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Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…
Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
Systems where all energy eigenstates are localized are known to display an emergent local integrability, in the sense that one can construct an extensive number of operators that commute with the Hamiltonian and are localized in real space.…
Dust particles immersed within a plasma environment, such as those found in planetary rings or comets, will acquire an electric charge. If the ratio of the inter-particle potential energy to average kinetic energy is large enough the…
The problem of finding the most efficient way to pack spheres has an illustrious history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal in the 60's. This problem finds applications…
Governing equations are fundamental for describing and predicting dynamic urban geographic systems. Unlike physical systems guided by first principles, urban spatiotemporal phenomena emerge from coupled geographic processes that lack…
Using computed x-ray tomography we determine the three dimensional (3d) structure of binary hard sphere mixtures as a function of composition and size ratio of the particles, q. Using a recently introduced four-point correlation function we…
Systems of particles interacting with "stealthy" pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely…
The eigenproblem for thin shells of revolution under uncertainty in material parameters is discussed. Here the focus is on the smallest eigenpairs. Shells of revolution have natural eigenclusters due to symmetries, moreover, the eigenpairs…
Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening…
Determination of \emph{optimal} arrangements of $N$ particles on a sphere is a well-known problem in physics. A famous example of such is the Thomson problem of finding equilibrium configurations of electrical charges on a sphere. More…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
This paper proposes a phase space to compare the static packings of a granular system compatible to a macrostate that is set by the external stress. The nature of this phase space is analyzed, showing that the consideration of the allowed…
Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood…
We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time $t$ and position in space x also depend on the…