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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…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial…
We review novel data analysis techniques developed or adapted for the field of coronal seismology. We focus on methods from the last ten years that were developed for extreme ultraviolet (EUV) imaging observations of the solar corona, as…
Time-reversed evolution has substantial implications in physics, including prominent applications in refocusing of classical waves or spins and fundamental researches such as quantum information scrambling. In quantum metrology, nonlinear…
We explore the effect of an inhomogeneous mass density field on frequencies and wave profiles of torsional Alfven oscillations in solar coronal loops. Dispersion relations for torsional oscillations are derived analytically in limits of…
We present an extended version of the Constant Time Lag analytical approach for the tidal evolution of circumbinary planets introduced in our previous work. The model is self-consistent, in the sense that all tidal interactions between…
Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term…
Observations of the solar surface reveal the presence of flows with length scales of around $35$ Mm, commonly referred to as supergranules. Inferring the sub-surface flow profile of supergranules from measurements of the surface and…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal…
We investigate sudden quenches across the critical point in the transverse field Ising chain with a perturbing non-integrable next-nearest-neighbour interaction. Expressions for the return (Loschmidt) amplitude and associated rate function…
We consider seismic imaging to include seismic inversion. Imaging could use approximate operator or time instead of depth. Processing in time is an important part of seismic imaging as well as processing in depth. We can classify seismic…
Propagating slow waves in coronal loops exhibit a damping which depends upon the frequency of the waves. In this study we aim to investigate the relationship of the damping length (L$_d$) with the frequency of the propagating wave. We…
A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities, which manifest themselves as interfaces between different phases in…
The transition to turbulence in Taylor-Couette flow often occurs via a sequence of supercritical bifurcations to progressively more complex, yet stable, flows. We describe a subcritical laminar-turbulent transition in the counter-rotating…
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical…