Fluctuation of a planar Brownian loop capturing a large area

We consider a planar Brownian loop that is run for a time and conditioned on the event that its range encloses the unusually high area of , with being large. The conditioned process, denoted by , was proposed by Senya Shlosman as a model for the fluctuation of a phase boundary. We study the deviation of the range of from a circle of radius . This deviation is measured by the inradius and outradius , which are the maximal radius of a disk enclosed by the range of , and the minimal radius of a disk that contains this range. We prove that, in a typical realization of the conditioned measure, each of these quantities differs from by at most .

     

Universal finitary codes with exponential tails

In 1977, Keane and Smorodinsky showed that there exists a finitaryhomomorphism from any finite-alphabet Bernoulli process to anyother finite-alphabet Bernoulli process of strictly lower entropy.In 1996, Serafin proved the existence of a finitary homomorphismwith finite expected coding length. In this paper, we constructsuch a homomorphism in which the coding length has exponentialtails. Our construction is source-universal, in the sense thatit does not use any information on the source distribution otherthan the alphabet size and a bound on the entropy gap betweenthe source and target distributions. We also indicate how ourmethods can be extended to prove a source-specific version ofthe result for Markov chains.     

Polymer and biopolymer mediated self-assembly of gold nanoparticles

Gold nanoparticle-polymer composites are versatile and diverse functional materials, with applications in optical, electronic and sensing devices. This tutorial review focuses on the use of polymers to control the assembly of gold nanoparticles. Examples of synthetic polymers and biopolymers are provided, as well as applications of the composite materials in sensing and memory devices.     

An LIL for cover times of disks by planar random walk and Wiener sausage

Let be the radius of the largest disk covered after steps of a simple random walk. We prove that almost surely

where denotes 3 iterations of the function. This is motivated by a question of Erdos and Taylor. We also obtain the analogous result for the Wiener sausage, refining a result of Meyre and Werner.

     

Effect of metal cations on polydiacetylene Langmuir films

Polydiacetylene (PDA) Langmuir films (LFs) are a unique class of materials that couple a highly aligned conjugated backbone with tailorable pendant side groups and terminal functionalities. The films exhibit chromatic transitions from monomer to blue polymer and finally to a red phase that can be activated optically, thermally, chemically, and mechanically. The properties of PDA LFs are strongly affected by the presence of metal cations in the aqueous subphase of the film due to their interaction with the carboxylic head groups of the polymer. In the present study the influence of divalent cadmium, barium, copper, and lead cations on the structural, morphological, and optical properties of PDA LFs was investigated by means of surface pressure-molecular area (π-A) isotherms, atomic force microscopy, optical absorbance, and Raman spectroscopy. The threshold concentrations for the influence of metal cations on the film structure, stability, and phase transformation were determined by π-A analyses. It was found that each of the investigated cations has a unique influence on the properties of PDA LFs. Cadmium cations induce moderate phase transition kinetics with reduced domain size and fragmented morphology. Barium cations contribute to stabilization of the PDA blue phase and enhanced linear strand morphology. On the other hand, copper cations enhance rapid formation of the PDA red phase and cause fragmented morphology of the film, while the presence of lead cations results in severe perturbation of the film with only a small area of the film able to be effectively polymerized. The influence of the metal cations is correlated with the solubility product (K(sp)), association strength, and ionic-covalent bond nature between the metal cations and the PDA carboxylic head groups.     

Comparative study of the photoprotolytic reactions of D-luciferin and oxyluciferin

Optical steady-state and time-resolved spectroscopic methods were used to study the photoprotolytic reaction of oxyluciferin, the active bioluminescence chromophore of the firefly's luciferase-catalyzed reaction. We found that like D-luciferin, the substrate of the firefly bioluminescence reaction, oxyluciferin is a photoacid with pK(a)* value of ～0.5, whereas the excited-state proton transfer (ESPT) rate coefficient is 2.2 × 10(10) s(-1), which is somewhat slower than that of D-luciferin. The kinetic isotope effect (KIE) on the fluorescence decay of oxyluciferin is 2.5 ± 0.1, the same value as that of D-luciferin. Both chromophores undergo fluorescence quenching in solutions with a pH value below 3.     

Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition

We study a version of the stochastic “tug-of-war” game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function is shifted by an appropriate constant, the values of the game after n steps converge in the continuous case and the case of finite graphs with loops. Using this we prove the existence of solutions to the infinity Laplace equation with vanishing Neumann boundary condition.     

Self-trapping of optical beams through thermophoresis

We demonstrate, theoretically and experimentally, self-trapping of optical beams in nanoparticle suspensions by virtue of thermophoresis. We use light to control the local concentration of nanoparticles, and increase their density at the center of the optical beam, thereby increasing the effective refractive index in the beam vicinity, causing the beam to self-trap.     

Mesoscopic stoner instability in metallic nanoparticles revealed by shot noise

We study sequential tunneling through a metallic nanoparticle close to the Stoner instability coupled to parallel magnetized electrodes. Increasing the bias voltage successively opens transport channels associated with excitations of the nanoparticle's total spin. For the current this leads just to a steplike increase. The Fano factor, in contrast, shows oscillations between large super-Poissonian and sub-Poissonian values as a function of bias voltage. We explain the enhanced Fano factor in terms of generalized random-telegraph noise and propose the shot noise as a convenient tool to probe the mesoscopic Stoner instability.