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Journal articles on the topic 'Kinetic theory of active particles'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Feliachi, Ouassim, Marc Besse, Cesare Nardini, and Julien Barré. "Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 11 (November 1, 2022): 113207. http://dx.doi.org/10.1088/1742-5468/ac9fc6.

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Abstract Kinetic and hydrodynamic theories are widely employed for describing the collective behavior of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each particle interacts weakly with many others, so that the total forces and torques exerted on each of them is of order unity at all times. Such limit is however not relevant for dilute systems that mostly interact via alignment; there, collisions are rare and make the self-propulsion direction to change abruptly. We derive a fluctuating kinetic theory, and the corresponding fluctuating hydrodynamics, for aligning self-propelled particles in the limit of dilute systems. We discover that fluctuations at kinetic level are not Gaussian and depend on the interactions among particles, but that only their Gaussian part survives in the hydrodynamic limit. At variance with fluctuating hydrodynamics for weakly interacting particles, we find that the noise variance at hydrodynamic level depends on the interaction rules among particles and is proportional to the square of the density, reflecting the binary nature of the aligning process. The results of this paper, which are derived for polar self-propelled particles with polar alignment, could be straightforwardly extended to polar particles with nematic alignment or to fully nematic systems.

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2

Nieto, J. "The (kinetic) theory of active particles applied to learning dynamics." Physics of Life Reviews 16 (March 2016): 152–53. http://dx.doi.org/10.1016/j.plrev.2016.01.017.

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3

Chauviere, A., and I. Brazzoli. "On the discrete kinetic theory for active particles. Mathematical tools." Mathematical and Computer Modelling 43, no. 7-8 (April 2006): 933–44. http://dx.doi.org/10.1016/j.mcm.2005.10.001.

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4

Benfenati, A., and V. Coscia. "Nonlinear microscale interactions in the kinetic theory of active particles." Applied Mathematics Letters 26, no. 10 (October 2013): 979–83. http://dx.doi.org/10.1016/j.aml.2013.04.007.

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5

Nieto, J. "The kinetic theory of active particles as a biological systems approach." Physics of Life Reviews 12 (March 2015): 81–82. http://dx.doi.org/10.1016/j.plrev.2015.01.015.

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6

Burini, D., S. De Lillo, and L. Gibelli. "Collective learning modeling based on the kinetic theory of active particles." Physics of Life Reviews 16 (March 2016): 123–39. http://dx.doi.org/10.1016/j.plrev.2015.10.008.

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7

Bellomo, Nicola, and Abdelghani Bellouquid. "On the mathematical kinetic theory of active particles with discrete states." Mathematical and Computer Modelling 44, no. 3-4 (August 2006): 397–404. http://dx.doi.org/10.1016/j.mcm.2006.01.025.

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8

Hill, K. M., and Danielle S. Tan. "Segregation in dense sheared flows: gravity, temperature gradients, and stress partitioning." Journal of Fluid Mechanics 756 (September 1, 2014): 54–88. http://dx.doi.org/10.1017/jfm.2014.271.

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AbstractIt is well-known that in a dense, gravity-driven flow, large particles typically rise to the top relative to smaller equal-density particles. In dense flows, this has historically been attributed to gravity alone. However, recently kinetic stress gradients have been shown to segregate large particles to regions with higher granular temperature, in contrast to sparse energetic granular mixtures where the large particles segregate to regions with lower granular temperature. We present a segregation theory for dense gravity-driven granular flows that explicitly accounts for the effects of both gravity and kinetic stress gradients involving a separate partitioning of contact and kinetic stresses among the mixture constituents. We use discrete-element-method (DEM) simulations of different-sized particles in a rotated drum to validate the model and determine diffusion, drag, and stress partition coefficients. The model and simulations together indicate, surprisingly, that gravity-driven kinetic sieving is not active in these flows. Rather, a gradient in kinetic stress is the key segregation driving mechanism, while gravity plays primarily an implicit role through the kinetic stress gradients. Finally, we demonstrate that this framework captures the experimentally observed segregation reversal of larger particles downward in particle mixtures where the larger particles are sufficiently denser than their smaller counterparts.

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9

Brazzoli, I., and A. Chauviere. "On the Discrete Kinetic Theory for Active Particles. Modelling the Immune Competition." Computational and Mathematical Methods in Medicine 7, no. 2-3 (2006): 143–57. http://dx.doi.org/10.1080/10273660600968911.

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This paper deals with the application of the mathematical kinetic theory for active particles, with discrete activity states, to the modelling of the immune competition between immune and cancer cells. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of the models. Two specific models are derived in the second part, while some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition. A final critical outlines some research perspectives.

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10

Brazzoli, I. "From the discrete kinetic theory to modelling open systems of active particles." Applied Mathematics Letters 21, no. 2 (February 2008): 155–60. http://dx.doi.org/10.1016/j.aml.2007.02.018.

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11

Alonso-Matilla, Roberto, Barath Ezhilan, and David Saintillan. "Microfluidic rheology of active particle suspensions: Kinetic theory." Biomicrofluidics 10, no. 4 (July 2016): 043505. http://dx.doi.org/10.1063/1.4954193.

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12

Ezhilan, Barath, and David Saintillan. "Transport of a dilute active suspension in pressure-driven channel flow." Journal of Fluid Mechanics 777 (July 20, 2015): 482–522. http://dx.doi.org/10.1017/jfm.2015.372.

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Confined suspensions of active particles show peculiar dynamics characterized by wall accumulation, as well as upstream swimming, centreline depletion and shear trapping when a pressure-driven flow is imposed. We use theory and numerical simulations to investigate the effects of confinement and non-uniform shear on the dynamics of a dilute suspension of Brownian active swimmers by incorporating a detailed treatment of boundary conditions within a simple kinetic model where the configuration of the suspension is described using a conservation equation for the probability distribution function of particle positions and orientations, and where particle–particle and particle–wall hydrodynamic interactions are neglected. Based on this model, we first investigate the effects of confinement in the absence of flow, in which case the dynamics is governed by a swimming Péclet number, or ratio of the persistence length of particle trajectories over the channel width, and a second swimmer-specific parameter whose inverse measures the strength of propulsion. In the limit of weak and strong propulsion, asymptotic expressions for the full distribution function are derived. For finite propulsion, analytical expressions for the concentration and polarization profiles are also obtained using a truncated moment expansion of the distribution function. In agreement with experimental observations, the existence of a concentration/polarization boundary layer in wide channels is reported and characterized, suggesting that wall accumulation in active suspensions is primarily a kinematic effect that does not require hydrodynamic interactions. Next, we show that application of a pressure-driven Poiseuille flow leads to net upstream swimming of the particles relative to the flow, and an analytical expression for the mean upstream velocity is derived in the weak-flow limit. In stronger imposed flows, we also predict the formation of a depletion layer near the channel centreline, due to cross-streamline migration of the swimming particles towards high-shear regions where they become trapped, and an asymptotic analysis in the strong-flow limit is used to obtain a scale for the depletion layer thickness and to rationalize the non-monotonic dependence of the intensity of depletion upon flow rate. Our theoretical predictions are all shown to be in excellent agreement with finite-volume numerical simulations of the kinetic model, and are also supported by recent experiments on bacterial suspensions in microfluidic devices.

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13

Burini, D., and N. Chouhad. "Hilbert method toward a multiscale analysis from kinetic to macroscopic models for active particles." Mathematical Models and Methods in Applied Sciences 27, no. 07 (April 11, 2017): 1327–53. http://dx.doi.org/10.1142/s0218202517400176.

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This paper develops a Hilbert type method to derive models at the macroscopic scale for large systems of several interacting living entities whose statistical dynamics at the microscopic scale is delivered by kinetic theory methods. The presentation is in three steps, where the first one presents the structures of the kinetic theory approach used toward the aforementioned analysis; the second step presents the mathematical method; while the third step provides a number of specific applications. The approach is focused on a simple system and with a binary mixture, where different time-space scalings are used. Namely, parabolic, hyperbolic, and mixed in the case of a mixture.

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14

Bellomo, Nicola, Giovanni Dosi, Damián A. Knopoff, and Maria Enrica Virgillito. "From particles to firms: on the kinetic theory of climbing up evolutionary landscapes." Mathematical Models and Methods in Applied Sciences 30, no. 07 (June 10, 2020): 1441–60. http://dx.doi.org/10.1142/s021820252050027x.

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This paper constitutes the first attempt to bridge the evolutionary theory in economics and the theory of active particles in mathematics. It seeks to present a kinetic model for an evolutionary formalization of economic dynamics. The new derived mathematical representation intends to formalize the processes of learning and selection as the two fundamental drivers of evolutionary environments [G. Dosi, M.-C. Pereira and M.-E. Virgillito, The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics, Ind. Corp. Change, 26 (2017) 187–210]. To coherently represent the aforementioned properties, the kinetic theory of active particles [N. Bellomo, A. Bellouquid, L. Gibelli and N. Outada, A Quest Towards a Mathematical Theory of Living Systems (Birkhäuser-Springer, 2017)] is here further developed, including the complex interaction of two hierarchical functional subsystems. Modeling and simulations enlighten the predictive ability of the approach. Finally, we outline the potential avenues for future research.

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15

Bellomo, Nicola, Abdelghani Bellouquid, Juanjo Nieto, and Juan Soler. "Modeling chemotaxis from $L^2$--closure moments in kinetic theory of active particles." Discrete & Continuous Dynamical Systems - B 18, no. 4 (2013): 847–63. http://dx.doi.org/10.3934/dcdsb.2013.18.847.

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16

Bianca, C. "On the modelling of space dynamics in the kinetic theory for active particles." Mathematical and Computer Modelling 51, no. 1-2 (January 2010): 72–83. http://dx.doi.org/10.1016/j.mcm.2009.08.044.

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17

Benfenati, A., and V. Coscia. "Modeling opinion formation in the kinetic theory of active particles I: spontaneous trend." ANNALI DELL'UNIVERSITA' DI FERRARA 60, no. 1 (March 13, 2014): 35–53. http://dx.doi.org/10.1007/s11565-014-0207-2.

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18

Knopoff, Damian A., and Juan M. Sánchez Sansó. "A kinetic model for horizontal transfer and bacterial antibiotic resistance." International Journal of Biomathematics 10, no. 04 (March 28, 2017): 1750051. http://dx.doi.org/10.1142/s1793524517500516.

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This paper presents a mathematical model for bacterial growth, mutations, horizontal transfer and development of antibiotic resistance. The model is based on the so-called kinetic theory for active particles that is able to capture the main complexity features of the system. Bacterial and immune cells are viewed as active particles whose microscopic state is described by a scalar variable. Particles interact among them and the temporal evolution of the system is described by a generalized distribution function over the microscopic state. The model is derived and tested in a couple of case studies in order to confirm its ability to describe one of the most fundamental problems of modern medicine, namely bacterial resistance to antibiotics.

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19

Bellomo, N., and F. Brezzi. "Collective dynamics in science and society." Mathematical Models and Methods in Applied Sciences 31, no. 06 (June 15, 2021): 1053–58. http://dx.doi.org/10.1142/s0218202521020012.

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This editorial paper presents the articles published in a special issue devoted to active particle methods applied to modeling, qualitative analysis, and simulation of the collective dynamics of large systems of interacting living entities in science and society. The modeling approach refers to the mathematical tools of behavioral swarms theory and to the kinetic theory of active particles. Applications focus on classical problems of swarms theory, on crowd dynamics related to virus contagion problems, and to multiscale problems related to the derivation of models at a large scale from the mathematical description at the microscopic scale. A critical analysis of the overall contents of the issue is proposed, with the aim to provide a forward look to research perspectives.

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20

Qi, Jin Peng, Ying Zhu, and Yong Sheng Ding. "A Mathematical Framework for Cellular Repair Mechanisms under Genomic Stress Based on Kinetic Theory Approach." Applied Mechanics and Materials 52-54 (March 2011): 7–12. http://dx.doi.org/10.4028/www.scientific.net/amm.52-54.7.

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Generally, a cell can trigger its self-defense mechanism in response to genomic stress under acute perturbations from outer environment. To investigate the dynamic kinetics of cellular repair mechanisms in fighting against genomic stress, a mathematical model of representing and analyzing DNA damage generation and repair process is proposed under acute Ion Radiation (IR) by using the Kinetic Theory of Active Particles (KTAP). In this paper, we focus on describing a mathematical framework of Cellular Repair System (CRS). We also present the dynamic processes of Double Strand Breaks (DSBs) and Repair Protein (RP) generating, DSB-protein complexes (DSBCs) synthesizing, and toxins accumulating under continuous radiation time.

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21

DELITALA, M., P. PUCCI, and M. C. SALVATORI. "FROM METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES TO MODELING VIRUS MUTATIONS." Mathematical Models and Methods in Applied Sciences 21, supp01 (April 2011): 843–70. http://dx.doi.org/10.1142/s0218202511005398.

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The paper presents a model of virus mutations and evolution of epidemics in a system of interacting individuals, where the intensity of the pathology, described by a real discrete positive variable, is heterogeneously distributed, and the virus is in competition with the immune system or therapeutical actions. The model is developed within the framework of the Kinetic Theory of Active Particles. The paper also presents a qualitative analysis developed to study the well-posedness of the mathematical problem associated to the general framework. Finally, simulations show the ability of the model to predict some interesting emerging phenomena, such as the mutation to a subsequent virus stage, the heterogeneous evolution of the pathology with the co-presence of individual carriers of the virus at different levels of progression, and the presence of oscillating time phases with either virus prevalence or immune system control.

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22

De Angelis, Elena, and Bertrand Lods. "On the kinetic theory for active particles: A model for tumor–immune system competition." Mathematical and Computer Modelling 47, no. 1-2 (January 2008): 196–209. http://dx.doi.org/10.1016/j.mcm.2007.02.016.

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23

DE LILLO, S., M. DELITALA, and M. C. SALVATORI. "MODELLING EPIDEMICS AND VIRUS MUTATIONS BY METHODS OF THE MATHEMATICAL KINETIC THEORY FOR ACTIVE PARTICLES." Mathematical Models and Methods in Applied Sciences 19, supp01 (August 2009): 1405–25. http://dx.doi.org/10.1142/s0218202509003838.

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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.

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24

BELLOUQUID, ABDELGHANI, ELENA DE ANGELIS, and DAMIAN KNOPOFF. "FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY." Mathematical Models and Methods in Applied Sciences 23, no. 05 (February 21, 2013): 949–78. http://dx.doi.org/10.1142/s0218202512500650.

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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.

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25

Bellomo, N., A. Bellouquid, and M. Delitala. "From the mathematical kinetic theory of active particles to multiscale modelling of complex biological systems." Mathematical and Computer Modelling 47, no. 7-8 (April 2008): 687–98. http://dx.doi.org/10.1016/j.mcm.2007.06.004.

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26

Bellomo, Nicola, Maria Letizia Bertotti, and Marcello Delitala. "From the kinetic theory of active particles to the modeling of social behaviors and politics." Quality & Quantity 41, no. 4 (February 16, 2007): 545–55. http://dx.doi.org/10.1007/s11135-007-9073-7.

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27

CATTANI, C., and A. CIANCIO. "HYBRID TWO SCALES MATHEMATICAL TOOLS FOR ACTIVE PARTICLES MODELLING COMPLEX SYSTEMS WITH LEARNING HIDING DYNAMICS." Mathematical Models and Methods in Applied Sciences 17, no. 02 (February 2007): 171–87. http://dx.doi.org/10.1142/s0218202507001875.

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This paper deals with the derivation of hybrid mathematical structures to describe the behavior of large systems of active particles by ordinary differential equations with stochastic coefficients whose evolution is modelled by equations of the mathematical kinetic theory. A preliminary analysis shows how the above tools can be used to model complex systems of interest in applied sciences, with special attention to the immune competition.

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28

De Angelis, E. "On the mathematical theory of post-Darwinian mutations, selection, and evolution." Mathematical Models and Methods in Applied Sciences 24, no. 13 (September 17, 2014): 2723–42. http://dx.doi.org/10.1142/s0218202514500353.

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This paper is devoted to the modeling, qualitative analysis and simulation of Darwinian selection phenomena and their evolution. The approach takes advantage of the mathematical tools of the kinetic theory of active particles which are applied to describe the selective dynamics of evolution processes. The first part of the paper focuses on a mathematical theory that has been developed to describe mutations and selection processes. The second part deals with different modeling strategies and looks ahead to research perspectives.

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29

Bellomo, Nicola, and Bruno Carbonaro. "On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim." Differential Equations and Nonlinear Mechanics 2006 (2006): 1–26. http://dx.doi.org/10.1155/denm/2006/86816.

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This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.

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30

Knopoff, Damián A., Juanjo Nieto, and Luis Urrutia. "Numerical Simulation of a Multiscale Cell Motility Model Based on the Kinetic Theory of Active Particles." Symmetry 11, no. 8 (August 3, 2019): 1003. http://dx.doi.org/10.3390/sym11081003.

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In this work, we deal with a kinetic model of cell movement that takes into consideration the structure of the extracellular matrix, considering cell membrane reactions, haptotaxis, and chemotaxis, which plays a key role in a number of biological processes such as wound healing and tumor cell invasion. The modeling is performed at a microscopic scale, and then, a scaling limit is performed to derive the macroscopic model. We run some selected numerical experiments aimed at understanding cell movement and adhesion under certain documented situations, and we measure the alignment of the cells and compare it with the pathways determined by the extracellular matrix by introducing new alignment operators.

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31

Bellomo, Nicola, Abdelghani Bellouquid, and Juan Soler. "From the mathematical kinetic theory for active particles on the derivation of hyperbolic macroscopic tissue models." Mathematical and Computer Modelling 49, no. 11-12 (June 2009): 2083–93. http://dx.doi.org/10.1016/j.mcm.2008.07.004.

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32

Bellomo, N., and M. Delitala. "On the coupling of higher and lower scales using the mathematical kinetic theory of active particles." Applied Mathematics Letters 22, no. 5 (May 2009): 646–50. http://dx.doi.org/10.1016/j.aml.2008.05.005.

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33

Noussair, Ahmed. "On a population dynamic model of active cells with direct interaction." Mathematical Modelling of Natural Phenomena 12, no. 6 (2017): 171–91. http://dx.doi.org/10.1051/mmnp/2017077.

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Through two case studies, this paper deals with a new class of population dynamic models inspired from the kinetic theory for active particles modelling cell to cell interactions with a transfer processes between cells. The first case study problem is related to the transfer of proteins motivated by advantages of cell transfer therapies for the treatment of cancers. The second case concerns the activity transfer between immune and tumor cells. We provide some numerical tests and we prove the convergence of the solutions from the discrete model to the continuous model.

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34

Burini, D., S. De Lillo, and G. Fioriti. "Influence of drivers ability in a discrete vehicular traffic model." International Journal of Modern Physics C 28, no. 03 (March 2017): 1750030. http://dx.doi.org/10.1142/s0129183117500309.

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A vehicular traffic model is presented, based on the so-called Kinetic Theory of Active Particles. Vehicles are characterized by a lattice of discrete speeds and by the driving ability of the drivers. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are consistent with experimental measurements of traffic flow.

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35

De Lillo, S., G. Fioriti, and M. L. Prioriello. "On the modeling of epidemics under the influence of risk perception." International Journal of Modern Physics C 28, no. 04 (April 2017): 1750051. http://dx.doi.org/10.1142/s0129183117500516.

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An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.

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36

BELLOMO, N., D. KNOPOFF, and J. SOLER. "ON THE DIFFICULT INTERPLAY BETWEEN LIFE, "COMPLEXITY", AND MATHEMATICAL SCIENCES." Mathematical Models and Methods in Applied Sciences 23, no. 10 (July 12, 2013): 1861–913. http://dx.doi.org/10.1142/s021820251350053x.

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This paper presents a revisiting, with developments, of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions. The approach is based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games. The basic idea consists in looking for a general mathematical structure suitable to capture the main features of living, hence complex, systems. Hopefully, this structure is a candidate towards the challenging objective of designing a mathematical theory of living systems. These topics are treated in the first part of the paper, while the second one applies it to specific case studies, namely to the modeling of crowd dynamics and of the immune competition.

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37

Calvo, Juan, Juanjo Nieto, and Mohamed Zagour. "Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions." Symmetry 11, no. 9 (September 2, 2019): 1093. http://dx.doi.org/10.3390/sym11091093.

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This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights.

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38

De Angelis, E., and M. Delitala. "Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles." Mathematical and Computer Modelling 43, no. 11-12 (June 2006): 1310–28. http://dx.doi.org/10.1016/j.mcm.2005.01.039.

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39

Bellomo, N., B. Carbonaro, and L. Gramani. "On the kinetic and stochastic games theory for active particles: Some reasonings on open large living systems." Mathematical and Computer Modelling 48, no. 7-8 (October 2008): 1047–54. http://dx.doi.org/10.1016/j.mcm.2007.12.010.

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40

Arlotti, L., and E. De Angelis. "On the initial value problem of a class of models of the kinetic theory for active particles." Applied Mathematics Letters 24, no. 3 (March 2011): 257–63. http://dx.doi.org/10.1016/j.aml.2010.09.015.

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41

BELLOMO, NICOLA, ABDELGHANI BELLOUQUID, JUAN NIETO, and JUAN SOLER. "MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS." Mathematical Models and Methods in Applied Sciences 20, no. 07 (July 2010): 1179–207. http://dx.doi.org/10.1142/s0218202510004568.

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This paper deals with the derivation of macroscopic tissue models from the underlying description delivered by a class of equations that models binary mixtures of multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of the biological functions and proliferative and destructive events. The asymptotic analysis deals with suitable parabolic and hyperbolic limits, and is specifically focused on the modeling of the chemotaxis phenomena.

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42

Kim, Daewa, Kaylie O’Connell, William Ott, and Annalisa Quaini. "A kinetic theory approach for 2D crowd dynamics with emotional contagion." Mathematical Models and Methods in Applied Sciences 31, no. 06 (April 17, 2021): 1137–62. http://dx.doi.org/10.1142/s0218202521400030.

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In this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians’ behavior. Our approach is based on the methods of the kinetic theory of active particles. The model allows us to weight between two competing behaviors depending on fear level: the search for less congested areas and the tendency to follow the stream unconsciously (herding). The fear level of each pedestrian influences their walking speed and is influenced by the fear levels of their neighbors. Numerically, we solve our pedestrian model with emotional contagion using an operator splitting scheme. We simulate evacuation scenarios involving two groups of interacting pedestrians to assess how domain geometry and the details of fear propagation impact evacuation dynamics. Further, we reproduce the evacuation dynamics of an experimental study involving distressed ants.

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43

BELLOMO, N., A. BELLOUQUID, J. NIETO, and J. SOLER. "ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES." Mathematical Models and Methods in Applied Sciences 22, no. 01 (January 2012): 1130001. http://dx.doi.org/10.1142/s0218202512005885.

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This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.

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44

Bellomo, N., A. Bellouquid, and N. Chouhad. "From a multiscale derivation of nonlinear cross-diffusion models to Keller–Segel models in a Navier–Stokes fluid." Mathematical Models and Methods in Applied Sciences 26, no. 11 (October 2016): 2041–69. http://dx.doi.org/10.1142/s0218202516400078.

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This paper deals with a micro–macro derivation of a variety of cross-diffusion models for a large system of active particles. Some of the models at the macroscopic scale can be viewed as developments of the classical Keller–Segel model. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. The second part is devoted to the design of the micro–macro general framework, where methods of the kinetic theory are used to model the dynamics of the system including the case of coupling with a fluid. The third part deals with the derivation of macroscopic models from the underlying description, delivered within a general framework of the kinetic theory.

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Budnik, A. P., L. V. Deputatova, V. E. Fortov, V. P. Lunev, and V. I. Vladimirov. "Simulation of Kinetic Processes, Optical and Neutron Properties of the Nuclear-Excited Dusty Plasma of Noble Gases." Ukrainian Journal of Physics 56, no. 12 (February 2, 2022): 1260. http://dx.doi.org/10.15407/ujpe56.12.1260.

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A model of kinetic processes in the argon-xenon gas plasma with the admixture of uranium nanoclusters is developed. This dusty plasma seems to be perspective as an active laser medium in the technologies of direct conversion of the nuclear energy into coherent light. The process of formation of quasistationary states in plasma and the influence of uranium nanoclusters are considered in the developed mathematical model of the kinetic processes in the argon-xenon gas excited by nuclear fission fragments. The suggested system of equations allows one to describe the kinetic processes in the plasma with presence of the uranium dust in a self-consistent way. The model include the evolutionary equations for the distribution function of electron velocities and for concentrations of a different components of plasma, including charged uranium nanoclusters. The model takes 44 components of plasma and 507 plasma-chemical processes into account. The method of solution of such equations is suggested, and the program complex realizing this method is developed. The influence of the dust concentration on the optical and neutronic properties of the plasma media is studied in calculations. The calculation of the neutron multiplication factor for the laser active infinite medium containing uranium dust particles is performed with the use of MCNP-5 code. The neutron cross-sections needed for calculations were taken from the ENDF/b-VI library. The attenuation of electromagnetic waves by uranium dust particles was calculated in the frame of the Mie theory for various spherical particle sizes and different wavelengths. Real and imaginary parts of the refraction coefficient for uranium needed for this calculation were taken from the experimental and theoretical works.

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BELLOMO, NICOLA, and GUIDO FORNI. "LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS." Mathematical Models and Methods in Applied Sciences 16, no. 07 (July 2006): 1001–29. http://dx.doi.org/10.1142/s0218202506001443.

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This paper deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by a few biological functions which are able to modify the above laws. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The last part of the paper deals with a critical analysis and with the indication of research perspectives concerning the challenging target of developing a biological-mathematical theory for the living matter.

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Burini, Diletta, Elena De Angelis, and Miroslaw Lachowicz. "A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactions." Communications in Applied and Industrial Mathematics 9, no. 2 (December 1, 2018): 106–18. http://dx.doi.org/10.2478/caim-2018-0018.

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Abstract In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.

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Knopoff, Damián A., and Germán A. Torres. "On an optimal control strategy in a kinetic social dynamics model." Communications in Applied and Industrial Mathematics 9, no. 2 (December 1, 2018): 22–33. http://dx.doi.org/10.2478/caim-2018-0014.

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Abstract Kinetic models have so far been used to model wealth distribution in a society. In particular, within the framework of the kinetic theory for active particles, some important models have been developed and proposed. They involve nonlinear interactions among individuals that are modeled according to game theoretical tools by introducing parameters governing the temporal dynamics of the system. In this present paper we propose an approach based on optimal control tools that aims to optimize this evolving dynamics from a social point of view. Namely, we look for time dependent control variables concerning the distribution of wealth that can be managed, for instance, by the government, in order to obtain a given social profile.

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De Lillo, S., M. C. Salvatori, and N. Bellomo. "Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity." Mathematical and Computer Modelling 45, no. 5-6 (March 2007): 564–78. http://dx.doi.org/10.1016/j.mcm.2006.07.005.

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KNOPOFF, D. "ON A MATHEMATICAL THEORY OF COMPLEX SYSTEMS ON NETWORKS WITH APPLICATION TO OPINION FORMATION." Mathematical Models and Methods in Applied Sciences 24, no. 02 (December 12, 2013): 405–26. http://dx.doi.org/10.1142/s0218202513400137.

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This paper presents a development of the so-called kinetic theory for active particles to the modeling of living, hence complex, systems localized in networks. The overall system is viewed as a network of interacting nodes, mathematical equations are required to describe the dynamics in each node and in the whole network. These interactions, which are nonlinearly additive, are modeled by evolutive stochastic games. The first conceptual part derives a general mathematical structure, to be regarded as a candidate towards the derivation of models, suitable to capture the main features of the said systems. An application on opinion formation follows to show how the theory can generate specific models.

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