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J L Lebowitz

Publications and source records attributed to J L Lebowitz.

16 recordsLinked to original sources
PubMed2004

Boltzmann entropy for dense fluids not in local equilibrium.

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f=[f(x,v)] and the total energy E. We find that S(f(t),E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monotonicity of S(M(t))=S(M(X(t))) should hold generally for "typical" (the overwhelming majority of) initial microstates (phase points) X0 belonging to the initial macrostate M0, satisfying M(X0)=M(0). This is a consequence of Liouville's theorem when M(t) evolves according to an autonomous deterministic law.

Journal Article↗
PubMed2003

Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field.

An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.

Journal Article↗
PubMed2002

Exact free energy functional for a driven diffusive open stationary nonequilibrium system.

We obtain the exact probability exp[-LF([rho(x)])] of finding a macroscopic density profile rho(x) in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system L-->infinity. F, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, F is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in nonconvexity of F, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.

Journal Article↗
PubMed2002

Properties of stationary nonequilibrium states in the thermostatted periodic Lorentz gas: the multiparticle system.

We study the stationary nonequilibrium states of N-point particles moving under the influence of an electric field E among fixed obstacles (disk) in a two-dimensional torus. The total kinetic energy of the system is kept constant through a Gaussian thermostat that produces a velocity dependent mean field interaction between the particles. The current and the particle distribution functions are obtained numerically and compared for small /E/ with analytic solutions of a Boltzmann-type equation obtained by treating the collisions with the obstacles as random independent scatterings. The agreement is surprisingly good for both small and large N. The latter system in turn agrees with a self-consistent one-particle evolution expected to hold in the N-->infinity limit.

Journal Article↗
PubMed2001

Thermodynamic entropy production fluctuation in a two-dimensional shear flow model.

We investigate fluctuations in the momentum flux across a surface perpendicular to the velocity gradient in a stationary shear flow maintained by either thermostated deterministic or by stochastic boundary conditions. In the deterministic system the fluctuation relation for the probability of large deviations, which holds for the phase space volume contraction giving the Gibbs ensemble entropy production, never seems to hold for the flux which gives the hydrodynamic entropy production. In the stochastic case the fluctuation relation is found to hold for the total flux, as predicted by various exact results, but not for the flux across part of the surface. The latter appear to satisfy a modified fluctuation relation. Similar results are obtained for the heat flux in a steady state produced by stochastic boundaries at different temperatures.

Journal Article↗
PubMed2001

Free energy functional for nonequilibrium systems: an exactly solvable case.

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size N, the probability of any macroscopic density profile rho(x) is exp[-NF([rho])]; F thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for F is a nonlocal functional of rho, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.

Journal Article↗
PubMed2001

Surface-directed spinodal decomposition in binary fluid mixtures.

We consider the phase separation of binary fluids in contact with a surface, which is preferentially wetted by one of the components of the mixture. We review the results available for this problem and present numerical results obtained using a mesoscopic level simulation technique for the three-dimensional problem.

Journal Article↗
PubMed1980

Saliva from patients with cystic fibrosis inhibits amiloride-sensitive sodium transport.

A factor is present in the saliva and sweat from patients with cystic fibrosis (CF) which inhibits the reabsorption of sodium in the ducts of the salivary and sweat glands. Inasmuch as the physiology of sodium absorption is similar in salivary ducts and the distal colon, we have examined the sensitivity of the sodium absorption in the rat colon to saliva from CF patients. Sodium absorption by the rat colon, estimated as the shortcircuit current, was inhibited by saliva from both patients with CF and normal volunteers. However, only with CF saliva was the inhibition consistently proportional to the saliva concentration. Furthermore, the inhibitory activity of CF saliva was greater than the inhibition observed with saliva from age- and sex-matched controls (percentage of inhibition: CF = 20.1 +/- 2.2, and controls = 14.9 +/- 2.1; P < 0.02), and the inhibition of the colonic shortcircuit current was proportional to the activity measured by the ductal retrograde perfusion assay with the rat parotid gland (linear correlation coefficient = 0.634; P < 0.005). This latter assay is an accepted assay for CF factor activity. We conclude that the CF factor present in saliva probably interacts in a reversible manner with the amiloride-sensitive sodium transport system which is present in all sodium scavenging epithelia. The rat colon is a promising assay system for CF factor activity because the electrical measurements permit a rapid quantitative estimate of activity and a single piece of tissue can be used to measure the activity of several saliva samples.

Amiloride↗
PubMed1976

A mathematical model of the acute myeloblastic leukemic state in man.

A dynamical mathematical model of the acute myeloblastic leukemic state is proposed in which normal neutrophils and their precursors, and leukemic myeloblasts, proliferate as distinct but interacting cell populations. Each population has a Go compartment, consisting of resting cells, that acts as a control center to determine the rate of proliferation. These rates are assumed to depend on the total number of cells in the combined populations. The presence of the leukemic population destabilizes the homeostatic state of the normal population, which is stable in the absence of leukemic cells, and drives the system to a new stable state consisting entirely of leukemic cells and no normal cells. Calculations based on the theory suggest that it is able to simulate the kinetic features of this disease state, at least in its typical manifestations.

Cell Division↗
PubMed1976

A mathematical model of the chemotherapeutic treatment of acute myeloblastic leukemia.

Based on our previous mathematical model of the acute myeloblastic leukemic (AML) state in man, we superimpose a chemotherapeutic drug treatment regimen. Our calculations suggest that small changes in the protocol can have significant effects on the result of treatment. Thus, the optimal period between drug doses is the S-phase interval of the leukemic cells--about 20h--and the greater the number of doses administered in a given course treatment, the longer the rest interval should be before the next course is administered. For a patient with a "slow" growing AML cell population, remission can be achieved with one or two courses of treatment, and further suppression of the leukemic population can be achieved with continued courses of treatment. However, for patients with a "fast" growing AML cell population, a similar aggressive treatment regimen succeeds in achieving remission status only at the cost of very great toxic effects on the normal neutrophil population and its precursors.

Cytarabine↗
PubMed1971

Parameterization of in vivo leukemic cell populations.

A quantitative mathematical formalism which was previously introduced has been utilized to obtain the cell kinetic parameters which characterize the in vivo leukemic myeloblast cell populations in two patients studied by Clarkson and his coworkers. The principal tentative conclusions are: (a) all cells which are actively proliferating must enter the resting state following cell division; (b) about 90% of the cells are in the resting state; (c) the generation time of the cells in the active state is about 25 hr and is essentially the same as the generation time of normal myeloblast cells.

Cell Division↗