相关论文: Initialization and the quasi-geostrophic slow mani…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…
We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the…
This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…
Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a…
Interfacial waves arising in a two-phase swirling flow driven by a low-frequency rotating magnetic field (RMF) are studied. At low RMF frequencies, of the order of 1-10 Hz, the oscillatory part of the induced Lorenz force becomes comparable…
We introduce a highly-parallelizable architecture for estimating parameters of compact binary coalescence using gravitational-wave data and waveform models. Using a spherical harmonic mode decomposition, the waveform is expressed as a sum…
Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…
We present a novel method for computing slow manifolds and their fast fibre bundles in geometric singular perturbation problems. This coordinate-independent method is inspired by the parametrisation method introduced by Cabr\'e, Fontich and…
Atmospheric ozone is a crucial absorber of solar radiation and an important greenhouse gas. However, most climate models participating in the Coupled Model Intercomparison Project (CMIP) still lack an interactive representation of ozone due…
As Einstein's equations for binary compact object inspiral have only been approximately or intermittently solved by analytic or numerical methods, the models used to infer parameters of gravitational wave (GW) sources are subject to…
We quantise and solve the dynamics of gravitational waves in a quantum Friedmann-Lemaitre-Robertson-Walker spacetime filled with perfect fluid. The classical model is formulated canonically. The Hamiltonian constraint is de-parametrised by…
The low solar atmosphere is composed of mostly neutral particles, but the importance of the magnetic field for understanding observed dynamics means that interactions between charged and neutral particles play a very important role in…
We introduce an algorithm to marginalize the likelihood for a gravitational wave signal from a quasi-circular binary merger over its extrinsic parameters, accounting for the effects of higher harmonics and spin-induced precession. The…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing…