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The driven, cylindrical, free interface between two miscible, Stokes fluids with high viscosity contrast have been shown to exhibit dispersive hydrodynamics. A hallmark feature of dispersive hydrodynamic media is the dispersive resolution…
We consider a class of time-dependent inclusions in Hilbert spaces for which we state and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities, convex analysis and fixed point theory. Then we…
Coupled waveguides are convenient at implementing useful optical transformations. In this letter, we investigate the uncertainty of transformation by two coupled waveguides that stems from the perturbations of waveguide's mode indices~---…
We consider a system of multiple insulating rigid bodies moving inside of an electrically conducting compressible fluid. In this system we take into account the interaction of the fluid with the bodies as well as with the electromagnetic…
This paper is dedicated to the study of the orthogonal decomposition of spatially and temporally distributed signals in fluid-structure interaction problems. First application is concerned with the analysis of wall-pressure distributions…
We derive an explicit relationship between the moment of inertia and the quadrupole response function of an interacting gas confined in a harmonic trap. The relationship holds for both Bose and Fermi systems and is well suited to reveal the…
Numerical solutions of the mode-coupling theory (MCT) equations for a hard-sphere fluid confined between two parallel hard walls are elaborated. The governing equations feature multiple parallel relaxation channels which significantly…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
In this review, we extend the Boundary Control method\, -- \,an approach to inverse problems based on control theory for dynamical systems \, -- \,to inverse problems for discrete dynamical systems. We apply our results to classical moment…
We have investigated the motion of a single optically trapped colloidal particle close to a limiting wall at time scales where the inertia of the surrounding fluid plays a significant role. The velocity autocorrelation function exhibits a…
This paper offers a comprehensive performance analysis of the distributed continuous-time filtering in the presence of modeling errors. First, we introduce two performance indices, namely the nominal performance index and the estimation…
We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a…
We study the link between generalization and interference in temporal-difference (TD) learning. Interference is defined as the inner product of two different gradients, representing their alignment. This quantity emerges as being of…
The key idea behind PID Passivity-based Control (PID-PBC) is to leverage the passivity property of PIDs (for all positive gains) and wrap the PID controller around a passive output to ensure global stability in closed-loop. However, the…
Turbulence modeling remains a longstanding challenge in fluid dynamics. Recent advances in data-driven methods have led to a surge of novel approaches aimed at addressing this problem. This work builds upon our recent work [Phys. Rev.…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
In this paper, we consider the direct and inverse problem of scattering of time-harmonic waves by an unbounded rough interface with a buried impenetrable obstacle. We first study the well-posedness of the direct problem with a local source…
Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the…
Self-potential (SP) data are of interest to vadose zone hydrology because of their direct sensitivity to water flow and ionic transport. There is unfortunately little consensus in the literature about how to best model SP data under…
Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is…