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Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
The use of few-femtosecond, extreme ultraviolet (XUV) pulses, produced by high-order harmonic generation, in combination with few-femtosecond infrared (IR) pulses in pump-probe experiments has great potential to disclose ultrafast dynamics…
Digitalizing real-world analog signals typically involves sampling in time and discretizing in amplitude. Subsequent signal reconstructions inevitably incur an error that depends on the amplitude resolution and the temporal density of the…
Diffraction imaging of non-equilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension.…
In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale problems, where the spatial heterogeneities are at subgrid…
We develop a representation of reverse-time migration in terms of Fourier integral operators the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation…
The aim of this paper is to study the feasibility of time-reversal methods in a non homogeneous elastic medium, from data recorded in an acoustic medium. We aim to determine, from partial aperture boundary measurements, the presence and…
Temporal modulation of material parameters offers unprecedented control over wave dynamics, enabling phenomena beyond the capabilities of static systems. Here we introduce and analyze a robust mechanism for time rewinding, whereby a…
Underwater acoustic recognition for ship-radiated signals has high practical application value due to the ability to recognize non-line-of-sight targets. However, due to the difficulty of data acquisition, the collected signals are scarce…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
Sampling is classically performed by recording the amplitude of an input signal at given time instants; however, sampling and reconstructing a signal using multiple devices in parallel becomes a more difficult problem to solve when the…
In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…
The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…
Time-reversal symmetry allows waves to retrace their paths through complex media and refocus at their origin. However, incomplete capture and reversal of scattered waves often limits pulse recompression. We address this challenge for…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
Nonreciprocal wave propagation allows for directional energy transport. In this work, we systematically investigate wave dynamics in an elastic lattice that combines nonreciprocal stiffness with viscous damping. After establishing how…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…