Search results for "Ordinary differential equation"
showing 8 items of 98 documents
Analogical Modeling and Numerical Simulation for Sintering Phenomena
2013
In this paper the authors propose an approach for analogical modeling and numerical simulation of the phenomena of sintering, taking into account different cases depending on the type of energy used in the process of aggregation and the nature of the material powder, using a software which simulates the propagation and the control of the temperature. Many physical phenomena encountered in science and engineering can be described mathematically through partial differential equations (PDE) and ordinary differential equations (ODE) such as propagation phenomena, engineering applications, hydrotechnics, chemistry, pollution a.s.o. There may be situations when the exact establish of the analytic…
A mathematical tool for describing the behaviour of a dense effluent discharge
2009
In many cases a dense effluent has to be discharged in the environment with possible harmful consequences. The preferred design for the relevant discharge unit is that of a simple or multi-port diffuser issuing jets at a given inclination above the horizontal. This work presents the follow-on developments of a model previously proposed to predict the behaviour of inclined dense jets issuing in a stagnant environment. It consists of a set of three ordinary differential equations that can be solved by standard numerical methods. Model outputs include information on the trajectory, spreading and dilution of inclined dense jets, return point position and concentration. Interestingly the model a…
Basic kinetic model for the reaction yielding linear polyurethanes. II
1995
On the basis of the gradual polyaddition kinetic model developed earlier, an attempt was made to provide a generalized mathematical model for the set of reactions yielding linear polyurethanes. The model is a system of first-order ordinary differential equations. It was assumed at the present stage of this model that the rate constants for the reaction considered do not change. The model developed was then solved numerically. Average molecular weight of the polymer and composition data for oligomers were calculated for a constant volume batch reactor and varied process parameters. The GPC method, which was tested for model urethane oligomers, was employed to verify the model developed. The …
Non-standard Problems in an Ordinary Differential Equations Course
2018
International audience; We report first results from a teaching intervention in an ordinary differential equations (ODEs) course for engineering students. Our aim is to challenge traditional approaches to teaching of Existence and Uniqueness Theorems (EUTs) through the design of problems that students cannot solve by applying well-rehearsed techniques or familiar methods. We analyse how the use of nonstandard problems contributes to the development of students' conceptual understanding of EUTs and ODEs.
EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES
1995
The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbat…
A two-point boundary value formulation of a mean-field crowd-averse game
2014
Abstract We consider a population of “crowd-averse” dynamic agents controlling their states towards regions of low density. This represents a typical dissensus behavior in opinion dynamics. Assuming a quadratic density distribution, we first introduce a mean-field game formulation of the problem, and then we turn the game into a two-point boundary value problem. Such a result has a value in that it turns a set of coupled partial differential equations into ordinary differential equations.
A note on some fundamental results in complete gauge spaces and application
2015
We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.
An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields
2004
[1] A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero- and the first-order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second-order approximation of the concentration and its fluxes inside each element. Limitati…