Biomedical subjects

M Kardar

Publications and source records attributed to M Kardar.

At least 19 recordsLinked to original sources

PubMed2006

Casimir Interaction between a plate and a cylinder.

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay approximately L/[H3 ln(H/R)] at large plate-cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.

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PubMed2005

Attractive Casimir forces in a closed geometry.

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.

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PubMed2003

Tight and loose shapes in flat entangled dense polymers.

We investigate the effects of topological constraints (entanglements) on two-dimensional polymer loops in the dense phase, and at the collapse transition (theta-point). Previous studies have shown that in the dilute phase the entangled region becomes tight, and is thus localised on a small portion of the polymer. We find that the entropic force favouring tightness is considerably weaker in dense polymers. While the simple figure-eight structure, created by a single crossing in the polymer loop, localises weakly, the trefoil knot and all other prime knots are loosely spread out over the entire chain. In both the dense and theta conditions, the uncontracted-knot configuration is the most likely shape within a scaling analysis. By contrast, a strongly localised figure-eight is the most likely shape for dilute prime knots. Our findings are compared to recent simulations.

Journal Article↗

PubMed2001

Probing the strong boundary shape dependence of the Casimir force.

We study the geometry dependence of the Casimir energy for deformed metal plates by a path integral quantization of the electromagnetic field. For the first time, we give a complete analytical result for the deformation induced change in Casimir energy delta E in an experimentally testable, nontrivial geometry, consisting of a flat and a corrugated plate. Our results show an interesting crossover for delta E as a function of the ratio of the mean plate distance H, to the corrugation length lambda: For lambda< >H.

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PubMed2001

Macroscopic equations for pattern formation in mixtures of microtubules and molecular motors.

Inspired by patterns observed in mixtures of microtubules and molecular motors, we propose continuum equations for the evolution of motor density and microtubule orientation. The chief ingredients are the transport of motors along tubules, and the alignment of tubules in the process. The macroscopic equations lead to aster and vortex patterns in qualitative agreement with experiments. While the early stages of evolution of tubules are similar to coarsening of spins following a quench, the rearrangement of motors leads to arrested coarsening at low densities. Even in one dimension, the equations exhibit a variety of interesting behaviors, such as symmetry breaking, moving fronts, and motor localization.

Microtubules↗

PubMed2001

Free energy self-averaging in protein-sized random heteropolymers.

Current theories of heteropolymers are inherently macroscopic, but are applied to mesoscopic proteins. To compute the free energy over sequences, one assumes self-averaging--a property established only in the macroscopic limit. By enumerating the states and energies of compact 18, 27, and 36mers on a lattice with an ensemble of random sequences, we test the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is valid at the scale of real proteins. The results validate sequence design methods which exponentially speed up computational design and simplify experimental realizations.

Models, Chemical↗

PubMed2001

Modified critical correlations close to modulated and rough surfaces.

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affine rough surface. We find that a large enough roughness exponent can modify surface critical behavior.

Journal Article↗

PubMed2000

Thermodynamic fingerprints of disorder in flux line lattices and other glassy mesoscopic systems

We examine probability distributions for thermodynamic quantities in finite-sized random systems close to criticality. Guided by available exact results, a general ansatz is proposed for replicated free energies, which leads to scaling forms for cumulants of various macroscopic observables. For the specific example of a planar flux line lattice in a two-dimensional superconducting film near H(c1), we provide detailed scaling results for the statistics of the magnetic flux density, susceptibility, heat capacity, and their cross correlations, which can be tested in a recently used experimental setup [Bolle et al., Nature (London) 399, 43 (1999)].

Journal Article↗

PubMed2000

Phase ordering and roughening on growing films.

We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimensions, we find a variety of different scaling behaviors, depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations.

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PubMed1996