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An abstract framework for constructing stable decompositions of the spaces corresponding to general symmetric positive definite problems into "local" subspaces and a global "coarse" space is developed. Particular applications of this…
Using an isothermal MHD code, we have performed three-dimensional, high-resolution simulations of the Parker instability. The initial equilibrium system is composed of exponentially-decreasing isothermal gas and magnetic field (along the…
The objective of the paper is to identify laws and mechanisms that allow the creation of more order from disorder using natural means i.e., without the help of conscious beings. While this is not possible for the collection of all dynamical…
Spin chains with quenched disorder exhibit rich critical behavior, often captured by real-space renormalization group (RSRG) techniques. However, the physics of such systems in the presence of random measurements (i.e., non-Hermitian…
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…
Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be…
In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
Free energy landscapes encode the kinetics, intermediates, and transition states that govern molecular processes and are thus a key target of single biomolecule research. Typical approaches to deriving optimal, error-minimizing,…
This paper presents a robust control synthesis and analysis framework for nonlinear systems with uncertain initial conditions. First, a deep learning-based lifting approach is proposed to approximate nonlinear dynamical systems with linear…
Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…
Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a review of the concepts underpinning the framework and the circumstances under which it is expected to be useful. A particular emphasis is placed on the…
The fully developed turbulence with weak anisotropy is investigated by means of renormalization group approach (RG) and double expansion regularization for dimensions $d\ge 2$. Some modification of the standard minimal substraction scheme…
As a quantum-informative window into quantum many-body physics, the concept and application of entanglement renormalization group (ERG) have been playing a vital role in the study of novel quantum phases of matter, especially long-range…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak…
Although resetting has widespread applicability, applying it to the dynamics in the presence of spatial quenched disorder, which is essential in many physical problems, is challenging. In this study, we consider a well-known one-dimensional…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…