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The prescribed-time stabilization problem for a general class of nonlinear systems with unknown input gain and appended dynamics (with unmeasured state) is addressed. Unlike the asymptotic stabilization problem, the prescribed-time…
We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with $n$ degrees of freedom (DOF) possesses $n$ nontrivial integrals of motion, and can…
Long-term time series forecasting is a long-standing challenge in various applications. A central issue in time series forecasting is that methods should expressively capture long-term dependency. Furthermore, time series forecasting…
The central result about fast rotating-flow structures is the Taylor-Proudman theorem (TPT) which connects various aspects of the dynamics. Taylor's geometrical proof of TPT is reproduced and extended substantially, with Lie's theory for…
A new concept, called the spatio-temporal transfer function (STTF), is introduced to characterise a class of linear time-invariant (LTI) spatio-temporal dynamical systems. The spatio-temporal transfer function is a natural extension of the…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
The classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
A Fourier transform method is introduced for a class of hybrid time-frequency methods that solve the acoustic scattering problem in regimes where the solution exhibits both highly oscillatory behavior and slow decay in time. This extends…
An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled non-linear equations that can be…
Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…
An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…
This paper presents the extension from flat spacetime into curved spacetime of the area of theoretical investigation that has been known as topological gauge field theory. The extension here presented is based upon a new derivation of the…
Determining onflow parameters is crucial from the perspectives of wind tunnel testing and regular flight and wind turbine operations. These parameters have traditionally been predicted via direct measurements which might lead to challenges…
Using the Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the Callen-Welton theorem is…
The 'vertical modes and horizontal rays' method, commonly applied for simulating acoustic wave propagation in shallow water is advanced in this research. Our approach to this method involves the use of the so-called space-time rays, which…