Related papers: The eigenspectra of Indian musical drums
Amorphous solids, like metallic glasses, exhibit an excess of low frequency vibrational states reflecting the break-up of sound due to the strong structural disorder inherent to these materials. Referred to as the boson peak regime of…
In synchronization problems, the goal is to estimate elements of a group from noisy measurements of their ratios. A popular estimation method for synchronization is the spectral method. It extracts the group elements from eigenvectors of a…
Can one hear the shape of a drum? was proposed by Kac in 1966. The simple answer is NO as shown through the construction of iso-spectral domains. There already exists 17 families of planar domains which are non-isometric but display the…
Identifying pure components in mixtures is a common yet challenging problem. The associated unmixing process requires the pure components, also known as endmembers, to be sufficiently spectrally distinct. Even with this requirement met,…
Sloshing eigenvalues and eigenfunctions are studied for vertical cylinders of constant, finite depth occupied by a two-layer fluid. Two families of eigenfrequencies are obtained in the form expressing them explicitly via the eigenvalues of…
We consider the dynamics of bodies with "active" microstructure described by vector-valued phase fields. For waves with time-varying amplitude, the associated evolution equation involves a matrix that can be non-normal, depending on the…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
Moved by the need for rigorous and reliable numerical tools for the analysis of peridynamic materials, the authors propose a model able to capture the dispersive features of nonlocal soliton-like solutions obtained by a peridynamic…
We present two approximation methods for computing eigenfrequencies and eigenmodes of large-scale nonlinear eigenvalue problems resulting from boundary element method (BEM) solutions of some types of acoustic eigenvalue problems in…
We show that for a general system of N s-wave point scatterers, there are always N eigenmodes. These eigenmodes or eigenchannels play the same role as spherical harmonics for a spherically symmetric target--they give a phase shift only. In…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
Unsupervised estimation of the dimensionality of hyperspectral microspectroscopy datasets containing pure and mixed spectral features, and extraction of their representative endmember spectra, remains a challenge in biochemical data mining.…
We investigate the eigenstructure of matrix formulations used for modeling scattering processes within materials in transmission electron microscopy. Dynamical scattering is crucial for describing the interaction between an electron wave…
In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
The investigation of metasurface, which is of great current interest, has opened up new degrees of freedom to research metamaterials. In this paper, we propose an ultrathin acoustic metasurface consisting of a series of structurally simple…
In this paper, we propose an efficient technique for estimating individual power spectral density (PSD) components, i.e., PSD of each desired sound source as well as of noise and reverberation, in a multi-source reverberant sound scene with…
Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such…
In this survey paper we review classical results and recent progress about a certain topic in the spectral theory of two-dimensional canonical systems. Namely, we consider the questions whether the spectrum $\sigma$ is discrete, and if it…
The eigendecomposition of the coupling matrix of large biological networks is central to the study of the dynamics of these networks. For neural networks, this matrix should reflect the topology of the network and conform with Dale's law…