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At least 829 records · Page 46Linked to original sources
PubMed1999

Theoretical model of diatomic molecules interacting on a two-dimensional lattice.

The coverage-dependent binding energy of interacting dimers is investigated using the lattice gas model. Dimers with distinguishable ends are assumed to interact if they occupy only nearest-neighbor lattice sites. The interaction energy between a pair of dimers will be repulsive if identical ends are in nearest-neighbor positions and attractive if they are not. The grand partition function is derived by using the Bethe approximation. The energy of the system of interacting dimers is evaluated as a function of the lattice coverage at different temperatures and pair interaction potentials. Under the same conditions the average number of all types of nearest-neighbors is evaluated.

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PubMed2001

Theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions.

In a recent study, the initial rise of the mutual information between the firing rates of N neurons and a set of p discrete stimuli has been analytically evaluated, under the assumption that neurons fire independently of one another to each stimulus and that each conditional distribution of firing rates is Gaussian. Yet real stimuli or behavioral correlates are high dimensional, with both discrete and continuously varying features. Moreover, the Gaussian approximation implies negative firing rates, which is biologically implausible. Here, we generalize the analysis to the case where the stimulus or behavioral correlate has both a discrete and a continuous dimension, like orientation and shape could be in a visual stimulus, or type and direction in a motor action. The functional relationship between the firing patterns and the continuous correlate is expressed through the tuning curve of the neuron, using two different parameters to modulate its width and its flatness. In the case of large noise, we evaluate the mutual information up to the quadratic approximation as a function of population size. We also show that in the limit of large N and assuming that neurons can discriminate between continuous values with a resolution Delta(theta), the mutual information grows to infinity like ln(1/Delta(theta)) when Delta(theta) goes to zero. Then we consider a more realistic distribution of firing rates, truncated at zero, and we prove that the resulting correction, with respect to the Gaussian firing rates, can be expressed simply as a renormalization of the noise parameter. Finally, we demonstrate the effect of averaging the distribution across the discrete dimension, evaluating the mutual information only with respect to the continuously varying correlate.

Action Potentials↗
PubMed2003

Theoretical model of x-ray scattering as a dense matter probe.

We present analytical expressions for the dynamic structure factor, or form factor S(k,omega), which is the quantity describing the x-ray cross section from a dense plasma or a simple liquid. Our results, based on the random phase approximation for the treatment on the charged particle coupling, can be applied to describe scattering from either weakly coupled classical plasmas or degenerate electron liquids. Our form factor correctly reproduces the Compton energy down-shift and the known Fermi-Dirac electron velocity distribution for S(k,omega) in the case of a cold degenerate plasma. The usual concept of scattering parameter is also reinterpreted for the degenerate case in order to include the effect of the Thomas-Fermi screening. The results shown in this work can be applied to interpreting x-ray scattering in warm dense plasmas occurring in inertial confinement fusion experiments or for the modeling of solid density matter found in the interior of planets.

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PubMed2003

Theoretical model for the discrete flexoelectric effect and a description for the sequence of intermediate smectic phases with increasing periodicity.

A general phenomenological description and a simple molecular model is proposed for the "discrete" flexoelectric effect in tilted smectic liquid crystal phases. This effect defines a polarization in a smectic layer induced by a difference of director orientations in the two smectic layers adjacent to it. It is shown that the "discrete" flexoelectric effect is determined by electrostatic dipole-quadrupole interaction between positionally correlated molecules located in adjacent smectic layers, while the corresponding dipole-dipole interaction is responsible for a coupling between polarization vectors in neighboring layers. It is shown that a simple phenomenological model of a ferrielectric smectic liquid crystal, which has recently been proposed in the literature, can be used to describe the whole sequence of intermediate chiral smectic C* phases with increasing periods, and to determine the nonplanar structure of each phase without additional assumptions. In this sequence the phases with three- and four-layer periodicities have the same structure, as observed in the experiment. The theory predicts also the structure of intermediate phases with longer periods that have not been studied experimentally so far. The structures of intermediate phases with periodicities of up to nine layers are presented together with the phase diagrams, and a relationship between molecular chirality and the three-dimensional structure of intermediate phases is discussed. It is considered also how the coupling between the spontaneous polarization determined by molecular chirality and the induced polarization determined by the discrete flexoelectric effect stabilizes the nonplanar structure of intermediate phases.

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PubMed2000

Stresses in silos: comparison between theoretical models and new experiments

We present precise and reproducible mean pressure measurements at the bottom of a cylindrical granular column. If a constant overload is added, the pressure is linear in overload and nonmonotonic in the column height. The results are quantitatively consistent with a local, linear relation between stress components, as was recently proposed by some of us. They contradict the simplest classical (Janssen) approximation, and may rather severely test competing models.

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PubMed2000

Theoretical model for the superconducting and magnetically ordered borocarbides

We present a theory of superconductivity in the presence of a general magnetic structure in a form suitable for the description of complex magnetic phases encountered in borocarbides. The theory, complemented with some details of the band structure and with the magnetic phase diagram, may explain the nearly reentrant behavior and the anisotropy of the upper critical field of HoNi2B2C. The onset of the helical magnetic order depresses superconductivity via the reduction of the interaction between phonons and electrons caused by the formation of magnetic Bloch states. At mean field level, no additional suppression of superconductivity is introduced by the incommensurability of the helical phase.

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PubMed2006

Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: a magnetic levitation investigation and theoretical model.

A magnetic field gradient was used to draw down a low density paramagnetic fluid below a more dense fluid in a Hele-Shaw cell. On turning off the field a Rayleigh-Taylor instability was observed in situ, and the growth of the most unstable wave vector was measured versus time. A theory for the instability that permits different viscosities for two immiscible fluids was developed, and good agreement was found with the experimental results. The technique of magnetic levitation promises to broaden significantly the accessible parameter space of gravitational interfacial instability experiments.

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