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  • 1
    Electronic Resource
    Electronic Resource
    The Genetic Control of Meiosis (1976)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Genetics 10 (1976), S. 53-134 
    Details
    ISSN: 0066-4197
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.ge.10.120176.000413
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  • 2
    Electronic Resource
    Electronic Resource
    Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria (1998)
    Springer
    Archive for rational mechanics and analysis 142 (1998), S. 193-218 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. We study, globally in time, the velocity distribution f(v,t) of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field E. The density f satisfies a Boltzmann-type kinetic equation containing a fully nonlinear electron‐electron collision term as well as linear terms representing collisions with reservoir particles having a specified Maxwellian distribution. We show that when the constant in front of the nonlinear collision kernel, thought of as a scaling parameter, is sufficiently strong, then the L 1 distance between f and a certain time-dependent Maxwellian stays small uniformly in t. Moreover, the mean and variance of this time‐dependent Maxwellian satisfy a coupled set of nonlinear ordinary differential equations that constitute the “hydrodynamical” equations for this kinetic system. This remains true even when these ordinary differential equations have non‐unique equilibria, thus proving the existence of multiple stable stationary solutions for the full kinetic model. Our approach relies on scale‐independent estimates for the kinetic equation, and entropy production estimates. The novel aspects of this approach may be useful in other problems concerning the relation between the kinetic and hydrodynamic scales globally in time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002050050090
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  • 3
    Electronic Resource
    Electronic Resource
    The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 389-412 
    Details
    ISSN: 1572-9613
    Keywords: Hydrodynamic limit ; stationary Navier-Stokes equations ; kinetic theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183355
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  • 4
    Electronic Resource
    Electronic Resource
    Solutions to the Boltzmann Equation in the Boussinesq Regime (1998)
    Springer
    Journal of statistical physics 90 (1998), S. 1129-1178 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; hydrodynamic scaling ; Boussinesq equation ; Rayleigh–Benard convection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a gas in a horizontal slab in which the top and bottom walls are kept at different temperatures. The system is described by the Boltzmann equation (BE) with Maxwellian boundary conditions specifying the wall temperatures. We study the behavior of the system when the Knudsen number ∈ is small and the temperature difference between the walls as well as the velocity field is of order ∈, while the gravitational force is of order ∈2. We prove that there exists a solution to the BE for % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaerbmv% 3yPrwyGm0BUn3BSvgaiuaacaWF1oWaaeWaaeaacaaIWaGaaiilamaa% naaabaGaamiDaaaaaiaawIcacaGLPaaaaaa!4184! which is near a global Maxwellian, and whose moments are close, up to order ∈2, to the density, velocity and temperature obtained from the smooth solution of the Oberbeck–Boussinesq equations assumed to exist for % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamrr1n% gBPrwtHrhAYaqeguuDJXwAKbstHrhAGq1DVbacfaGae8hzIq4aa0aa% aeaacaWG0baaaaaa!4322! .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023223226585
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  • 5
    Electronic Resource
    Electronic Resource
    Navier–Stokes Limit for a Thermal Stochastic Lattice Gas (1999)
    Springer
    Journal of statistical physics 96 (1999), S. 653-713 
    Details
    ISSN: 1572-9613
    Keywords: stochastic particle systems ; hydrodynamic limit ; Navier–Stokes equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study a stochastic particle system on the lattice whose particles move freely according to a simple exclusion process and change velocities during collisions preserving energy and momentum. In the hydrodynamic limit, under diffusive space-time scaling, the local velocity field u satisfies the incompressible Navier–Stokes equation, while the temperature field θ solves the heat equation with drift u. The results are also extended to include a suitably resealed external force.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004618924291
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  • 6
    Electronic Resource
    Electronic Resource
    The Boltzmann Equation for a One-Dimensional Quantum Lorentz Gas (1999)
    Springer
    Communications in mathematical physics 204 (1999), S. 619-649 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We study the macroscopic behavior of a quantum particle under the action of randomly distributed scatterers on the real line. Each scatterer generates a δ-potential. We prove that, in the low density limit, the Wigner function of the system converges to a probability distribution satisfying a classical linear Boltzmann equation, with a scattering cross section computed according to the Quantum Mechanical rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050659
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  • 7
    Electronic Resource
    Electronic Resource
    The Boltzmann equation for weakly inhomogeneous data (1987)
    Springer
    Communications in mathematical physics 111 (1987), S. 393-407 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We solve the initial value problem associated to the nonlinear Boltzmann equation in the case in which the initial distribution has sufficiently small spatial gradients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238905
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  • 8
    Electronic Resource
    Electronic Resource
    Hydrodynamics of stochastic cellular automata (1989)
    Springer
    Communications in mathematical physics 125 (1989), S. 127-145 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We investigate a stochastic version of cellular automata used for simulating hydrodynamical flows, e.g. the HPP and FHP models. The extra stochasticity consists of “random exchanges” between neighboring cells which conserve momentum. We prove that, in suitable limits, these models satisfy the appropriate continuous Boltzmann and hydrodynamic equations, the same as those conjectured for the original models (except that there is no negative viscosity contribution). The results are obtained by proving a very strong form of propagation of chaos and by using Hilbert-Chapman-Enskog type expansions. Explicit proofs are presented for the stochastic HPP model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217773
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  • 9
    Electronic Resource
    Electronic Resource
    Hydrodynamic limit of the stationary Boltzmann equation in a slab (1994)
    Springer
    Communications in mathematical physics 160 (1994), S. 49-80 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the stationary solution of the Boltzmann equation in a slab with a constant external force parallel to the boundary and complete accommodation condition on the walls at a specified temperature. We prove that when the force is sufficiently small there exists a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip boundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099789
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  • 10
    Electronic Resource
    Electronic Resource
    Cellulose-based hydrogels as body water retainers (2000)
    Springer
    Journal of materials science 11 (2000), S. 247-253 
    Details
    ISSN: 1573-4838
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract In this work the possibility of using hydrogels as body water retainers for a therapeutic aid in pathologies such as oedemas of various origins was explored. For such a purpose, the material requires a good compatibility and a controlled swelling capacity without altering the body electrolyte homeostasis. The hydrogel was designed to meet the swelling requirements with the physiological constraints and its biocompatibility was assessed either in vitro or in vivo. Absorption tests were performed in order to define the swelling behavior by varying the pH and ion content of the external solution. The hydrogel swelling capacity was assessed in the presence of various solvents, in order to evaluate its absorption capacity in solutions similar to biological fluids. In addition, the capacity of the gel to modify electrolyte homeostasis by adsorbing ions such as calcium, potassium and sodium was tested. In order to assess the gel biocompatibility after contact of the hydrogel with intestinal cells, arachidonic acid relase was determined. No significant intracellular increase of free arachidonic acid was found in the cells after up to 2 h of contact with the gel. The results suggest that, as far as brief periods are concerned, the gel does not cause an inflammatory response in intestinal cells. ©2000 Kluwer Academic Publishers
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008980629714
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