Related papers: Convolution Quadrature for Wave Simulations
Wave equations for some curved spacetimes may involve functions that prevent a solution in a closed form. In some cases, these functions can be eliminated by transformations and the solutions can be found analytically. In the cases where…
This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
In finite-volume-based flow simulations, absorbing layers are widely used to reduce pressure wave reflections at boundaries of the computational domain. A disadvantage of absorbing layers is that they contain case-dependent parameters; thus…
We present a pedagogical introduction to some key computations in gravitational waves via a side-by-side comparison with the quadrupole contribution of electromagnetic radiation. Subtleties involving gauge choices and projections over…
People are witnessing quantum computing revolutions nowadays. Progress in the number of qubits, coherence times and gate fidelities are happening. Although quantum error correction era has not arrived, the research and development of…
A wavelet scattering network computes a translation invariant image representation, which is stable to deformations and preserves high frequency information for classification. It cascades wavelet transform convolutions with non-linear…
Simulations of scattering processes are essential in understanding the physics of our universe. Computing relevant scattering quantities from ab initio methods is extremely difficult on classical devices because of the substantial…
We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…
We propose an accurate numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even in the presence of high wavenumbers. The proposed scheme…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
We compute the waves propagating on a compact 3-manifold of constant positive curvature with a non trivial topology: the Poincar\'e dodecahedral space that is a plausible model of multi-connected universe. We transform the Cauchy problem to…
We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum…
Beginning with addition and multiplication which are intrinsic to a Koch-type curve, I formulate and solve a wave equation that describes wave propagation along a fractal coastline. As opposed to the examples known from the literature I do…
A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…