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In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
We present a study of three-mode parametric instability in large-scale gravitational-wave detectors. Previous work used a linearised model to study the onset of instability. This paper presents a non-linear study of this phenomenon, which…
Equilibrium fluid configurations for close binary systems can become {\em globally unstable\/}. Instabilities arise from the strong tidal interaction between the two components, which tends to make the effective two-body potential governing…
While quantum mechanics imposes a fundamental limit on the precision of interferometric measurements of mechanical motion due to measurement backaction, the nonlinear nature of the coupling also leads to parametric instabilities that place…
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the…
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping…
The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…
Ensuring nominal asymptotic stability of the Nonlinear Model Predictive Control controller is not trivial. Stabilizing ingredients such as terminal penalty term and terminal region are crucial in establishing the asymptotic stability.…
The superb precision of an atomic clock is derived from its stability. Atomic clocks based on optical (rather than microwave) frequencies are attractive because of their potential for high stability, which scales with operational frequency.…
The presence of defects in solids formed by active particles breaks their discrete translational symmetry. As a consequence, many of their properties become space-dependent and different from those characterizing perfectly ordered…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…
This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in ``cigar-shaped'' (1D) attractive BECs and the transverse…
This paper presents our investigation into the modification of a finite-width internal gravity wave beam arising from triadic resonance instability. We present both experimental and weakly non-linear modelling to examine this instability…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We present an investigation of the electromagnetic instabilities which are trig gered when an ultra relativistic electron beam passes through a plasma. The linear growth rate is computed for every direction of propagation of the unstable…
Many astrophysical plasmas are prone to beam-plasma instabilities. For relativistic and dilute beams, the {\it spectral} support of the beam-plasma instabilities is narrow, i.e., the linearly unstable modes that grow with rates comparable…
We examine the stability of a spherically symmetric regular black hole when subjected to perturbations from a charged scalar field. This particular black hole is constructed by deforming the Minkowski spacetime. It has been observed that…
The linear stability of stalled accretion shocks is investigated in the context of core collapse of type II supernovae. We focus on a particular instability mechanism based on the coupling of acoustic perturbations with advected ones…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…