Stochastic regularization method for backward Cauchy problem in Banach spaces

We consider a stochastic regularization method for solving the backward Cauchy problem in Banach spaces. An order of convergence is obtained on sourcewise representative elements.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

An alternating potential based approach for a Cauchy problem for the Laplace equation in a planar domain with a cut

We consider a Cauchy problem for the Laplace equation in a bounded region containing a cut, where the region is formed by removing a sufficiently smooth arc (the cut) from a bounded simply connected domain D. The aim is to reconstruct the solution on the cut from the values of the solution and its normal derivative on the boundary of the domain D. We propose an alternating iterative method which involves solving direct mixed problems for the Laplace operator in the same region. These mixed problems have either a Dirichlet or a Neumann boundary condition imposed on the cut and are solved by a potential approach. Each of these mixed problems is reduced to a system of integral equations of the first kind with logarithmic and hypersingular kernels and at most a square root singularity in the densities at the endpoints of the cut. The full discretization of the direct problems is realized by a trigonometric quadrature method which has super-algebraic convergence. The numerical examples presented illustrate the feasibility of the proposed method.

Isotropic finite volume discretization

Finite volume methods traditionally employ dimension by dimension extension of the one-dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured Cartesian mesh in multiple dimensions. This simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution. The resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines. In this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error. Explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions, respectively. It is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next-nearest and next-next-nearest neighbors in three dimensions. Use of these isotropic expressions alone in a standard finite volume framework, however, is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and/or spatially non-uniform. The rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form. Various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms, while preserving the formal order of accuracy and discrete conservation of the original finite volume method, are developed. Numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method. Prominent anisotropic errors, such as spurious asymmetric distortions on a circular reaction-diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization. Furthermore, for a given spatial resolution, a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two-dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization. (C) 2014 Elsevier Inc. All rights reserved.

Full and Model-Reduced Structure-Preserving Simulation of Incompressible Fluids

This thesis outlines the construction of several types of structured integrators for incompressible fluids. We first present a vorticity integrator, which is the Hamiltonian counterpart of the existing Lagrangian-based fluid integrator. We next present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness to coarse spatial and temporal resolutions of geometric integrators, and the simplicity of homogenized boundary conditions on regular grids to deal with arbitrarily-shaped domains with sub-grid accuracy.

Both these numerical methods involve approximating the Lie group of volume-preserving diffeomorphisms by a finite-dimensional Lie-group and then restricting the resulting variational principle by means of a non-holonomic constraint. Advantages and limitations of this discretization method will be outlined. It will be seen that these derivation techniques are unable to yield symplectic integrators, but that energy conservation is easily obtained, as is a discretized version of Kelvin's circulation theorem.

Finally, we outline the basis of a spectral discrete exterior calculus, which may be a useful element in producing structured numerical methods for fluids in the future.

Analysis of irregular microstrip structures using a full wave MoM scheme

[EN]This article presents the results obtained in the analysis of irregular microstrip structures using a full wave method of moments scheme. The irregular microstrip structures are divided into rectangular subdomains. The EFIE is discretized an solved over the subdomains using a Galerkin type scheme. Base and weight functions are piece wise sinusoidals (PWS) or triangular. Delta gap voltage generators are used as sources]. Green functions are computed using a freely available library developed by our research group. All the calculations are carried out in the so called ”spatial domain” so there is no need of using regular grids during the discretization process.

Full-time is a given here : part-time versus full-time job quality

This study explores full-time workers' understanding of and assumptions about part-time work against six job quality components identified in recent literature. Forty interviews were conducted with employees in a public sector agency in Australia, a study context where part-time work is ostensibly 'good quality' and is typically long term, voluntary, involving secure contracts (i.e. permanent rather than casual) and having predictable hours distributed evenly over the week and year. Despite strong collective bargaining arrangements as well as substantial legal and industrial obligations, the findings revealed some serious concerns for part-time job quality. These concerns included reduced responsibilities and lesser access to high status roles and projects, a lack of access to promotion opportunities, increased work intensity and poor workplace support. The highly gendered, part-time labour market also means that it is women who disproportionately experience this disadvantage. To foster equity, greater attention needs to focus on monitoring and enhancing job quality, regardless of hours worked.

Full scale fire tests of a new light gauge steel floor-ceiling system

Cold-formed steel members can be assembled in various combinations to provide cost-efficient and safe light gauge floor systems for buildings. Such Light gauge Steel Framing (LSF) systems are widely accepted in industrial and commercial building construction. An example application is in floor-ceiling systems. Light gauge steel floor-ceiling systems must be designed to serve as fire compartment boundaries and provide adequate fire resistance. Fire-rated floor-ceiling assemblies formed with new materials and construction methodologies have been increasingly used in buildings. However, limited research has been undertaken in the past and hence a thorough understanding of their fire resistance behaviour is not available. Recently a new composite floor-ceiling system has been developed to provide higher fire rating under standard fire conditions. But its increased fire rating could not be determined using the currently available design methods. Therefore a research project was carried out to investigate its structural and fire resistance behaviour under standard fire conditions. In this research project full scale experimental tests of the new LSF floor system based on a composite ceiling unit were undertaken using a gas furnace at the Queensland University of Technology. Both the conventional and the new steel floor-ceiling systems were tested under structural and fire loads. Full scale fire tests provided a good understanding of the fire behaviour of the LSF floor-ceiling systems and confirmed the superior performance of the new composite system. This paper presents the details of this research into the structural and fire behaviour of light gauge steel floor systems protected by the new composite panel, and the results.

Placing the creative sector in innovation : the full gamut

This paper examines the place of the creative sector -- the arts, design, media and communications -- within the framework of contemporary innovation. The historical focus on science-and-technology by innovation policy makers has spurred many within the creative sector to argue how and why it also contributes to innovation. Drawing on a wide range of English-speaking research and policy documents, the full gamut of places for the creative sector in innovation is surveyed. The paper ends by scoping out the conceptual and empirical research that is required if ideas about innovation in the creative sector are to take up a mature position within innovation studies and related policy.

The mobile Internet and small business : an exploratory study of needs, uses and adoption with full-adopters of technology

The technological environment in which contemporary small and medium-sized enterprises (SMEs) operate can only be described as dynamic. The exponential rate of technological change, characterised by perceived increases in the benefits associated with various technologies, shortening product life cycles and changing standards, provides for the SME a complex and challenging operational context. The primary aim of this research was to concentrate on those SMEs that had already adopted technology in order to identify their needs for the new mobile data technologies (MDT), the mobile Internet. The research design utilised a mixed approach whereby both qualitative and quantitative data was collected to address the question. Overall, the needs of these SMEs for MDT can be conceptualised into three areas where the technology will assist business practices; communication, eCommerce and security.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.