Existence of stationary solutions in kinetic models with Gaussian thermostats

Mathematical Methods in the Applied Sciences

Volumn 36, Issue 13, 2013, Pages 1768-1775

  Bianca, Carlo ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

fixed point; integro differential equation; kinetic theory; measure theory; steady states

Indexed keywords

EXTERNAL FORCE FIELD; FIXED POINTS; GAUSSIAN THERMOSTATS; MEASURE THEORY; OUT OF EQUILIBRIUM; QUADRATIC NONLINEARITIES; STATIONARY SOLUTIONS; STEADY STATE;

DIFFERENTIAL EQUATIONS; INTEGRODIFFERENTIAL EQUATIONS; KINETIC THEORY; NONLINEAR ANALYSIS; THERMOSTATS;

KINETICS;

EID: 84880775345     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.2722     Document Type: Article

References (24)

1. Derrida B,. Non-equilibrium steady states: fluctuations and large deviations of the density and of the current. Journal of Statistical Mechanics 2007; 2007: P07023-1-P07023-45.
2. Dickson A, Dinner AR,. Enhanced sampling of nonequilibrium steady states. Annual Review of Physical Chemistry 2010; 61: 441-459.
3. Eckmann JP, Pillet CA, Rey-Bellet L,. Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures. Communications in Mathematical Physics 1999; 201: 657-697.
4. Fruleux A, Kawai R, Sekimoto K,. Momentum transfer in nonequilibrium steady states. Physical Review Letters 2012; 108 (16): 160601-1-160601-5.
5. Gelinc MF, Kosov DS,. Asymptotic nonequilibrium steady-state operators. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2009; 80: 022101-1-022101-4.
6. Ge H, Qian M, Qian H,. Stochastic theory of nonequilibrium steady states. Part II: Applications in chemical biophysics. Physics Reports 2012; 510: 87-118.
7. Hurowitz D, Rahav S, Cohen D,. The non-equilibrium steady state of sparse systems with non-trivial topology. Europhysics letters 2012; 98: 20002-1-20002-6.
8. Kwon C, Ao P,. Nonequilibrium steady state of a stochastic system driven by a nonlinear drift force. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 2001; 84: 061106-1-061106-9.
9. Tjhung E, Cates ME, Marenduzzo D,. Nonequilibrium steady states in polar active fluids. Soft Matter 2011; 7: 7453-7464.
10. Callen HB,. Thermodynamics and An Introduction to Thermostatistics, Second edition. Wiley: New York, 1985.
11. De Groot SR, Mazur P,. Non-equilibrium Thermodynamics. North-Holland Publishing Company: Amsterdam, The Netherlands, 1969.
12. Bianca C,. Kinetic theory for active particles modelling coupled to Gaussian thermostats. Applied Mathematical Sciences 2012; 6: 651-660.
13. Bianca C,. An existence and uniqueness theorem for the Cauchy problem for thermostatted-KTAP models. International Journal of Mathematics Analysis 2012; 6: 813-824.
14. Bianca C,. Onset of nonlinearity in thermostatted active particles models for complex systems. Nonlinear Analysis: Real World Applications 2012; 13: 2593-2608.
15. Bianca C,. Thermostatted kinetic equations as models for complex systems in physics and life sciences. Physics of Life Reviews. DOI: 10.1016/j.plrev. 2012.08.001.
16. Min W, Jiang L, Yu J, Kou SC, Qian H, Xie XS,. Nonequilibrium steady state of a nanometric biochemical system: determining the thermodynamic driving force from single enzyme turnover time traces. Nano Letters 2005; 5: 2373-2378. (Pubitemid 43088880)
17. Simmons JS, Taylor GW,. Nonequilibrium steady-state statistics and associated effects for insulators and semiconductors containing an arbitrary distribution of traps. Physical Review B: Condensed Matter and Materials Physics 1971; 4: 502-511.
18. Bianca C,. Modeling complex systems by functional subsystems representation and thermostatted-KTAP methods. Applied Mathematics & Information Sciences 2012; 6: 495-499.
19. Morris GP, Dettmann CP,. Thermostats: analysis and application. Chaos; 8: 321-336.
20. Ruelle D,. Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. Journal of Statistical Physics; 95: 393-468.
21. Gauss KF,. Uber ein Neues Allgemeines Grundgesatz der Mechanik. Journal Fur Die Reine Und Angewandte Mathematik 1829; 4: 232-235.
22. Wennberg B, Wondmagegne Y,. Stationary states for the Kac equation with a Gaussian thermostat. Nonlinearity 2004; 14: 633-648. (Pubitemid 38390016)
23. Bagland V,. Well-posedness and large time behaviour for the non-cutoff Kac equation with a Gaussian thermostat. Journal of Statistical Physics 2010; 138: 838-875.
24. Bianca C,. On the modelling of space dynamics in the kinetic theory for active particles. Mathematical and Computer Modelling 2010; 51: 72-83.