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Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…
We propose a variational wave function to represent quantum skyrmions as bosonic operators. The operator faithfully reproduces two fundamental features of quantum skyrmions: their classical magnetic order and a "quantum cloud" of local…
We introduce a concept of the operator (non-commutative) projective line PH defined by a Hilbert space H and a symplectic structure on it. Points of PH are Lagrangian subspaces of H. If a particular Lagrangian subspace is fixed then we can…
A method of binaural rendering from microphone array signals of arbitrary geometry is proposed. To reproduce binaural signals from microphone array recordings at a remote location, a spherical microphone array is generally used for…
We have proposed and demonstrated a scalable and efficient scheme for programmable unitary operations in orbital angular momentum (OAM) domain. Based on matrix decomposition into diagonal and Fourier factors, arbitrary matrix operators can…
Purpose: Field monitoring using field probes allows for accurate measurement of magnetic field perturbations, such as from eddy currents, during MRI scanning. However, errors may result when the spatial variation of the fields is not…
In this paper, the frequency-domain sound field is regarded as an element of some band-limited function space, and a representation of the field as a linear combination of the reproducing kernel in that space is proposed. This model has the…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
Acoustic radiation force and torque arising from wave scattering are commonly used to manipulate micro-objects without contact. We applied the partial wave expansion series and the conformal transformation approach to estimate the radiation…
Variational wave functions containing electronic pairing and suppressed charge fluctuations (i.e., projected BCS states) have been proposed as the paradigm for disordered magnetic systems (including spin liquids). Here we discuss the…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…
Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…
Parametric sound field synthesis methods, such as the Spatial Decomposition Method (SDM) and Higher-Order Spatial Impulse Response Rendering (HO-SIRR), are widely used for the analysis and auralization of sound fields. This paper studies…
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…
Hybrid systems can express a plethora of physical phenomena and systems as they can combine continuous and discrete dynamics. There exist several tools that enable the reachability analysis of hybrid systems modeled as hybrid automata.…
Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…
A general spherical harmonics method is described for extracting anisotropic pair distribution functions (PDF) in this work. In the structural study of functional crystallized materials, the investigation of the local structures under the…