Keijo Ruotsalainen

Essential spectrum of a periodic elastic waveguide may contain arbitrarily many gaps

We construct a family of periodic elastic waveguides Π h , depending on a small geometrical parameter, with the following property: as h → +0, the number of gaps in the essential spectrum of the elasticity system on Π h grows unboundedly.

A gap in the spectrum of the Neumann–Laplacian on a periodic waveguide

We study a spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder which contains a periodic arrangement of inclusions. On the boundary of the waveguide, we consider both Neumann and Dirichlet conditions. We prove that provided the diameter of the inclusion is small enough the spectrum of Laplace operator contains band gaps, i.e. there are frequencies that do not propagate through the waveguide. The existence of the band gaps is verified using the asymptotic analysis of elliptic operators.

Analysis of Minimum Hellinger Distance Identification for Digital Phase Modulation

This paper presents a modulation identification (MOD ID) method for digital M-ary phase-shift keying (M-PSK) under additive white Gaussian channel, using the minimum Hellinger distance (MHD). When compared with the maximum likelihood (ML) method, the MHD has two significant advantages, low complexity and robustness against perturbations. In addition, the MHD is implementable for MOD ID by partitioning the I-Q plane. Our contribution is as follows. We obtain theoretical results for the modulation identification error probability of the MHD. Employing the Hellinger distance criteria, we present a sub-optimal partition design. Computer simulation experiments compare the MHD and the ML methods regarding the MOD ID performance and show that difference in performance is around 2dB in ideal channel.

Wireless system for the continuous observation of whole-body vibration in heavy machinery

Several occupational groups are exposed to substantial amounts of vibration daily due to normal working routines, like operating heavy equipment or driving vehicles on uneven surfaces. Vibration that affects the whole human body and is transferred to the body through supporting systems such as the seat or floor is defined as whole-body vibration (WBV). Studies have shown that longterm exposure to WBV creates adverse health effects, of which lower back pain is the most common. Such symptoms may affect a persons quality of life or even cause incapacitation. Even though a correlation between health problems and long-term WBV exposure is evident, mechanisms behind the symptoms have remained unexplained. This paper presents a novel approach to the continuous observation of WBV in heavy machinery. The key elements of the approach are the incorporation of a measurement system into heavy machinery, enhanced comfort, ease of use, and cost-effectiveness. Small alternative sensor devices that improve comfort with respect to the standardized method were investigated in wired and wireless form. Wireless data transmission was then utilized to provide effortless and cost-effective data acquisition from the machinery to the remote server. The system was able to execute the calculations, transfer the resulting parameters to a remote server where information about predominant vibration conditions could be accessed instantaneously, and acquire and store raw acceleration data for further research.

Unitary Space–Time Constellation Design Based on the Chernoff Bound of the Pairwise Error Probability

Unitary space-time constellation design is considered for noncoherent multiple-antenna communications, where neither the transmitter nor the receiver knows the fading coefficients of the channel. By employing the Clarkes subdifferential theorem of the sum of the kappa largest singular values of a unitary matrix, we present a numerical optimization procedure for finding unitary space-time signal constellations of any dimension. The Chernoff bound of the pairwise error probability is used directly as a design criterion. The constellations are found by performing gradient descent search on a family ldquosurrogaterdquo functions that converge to the maximum pairwise error probability. The complexity of the search procedure increases with the dimension and the size of the constellation, but it can be considered to be acceptable for an off-line design procedure. Since the designed constellations are unstructured, and, thus, require an exhaustive search over all codewords in decoding, their main practical value is to serve as constellation design performance benchmarks. We compare the performance of the new constellations to that of some other well-known constellations. Computer simulation results illustrate typically about 0.4-3.5 dB performance gains.

Spectral gaps for water waves above a corrugated bottom

In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell.

On the spline collocation method for the single layer equation related to time-fractional diffusion

The boundary element spline collocation method is studied for the time-fractional diffusion equation in a bounded two-dimensional domain. We represent the solution as the single layer potential which leads to a Volterra integral equation of the first kind. We discretize the boundary integral equation with the spline collocation method on uniform meshes both in spatial and time variables. In the stability analysis we utilize the Fourier analysis technique developed for anisotropic pseudodifferential equations. We prove that the collocation solution is quasi-optimal under some stability condition for the mesh parameters. We have to assume that the mesh parameter in time satisfies

REMARKS ON THE BOUNDARY ELEMENT METHOD FOR STRONGLY NONLINEAR PROBLEMS

(h_t=c h^{\frac{2}{\alpha}})

Bound states of waveguides with two right-angled bends

, where (h) is the spatial mesh parameter.

A novel design of unitary space-time constellations

Recently in several papers the boundary element method has been applied to nonlinear problems. In this paper we extend the analysis to strongly nonlinear boundary value problems. We shall prove the convergence and the stability of the Galerkin method in if -spaces. Optimal order error estimates in if space then follow. We use the theory of ^4-proper mappings and monotone operators to prove convergence of the method. We note that the analysis includes the u 4 -nonlinearity, which is encountered in heat radiation problems. For some time the analysis of boundary element methods (i.e. BEM) has interested many authors. At the same time the development of computational software has made the boundary element method an alternative to the more conventional finite element techniques in engineering applications. And when the implementation of the boundary element method is done ingeniously (cf. [13] for the panel clustering method), it will be in fact as efficient in computing the approximate solution to linear elliptic boundary value problems as other methods available. The efficiency here refers to both complexity and accuracy of the method. The purpose of this paper is to extend the analysis of the boundary element methods to nonlinear problems started in [21]. There the Galerkin boundary element method was studied for the first time for a mildly nonlinear boundary integral equation, which was obtained by the direct formulation of the nonlinear boundary value problem. Later in [20] the analysis was extended