A KINETIC DESCRIPTION OF PARTICLE FRAGMENTATION

2006 ◽  
Vol 16 (06) ◽  
pp. 933-948 ◽  
Author(s):  
PIERRE-EMMANUEL JABIN ◽  
JUAN SOLER
Keyword(s):  
Kinetic Theory ◽  
Internal Energy ◽  
General Model ◽  
External Medium ◽  
Mathematical Approach ◽  
Kinetic Description ◽  
Particle Fragmentation ◽  
Proposed Model ◽  
Internal Configuration ◽  
Fragmentation Processes

This paper is concerned with the formulation and analysis of particle fragmentation by a mathematical approach of the kinetic theory. We consider a fairly general model which may require a description of the internal configuration of each particle, like internal energy. The fragmentation process is assumed to occur due to the configuration of the corresponding particle; an easy modification would allow one to consider the interaction with some external medium (typically a fluid) but we do not deal with fragmentation processes induced by particles collision here. The proposed model is therefore linear and may be analyzed with the use of correct entropies.

Analysis of Dynamics of Infected Active and Uninfected Active Populations Leading to Pandemics using a Discrete Model of Two Interacting Pacemakers Taking into Account the Time of Refractoriness

2020 ◽  
pp. 1-4
Author(s):  
Sergey Belyakin ◽  
◽  
Sergey Shuteev ◽  
Keyword(s):  
General Model ◽  
Discrete Model ◽  
Strong Difference ◽  
Proposed Model ◽  
Minimum Number ◽  
Analysis Of Dynamics

In this publication, we generalize the proposed model of two interacting oscillators in the case of a strong difference in their periods (when the pacemaker pulses do not alternate) and propose a General model describing a network of oscillators coupled globally. Our goal is to make the model as simple as possible and enter the minimum number of parameters. Therefore, we will fully characterize the pacemaker of their internal lengths of the cycle and re-present them as pulse oscillators. Interaction of pacemakers is described by PRC

scholarly journals Model-based assessment of the impact of driver-assist vehicles using kinetic theory

2020 ◽  
Vol 71 (5) ◽  
Author(s):  
Benedetto Piccoli ◽  
Andrea Tosin ◽  
Mattia Zanella
Keyword(s):  
Kinetic Theory ◽  
Autonomous Vehicles ◽  
Control Strategies ◽  
Field Studies ◽  
Kinetic Approach ◽  
Kinetic Description ◽  
Traffic Models ◽  
Nice Agreement ◽  
Theoretical Evidence ◽  
The Impact

Abstract In this paper, we consider a kinetic description of follow-the-leader traffic models, which we use to study the effect of vehicle-wise driver-assist control strategies at various scales, from that of the local traffic up to that of the macroscopic stream of vehicles. We provide theoretical evidence of the fact that some typical control strategies, such as the alignment of the speeds and the optimisation of the time headways, impact on the local traffic features (for instance, the speed and headway dispersion responsible for local traffic instabilities) but have virtually no effect on the observable macroscopic traffic trends (for instance, the flux/throughput of vehicles). This unobvious conclusion, which is in very nice agreement with recent field studies on autonomous vehicles, suggests that the kinetic approach may be a valid tool for an organic multiscale investigation and possibly the design of driver-assist algorithms.

FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY

2013 ◽  
Vol 23 (05) ◽  
pp. 949-978 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
ELENA DE ANGELIS ◽  
DAMIAN KNOPOFF
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Biological Function ◽  
Early Stage ◽  
Black Swan ◽  
Mathematical Approach ◽  
Hallmarks Of Cancer ◽  
Active Particles ◽  
Scalar Variable ◽  
Large Systems

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

MODELLING EPIDEMICS AND VIRUS MUTATIONS BY METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES

2009 ◽  
Vol 19 (supp01) ◽  
pp. 1405-1425 ◽  
Author(s):  
S. DE LILLO ◽  
M. DELITALA ◽  
M. C. SALVATORI
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Numerical Simulations ◽  
Mathematical Approach ◽  
Heterogeneous Distribution ◽  
Active Particles

The present study is devoted to modelling the onset and the spread of epidemics. The mathematical approach is based on the generalized kinetic theory for active particles. The modelling includes virus mutations and the role of the immune system. Moreover, the heterogeneous distribution of patients is also taken into account. The structure allows the derivation of specific models and of numerical simulations related to real systems.

MODEL KINETIC EQUATION FOR THE DISTRIBUTION OF DISCRETIZED INTERNAL ENERGY

1994 ◽  
Vol 04 (05) ◽  
pp. 669-675 ◽  
Author(s):  
K. NANBU
Keyword(s):  
Kinetic Equation ◽  
Kinetic Theory ◽  
Internal Energy ◽  
Boltzmann Distribution ◽  
Model Kinetic Equation ◽  
Discrete Velocity ◽  
Second Moment ◽  
Exponential Relaxation ◽  
H Theorem

Kinetic equation for discretized internal energy is obtained by using the idea underlying the discrete-velocity kinetic theory. The equation satisfies the Boltzmann H-theorem. The solution of this equation in equilibrium is the Boltzmann distribution. The second moment of distribution shows an exponential relaxation.

scholarly journals Density fluctuations in granular piles traversing the glass transition: A grain-scale characterization via the internal energy

2022 ◽  
Vol 8 (2) ◽  
Author(s):  
Paula A. Gago ◽  
Stefan Boettcher
Keyword(s):  
Glass Transition ◽  
Kinetic Theory ◽  
Internal Energy ◽  
Density Fluctuations ◽  
Granular Pile ◽  
Granular Piles ◽  
Scale Characterization

The grain-scale dynamics of the internal energy inside a tapped granular pile is studied, advancing on a kinetic theory of grains.

scholarly journals What is life? A perspective of the mathematical kinetic theory of active particles

2021 ◽  
pp. 1-46
Author(s):  
Nicola Bellomo ◽  
Diletta Burini ◽  
Giovanni Dosi ◽  
Livio Gibelli ◽  
Damian Knopoff ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Case Studies ◽  
General Framework ◽  
Living Systems ◽  
Mathematical Approach ◽  
Collective Behaviors ◽  
Research Perspectives ◽  
Active Particles ◽  
Look Ahead

The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives.

Can Physics Help Athletes Run Faster on a Curve Track

2018 ◽  
Vol 7 (3) ◽  
pp. 24-31
Author(s):  
Katherine Han
Keyword(s):  
Kinetic Theory ◽  
General Model ◽  
Running Speed ◽  
Centrifugal Effect ◽  
Tilting Angle ◽  
Curve Track ◽  
Curved Track

Sprinting on a curve is slower than sprinting on a straight lane. To explain this phenomenon, various models based on a combination of biological and physical assumptions have been developed. These models depend on detailed parameters that significantly differ for each individual athlete. Here, we propose a general model solely based on kinetic theory of physics that can be universally applied to all athletes. By solving the force and torque equations for the running speed of the athletes on a curved track, we analyzed sprinting speeds between the inner and outer curves. Applying the data from the classic works into our models, we find that our results and conclusions are mostly aligned with the previous works while our approach is built on the accurate physics principles and contains no uncontrollable parameters. Further we show how runners can alleviate the centrifugal effect of curved track by tilting their bodies and we quantitatively determine the optimal tilting angle for a given curvature.

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