Biomedical subjects

M Widom

Publications and source records attributed to M Widom.

At least 19 recordsLinked to original sources

PubMed2004

First-principles prediction of a decagonal quasicrystal containing boron.

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants whose deterministic decoration of tiles by atoms can be extended quasiperiodically. Experimentally observed disorder corresponds to phason fluctuations. First-principles total energy calculations find many distinct tilings close to stability and suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B38Mg17Ru45 forms a metastable decagonal quasicrystal that may be thermodynamically stable at high temperatures.

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PubMed2001

Saffman-Taylor problem on a sphere.

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.

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PubMed2000

Gravity-driven instability in a spherical Hele-Shaw cell.

A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.

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PubMed2000

Parallel flow in hele-shaw cells with ferrofluids

Parallel flow in a Hele-Shaw cell occurs when two immiscible liquids flow with relative velocity parallel to the interface between them. The interface is unstable due to a Kelvin-Helmholtz type of instability in which fluid flow couples with inertial effects to cause an initial small perturbation to grow. Large amplitude disturbances form stable solitons. We consider the effects of applied magnetic fields when one of the two fluids is a ferrofluid. The dispersion relation governing mode growth is modified so that the magnetic field can destabilize the interface even in the absence of inertial effects. However, the magnetic field does not affect the speed of wave propogation for a given wave number. We note that the magnetic field creates an effective interaction between the solitons.

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PubMed2000

Ferromagnetic liquid thin films under applied field

Theoretical calculations, computer simulations, and experiments indicate the possible existence of a ferromagnetic liquid state, although definitive experimental evidence is lacking. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture. Since liquid droplets are deformable, the droplet shape is coupled with the magnetization texture. In a thin-film geometry in zero applied field, the droplet has a circular shape and a rotating magnetization texture with a point vortex at the center. We calculate the elongation and magnetization texture of such a ferromagnetic thin-film liquid droplet confined between two parallel plates under a weak applied magnetic field. The vortex stretches into a domain wall and exchange forces break the reflection symmetry. This behavior contrasts qualitatively and quantitatively with the elongation of paramagnetic thin films.

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PubMed2000

Rayleigh-taylor instability with magnetic fluids: experiment and theory

We present experiments showing the Rayleigh-Taylor instability at the interface between a dense magnetic liquid and an immiscible less dense liquid. The liquids are confined in a Hele-Shaw cell and a magnetic field is applied perpendicular to the cell. We measure the wavelength and the growth rate at the onset of the instability as a function of the external magnetic field. The wavelength decreases as the field increases. The amplitude of the interface deformation grows exponentially with time in the early stage, and the growth rate is an increasing function of the field. These results are compared to theoretical predictions given in the framework of linear stability analysis.

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PubMed1999

Elongation of confined ferrofluid droplets under applied fields.

Ferrofluids are strongly paramagnetic liquids. We study the behavior of ferrofluid droplets confined between two parallel plates with a weak applied field parallel to the plates. The droplets elongate under the applied field to reduce their demagnetizing energy and reach an equilibrium shape where the magnetic forces balance against the surface tension. This elongation varies logarithmically with aspect ratio of droplet thickness to its original radius, in contrast to the behavior of unconfined droplets. Experimental studies of a ferrofluid-water-surfactant emulsion confirm this prediction.

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PubMed1995