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We determine the nucleation rates of hard spheres using brute-force molecular dynamics simulations. We overcome nucleation barriers of up to $28 k_B T$, leading to a rigorous test of nucleation rates obtained from rare-event methods and…

Nucleation at large metastability is still largely an unsolved problem, although is a problem of tremendous current interest, with wide practical value. It is well-accepted that the classical nucleation theory (CNT) fails to provide a…

We consider the demixing of a binary fluid mixture, under gravity, which is steadily driven into a two phase region by slowly ramping the temperature. We assume, as a first approximation, that the system remains spatially isothermal, and…

When a bubble of air rises to the top of a highly viscous liquid, it forms a dome-shaped protuberance on the free surface. Unlike a soap bubble, it bursts so slowly as to collapse under its own weight simultaneously, and folds into a…

The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent's view about crisp and non crisp objects over a set of…

The hypercube 2-segmentation problem is a certain biclustering problem that was previously claimed to be NP-hard, but for which there does not appear to be a publicly available proof of NP-hardness. This manuscript provides such a proof.

We present laboratory experiments of a vertically vibrated granular medium consisting of 1 mm diameter glass beads with embedded 8 mm diameter intruder glass beads. The experiments were performed in the laboratory as well as in a parabolic…

We study Mandelbrot's percolation process in dimension $d \geq 2$. The process generates random fractal sets by an iterative procedure which starts by dividing the unit cube $[0,1]^d$ in $N^d$ subcubes, and independently retaining or…

The material of the article is devoted to the most complicated and interesting problem -- a problem of P = NP?. This research was presented to mathematical community in Hyderabad during International Congress of Mathematicians. But there it…

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…

Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient…

It is known that in a certain case, the secondary Bjerknes force, which is a radiation force acting between pulsating bubbles, changes, e.g., from attraction to repulsion as the bubbles approach each other. In this paper, a theoretical…

This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…

We investigate systems of nature where the common physical processes diffusion and fragmentation compete. We derive a rate equation for the size distribution of fragments. The equation leads to a third order differential equation which we…

The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequently, the solvability of systems of equations corresponding…

The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a…

We use direct numerical simulation (DNS) to explore the effect of tilt on two-dimensional turbulent thermal convection on a half-soap bubble that is heated at its equator.In the DNS, the bubble is tilted by an angle…

It is shown that diffusion-limited classical nucleation theory (CNT) can be recovered as a simple limit of the recently proposed dynamical theory of nucleation based on fluctuating hydrodynamics (Lutsko, JCP 136, 034509 (2012)). The same…

Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at…

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…