Subhadip Raychaudhuri

Maximal height scaling of kinetically growing surfaces.

The scaling properties of the maximal height of a growing self-affine surface with a lateral extent L are considered. In the late-time regime its value measured relative to the evolving average height scales like the roughness: h*(L) approximately L alpha. For large values its distribution obeys logP(h*(L)) approximately (-)A(h*(L)/L(alpha))(a). In the early-time regime where the roughness grows as t(beta), we find h*(L) approximately t(beta)[lnL-(beta/alpha)lnt+C](1/b), where either b = a or b is the corresponding exponent of the velocity distribution. These properties are derived from scaling and extreme-value arguments. They are corroborated by numerical simulations and supported by exact results for surfaces in 1D with the asymptotic behavior of a Brownian path.

Effective membrane model of the immunological synapse.

The immunological synapse is a patterned collection of different types of receptors and ligands that forms in the intercellular junction between T cells and antigen presenting cells during recognition. The synapse is implicated in information transfer between cells, and is characterized by different spatial patterns of receptors at different stages in the life cycle of T cells. We obtain a minimalist model that captures this experimentally observed phenomenology. A functional renormalization group analysis provides further insights.

Excitonic Funneling in Extended Dendrimers with Nonlinear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial treelike light-harvesting antennas (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the nonlinearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.

Movies, measurement, and modeling: the three Ms of mechanistic immunology.

Immunological phenomena that were once deduced from genetic, biochemical, and in situ approaches are now being witnessed in living color, in three dimensions, and in real time. The information in time-lapse imaging can provide valuable mechanistic insight into a host of processes, from cell migration to signal transduction. What we need now are methods to quantitate these new visual data and to exploit computational resources and statistical mechanical methods to develop mechanistic models.

Scaling behavior of cyclical surface growth

The scaling behavior of cyclical surface growth (e.g., deposition/desorption), with the number of cycles, n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents inherited from the dominant process while the effective amplitudes are determined by both. Relevant nonlinear effects in the primary processes may remain so or be rendered irrelevant. Numerical simulations for several pairs of generic primary processes confirm these conclusions. Experimental results for the surface roughness during cyclical electrodeposition/dissolution of silver show a power-law dependence on n, consistent with the scaling description.

Disorder and funneling effects on exciton migration in treelike dendrimers

The center-bound excitonic diffusion on dendrimers subjected to several types of nonhomogeneous funneling potentials is considered. We first study the mean first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations g to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature T is lowered. This is a transition from a high-T regime in which all paths contribute to the MFPT to a low-T regime in which only a few of them do. We further explore the funneling within a realistic nonlinear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the time-dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with g but crosses over, beyond a molecular-specific and T-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the small world model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power law or to a logarithmic scaling with g, depending on the strength of the funneling force.

Roughness scaling in cyclical surface growth.

The scaling behavior of cyclical growth (e.g., cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical processes by substituting the number of cycles n for the time. The roughness is predicted to grow as n(beta) where beta is the cyclical growth exponent. The roughness saturates to a value that scales with the system size L as L(alpha), where alpha is the cyclical roughness exponent. The relations between the cyclical exponents and the corresponding exponents of the primary processes are studied. Exact relations are found for cycles composed of primary linear processes. An approximate renormalization group approach is introduced to analyze nonlinear effects in the primary processes. The analytical results are backed by extensive numerical simulations of different pairs of primary processes, both linear and nonlinear. Experimentally, silver surfaces are grown by a cyclical process composed of electrodeposition followed by 50% electrodissolution. The roughness is found to increase as a power law of n, consistent with the scaling behavior anticipated theoretically. Potential applications of cyclical scaling include accelerated testing of rechargeable batteries and improved chemotherapeutic treatment of cancerous tumors.

Scaling behaviour of randomly alternating surface growth processes

The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given distribution functions. We analytically address processes in which the two primary processes are linear and extend the conclusions to nonlinear processes as well. The growth scaling exponent of the average roughness with the number of applications is found to be determined by the long time tail of the distribution functions. For processes in which both mean application times are finite, the scaling behaviour follows that of the corresponding cyclical process in which the uniform application time of each primary process is given by its mean. If the distribution functions decay with a small enough power law for the mean application times to diverge, the growth exponent is found to depend continuously on this power-law exponent. In contrast, the roughness exponent does not depend on the timing of the applications. The analytical results are supported by numerical simulations of various pairs of primary processes and with different distribution functions. Self-affine surfaces grown by two randomly alternating processes are common in nature (e.g., due to randomly changing weather conditions) and in man-made devices such as rechargeable batteries.