Using the method of separate variables, the three-dimensional magnet field solution expressed in Fourier’s expansion for permanent magnet (PM) machines with finite axial magnet length is presented in this paper. From the analytic results obtained, much useful and interesting design information for PM machines in three dimensions may be quantitatively deduced. Design curves of the leakage factor...

Abstract. Extending results of Oh and Zumbrun in dimensions d ≥ 3, we establish nonlinear stability and asymptotic behavior of spatially periodic traveling-wave solutions of viscous systems of conservation laws in critical dimensions d = 1, 2, under a natural set of spectral stability assumptions introduced by Schneider in the setting of reaction diffusion equations. The key new steps in the an...

In this article we continue our analysis of Schrödinger operators with a random potential using scattering theory. In particular the theory of Krein’s spectral shift function leads to an alternative construction of the density of states in arbitrary dimensions. For arbitrary dimension we show existence of the spectral shift density, which is defined as the bulk limit of the spectral shift funct...

Environmental sounds present a difficult problem for sound modeling because spectral and temporal cues are tightly correlated. These sounds form classes that cannot be handled by traditional synthesis methods. Micro-level representations provide ways to control spectral and spatial cues in sound synthesis and meso-level representations determine the temporal structure of sound events. By constr...

A snapshot Image Mapping Spectrometer (IMS) with high sampling density is developed for hyperspectral microscopy, measuring a datacube of dimensions 285 x 285 x 60 (x, y, lambda). The spatial resolution is approximately 0.45 microm with a FOV of 100 x 100 microm(2). The measured spectrum is from 450 nm to 650 nm and is sampled by 60 spectral channels with average sampling interval approximately...

This work describes numerical methods for the joint reconstruction and segmentation of spectral images taken by compressive sensing coded aperture snapshot spectral imagers (CASSI). In a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation of both spectral information and 2D spatial information of a scene, resulting in significant savings in ...

Sparsity-based models have enabled significant advances in many image processing tasks. Hyperspectral imagery (HSI) in particular has benefited from these approaches due to the significant low-dimensional structure in both spatial and spectral dimensions. Specifically, previous work has shown that sparsity models can be used for spectral super-resolution, where spectral signatures with HSI-leve...

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them " partially integrable ". Such a construction is achieved using a suitable modification of the classical dressing scheme, consisting in assuming that the kernel of the basic int...

We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound states of the two dimensional time-independent Schrödinger equation. We first illustrate the use of this method on an exactly solvable case and then use it on ...

Spectral algorithms for learning low-dimensional data manifolds have largely been supplanted by deep learning methods in recent years. One reason is that classic spectral manifold learning methods often learn collapsed embeddings that do not fill the embedding space. We show that this is a natural consequence of data where different latent dimensions have dramatically different scaling in obser...