Some theorems about spectrum and finite element approach for eigenvalue problems for elastic bodies with voids

The paper concerns eigenvalue problems for elastic bodies with voids in contact with massive rigid plane punches. The linear theory of elastic materials with voids according to the Cowin–Nunziato model is used. A variational principle is constructed which has the properties of minimality, similar to the well-known variational principle for problems with pure elastic media. The discreteness of the spectrum and completeness of the eigenfunctions are proved. As a consequence of variational principles, the properties of an increase or a decrease in the natural frequencies, when the mechanical and “porous” boundary conditions and the modulus of elastic solid with voids change, are established. A finite element method is proposed for numerical solution of eigenvalue problems for elastic media with voids. Some effective block algorithms for finite element eigenvalue problems with partial coupling are described. Numerical experiments are presented for determining the first eigenfrequencies of an axisymmetric elastic body with voids.     

A treatment of discontinuities for nonlinear systems with linearly degenerate fields

In this paper we propose an artificial compression technique to avoid the numerical diffusion that standard numerical methods present in contact discontinuities. The main idea is to replace contact discontinuities by shocks. For nonlinear 1D systems we replace locally linearly degenerate fields by genuinely nonlinear fields, in such a way the solution does not vary. We apply this technique to a family of numerical schemes and we deduce that this can be seen as a discretization of the system modified by a new term, when we are in a jump of a contact discontinuity. We have also extended this technique for the multidimensional case. We prove by applying the artificial compression technique that the numerical scheme is stable under the same CFL condition. We also present different numerical schemes: Sod’s problem for 1D Euler equations, transport of a discontinuity, a stationary contact discontinuity and in the multidimensional case the transversal transport of two different geometries. We observe that in all cases the numerical diffusion is reduced.     

Optimal representation of non-stationary random fields with finite numbers of samples: A linear MMSE framework

In this article we consider the representation of a finite-energy non-stationary random field with a finite number of samples. We pose the problem as an optimal sampling problem where we seek the optimal sampling interval under the mean-square error criterion, for a given number of samples. We investigate the optimum sampling rates and the resulting trade-offs between the number of samples and the representation error. In our numerical experiments, we consider a parametric non-stationary field model, the Gaussian–Schell model, and present sampling schemes for varying noise levels and for sources with varying numbers of degrees of freedom. We discuss the dependence of the optimum sampling interval on the problem parameters. We also study the sensitivity of the error to the chosen sampling interval.     

A magnetic resonance compatible surgical manipulator: part of a unified support system for the diagnosis and treatment of heart disease

A prototype of a magnetic resonance (MR)-compatible surgical manipulator was designed and evaluated. The manipulator is designed so as to fit into vertical magnetic field open-configuration MR imagers. Moreover, it is designed to work without being fixed to an MR imager, and its electrical circuits and lines of actuators and sensors are independent of the room shield so that it could be installed in various kinds of settings at many MR imager sites without any additional construction. The MR compatibility of the manipulator was evaluated: no noticeable deformation was observed in the MR images even when the manipulator was in motion. Although the signal-to-noise deterioration ratio was higher than that previously reported, the MR images were thought to be good enough for recognizing the whole structure of a targeted organ and for following the relative position of the manipulator tip with regard to the target, i.e. MR tracking.     

A unified setting for decoupling with preview and fixed-lag smoothing in the geometric context

Exact decoupling with preview, perfect tracking of previewed references, unknown-input state observation with fixed lag, and left inversion with fixed lag are considered from a unifying perspective where exact decoupling with preview is the basic problem. Necessary and sufficient constructive conditions for decoupling with finite preview are proved in the geometric framework. Structural and stabilizability conditions are considered separately and the use of self-bounded controlled invariant subspaces allows the dynamic compensator with the minimal unassignable dynamics to be straightforwardly derived. A steering along zeros technique is devised to guarantee decoupling with stability also in the presence of unstable unassignable dynamics of the minimal self-bounded controlled invariant.     

On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers

The paper is concerned with the numerical simulation of compressible flow with wide range of Mach numbers. We present a new technique which combines the discontinuous Galerkin space discretization, a semi-implicit time discretization and a special treatment of boundary conditions in inviscid convective terms. It is applicable to the solution of steady and unsteady compressible flow with high Mach numbers as well as low Mach number flow at incompressible limit without any modification of the Euler or Navier–Stokes equations.     

Formal and incremental construction of distributed algorithms: On the distributed reference counting algorithm

The development of distributed algorithms and, more generally, distributed systems, is a complex, delicate and challenging process. Refinement techniques of (system) models improve the process by using a proof assistant, and by applying a design methodology aimed at starting from the most abstract model and leading, in an incremental way, to the most concrete model, for producing a distributed solution. We show, using the distributed reference counting (DRC) problem as our study, how models can be produced in an elegant and progressive way, thanks to the refinement and how the final distributed algorithm is built starting from these models. The development is carried out within the framework of the event B method and models are validated with a proof assistant.     

On the absence of global solutions for quantum versions of Schrödinger equations and systems

We, first, consider the quantum version of the nonlinear Schrödinger equation

$i^q{D}_{q|t}u(t,x)+\Delta u(qt,x)=\lambda |u(qt,x){|}^p,t>0,x\in {\mathbb{R}}^N,$

where $0<q<1$, $i^q$ is the principal value of $i^q$, $D_{q|t}$ is the $q$-derivative with respect to $t$, $\Delta$ is the Laplacian operator in ${\mathbb{R}}^N$, $\lambda \in ??\left\{0\right\}$, $p>1$, and $u(t,x)$ is a complex-valued function. Sufficient conditions for the nonexistence of global weak solution to the considered equation are obtained under suitable initial data. Next, we study the system of nonlinear coupled equations

$i^q{D}_{q|t}u(t,x)+\Delta u(qt,x)=\lambda |v(qt,x){|}^p,t>0,x\in {\mathbb{R}}^N,$

$i^q{D}_{q|t}v(t,x)+\Delta v(qt,x)=\lambda |u(qt,x){|}^m,t>0,x\in {\mathbb{R}}^N,$     

A unified approach to the change of resolution: space and gray-level

It is shown that by defining a suitable measure for the comparison of images, changes in resolution can be treated with the same tool as changes in color resolution. A gray-tone image, for example, can be compared to a half-tone image having only two colors (black and white), but of higher spatial resolution. A graph-theoretical definition of the basic measure used is introduced. This is followed by application to spatial resampling and gray-level requantization. This results in a hybrid treatment of resolution, and the possibility of trading spatial for gray-level resolution and vice versa.<>     

Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position

Suggested by the structure of the visual nervous system, a new algorithm is proposed for pattern recognition. This algorithm can be realized with a multilayered network consisting of neuron-like cells. The network, “neocognitron”, is self-organized by unsupervised learning, and acquires the ability to recognize stimulus patterns according to the differences in their shapes: Any patterns which we human beings judge to be alike are also judged to be of the same category by the neocognitron. The neocognitron recognizes stimulus patterns correctly without being affected by shifts in position or even by considerable distortions in shape of the stimulus patterns.     

On the control of noise in finite element tidal computations: A semi-implicit approach

Numerical solution of the two-dimensional shallow water equations is achieved by coupling the finite element method in space with finite difference time stepping schemes. Solutions obtained with an efficient leapfrog model are found to contain severe short-wavelength oscillations in space when compared to analytic solutions. An alternative semi-implicit formulation in the time domain, which retains most of the economical advantages of the leapfrog scheme is developed and tested. A significant reduction in the mode-to-node oscillations and improved agreement with analytical solutions are obtained. Both linear triangles and quadratic isoparametric quadrilaterals are examined. Emphasis is on the numerical behavior of the schemes tested and a comparison with a field case is not attempted.     

A unified methodology for the evaluation of accessibility and usability of mobile applications

This article reports a unified methodology developed to evaluate the accessibility and usability of mobile computing applications, which is intended to guarantee universal access as far as possible. As a basis for the methodology, this paper presents an analysis of the accessibility guidelines, conducted to take into account the specificity of mobile systems, as well as a set of usability heuristics, specifically devised for mobile computing. Finally, it presents the results of the application of the proposed methodology to applications that have been semi-automatically developed by the MAIS Designer, a new design tool that provides applications suited to different mobile devices.     

A unified approach for the evaluation of quay crane scheduling models and algorithms

Scheduling of quay cranes at container terminals is a field of growing interest in research and practice. In the literature, we find diverse models for quay crane scheduling that consider the service of container vessels at different levels of detail. Currently, however, there exists no basis to compare the quality of planning that is achieved from these models. There is also no platform available that allows comparing different solution procedures and investigating conditions where they perform well or poorly. This paper presents a unified approach for evaluating the performance of different model classes and solution procedures. The approach is demonstrated by investigating the suitability of three models within a comprehensive computational study.     

Pseudorandom generators for CC0[p] and the Fourier spectrum of low-degree polynomials over finite fields

In this paper, we give the first construction of a pseudorandom generator, with seed length O(log n), for CC⁰[p], the class of constant-depth circuits with unbounded fan-in MOD _p gates, for some prime p. More accurately, the seed length of our generator is O(log n) for any constant error ${\epsilon > 0}$ . In fact, we obtain our generator by fooling distributions generated by low-degree polynomials, over ${\mathbb{F}_p}$ , when evaluated on the Boolean cube. This result significantly extends previous constructions that either required a long seed (Luby et al. 1993) or could only fool the distribution generated by linear functions over ${\mathbb{F}_p}$ , when evaluated on the Boolean cube (Lovett et al. 2009; Meka & Zuckerman 2009). En route of constructing our PRG, we prove two structural results for low-degree polynomials over finite fields that can be of independent interest.

1. Let f be an n-variate degree d polynomial over ${\mathbb{F}_p}$ . Then, for every ${\epsilon > 0}$ , there exists a subset ${S \subset [n]}$ , whose size depends only on d and ${\epsilon}$ , such that ${\sum_{\alpha \in \mathbb{F}_p^n: \alpha \ne 0, \alpha_S=0}|\hat{f}(\alpha)|^2 \leq \epsilon}$ . Namely, there is a constant size subset S such that the total weight of the nonzero Fourier coefficients that do not involve any variable from S is small.
2. Let f be an n-variate degree d polynomial over ${\mathbb{F}_p}$ . If the distribution of f when applied to uniform zero–one bits is ${\epsilon}$ -far (in statistical distance) from its distribution when applied to biased bits, then for every ${\delta > 0}$ , f can be approximated over zero–one bits, up to error δ, by a function of a small number (depending only on ${\epsilon,\delta}$ and d) of lower degree polynomials.

     

Model reduction and perturbation analysis of wave finite element formulations for computing the forced response of coupled elastic systems involving junctions with uncertain eigenfrequencies

The wave finite element method is investigated for computing the low- and mid-frequency forced response of coupled elastic systems involving straight structures with junctions. The relevance of the method is discussed when a component mode synthesis procedure is used for modeling the junctions. A norm-wise selection criterion is proposed so as to reduce efficiently the number of junction modes retained in the wave-based formulations. Component-wise perturbation bounds of the wave-based displacement/force solutions are also derived to address slight uncertainties for the junction eigenfrequencies. Numerical comparisons with standard finite element solutions as well as Monte Carlo simulations highlight the relevance of the formulation.