Related papers: Gelation Paradox
By analogy with conjectures for random matrices, Fyodorov-Hiary-Keating and Fyodorov-Keating proposed precise asymptotics for the maximum of the Riemann zeta function in a typical short interval on the critical line. In this paper, we…
The YbF molecule is a sensitive system for measuring the electron's electric dipole moment. The precision of this measurement can be improved by direct laser cooling of the molecules to ultracold temperature. However, low-lying electronic…
Resistivity saturation is observed in many metallic systems with a large resistivity, i.e., when the resistivity has reached a critical value, its further increase with temperature is substantially reduced. This typically happens when the…
We review the recently proposed elastic approach to glass transition. This approach is based on a simple and a physically transparent idea of elastic interactions between local relaxation events in a liquid. Central to this picture is the…
We consider the two dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball $\{r\leq \lambda(t)\}$. We revisit the pioneering analysis of [20] and prove the existence in the radial class of…
Moment expansions are used as model reduction technique in kinetic gas theory to approximate the Boltzmann equation. Rarefied gas models based on so-called moment equations became increasingly popular recently. However, in a seminal paper…
The chemical reactions are very complex, and include oscillation, condensation, catalyst and self-organization, etc. In these case changes of entropy may increase or decrease. The second law of thermodynamics is based on an isolated system…
It is generally assumed that solid hydrogen will transform into a metallic alkali-like crystal at sufficiently high pressure. However, some theoretical models have also suggested that compressed hydrogen may form an unusual two-component…
Properties of water have been well elucidated for temperatures above $\sim$230 K and yet mysteries remain in the deeply supercooled region. By performing extensive molecular dynamics simulations on this supercooled region, we find that…
The most puzzling aspect of the 'strange metal' behavior of correlated electron compounds is that the linear in temperature resistivity often extends down to low temperatures, lower than natural microscopic energy scales. We consider…
Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich and colloid-poor regions. Gelation results when interconnected colloid-rich regions solidify. We show that this occurs when these regions undergo a glass…
We examine gas accretion and subsequent star formation in representative galaxies from the McMaster Unbiased Galaxy Simulations (Stinson et al. 2010). Accreted gas is bimodal with a natural temperature division at $10^5$ K, near the peak of…
A comprehensive theory encompassing the kinetics of sol-to-gel transition is yet to be formulated due to break-down of the mean-field Smoluchowski Equation. Using high temporal-resolution Monte Carlo simulation of irreversible aggregation…
We conducted experiments to directionally freeze agar hydrogel drops with different polymer concentrations, on a copper substrate maintained at low temperature. Unlike the water droplet studied in the literature, where the liquid part can…
Let $d(n)$ be the number of divisors of $n$, let $$ \Delta(x) := \sum_{n\le x}d(n) - x(\log x + 2\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\zeta(s)$ denote the Riemann zeta-function. Several…
A microscopic picture of the ``preparation'' of a crystal to the transition to liquid state at the approach to melting temperature is proposed. Basing on simple crystallogeometric considerations and the analysis of the computational results…
A picture for thermodynamics of the glassy state is introduced. It assumes that one extra parameter, the effective temperature, is needed to describe the glassy state. This explains the classical paradoxes concerning the Ehrenfest relations…
Well before the atomistic nature of matter was experimentally established, Ludwig Boltzmann's audacious effort to explain the macroscopic world of human experience in terms of the workings of an unseen microscopic world met with vigorous…
The rapid structural and vibrational entropy decrease with decreasing temperature in undercooled liquids is explained in terms of the disappearance of local structural instabilities, which freeze in at the glass temperature as boson peak…
Supercooled Stefan problems describe the evolution of the boundary between the solid and liquid phases of a substance, where the liquid is assumed to be cooled below its freezing point. Following the methodology of Delarue, Nadtochiy and…