Thermostatted kinetic equations as models for complex systems in physics and life sciences

Thermostatted Kinetic Models: Open Problems

“…The thermostatted kinetic framework proposed in this editorial article generalizes the thermostatted kinetic frameworks of the *Corresponding author: Carlo Bianca, Dipartimento di Scienze Matematiche, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy, E-mail: 016317@polito.it pertinent literature; see the recent review paper [9], to complex systems where the space and velocity variables have an important role. Nevertheless we are aware that mathematical problems are still open.…”

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

“…Recently the thermostatted kinetic theory has been proposed as a new paradigm for the modeling of complex biological systems composed by a large number of entities [168]. This framework is based on a new system biology approach that looks at the entities composing the system for their ability to express a specific strategy or function.…”

“…Indeed PDE solvers are even more computationally intensive than ODE solvers. In contrast to the general framework with internal structure, the thermostatted kinetic theory for active particles (that can be considered as a generalized model with internal structure) has the advantage that can take into account the modeling of nonequilibrium steady states that are typical of the biological systems [168,170].…”

Kinetic Equations of Active Soft Matter

“…It should be noted wide applications of these evolution equations to the description of collective processes of various nature [1][2][3][4][5][6][7][8][9][10][11][12][13][14], in particular, the collective behavior of complex systems of mathematical biology [13][14][15][16][17][18][19][20][21][22][23]. We emphasize that the considerable advance in solving the problem of rigorous modeling of the kinetic evolution of systems with a large number of constituents (entities) of mathematical biology, in particular, systems of large number of cells, is recently observed [20][21][22][23][24][25][26] (and see references cited therein).…”