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Jean-Pierre Hansen

Publications and source records attributed to Jean-Pierre Hansen.

10 recordsLinked to original sources
PubMed2006

Solving the Fokker-Planck kinetic equation on a lattice.

We propose a discrete lattice version of the Fokker-Planck kinetic equation in close analogy with the lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension D. A generalized Hermite-Gauss procedure is used to construct a discretized kinetic equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations. The linear stability of the algorithm with respect to the finite time step Delta t is characterized by the eigenvalues of the collision matrix. A heuristic second-order algorithm in Delta t is applied to investigate the time evolution of the distribution function of simple model systems, and compared to known analytical solutions. Preliminary investigations of sedimenting Brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the Lattice-Fokker-Planck algorithm to simulate nontrivial situations. Interactions between Brownian particles may be accounted for by adding a standard Bhatnagar-Gross-Krook collision operator to the discretized Fokker-Planck kernel.

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PubMed2006

Dielectric response of a polar fluid trapped in a spherical nanocavity.

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is accounted for by appropriate image charges. We focus on the influence of the external permittivity epsilon(') on the static and dynamic properties of the confined fluid. The density profile and local orientational order parameter of the dipoles turn out to be remarkably insensitive to epsilon('). Permittivity profiles epsilon(r) inside the spherical cavity are calculated from a generalized Kirkwood formula. These profiles oscillate in phase with the density profiles and go to a "bulk" value epsilon(b) away from the confining surface; epsilon(b) is only weakly dependent on epsilon('), except for epsilon(')=1 (vacuum), and is strongly reduced compared to the permittivity of a uniform (bulk) fluid under comparable thermodynamic conditions. The dynamic relaxation of the total dipole moment of the sample is found to be strongly dependent on epsilon(') and to exhibit oscillatory behavior when epsilon(')=1; the relaxation is an order of magnitude faster than in the bulk. The complex frequency-dependent permittivity epsilon(omega) is sensitive to epsilon(') at low frequencies, and the zero-frequency limit epsilon(omega=0) is systematically lower than the bulk value epsilon(b) of the static permittivity.

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PubMed2006

Multiscale coarse graining of diblock copolymer self-assembly: from monomers to ordered micelles.

Starting from a microscopic lattice model, we investigate clustering, micellization, and micelle ordering in semidilute solutions of AB diblock copolymers in a selective solvent. To bridge the gap in length scales, from monomers to ordered micellar structures, we implement a two-step coarse-graining strategy, whereby the AB copolymers are mapped onto ultrasoft dumbells with monomer-averaged effective interactions between the centers of mass of the blocks. Monte Carlo simulations of this coarse-grained model yield clear-cut evidence for self-assembly into micelles with a mean aggregation number n approximately 100 beyond a critical concentration. At a slightly higher concentration the micelles spontaneously undergo a disorder-order transition to a cubic phase. We determine the effective potential between these micelles from first principles.

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PubMed2006

Phase separation of a model binary polymer solution in an external field.

The phase separation of a simple binary mixture of incompatible linear polymers in solution is investigated using an extension of the sedimentation equilibrium method, whereby the osmotic pressure of the mixture is extracted from the density profiles of the inhomogeneous mixture in a gravitational field. In Monte Carlo simulations the field can be tuned to induce significant inhomogeneity, while keeping the density profiles sufficiently smooth for the macroscopic condition of hydrostatic equilibrium to remain applicable. The method is applied here for a simplified model of ideal but mutually avoiding polymers, which readily phase separate at relatively low densities. The Monte Carlo data are interpreted with the help of an approximate bulk phase diagram calculated from a simple, second-order virial coefficient theory. By derivation of effective potentials between polymer centers of mass, the binary mixture of polymers is coarse-grained to a "soft colloid" picture reminiscent of the Widom-Rowlinson model for incompatible atomic mixtures. This approach significantly speeds up the simulations and accurately reproduces the behavior of the full monomer resolved model.

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PubMed2005

Corrections to scaling and crossover from good- to theta-solvent regimes of interacting polymers.

We exploit known properties of universal ratios, involving the radius of gyration R(g), the second and third virial coefficients B(2) and B(3), and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good- to theta-solvent regimes of polymers of finite length L. The scaling limit and finite-L corrections to scaling are investigated in the good-solvent case and close to the theta temperature. Detailed interpolation formulas are derived from Monte Carlo data and results for the Edwards two-parameter model, providing estimates of universal ratios as functions of the observable ratio A(2)=B(2)/R(g) (3) over the whole temperature range, from the theta point to the good-solvent regime. The convergence with L (L< or =8000) is found to be satisfactory under good-solvent conditions, but longer chains would be required to match theoretical predictions near the theta point, due to logarithmic corrections. A quantitative estimate of the universal ratio A(3)=B(3)/R(g) (6) as a function of temperature shows that the third virial coefficient remains positive throughout, and goes through a pronounced minimum at the theta temperature, which goes to zero as 1/ln L in the scaling limit.

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PubMed2004

Kinetic models of ion transport through a nanopore.

Kinetic equations for the stationary state distribution function of ions moving through narrow pores are solved for a number of 1D models of single ion transport. Ions move through pores of length L, under the action of a constant external field and of a concentration gradient. The interaction of single ions with the confining pore surface and with water molecules inside the pore are modeled by a Fokker-Planck term in the kinetic equation, or by uncorrelated collisions with thermalizing centers distributed along the pore. The temporary binding of ions to polar residues lining the pore is modeled by stopping traps or energy barriers. Analytic expressions for the stationary ion current through the pore are derived for several versions of the model, as functions of key physical parameters. In all cases, saturation of the current at high fields is predicted. Such simple models, for which results are analytic, may prove useful in the study of the current/voltage relations of ion channels through membranes.

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PubMed2004

Floating liquid phase in sedimenting colloid-polymer mixtures.

Density functional theory and computer simulation are used to investigate sedimentation equilibria of colloid-polymer mixtures within the Asakura-Oosawa-Vrij model of hard sphere colloids and ideal polymers. When the ratio of buoyant masses of the two species is comparable to the ratio of differences in density of the coexisting bulk (colloid) gas and liquid phases, a stable "floating liquid" phase is found, i.e., a thin layer of liquid sandwiched between upper and lower gas phases. The full phase diagram of the mixture under gravity shows coexistence of this floating liquid phase with a single gas phase or a phase involving liquid-gas equilibrium; the phase coexistence lines meet at a triple point. This scenario remains valid for general asymmetric binary mixtures undergoing bulk phase separation.

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PubMed2002

Intermittent permeation of cylindrical nanopores by water.

Molecular-dynamics simulations of water molecules in nanometer sized cylindrical channels connecting two reservoirs show that the permeation of water is very sensitive to the channel radius and to electric polarization of the embedding material. At threshold, the permeation is intermittent on a nanosecond time scale, and strongly enhanced by the presence of an ion inside the channel, providing a possible mechanism for gating. Confined water remains surprisingly fluid and bulklike. Its behavior differs strikingly from that of a reference Lennard-Jones fluid, which tends to contract into a highly layered structure inside the channel.

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