Asymptotes of macroscopic observables in Gibbs measures of general interacting particle systems

This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the number of particles tends to infinity. Our main results are concentration bounds, and estimates on the Laplace transform of fluctuations. The main technique is a regularization procedure for general interaction kernels, based on an associated parabolic flow

Large Deviations Principle for the tagged empirical field of a general interacting gas

This paper deals with rare events in a general {interacting gas} at high temperature, by means of Large Deviations Principles. The main result is an LDP for the tagged empirical field, which features the competition of an energy term and an entropy term. The approach to proving this Large Deviations Principle is to first deduce one for the tagged empirical field of non-interacting particles at high temperature, and upgrade that result to interacting particle systems.Comment: Expanded section on construction of configuration

Large Deviation Principle for local empirical measure of Coulomb gases at intermediate temperature regime

This paper deals with Coulomb gases at an intermediate temperature regime. We define a local empirical field and identify a critical temperature scaling. We show that if the scaling of the temperature is supercritical, the local empirical field satisfies an LDP with an entropy-based rate function. We also show that if the scaling of the temperature is subcritical, the local empirical field satisfies an LDP with an energy-based rate function. In the critical temperature scaling regime, we derive an LDP-type result in which the "rate function" features the competition of an entropy and energy terms. An important idea in this work is to exploit the different scaling relations satisfied by the Coulomb energy and the entropy

Generalized transport inequalities and concentration bounds for Riesz-type gases

This paper explores the connection between a generalized Riesz electric energy and norms on the set of probability measures defined in terms of duality. We derive functional inequalities linking these two notions, recovering and generalizing existing Coulomb transport inequalities. We then use them to prove concentration of measure around the equilibrium and thermal equilibrium measures. Finally, we leverage these concentration inequalities to obtain Moser-Trudinger-type inequalities, which may also be interpreted as bounds on the Laplace transform of fluctuations.Comment: Typos fixed. We thank Martin Rouault for spotting the

Antimicrobial Properties and Characterization of Polymer/Composite Nanofibers

Pathogenic bacteria have been the cause of many illnesses worldwide due to their rapid growth and reproduction in food and water. Bacteria-resistant antibiotics and kidney complications due to overuse of antibiotics has remained a large public health concern. The goal of this research project was to find an alternative by producing nanofibers that inhibit microbial growth utilizing Forcespinning technology. The Forcespinning of poly(acrylic acid) (PAA) with Single Wall Carbon Nanotubes functionalized with OH (SWCNT-OH) and Ag + flakes were carried out on solutions with different concentrations. Scanning electron microscopy was used to view fiber morphology and investigate the average nanofiber diameter. Raman spectroscopy was used to observe the molecular vibrations of the samples investigated, thermal gravimetric analysis was used to compare various samples, dynamic scanning calorimetry was used to observe shifts in the glass transition temperature of PAA at different heating rates, and preliminary antimicrobial properties of the nanofibers was investigated