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Biomedical subjects

P Gaspard

Publications and source records attributed to P Gaspard.

At least 19 recordsLinked to original sources
PubMed2001

Transport and dynamics on open quantum graphs.

We study the classical limit of quantum mechanics on graphs by introducing a Wigner function for graphs. The classical dynamics is compared to the quantum dynamics obtained from the propagator. In particular, we consider extended open graphs whose classical dynamics generate a diffusion process. The transport properties of the classical system are revealed in the scattering resonances and in the time evolution of the quantum system.

Journal Article↗
PubMed2001

Liouvillian dynamics of the Hopf bifurcation.

Two-dimensional vector fields undergoing a Hopf bifurcation are studied in a Liouville-equation approach. The Liouville equation rules the time evolution of statistical ensembles of trajectories issued from random initial conditions, but evolving under the deterministic dynamics. The time evolution of the probability densities of such statistical ensembles can be decomposed in terms of the spectrum of the resonances (i.e., the relaxation rates) of the Liouvillian operator or the related Frobenius-Perron operator. The spectral decomposition of the Liouvillian operator is explicitly constructed before, at, and after the Hopf bifurcation. Because of the emergence of time oscillations near the Hopf bifurcation, the resonance spectrum turns out to be complex and defined by both relaxation rates and oscillation frequencies. The resonance spectrum is discrete far from the bifurcation and becomes continuous at the bifurcation. This continuous spectrum is caused by the critical slowing down of the oscillations occurring at the Hopf bifurcation and it leads to power-law relaxation as 1/square root of [t] of the probability densities and statistical averages at long times t-->infinity. Moreover, degeneracy in the resonance spectrum is shown to yield a Jordan-block structure in the spectral decomposition.

Journal Article↗
PubMed2001

Diffusion of particles bouncing on a one-dimensional periodically corrugated floor.

We report on a class of spatially extended mechanical systems sustaining a transport process of diffusive type. These systems consist of a point particle subject to a constant vertical acceleration and bouncing on a one-dimensional periodically corrugated floor. We show that the deterministic dynamics of these systems is chaotic with small elliptic islands for many parameter values. The motion of particles perturbed by a small noise has a horizontal diffusion that is normal. In such a case, we show that the diffusion coefficient oscillates periodically as the energy of particles increases. In the absence of noise, there still exists an effective numerical value for the diffusion coefficient and this value has an irregular dependence on energy.

Journal Article↗
PubMed2001

Classical dynamics on graphs.

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes.

Journal Article↗
PubMed2001

Fractals and dynamical chaos in a two-dimensional Lorentz gas with sinks.

We consider a two-dimensional periodic reactive Lorentz gas, in which a moving point particle undergoes elastic collisions on fixed hard disks and annihilates on absorbing disks, called sinks. We present clear evidence of the existence of a fractal repeller in this open system. Moreover, we establish a relation between the reaction rate, describing the macroscopic evolution of the system, and two characteristic quantities of the microscopic chaos: the average Lyapunov exponent and the Hausdorff codimension of the fractal repeller.

Journal Article↗
PubMed2001

Fractality of the hydrodynamic modes of diffusion.

Transport by normal diffusion can be decomposed into hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with 2 degrees of freedom, the fine scale structures of these modes are singular and fractal, characterized by a Hausdorff dimension given in terms of Ruelle's topological pressure. For long-wavelength modes, we relate the Hausdorff dimension to the diffusion coefficient and the Lyapunov exponent. This relationship is tested numerically on two Lorentz gases, one with hard repulsive forces, the other with attractive, Yukawa forces. The agreement with theory is excellent.

Journal Article↗
PubMed2000

Entropy production, fractals, and relaxation to equilibrium

The theory of entropy production in nonequilibrium, Hamiltonian systems, previously described for steady states using partitions of phase space, is here extended to time dependent systems relaxing to equilibrium. We illustrate the main ideas by using a simple multibaker model, with some nonequilibrium initial state, and we study its progress toward equilibrium. The central results are (i) the entropy production is governed by an underlying, exponentially decaying fractal structure in phase space, (ii) the rate of entropy production is largely independent of the scale of resolution used in the partitions, and (iii) the rate of entropy production is in agreement with the predictions of nonequilibrium thermodynamics.

Journal Article↗
PubMed2000

Nonlinear Schrodinger flow in a periodic potential

We report a study of solutions of the defocusing nonlinear Schrodinger equation in a spatially periodic potential. The ground-state solution and the steady flows of the system are studied analytically. Above a critical current, a steady state no longer exists and time-dependent solutions are generated, which are numerically simulated and described.

Journal Article↗
PubMed1997

[Treatment of sludge from purification stations with the purpose of ameliorating soils intended for agriculture: parasitic contamination and model development with a view to managing the sanitation risk].

Helminth eggs (Ascaris, Taenia...) present in urban sludge constitute a sanitary risk when used for the enrichment of agricultural soil. These eggs are very resistant in the environment and their survival could reach 6 months to one year in soils. To control the risks for the public health, we have to determine parameters leading to the eggs destruction in soils. Then the aim of the work is to study several conditions (humidity, temperature, texture,...) that could influence the survival of intestinal nematode eggs in various types of soil. Survival experiments were carried out in clayey soil, silty-loam soil and sandy soils with humidity levels corresponding to: field capacities, wilting point and variation between this 2 limit point (storage temperatures 4 degrees C, 19 degrees C and 30 degrees C). The result of this study has shown that the temperature conditioned for a great part the survival of the eggs in all types of soils with survival times superior at two year with a temperature of 4 degrees C. Between survivals at 20 degrees C and 30 degrees C, no difference has been observed. The humidity is the second parameter that condition the egg survival with a good viability preservation at the wilting point. This study also shows better survival in the conditions of deep soil with the protection of the egg from drying. With these data and with the simulation of continental temperate conditions, a contamination rate of 0.35% could be found on the surface soil after one year and a more important rate in the deep soil with 10.6%. The last step is the validation of this model and calculated values seem to be a good evaluation of the results found on fields. All these data must be take into account for the establishment of the regulation about the urban sludge reused for agricultural purpose.

Agriculture↗
PubMed1995

Intracoronary stenting without coumadin: one month results of a French multicenter study.

In order to simplify post-coronary stenting treatment and to obtain a lower rate of complications, especially in bailout situations, seven French institutions treated 246 stented patients with 0.25 g/day of ticlopidine, 0.1 g/day of IV aspirin, and 2 days of heparin followed by low-molecular-weight heparin for 1 month. Fifty percent of patients had a planned stenting procedure, and 50% had an unplanned procedure, including 29 (11.8%) in bailout situations. Subacute occlusion occurred in three (1.2%) patients (one death, two non-Q-wave infarctions). During the 1 month follow-up period, another death was reported (non-stent-related), two elective coronary artery bypass grafts were performed, and three additional patients presented with non-Q-wave myocardial infarctions. Nine (3.7%) patients had a groin complication that required blood transfusion or surgical repair. These results suggest that while waiting for the technological advancements of stents, postprocedural treatment that includes a low dosage of ticlopidine, aspirin, and low-molecular-weight heparin is a very effective alternative to conventional poststenting therapy.

Adult↗