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Atomic clocks have been transformational in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation. Next-generation optical atomic clocks can extend…
A new amplification method based on the optical Kerr instability is suggested and theoretically analyzed, with emphasis on the near to mid-infrared wavelength regime. Our analysis for CaF2 and KBr crystals shows that one to two cycle pulse…
The steady-state current-voltage response of ion-selective systems varies as the number of ion-selective components is varied. For the highly investigated unipolar system, including only one ion-selective component, it has been shown that…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A…
A desirable property of control systems is to be robust to inputs, that is small perturbations of the inputs of a system will cause only small perturbations on its outputs. But it is not clear whether this property is maintained at the…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
We study the evolution of an inverted spin ensemble coupled to a cavity. The inversion itself presents an inherent instability of the system; however, the inhomogeneous broadening of spin-resonance frequencies presents a stabilizing…
We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of…
The fidelity between the state of a continuously observed quantum system and the state of its associated quantum filter, is shown to be always a submartingale. The observed system is assumed to be governed by a continuous-time Stochastic…
For a relative equilibrium of a symmetric simple mechanical system, if the Morse index of the corresponding amended potential is odd, whether the nullity is zero or not, it is linearly unstable. We also provide a sufficient condition for…
It is shown that in perfectly quasi-isodynamic stellarators, trapped particles with a bounce frequency much higher than the frequency of the instability are stabilizing in the electrostatic and collisionless limit. The collisionless…
Electron dynamics in the bulk and at the surface of solid materials are well known to play a key role in a variety of physical and chemical phenomena. In this article we describe the main aspects of the interaction of low-energy electrons…
Neutrino-neutrino interactions in dense neutrino streams, like those emitted by a core-collapse supernova, can lead to self-induced neutrino flavor conversions. While this is a nonlinear phenomenon, the onset of these conversions can be…
This paper considers a disturbance attenuation problem for a linear discrete time invariant system under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in terms of relative…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently…
A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…