The purpose of this study is to address the open question of diffusion on a fractal lattice. Monte Carlo simulations were performed on systems containing two species of particles. B particles were subject to the general reactions  (i) B → 0 with rate l; (ii) n B → 0 with rate m; and (iii) B → (m + 1) B with rate s. These give rise to a fractal structure at the nonequilibrium phase transition between an active and absorbing phase. The A particles were allowed to diffuse only on sites occupied by B particles, and we compare their measured mean square displacement with the mean field result <x²> ~ t^(1-a) when B(t) ~ t^(-a).  At criticality, any deviation from this mean square result was smaller than our error in determining the exponents, but more interesting behavior was observed off criticality.

I will give a brief and qualitative review of a few experiments in the field of soft matter.  First, I will discuss some clever experiments designed to understand the stability of the shapes of lipid vesicles. Next is the surprising world of vibrated layers of sand, rich with unexpected patterns.  Finally we visit the dynamics of a ping-pong ball in a turbulent flow.  Students of all levels are urged to attend, as the talk will be of the "wow isn't this cool!" variety.

The late stages of coarsening systems exhibit features that demand explanation by the dynamic renormalization group: self-similarity, power-law growth, and universality. Unfortunately, a controlled renormalization group calculation has proved elusive, leaving us to guess the properties of the fixed point that controls the asymptotic dynamics guided by empirical evidence, consistency requirements, and a handful of exact solutions. New evidence has overturned some of the standard views on correlation function universality. I will present an argument which reconciles this discrepancy and which provides a clarification of which quantities are universal and a new larger set of universality classes.

The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamic Chern-Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern-Simons theory has a perturbative momentum expansion. The effective action obtained from the perturbation theory, although commutative at leading order, is also non-commutative. This non-commutative gauge symmetry is a quantum symmetry, which can only be fully realized through the inclusion of all orders in perturbation theory.

The effects of giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR) in magnetic multilayered structures and tunnel junctions are of fundamental interest and very promising for creating new generations of magnetic sensors and memory devices. A quantum theory of GMR in magnetic sandwiches is presented. The problem of relative importance of bulk and surface scattering is discussed. Another part of the talk is devoted to a theory of the tunnel magnetoresistance (TMR) in magnetic double barrier tunnel junctions. The magnetic double barrier structures are very promising to study fundamental phenomena and for the application in tunnelling magnetic random access memories (MRAM). Current-voltage characteristics of asymmetric and symmetric double barrier structures with the concept of ``magnetically controlled diodes'' are presented. The influence of statistics of random thickness fluctuations on transport properties and on quantum well states in the middle metallic layer is discussed.

Fibroblast growth factors (FGF) stimulates proliferation of many cell types, and are crucial in such processes as eg. wound healing. Cells have specific receptor (R) protein molecules on their surface which bind FGF for this purpose. FGF is also bound by Heparan Sulfate Proteoglycan (HSPG) molecules which are present on the cell surface. In vitro, both these complexes are unstable, with half-life of the order of 10-20 minutes, wheras in intact cells, the half-life of FGF-R complex is nearly 5 hours! To account for this increased stability, it has been proposed that R-FGF complex combines with HSPG via surface diffusion and forms the triad  R-FGF-HSPG. We examine the feasibility of this reaction using the well-known Smoluchowski theory and Monte Carlo simulations. Our results support the triad formation theory, and are in qualitative agreement with experimental data.

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature T_e (T_o). Detailed balance is violated so that the spin chain settles into a non-equilibrium stationary state, characterized by multiple interactions of increasing range and spin order.
We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the long-time, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

We describe a field-theoretic approach to calculate quantum shot noise in nanoscale conductors from first principles. Our starting point is the second-quantization field operator to calculate shot noise in terms of single quasi-particle wavefunctions obtained self-consistently within density functional theory. The approach is valid in both linear and nonlinear response and is particularly helpful in studying shot noise at the atomic-scale level. As an example we study shot noise in Si atomic wires and benzene molecule between metal electrodes. We find that shot noise is strongly nonlinear as a function of bias in Si atomic wires and it is enhanced for very short wires due to the large contribution from the metal electrodes, while for longer wires it shows an oscillatory behavior for even and odd number of atoms with opposite trend with respect to the conductance. We also observe that the shotnoise w.r.t. applied gate field in benzene molecule is enhanced wherever the conductance is suppressed.

Hysteresis in bistable systems driven by an oscillating external field has been an active research topic for over a century, but interesting problems and phenomena still remain. One of these are the asymptotic low-frequency dependence of the hysteresis-loop area (the energy dissipation) in systems driven by a sinusoidally varying field. Although this quantity is commonly analyzed as a power law, the power-law exponents reported by different groups differ widely. Here we present data that yield a solution to this dilemma: the loop area is actually described by a very wide crossover to a logarithmic low-frequency dependence on the inverse frequency, yielding different effective exponents in different frequency ranges. Another exciting phenomenon that has come to light in the last decade, is a dynamic phase transition between a symmetric dynamic phase at low driving frequencies, and a symmetry-broken phase at high frequencies. Here we present strong numerical and analytical evidence that the phase transition that separates these two dynamic phases belongs to the universality class of the equilibrium Ising model in zero field, despite the fact that the system under consideration is driven very far from equilibrium by the oscillating field.

We present numerical and theoretical results for models of magnetization switching in nanoparticles and ultrathin films. The models and computational methods include kinetic Ising models of highly anisotropic magnets which are simulated by dynamic Monte Carlo methods, and micromagnetics models of continuum-spin systems that are studied by finite-temperature Langevin simulations. The theoretical analysis builds on the fact that a magnetic particle that is magnetized in a direction antiparallel to the applied field is in a metastable state. Nucleation theory is therefore used to analyze magnetization reversal as the decay of this metastable phase to equilibrium. We present results on magnetization reversal in pure systems, as well as effects of impurities and surfaces, and hysteresis in magnets driven by oscillating external fields.

We use a mean-field approximation to study the Persistence properties of the zero-temperature coarsening dynamics of the one-dimensional q-state Potts model, by ignoring the correlations between diffusing interfacial points separating spins with different Potts state. We show that the persistent site pair correlation function has a scaling form which is the same for all values of the persistence exponent theta(q). We then show within the Independent Interval Approximation (IIA) that the distribution n(k,t) of separations k between two consecutive 
persistent spins at time t has the asymptotic scaling form n(k,t)=t^{-2Z} g(t,k/t^Z) where the dynamical exponent has the unusual form Z=max(1/2,theta). The behavior of the scaling function g(t,x) for large and small values of the arguments is found using the IIA. The unusual dynamical scaling form and the behavior of the scaling function is supported by numerical simulations.

It is well understood how a charged particle behaves under the influence of a large external magnetic field. Magnetic Resonance Imaging (MRI) harnesses this information in Fourier space as a clinical diagnostic tool. Using the underlying physics of MRI and its k-space representation, a quantitative and qualitative understanding of the nature of the tissues in the Central Nervous System (CNS) is explored. We will examine three techniques to estimate the solutions to the coupled Bloch equations governing nuclear spin exchange (Magnetization Transfer), and apply these solutions to understanding the phenomenological fingerprint of Magnetization Transfer in two de-myelinating diseases of the CNS: Adrenoleukodysrophy and Adrenomyeloneuropathy.

We consider diffusion-limited reactions A_i + A_j → 0 (1 ≤ i < j &le q) in d space dimensions. For q > 2 and d ≥ 2 we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is the same as for single-species pair annihilation A + A → 0. In d = 1, however, particle segregation occurs for all q < ∞. The total density decays according to a q dependent power law, n(t) ~ t^-a(q). Within a simplified version of the model a(q) = (q-1) / 2q can be determined exactly. Our findings are supported through Monte Carlo simulations.