Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles

Angelis, Elena De; Delitala, Marcello Edoardo

doi:10.1016/j.mcm.2005.01.039

Cited by 13 publications

(4 citation statements)

References 56 publications

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“…Finally, we mention that our model is an application of the generalized kinetic theory and is related to the derivation of macroscopic descriptions of the flow of large ensembles of dispersed elements in gas dynamics, traffic models, mathematical biology, and other applications. [29][30][31][32][33][34] In a sense, however, we address a limit opposite to standard kinetic modeling, since we obtain a nonlinear convective term, which is nonlocal with respect to the kinetic parameter, and have zero collision terms.…”

Section: Related Workmentioning

confidence: 99%

Centrifugal Settling of Polydisperse Suspensions with a Continuous Particle Size Distribution: A Generalized Kinetic Description

Bürger

García

2008

Drying Technology

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The settling of a polydisperse suspension with a continuous particle size distribution (PSD) can be modeled by an equation of the generalized kinetic theory, which represents the limit case of a system of conservation laws for a finite number of size classes. A previous model of gravity settling of such a mixture is extended to settling in a rotating tube or basket centrifuge. A numerical scheme to approximate solutions of the generalized kinetic equation is defined and simulations are presented, illustrating the formation of sediment and the effect of various centrifuge geometries. In particular, the model predicts the radial variation of the composition of the sediment forming at the outer wall.

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Section: Related Workmentioning

confidence: 99%

Centrifugal Settling of Polydisperse Suspensions with a Continuous Particle Size Distribution: A Generalized Kinetic Description

Bürger

García

2008

Drying Technology

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“…This proves assertion (5). Assertion (5) implies that is a solution of ODE (2.1) in set . By virtue of Remark 2.1 (applicable because of assumption ( 1)), the mentioned solution is unique in and can be denoted with .…”

Section: Uniformly Bounded Solutions Of Non-autonomous Ordinary Differential Equationsmentioning

confidence: 99%

“…• incorporation of the homeorhesis ODE model (4.1)-(4.7) into APGKT as a description of the internal state; this can complement and specify the general theory presented in such works as [1] and [5]; • numerical simulation of model (4.1)-(4.7) to obtain the homeorhesis manifestations in specific quantitative terms; this can allow to preliminary study the effects not accounted in the proposed model (e.g., the influence of the exogenous-signal intensity upon homeorhesis).…”

Section: Concluding Remarks and Directions For Future Researchmentioning

confidence: 99%

“…Advanced generalized-kinetic-theory (GKT) models for biological systems are developed for populations of active (or living) particles [1]- [5]. They are described with both the stochastic variables common in kinetic theory (such as the time, the particle random location and velocity) and the stochastic variables related to the internal state of an active particle.…”

Section: Introductionmentioning

confidence: 99%

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Modelling homeorhesis by ordinary differential equations

Mamontov

2007

Mathematical and Computer Modelling

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Homeorhesis is a necessary feature of any living system. If a system does not perform homeorhesis, it is nonliving. The present work develops the sufficient conditions for the ODE model to describe homeorhesis and suggests the structure of the model. The proposed homeorhesis model is fairly general. It treats homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on specific system and specific purposes of this analysis. An example of the specification is the PhasTraM model, the homeorhesis-aware nonlinear reaction-diffusion model for hyperplastic oncogeny in the previous works of the author. The qualitative agreement of the developed homeorhesis model with the living-system experimental results is noted. The work also shows that the basic mathematical models (such as the active-particle generalized kinetic theory) are substantially more important for the living-matter studies than in the case of nonliving matter. A few directions for future research are suggested as well.

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From Kinetic Theory for Active Particles to Modelling Immune Competition

Bellouquid

Delitala

2008

Selected Topics in Cancer Modeling

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Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles

Cited by 13 publications

References 56 publications

Centrifugal Settling of Polydisperse Suspensions with a Continuous Particle Size Distribution: A Generalized Kinetic Description

Centrifugal Settling of Polydisperse Suspensions with a Continuous Particle Size Distribution: A Generalized Kinetic Description

Modelling homeorhesis by ordinary differential equations

From Kinetic Theory for Active Particles to Modelling Immune Competition

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