Condensed Matter Students’ Symposium

Bringing stochastic resetting closer to reality

Ofir Tal-Friedman

Abstract:

Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where, upon resetting, the particle is returned to its initial position. My presentation will be separated into two parts:

1. While Diffusion with stochastic resetting serves as a paradigmatic model to study resetting phenomena in general, the lack of a well-controlled platform by which this process can be studied experimentally has been a major impediment to research in the field. I will present our experimental realization of colloidal particle diffusion and resetting via holographic optical tweezers. We provide the first experimental corroboration of central theoretical results and go on to measure the energetic cost of resetting in steady-state and first-passage scenarios. In both cases, we show that this cost cannot be made arbitrarily small because of fundamental constraints on realistic resetting protocols.

2. I will present our generalization of diffusion with resetting to account for situations where a particle is returned only a fraction of its distance to the origin, e.g., halfway. This model always attains a steady-state distribution, and as we change the fraction of resetting, the steady-state transitions from the known Laplace form obtained in the limit of full resetting to a Gaussian form, which is obtained close to the limit of no resetting. A similar transition is shown to be displayed by drift-diffusion. Finally, I will show the extension of our analysis to capture the temporal evolution of drift-diffusion with partial resetting, providing a bottom-up probabilistic construction that yields a closed-form solution for the time-dependent distribution of this process in Fourier-Laplace space.

Effects of size asymmetry in ionic solutions

Or Ben Yaakov

Abstract:

Electrostatic interactions between charges in aqueous solutions of small and macro-ions have been widely investigated in the past, as they govern the self-organization and dynamics of many soft matter systems. When the ionic solution is dilute, the interactions are well described by the renowned Poisson-Boltzmann theory. Yet, at higher concentrations, which are very common in Nature and industrial applications, steric interactions also become important, and a more refined theory is needed. One such modification is called the sterically modified Poisson-Boltzmann (smPB) theory. The theory takes into account the ionic finite size, but it  is restricted to solvent molecules and ions that have the same size.

In this talk, I will present an extension of the smPB theory, accounting for asymmetry in the ionic size and their valency. After presenting the model, I will examine numerical solutions of the ionic and electrostatic-potential profiles near charged surfaces. I will focus on the surprising effects of the solvent size on the ionic concentrations, and the importance of the valency-to-size ratio in concentrated solutions. Finally, I will discuss future directions and challenges, especially those involving several charged species.

Seminar Organizer: Dr. Dominik Juraschek