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Mehran Kardar

Publications and source records attributed to Mehran Kardar.

At least 73 records · Page 4Linked to original sources

Spin models inferred from patient data faithfully describe HIV fitness landscapes and enable rational vaccine design

Mutational escape from vaccine induced immune responses has thwarted the development of a successful vaccine against AIDS, whose causative agent is HIV, a highly mutable virus. Knowing the virus' fitness as a function of its proteomic sequence can enable rational design of potent vaccines, as this information can focus vaccine induced immune responses to target mutational vulnerabilities of the virus. Spin models have been proposed as a means to infer intrinsic fitness landscapes of HIV proteins from patient-derived viral protein sequences. These sequences are the product of non-equilibrium viral evolution driven by patient-specific immune responses, and are subject to phylogenetic constraints. How can such sequence data allow inference of intrinsic fitness landscapes? We combined computer simulations and variational theory á la Feynman to show that, in most circumstances, spin models inferred from patient-derived viral sequences reflect the correct rank order of the fitness of mutant viral strains. Our findings are relevant for diverse viruses.

physics.bio-ph↗

Interplay of roughness/modulation and curvature at proximity

We show that roughness or surface modulations change the distance dependence of (power-law) interactions between curved objects at proximity. The modified scaling law is then simply related to the order of the first non-vanishing coefficient of the Taylor expansion of the distribution of separations between the surfaces. The latter can in principle be estimated by scanning measurements, or computed for well characterized modulations, and then used to predict short-distance scaling behavior in disparate experiments. For example, we predict that the radiative heat transfer between a rough sphere and a plate approaches a constant with decreasing separation. Similar saturation is expected for the Casimir force between dielectric or metallic surfaces with appropriate modulations over distinct length scales.

quant-ph↗

Small distance expansion for radiative heat transfer between curved objects

We develop a small distance expansion for the radiative heat transfer between gently curved objects, in terms of the ratio of distance to radius of curvature. A gradient expansion allows us to go beyond the lowest order proximity transfer approximation. The range of validity of such expansion depends on temperature as well as material properties. Generally, the expansion converges faster for the derivative of the transfer than for the transfer itself, which we use by introducing a near-field adjusted plot. For the case of a sphere and a plate, the logarithmic correction to the leading term has a very small prefactor for all materials investigated.

quant-ph↗

A Scattering Approach to the Dynamical Casimir Effect

We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from accelerating boundaries. Applications are provided for objects with different shapes in various dimensions, and undergoing rotational or linear motion. Within this framework, photon generation is discussed in the context of a modulated optical mirror. For dispersive objects, we find general results solely in terms of the scattering matrix. Specifically, we discuss the vacuum friction on a rotating object, and the friction on an atom moving parallel to a surface.

quant-ph↗

Polymer-mediated entropic forces between scale-free objects

The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R_0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h<<R_0, separation is the only remaining relevant scale and the entropic force must take the form F=AkT/h. The amplitude A is universal, and can be related to exponents ηgoverning the anomalous scaling of polymer correlations in the presence of obstacles. We use analytical, numerical and epsilon-expansion techniques to compute the exponent ηfor a polymer attached to the tip of the cone (with or without an additional plate or cone) for ideal and self-avoiding polymers. The entropic force is of the order of 0.1 pN at 0.1 micron for a single polymer, and can be increased for a star polymer.

cond-mat.soft↗

Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects

We present a detailed derivation of heat radiation, heat transfer and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal non-equilibrium. The results can be expressed as basis-independent trace formulae in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave-expansions, we transform the results for radiation, transfer and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nano-spheres is typically invalid. We derive asymptotic formulae for heat transfer and non-equilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nano-sphere can levitate above a plate with the repulsive non-equilibrium force overcoming gravity -- an effect that is not due to radiation pressure.

quant-ph↗

Spontaneous emission by rotating objects: A scattering approach

We study the quantum electrodynamics (QED) vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel'dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis.

quant-ph↗

Casimir forces between cylinders at different temperatures

We study Casimir interactions between cylinders in thermal non-equilibrium, where the objects as well as the environment are held at different temperatures. We provide the general formula for the force, in a one reflection approximation, for cylinders of arbitrary radii and optical properties. As is the case for equilibrium, we find that the force for optically diluted cylinders can be obtained by appropriate summation of the corresponding result for spheres. We find that the non-equilibrium forces are generally larger than their equilibrium counterpart at separations greater than the thermal wavelength. They may also exhibit oscillations as function of separation, leading to stable points of zero net force. These effects are particularly pronounced for thin conducting cylinders (e.g. 40nm diameter nano-wires of tungsten) due to their large emissivity.

quant-ph↗

Heat radiation from long cylindrical objects

The heat radiated by objects small or comparable to the thermal wavelength can be very different from the classical blackbody radiation as described by the laws of Planck and Stefan-Boltzmann. We use methods based on scattering of electromagnetic waves to explore the dependence on size, shape, as well as material properties. In particular, we explore the radiation from a long cylinder at uniform temperature, discussing in detail the degree of polarization of the emitted radiation. If the radius of the cylinder is much smaller than the thermal wavelength, the radiation is polarized parallel to the cylindrical axis and becomes perpendicular when the radius is comparable to the thermal wavelength. For a cylinder of uniaxial material (a simple model for carbon nanontubes), we find that the influence of uniaxiality on the polarization is most pronounced if the radius is larger than a few microns, and quite small for submicron sizes typical for nanotubes.

quant-ph↗

Entropic force of polymers on a cone tip

We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by F=A kT/h. The universal amplitude A can be related to (geometry dependent) correlation exponents of long polymers. We compute A for phantom polymers, and for self-avoiding (including star) polymers by epsilon-expansion, as well as by numerical simulations in 3 dimensions.

cond-mat.stat-mech↗

The influence of T cell development on pathogen specificity and autoreactivity

T cells orchestrate adaptive immune responses upon activation. T cell activation requires sufficiently strong binding of T cell receptors on their surface to short peptides derived from foreign proteins bound to protein products of the major histocompatibility (MHC) gene products, which are displayed on the surface of antigen presenting cells. T cells can also interact with peptide-MHC complexes, where the peptide is derived from host (self) proteins. A diverse repertoire of relatively self-tolerant T cell receptors is selected in the thymus. We study a model, computationally and analytically, to describe how thymic selection shapes the repertoire of T cell receptors, such that T cell receptor recognition of pathogenic peptides is both specific and degenerate. We also discuss the escape probability of autoimmune T cells from the thymus.

physics.bio-ph↗

Dilution and resonance enhanced repulsion in non-equilibrium fluctuation forces

In equilibrium, forces induced by fluctuations of the electromagnetic field between electrically polarizable objects (microscopic or macroscopic) in vacuum are always attractive. The force may, however, become repulsive for microscopic particles coupled to thermal baths with different temperatures. We demonstrate that this non-equilibrium repulsion can be realized also between macroscopic objects, as planar slabs, if they are kept at different temperatures. It is shown that repulsion can be enhanced by (i) tuning of material resonances in the thermal region, and by (ii) reducing the dielectric contrast due to "dilution". This can lead to stable equilibrium positions. We discuss the realization of these effects for aerogels, yielding repulsion down to sub-micron distances at realistic porosities.

quant-ph↗

Non-equilibrium electromagnetic fluctuations: Heat transfer and interactions

The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in non-equilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.

quant-ph↗

Non-equilibrium Casimir forces: Spheres and sphere-plate

We discuss non-equilibrium extensions of the Casimir force (due to electromagnetic fluctuations), where the objects as well as the environment are held at different temperatures. While the formalism we develop is quite general, we focus on a sphere in front of a plate, as well as two spheres, when the radius is small compared to separation and thermal wavelengths. In this limit the forces can be expressed analytically in terms of the lowest order multipoles, and corroborated with results obtained by diluting parallel plates of vanishing thickness. Non-equilibrium forces are generally stronger than their equilibrium counterpart, and may oscillate with separation (at a scale set by material resonances). For both geometries we obtain stable points of zero net force, while two spheres may have equal forces in magnitude and direction resulting in a self-propelling state.

quant-ph↗

Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.

quant-ph↗

Formation and Stability of Synaptic Receptor Domains

Neurotransmitter receptor molecules, concentrated in postsynaptic domains along with scaffold and a number of other molecules, are key regulators of signal transmission across synapses. Employing experiment and theory, we develop a quantitative description of synaptic receptor domains in terms of a reaction-diffusion model. We show that interactions between only receptor and scaffold molecules, together with the rapid diffusion of receptors on the cell membrane, are sufficient for the formation and stable characteristic size of synaptic receptor domains. Our work reconciles long-term stability of synaptic receptor domains with rapid turnover and diffusion of individual receptors.

q-bio.NC↗

Casimir force between sharp-shaped conductors

Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest.

quant-ph↗

Casimir Force at a Knife's Edge

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $θ$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.

quant-ph↗