Justification of Godunov’s scheme in the multidimensional case

The classical Godunov scheme for the numerical solution of 3D gas dynamics equations is justified in the multidimensional case. An estimate is obtained for the error induced by replacing the exact solution of the multidimensional discontinuity breakup problem (known as the Riemann problem) with the solution of the 1D problems with the data on the left and right of the interface of each cell without considering the complicated flow in the neighborhood of the cells’ vertices. It is shown that, in the case of plane interfaces, the error has the first order of smallness in the time step and the approximate solution converges to the solution of semidiscrete equations as the time step vanishes. In fact, the time integration of these equations using the explicit Euler method represents the Godunov scheme.     

Studies of Work ‘in the Wild’

Computer Supported Cooperative Work (CSCW) -     

Experimental application and enhancement of the XFEM–GA algorithm for the detection of flaws in structures

The extended finite element formulation (XFEM) combined with genetic algorithms (GAs) have previously been shown to be very effective in the detection of flaws in structures. By this approach, the XFEM is used to model the forward problem and a GA is used as the optimization scheme, converging to the true flaw. The convergence is obtained by minimizing the error between sensor measurements and data obtained by solving the forward problem.The current study proposes several advances of this XFEM–GA algorithm, more specifically: (i) a novel genetic algorithm that accelerates the convergence of the scheme and alleviates entrapment in local optima, (ii) a generic XFEM formulation of an elliptical hole which is utilized to detect any type of flaw (cracks or holes) of any shape, and (iii) experimental verification of the approach for an arbitrary crack in a 2D plate.Convergence studies on various benchmark problems including the experimental verification clearly show the potential of this approach to detection of arbitrary flaws.     

Polylogarithms and the Asymptotic Formula for the Moments of Lebesgue’s Singular Function

Recall that Lebesgue’s singular function L(t) is defined as the unique solution to the equation L(t) = qL(2t) + pL(2t ? 1), where p, q > 0, q = 1 ? p, p ≠ q. The variables M _n = ∫₀¹t ⁿ dL(t), n = 0,1,… are called the moments of the function The principal result of this work is \({M_n} = {n^{{{\log }_2}p}}{e^{ - \tau (n)}}(1 + O({n^{ - 0.99}}))\), where the function τ(x) is periodic in log₂x with the period 1 and is given as \(\tau (x) = \frac{1}{2}1np + \Gamma '(1)lo{g_2}p + \frac{1}{{1n2}}\frac{\partial }{{\partial z}}L{i_z}( - \frac{q}{p}){|_{z = 1}} + \frac{1}{{1n2}}\sum\nolimits_{k \ne 0} {\Gamma ({z_k})L{i_{{z_k} + 1}}( - \frac{q}{p})} {x^{ - {z_k}}}\), \({z_k} = \frac{{2\pi ik}}{{1n2}}\), k ≠ 0. The proof is based on poissonization and the Mellin transform.     

Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities

Since the turn of the century experimental solid mechanics has undergone major changes with the generalized use of images. The number of acquired data has literally exploded and one of today’s challenges is related to the saturation of mining procedures through such big data sets. With respect to digital image/volume correlation one of tomorrow’s pathways is to better control and master this data flow with procedures that are optimized for extracting the sought information with minimum uncertainties and maximum robustness. In this paper emphasis is put on various hierarchical identification procedures. Based on such structures a posteriori model/data reductions are performed in order to ease and make the exploitation of the experimental information far more efficient. Some possibilities related to other model order reduction techniques like the proper generalized decomposition are discussed and new opportunities are sketched.     

Substructuring of a Signorini-type problem and Robin’s method for the Richards equation in heterogeneous soil

We prove a substructuring result for variational inequalities. It concerns but is not restricted to the Richards equation in heterogeneous soil, and it includes boundary conditions of Signorini’s type. This generalizes existing results for the linear case and leads to interface conditions known from linear variational equalities: continuity of Dirichlet and flux values in a weak sense. In case of the Richards equation, these are the continuity of the physical pressure and of the water flux, which is hydrologically reasonable. We use these interface conditions in a heterogeneous problem with piecewise constant soil parameters, which we address by the Robin method. We prove that, for a certain time discretization, the homogeneous problems in the subdomains including Robin and Signorini-type boundary conditions can be solved by convex minimization. As a consequence, we are able to apply monotone multigrid in the discrete setting as an efficient and robust solver for the local problems. Numerical results demonstrate the applicability of our approach.     

A new algorithm for the extraction of the surface waves for the Green’s function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green’s function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green’s function. The numerical results demonstrated the accuracy and efficiency of the proposed method.     

Equiparadoxicality of Yablo’s Paradox and the Liar

It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition.     

Boundary Effect in the Error Estimate of the Finite-Difference Scheme for Two-Dimensional Poisson’s Equation

We obtain the a priori error estimate of the rate of convergence of mesh solution to the generalized solution of two-dimensional Poisson equation in case of mixed boundary condition (boundary conditions of first and third kinds). We prove that the accuracy order is higher near the sides of the domain where the Dirichlet boundary condition is specified.     

Numerical Studies of Three-dimensional Stochastic Darcy’s Equation and Stochastic Advection-Diffusion-Dispersion Equation

Solute transport in randomly heterogeneous porous media is commonly described by stochastic flow and advection-dispersion equations with a random hydraulic conductivity field. The statistical distribution of conductivity of engineered and naturally occurring porous material can vary, depending on its origin. We describe solutions of a three-dimensional stochastic advection-dispersion equation using a probabilistic collocation method (PCM) on sparse grids for several distributions of hydraulic conductivity. Three random distributions of log hydraulic conductivity are considered: uniform, Gaussian, and truncated Gaussian (beta). Log hydraulic conductivity is represented by a Karhunen-Loève (K-L) decomposition as a second-order random process with an exponential covariance function. The convergence of PCM has been demonstrated. It appears that the accuracy in both the mean and the standard deviation of PCM solutions can be improved by using the Jacobi-chaos representing the truncated Gaussian distribution rather than the Hermite-chaos for the Gaussian distribution. The effect of type of distribution and parameters such as the variance and correlation length of log hydraulic conductivity and dispersion coefficient on leading moments of the advection velocity and solute concentration was investigated.     

Nicola Zabaglia and the School of Practical Mechanics of the Fabbrica of St. Peter’s in Rome

Nicola Zabaglia, master mason of the Fabbrica of St. Peter’s and inventor of many ingenious mechanical devices for restoration, was also the director of the “School of Practical Mechanics” for the education of young labourers. At a time when traditional operational experience was strongly rivalled by the coeval achievements in the theory of mechanics and its effect on building, the work of Zabaglia became an instrument of propaganda. Since empirical practice and the oral transmission of operational knowledge were called into question by the pressing progress of science as well as by new institutions, the works of Zabaglia and his talented students were not only an influential model of cohesion between architecture, building yard and applied mechanics, but also a melancholy epilogue of a practical tradition inexorably condemned to oblivion.     

Efficient approach and application of the Green’s functions in spatial domain in multilayered media

Based on the dipole source method, all components of the Green＇s functions in spectral domain are restructured concisely by four basis functions, and in terms of the two-level discrete complex image method （DCIM） with the high order Sommerfeld identities, an efficient algorithm for closed-form Green＇s functions in spatial domain in multilayered media is presented. This new work enjoys the advantages of the surface wave pole extraction directly carried out by the generalized integral path without troubles of that all components of Green＇s function in spectral domain should be reformed respectively in transmission line network analogy, and then the Green＇s functions for mixed-potential integral equation （MPIE） analysis in both near-field and far-field in multilayered media are obtained. In addition, the curl operator for coupled field in MPIE is avoided conveniently. It is especially applicable and useful to characterize the electromagnetic scattering by, and radiation in the presence of, the electrically large 3-D objects in multilayered media. The numerical results of the S-parameters of a microstrip periodic bandgap （PBG） filter, the radar cross section （RCS） of a large microstrip antenna array, the characteristics of scattering, and radiation from the three-dimensional （3-D） targets in multilayered media are obtained, to demonstrate better effectiveness and accuracy of this technique.     

On the Hopcroft’s minimization technique for DFA and DFCA

We show that the absolute worst case time complexity for Hopcroft’s minimization algorithm applied to unary languages is reached only for deterministic automata or cover automata following the structure of the de Bruijn words. A previous paper by Berstel and Carton gave the example of de Bruijn words as a language that requires $O(nlogn)$ steps in the case of deterministic automata by carefully choosing the splitting sets and processing these sets in a FIFO mode for the list of the splitting sets in the algorithm. We refine the previous result by showing that the Berstel/Carton example is actually the absolute worst case time complexity in the case of unary languages for deterministic automata. We show that the same result is valid also for the case of cover automata and an algorithm based on the Hopcroft’s method used for minimization of cover automata. We also show that a LIFO implementation for the splitting list will not achieve the same absolute worst time complexity for the case of unary languages both in the case of regular deterministic finite automata or in the case of the deterministic finite cover automata as defined by S. Yu.     

Valiant’s model and the cost of computing integers

Let (n) be the minimum number of arithmetic operations required to build the integer from the constants 1 and 2. A sequence x_n is said to be easy to compute if there exists a polynomial p such that for all It is natural to conjecture that sequences such as or n! are not easy to compute. In this paper we show that a proof of this conjecture for the first sequence would imply a superpolynomial lower bound for the arithmetic circuit size of the permanent polynomial. For the second sequence, a proof would imply a superpolynomial lower bound for the permanent or P PSPACE.     

Complexity analysis of the Pawlak’s flowgraph extension for re-identification in multi-camera surveillance system

The idea of Pawlak’s flowgraph turned out to be a useful and convenient container for a knowledge of objects’ behaviour and movements within the area observed with a multi-camera surveillance system. Utilization of the flowgraph for modelling behaviour admittedly requires certain extensions and enhancements, but it allows for combining many rules into a one data structure and for obtaining parameters describing how objects tend to move through the supervised area. The main aim of this article is presentation of the complexity analysis of proposed modification of flowgraphs. This analysis contains considerations of issues such as memory efficiency and computational complexity of operations on the flowgraph. The measures related to space and time efficiency were also included.     

Analysis of vertical eye movements in Parkinson’s disease and its potential for diagnosis

Applied Intelligence - It is well known that eye movements are highly affected by Parkinson’s disease. The majority of studies related to effects of Parkinson’s disease on eye movements...     

An examination of the Internet’s development as a disabling environment in the context of the social model of disability and anti-discrimination legislation in the UK and USA

Research indicates that inaccessible website design persists despite the existence of anti-discrimination legislation and the influence of the social model of disability on policy development. In this paper, the concept of universal access is examined in the light of the social model of disability in relation to both the physical and virtual environments. The manner in which disability is often deemed a design afterthought is highlighted. The need for universal access is then placed alongside a discussion of access to the Internet in relation to an ageing population and people with cognitive difficulties. Subsequently, anti-discrimination provisions are analysed in relation to how they support designers’ focus on an accepted normality to which reasonable adjustments need to be made, rather than the acquisition of full universal access.     

The Garden of Forking Paths – Forms of Scholarship and the ‘Formations’ Pre-Prints System for Cultural Studies and Related Fields

This paper describes and analyses a web-based pre-prints project in the UK's Electronic Libraries Programme in order to raise issues about the forms of scholarship that are best suited to online working. Specifically, the paper describes some of the underlying processes at work in academic research and seeks to match these, where appropriate, to forms of online working. In doing so, the paper describes in detail a scholarship of integration which seems well suited to online tools such as pre-prints systems, but speculates that such forms of scholarship are too seldom explicitly identified when academics refer to research as a totality. As a consequence the potential match between working practices and emerging tools may not be obvious to academic researchers. To investigate these issues further, the paper examines the degrees of formality involved in different kinds of online communication and describes how academic working practices might be supported by adapting established groupware tools such as Lotus Notes. The eLib Formations project, which is using Notes to develop an integrated pre-prints and e-journal system for research in cultural studies and related fields, is described in detail, focusing on the underlying technology and the overall design.