Related papers: Vector Resonant Relaxation and Statistical Closure…
Stars orbiting a supermassive black hole in the center of galaxies undergo very efficient diffusion in their orbital orientations: this is "Vector Resonant Relaxation". Such a dynamics is intrinsically non-linear, stochastic, and…
In the realm of complex systems, dynamics is often modeled in terms of a non-linear, stochastic, ordinary differential equation (SDE) with either an additive or a multiplicative Gaussian white noise. In addition to a well-established…
We develop the exact renormalization group approach as a way to evaluate the effective speed of propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Direct numerical simulations of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean…
We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss…
We use the renormalization group method to study model E of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using Martin-Siggia-Rose theorem, we obtain a field-…
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic…
This work proposes a technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems modeled as parameterized systems of algebraic equations. The proposed technique extends the…
We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated…
We use the technique of information relaxation to develop a duality-driven iterative approach to obtaining and improving confidence interval estimates for the true value of finite-horizon stochastic dynamic programming problems. We show…
We investigate the rate of orbital orientation dilution of young stellar clusters in the vicinity of supermassive black holes. Within the framework of vector resonant relaxation, we predict the time evolution of the two-point correlation…
We have developed a new simulation code aimed at studying the stellar dynamics of a galactic central star cluster surrounding a massive black hole. In order to include all the relevant physical ingredients (2-body relaxation, stellar mass…
We present a first-principles theory of Resonant Relaxation (RR) of a low mass stellar system orbiting a more massive black hole (MBH). We first extend the kinetic theory of Gilbert (1968) to include the Keplerian field of a black hole of…
We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called…
The Recent Fluid Deformation Closure (RFDC) model of lagrangian turbulence is recast in path-integral language within the framework of the Martin-Siggia-Rose functional formalism. In order to derive analytical expressions for the…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively employing a Gaussian…