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Mehran Kardar

Publications and source records attributed to Mehran Kardar.

7 recordsLinked to original sources

Information optimization in coupled audio-visual cortical maps.

Barn owls hunt in the dark by using cues from both sight and sound to locate their prey. This task is facilitated by topographic maps of the external space formed by neurons (e.g., in the optic tectum) that respond to visual or aural signals from a specific direction. Plasticity of these maps has been studied in owls forced to wear prismatic spectacles that shift their visual field. Adaptive behavior in young owls is accompanied by a compensating shift in the response of (mapped) neurons to auditory signals. We model the receptive fields of such neurons by linear filters that sample correlated audio-visual signals and search for filters that maximize the gathered information while subject to the costs of rewiring neurons. Assuming a higher fidelity of visual information, we find that the corresponding receptive fields are robust and unchanged by artificial shifts. The shape of the aural receptive field, however, is controlled by correlations between sight and sound. In response to prismatic glasses, the aural receptive fields shift in the compensating direction, although their shape is modified due to the costs of rewiring.

Acoustic Stimulation↗

Knots in charged polymers.

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.

Journal Article↗

Force-extension relations for polymers with sliding links.

Topological entanglements in polymers are mimicked by sliding rings (slip links) that enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip links create additional loops of variable sizes. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation. The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus-de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.

Journal Article↗

Tightness of slip-linked polymer chains.

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip links) enforce pair contacts between monomers. These slip links divide a closed ring polymer into a number of subloops which can exchange length among each other. In the ideal chain limit, we find the joint probability density function for the sizes of segments within such a slip-linked polymer chain (paraknot). A particular segment is tight (small in size) or loose (of the order of the overall size of the paraknot) depending on both the number of slip links it incorporates and its competition with other segments. When self-avoiding interactions are included, scaling arguments can be used to predict the statistics of segment sizes for certain paraknot configurations.

Journal Article↗

Equilibrium shapes of flat knots.

We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localized on a small portion of the larger ring polymer. Within this region, the original knot configuration can assume a hierarchy of contracted shapes, the dominating one given by just one small loop. This hierarchy is investigated in detail for the flat trefoil knot, and corroborated by Monte Carlo simulations.

DNA↗

Correlation functions near modulated and rough surfaces.

In a system with long-ranged correlations, the behavior of correlation functions is sensitive to the presence of a boundary. We show that surface deformations strongly modify this behavior as compared to a flat surface. The modified near surface correlations can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in the deformations in height from a flat surface. Detailed results are given for a regularly patterned surface, as well as for a self-affinely rough surface with roughness exponent zeta. By combining this perturbative calculation in height deformations with the field-theoretic renormalization-group approach, we also estimate the values of critical exponents governing the behavior of the decay of correlation functions near a self-affinely rough surface. We find that for the interacting theory, a large enough zeta can lead to a different surface critical behavior. We also provide scaling relations between roughness induced critical exponents for thermodynamic surface quantities.

Journal Article↗

Anomalous dynamics of translocation.

We study the dynamics of the passage of a polymer through a membrane pore (translocation), focusing on the scaling properties with the number of monomers N. The natural coordinate for translocation is the number of monomers on one side of the hole at a given time. Commonly used models that assume Brownian dynamics for this variable predict a mean (unforced) passage time tau that scales as N2, even in the presence of an entropic barrier. In particular, however, the time it takes for a free polymer to diffuse a distance of the order of its radius by Rouse dynamics scales with an exponent larger than two, and this should provide a lower bound to the translocation time. To resolve this discrepancy, we perform numerical simulations with Rouse dynamics for both phantom (in space dimensions d=1 and 2), and self-avoiding (in d=2) chains. The results indicate that for large N, translocation times scale in the same manner as diffusion times, but with a larger prefactor that depends on the size of the hole. Such scaling implies anomalous dynamics for the translocation process. In particular, the fluctuations in the monomer number at the hole are predicted to be nondiffusive at short times, while the average pulling velocity of the polymer in the presence of a chemical-potential difference is predicted to depend on N.

Journal Article↗