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The lattice data for the energy density of $SU(2)$ gauge theory are calculated with \nop~derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the \nop~beta function in accord with…
The pressure, and the energy and entropy densities are determined for the SU(3) gauge theory in $2 + 1$ dimensions from lattice Monte Carlo calculations in the interval $0.6 \leq T/T_c \leq 15$. The finite temperature lattices simulated…
The mechanical response of solid particles dispersed in a Newtonian fluid exhibits a wide range of nonlinear phenomena including a dramatic increase in the viscosity \cite{1-3} with increasing stress. If the volume fraction of the solid…
Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases…
Vortex shedding is an important physical phenomenon observed across many spatial and temporal scales in fluids. Previous experimental and theoretical studies have established a hierarchy of local and global reduced-order models for vortex…
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…
Through a detailed investigation of the $SU(3)$ gauge theory at finite temperature on lattices of various size we can control finite lattice cut-off effects in bulk thermodynamic quantities. We calculate the pressure and energy density of…
Motivated by experimental progress in cold atomic systems, we use and advance Localisation Landscape Theory (LLT), to examine two-dimensional systems with point-like random scatterers. We begin by showing that exact eigenstates cannot be…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
Radiation from a chaotic cavity filled with gain medium is considered. A set of coupled equations describing the photon density and the population of gain medium is proposed and solved. The spectral distribution and fluctuations of the…
Calorimeters operating in high-radiation environments are susceptible to damage, leading to increased noise that can significantly degrade energy resolution. A common way to mitigate noise is to apply a higher energy threshold on the cells,…
In glass forming liquids close to the glass transition point, even a very slight increase in the macroscopic density results in a dramatic slowing down of the macroscopic relaxation. Concomitantly, the local density itself fluctuates in…
Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with an approximate model of adsorption on lattice sites situated on a cylindrical surface. Using this model, the ground state energies of alternative lattice structures…
There are two competing paradigms in successful SAT solvers: Conflict-driven clause learning (CDCL) and stochastic local search (SLS). CDCL uses systematic exploration of the search space and has the ability to learn new clauses. SLS…
Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then…
Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local…
In part I: We find a series physical scales such as 1) Planck scale, 2) Minimal approximate grand unification SU(5), 3) the mass scale of the see saw model right handed or Majorana neutrinoes, some invented scale with many scalar bosons,…
We develop a semiclassical theory of laser oscillation into a chiral edge state of a topological photonic system endowed with a frequency-dependent gain. As an archetypal model of this physics, we consider a Harper-Hofstadter lattice…
A lattice of elastic Rayleigh rods organized in a parallelepiped geometry can be axially loaded up to an arbitrary amount without distortion and then be subject to incremental time-harmonic dynamic motion. At certain threshold levels of…
We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including…