Continuous Flow ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Chemical Reactor ◽  
Point Of View ◽  
General Point ◽  
Stochastic Description ◽  
One Dimensional ◽  
Reactor Operating ◽  
Parameter Values

A model of an isothermal one-dimensional continuous flow chemical reactor operating at the steady state was derived using a stochastic description of motion of the reacting molecules. The model enables evaluation of the conversion of the reacting components. At the limiting parameter values the model yields results identical to those of the simplified models conventionally used in chemical reactor engineering. The model also enables the applicability of Danckwerts' boundary conditions to be assessed from a more general point of view.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Stochastic Model of Non-Isothermal Flow Chemical Reactor

1996 ◽  
Vol 61 (2) ◽  
pp. 242-258 ◽  
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Stochastic Model ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Dispersion Model ◽  
Chemical Reactor ◽  
Segregation Index ◽  
One Dimensional ◽  
A Value ◽  
Isothermal Case ◽  
Flow Through

Recently developed stochastic model of a one-dimensional flow-through chemical reactor is extended in this paper also to the non-isothermal case. The model enables the evaluation of concentration and temperature profiles along the reactor. The results are compared with the commonly used one-dimensional dispersion model with Danckwerts' boundary conditions. The stochastic model also enables to evaluate a value of the segregation index.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Formulation of Boundary Conditions in Flow Systems

1994 ◽  
Vol 59 (2) ◽  
pp. 345-358
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Libor Vejmola
Keyword(s):  
Boundary Conditions ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Dispersion Model ◽  
Point Of View ◽  
General Point ◽  
Engineering Systems ◽  
Boundary Conditions For Diffusion ◽  
Flow Through ◽  
The One

Problems associated with the formulation of the boundary conditions for diffusion equations describing flow-through chemical-engineering systems from the point of view of stochastic process theory are discussed. An approach to modelling such systems is presented, allowing the one-dimensional diffusion (dispersion) model of a continuous flow mixer, commonly used in chemical engineering, to be reassessed from a rather general point of view.

scholarly journals A TWO-PARAMETER METHOD FOR CHAOS CONTROL AND TARGETING IN ONE-DIMENSIONAL MAPS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350003 ◽  
Author(s):  
DANIEL FRANCO ◽  
EDUARDO LIZ
Keyword(s):  
Chaos Control ◽  
Point Of View ◽  
Positive Equilibrium ◽  
Parameter Method ◽  
One Dimensional ◽  
Current State ◽  
Control Scheme ◽  
The Difference ◽  
One Dimensional Maps ◽  
Parameter Values

We investigate a method of chaos control in which intervention is proportional to the difference between the current state and a fixed value. We prove that this method allows to stabilize the most usual one-dimensional maps used in discrete-time models of population dynamics about a globally stable positive equilibrium. From the point of view of targeting, this technique is very flexible, and we show how to choose the control parameter values to lead the system towards the desired target. Another important feature of this control scheme in the ecological context is that it can be designed to prevent the risk of extinction in models with the so-called Allee effect. We provide a useful geometrical interpretation, and give some examples to illustrate our theoretical results.

scholarly journals Iteration of piecewise linear maps on an interval

1981 ◽  
Vol 24 (3) ◽  
pp. 433-451 ◽  
Author(s):  
James B. McGuire ◽  
Colin J. Thompson
Keyword(s):  
Invariant Measures ◽  
Piecewise Linear ◽  
Point Of View ◽  
Complete Analysis ◽  
Functional Composition ◽  
One Dimensional ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Parameter Values ◽  
Dense Set

A complete analysis is given of the iterative properties of two piece-piecewise linear maps on an interval, from the point of view of a doubling transformation obtained by functional composition and rescaling. We show how invariant measures may be constructed for such maps and that parameter values where this may be done form a dense set in a one-dimensional subset of parameter space.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Numerical Simulation of One-Dimensional Diffusion Process

1996 ◽  
Vol 61 (4) ◽  
pp. 512-535 ◽  
Author(s):  
Pavel Hasal ◽  
Vladimír Kudrna
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Stochastic Integral ◽  
Random Motion ◽  
One Dimensional ◽  
Dimensional Diffusion

Some problems are analyzed arising when a numerical simulation of a random motion of a large ensemble of diffusing particles is used to approximate the solution of a one-dimensional diffusion equation. The particle motion is described by means of a stochastic differential equation. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of simulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous results when used for solution of stochastic differential equations. General conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficient.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Dynamic Stochastic Model of Flow Mixer

1994 ◽  
Vol 59 (7) ◽  
pp. 1551-1570
Author(s):  
Vladimír Kudrna ◽  
Libor Vejmola ◽  
Pavel Hasal
Keyword(s):  
Time Distribution ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Extreme Values ◽  
Stochastic Diffusion ◽  
One Dimensional ◽  
Simplifying Assumptions ◽  
Dynamic Stochastic ◽  
The Common ◽  
The One

The one-dimensional stochastic diffusion model of a continuous flow mixer is proposed incorporating (contrary to commonly used diffusion models) a distribution of velocities of diffusing particles. Simplifying assumptions enabled us to derive an analytical expression for the liquid residence time distribution and concentration profile inside the mixer. For extreme values of parameters, the model becomes identical with the common idealized models usually adopted in chemical engineering.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Relations between Different Types of Diffusion Equations

1992 ◽  
Vol 57 (6) ◽  
pp. 1248-1261 ◽  
Author(s):  
Vladimír Kudrna ◽  
Daniel Turzík
Keyword(s):  
Differential Equations ◽  
Diffusion Equation ◽  
Stochastic Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Point Of View ◽  
Diffusion Equations ◽  
Complex Diffusion ◽  
Different Types ◽  
Individual Particles

The dependence is discussed between the "clasical" diffusion equation commonly used in chemical engineering and the stochastic differential equations which describe this diffusion from the point of view of micromotion of individual particles. The resulting equations can be useful above all for the modelling of more complex diffusion processes.

Present, Past and Future of IT Careers, a Review

2011 ◽  
pp. 218-243
Author(s):  
Adrián Hernández-López ◽  
Ricardo Colomo-Palacios ◽  
Ángel García-Crespo ◽  
Fernando Cabezas-Isla
Keyword(s):  
Organizational Culture ◽  
Vertical Movement ◽  
Point Of View ◽  
External Factors ◽  
Career Management ◽  
General Point ◽  
One Dimensional ◽  
Non Linear ◽  
Employee Relationships ◽  
Culture Differences

Careers have experienced an evolution parallel to society’s constant progress. Careers have migrated from hierarchical and unidirectional models within a single organization, to models that provide non-linear or vertical movement within the hierarchy, movement between organizations, changes in employer-employee relationships, etc. Furthermore, careers have transferred responsibility from organizations to individuals. Due to these changes, careers have been transmuted from the organizational pyramid to a globalized, boundaryless, and one-dimensional scheme. In addition, within the IT sector, external factors such as gender, organizational culture, differences in requirements between technical and nontechnical positions, among others, have also impacted career management. This chapter presents a review of the changes that have been undertaken in career management from a general point of view, to the peculiarities of the IT sector, and ultimately encompass some conclusions extracted from research.

Naive models as active expert system in bioengineering and chemical engineering

1988 ◽  
Vol 53 (7) ◽  
pp. 1476-1499 ◽  
Author(s):  
Mirko Dohnal
Keyword(s):  
Expert System ◽  
Case Studies ◽  
Chemical Engineering ◽  
Anaerobic Fermentation ◽  
Continuous Fermentation ◽  
Point Of View ◽  
Qualitative Variable ◽  
Human Thinking

A possibility of qualitative variable utilization for description and evaluation of phenomena and processes from non-formal human thinking point of view is presented. Paper gives methods of naïve modelling and realistically assesses results that can be awaited. The method is demonstrated on two case studies that are given in full details, namely continuous fermentation (fermentor, two separators) and anaerobic fermentation.

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