An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.

Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

CP-OQAM-OFDM based SC-FDMA: adjustable user bandwidth and space-time coding

The discrete Fourier transmission spread OFDM DFTS-OFDM) based single-carrier frequency division multiple access (SC-FDMA) has been widely adopted due to its lower peak-to-average power ratio (PAPR) of transmit signals compared with OFDM. However, the offset modulation, which has lower PAPR than general modulation, cannot be directly applied into the existing SC-FDMA. When pulse-shaping filters are employed to further reduce the envelope fluctuation of transmit signals of SC-FDMA, the spectral efficiency degrades as well. In order to overcome such limitations of conventional SC-FDMA, this paper for the first time investigated cyclic prefixed OQAMOFDM (CP-OQAM-OFDM) based SC-FDMA transmission with adjustable user bandwidth and space-time coding. Firstly, we propose CP-OQAM-OFDM transmission with unequally-spaced subbands. We then apply it to SC-FDMA transmission and propose a SC-FDMA scheme with the following features: a) the transmit signal of each user is offset modulated single-carrier with frequency-domain pulse-shaping; b) the bandwidth of each user is adjustable; c) the spectral efficiency does not decrease with increasing roll-off factors. To combat both inter-symbolinterference and multiple access interference in frequencyselective fading channels, a joint linear minimum mean square error frequency domain equalization using a prior information with low complexity is developed. Subsequently, we construct space-time codes for the proposed SC-FDMA. Simulation results confirm the powerfulness of the proposed CP-OQAM-OFDM scheme (i.e., effective yet with low complexity).

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

The first real-time worldwide ionospheric predictions network: an advance in support of spaceborne experimentation, on-line model validation, and space weather

We report on the first realtime ionospheric predictions network and its capabilities to ingest a global database and forecast F-layer characteristics and "in situ" electron densities along the track of an orbiting spacecraft. A global network of ionosonde stations reported around-the-clock observations of F-region heights and densities, and an on-line library of models provided forecasting capabilities. Each model was tested against the incoming data; relative accuracies were intercompared to determine the best overall fit to the prevailing conditions; and the best-fit model was used to predict ionospheric conditions on an orbit-to-orbit basis for the 12-hour period following a twice-daily model test and validation procedure. It was found that the best-fit model often provided averaged (i.e., climatologically-based) accuracies better than 5% in predicting the heights and critical frequencies of the F-region peaks in the latitudinal domain of the TSS-1R flight path. There was a sharp contrast however, in model-measurement comparisons involving predictions of actual, unaveraged, along-track densities at the 295 km orbital altitude of TSS-1R In this case, extrema in the first-principle models varied by as much as an order of magnitude in density predictions, and the best-fit models were found to disagree with the "in situ" observations of Ne by as much as 140%. The discrepancies are interpreted as a manifestation of difficulties in accurately and self-consistently modeling the external controls of solar and magnetospheric inputs and the spatial and temporal variabilities in electric fields, thermospheric winds, plasmaspheric fluxes, and chemistry.

The effects of explicit versus parameterized convection on the MJO in a large-domain high-resolution tropical case study. Part II: Processes leading to differences in MJO development

High-resolution simulations over a large tropical domain (∼20◦S–20◦N and 42◦E–180◦E) using both explicit and parameterized convection are analyzed and compared during a 10-day case study of an active Madden-Julian Oscillation (MJO) event. In Part II, the moisture budgets and moist entropy budgets are analyzed. Vertical subgrid diabatic heating profiles and vertical velocity profiles are also compared; these are related to the horizontal and vertical advective components of the moist entropy budget which contribute to gross moist stability, GMS, and normalized GMS (NGMS). The 4-km model with explicit convection and good MJO performance has a vertical heating structure that increases with height in the lower troposphere in regions of strong convection (like observations), whereas the 12-km model with parameterized convection and a poor MJO does not show this relationship. The 4-km explicit convection model also has a more top-heavy heating profile for the troposphere as a whole near and to the west of the active MJO-related convection, unlike the 12-km parameterized convection model. The dependence of entropy advection components on moisture convergence is fairly weak in all models, and differences between models are not always related to MJO performance, making comparisons to previous work somewhat inconclusive. However, models with relatively good MJO strength and propagation have a slightly larger increase of the vertical advective component with increasing moisture convergence, and their NGMS vertical terms have more variability in time and longitude, with total NGMS that is comparatively larger to the west and smaller to the east.

Work Domain Analysis for understanding medication safety in care homes in England: an exploratory study

Medication safety and errors are a major concern in care homes. In addition to the identification of incidents, there is a need for a comprehensive system description to avoid the danger of introducing interventions that have unintended consequences and are therefore unsustainable. The aim of the study was to explore the impact and uniqueness of Work Domain Analysis (WDA) to facilitate an in-depth understanding of medication safety problems within the care home system and identify the potential benefits of WDA to design safety interventions to improve medication safety. A comprehensive, systematic and contextual overview of the care home medication system was developed for the first time. The novel use of the Abstraction Hierarchy (AH) to analyse medication errors revealed the value of the AH to guide a comprehensive analysis of errors and generate system improvement recommendations that took into account the contextual information of the wider system.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Complementarity of neutron reflectometry and ellipsometry for the study of atmospheric reactions at the air–water interface

The combined application of neutron reflectometry (NR) and ellipsometry to determine the oxidation kinetics of organic monolayers at the air–water interface is described for the first time. This advance was possible thanks to a new miniaturised reaction chamber that is compatible with the two techniques and has controlled gas delivery. The rate coefficient for the oxidation of methyl oleate monolayers by gas-phase O3 determined using NR is (5.4 ± 0.6) × 10−10 cm2 per molecule per s, which is consistent with the value reported in the literature but is now better constrained. This highlights the potential for the investigation of faster atmospheric reactions in future studies. The rate coefficient determined using ellipsometry is (5.0 ± 0.9) × 10−10 cm2 per molecule per s, which indicates the potential of this more economical, laboratory-based technique to be employed in parallel with NR. In this case, temporal fluctuations in the optical signal are attributed to the mobility of islands of reaction products. We outline how such information may provide critical missing information in the identification of transient reaction products in a range of atmospheric surface reactions in the future.

Heat Conduction Equation Solution in the Presence of a Change of State in a Bounded Axisymmetric Cylindrical Domain

The heat conduction problem, in the presence of a change of state, was solved for the case of an indefinitely long cylindrical layer cavity. As boundary conditions, it is imposed that the internal surface of the cavity is maintained below the fusion temperature of the infilling substance and the external surface is kept above it. The solution, obtained in nondimensional variables, consists in two closed form heat conduction equation solutions for the solidified and liquid regions, which formally depend of the, at first, unknown position of the phase change front. The energy balance through the phase change front furnishes the equation for time dependence of the front position, which is numerically solved. Substitution of the front position for a particular instant in the heat conduction equation solutions gives the temperature distribution inside the cavity at that moment. The solution is illustrated with numerical examples. [DOI: 10.1115/1.4003542]

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

The Aedes aegypti larval transcriptome: a comparative perspective with emphasis on trypsins and the domain structure of peritrophins

The genome sequence of Aedes aegypti was recently reported. A significant amount of Expressed Sequence Tags (ESTs) were sequenced to aid in the gene prediction process. In the present work we describe an integrated analysis of the genomic and EST data, focusing on genes with preferential expression in larvae (LG), adults (AG) and in both stages (SG). A total of 913 genes (5.4% of the transcript complement) are LG, including ion transporters and cuticle proteins that are important for ion homeostasis and defense. From a starting set of 245 genes encoding the trypsin domain, we identified 66 putative LG, AG, and SG trypsins by manual curation. Phylogenetic analyses showed that AG trypsins are divergent from their larval counterparts (LG), grouping with blood-induced trypsins from Anopheles gambiae and Simulium vittatum. These results support the hypothesis that blood-feeding arose only once, in the ancestral Culicomorpha. Peritrophins are proteins that interlock chitin fibrils to form the peritrophic membrane (PM) that compartmentalizes the food in the midgut. These proteins are recognized by having chitin-binding domains with 6 conserved Cys and may also present mucin-like domains (regions expected to be highly O-glycosylated). PM may be formed by a ring of cells (type 2, seen in Ae. aegypti larvae and Drosophila melanogaster) or by most midgut cells (type 1, found in Ae. aegypti adult and Tribolium castaneum). LG and D. melanogaster peritrophins have more complex domain structures than AG and T. castaneum peritrophins. Furthermore, mucin-like domains of peritrophins from T. castaneum (feeding on rough food) are lengthier than those of adult Ae. aegypti (blood-feeding). This suggests, for the first time, that type 1 and type 2 PM may have variable molecular architectures determined by different peritrophins and/or ancillary proteins, which may be partly modulated by diet.

Independent Domain of Symmetric Encryption using Least SignificantBit : Computer Vision, Steganography and Cryptography Techniques

The rapid development of data transfer through internet made it easier to send the data accurate and faster to the destination. There are many transmission media to transfer the data to destination like e-mails; at the same time it is may be easier to modify and misuse the valuable information through hacking. So, in order to transfer the data securely to the destination without any modifications, there are many approaches like cryptography and steganography. This paper deals with the image steganography as well as with the different security issues, general overview of cryptography, steganography and digital watermarking approaches.  The problem of copyright violation of multimedia data has increased due to the enormous growth of computer networks that provides fast and error free transmission of any unauthorized duplicate and possibly manipulated copy of multimedia information. In order to be effective for copyright protection, digital watermark must be robust which are difficult to remove from the object in which they are embedded despite a variety of possible attacks. The message to be send safe and secure, we use watermarking. We use invisible watermarking to embed the message using LSB (Least Significant Bit) steganographic technique. The standard LSB technique embed the message in every pixel, but my contribution for this proposed watermarking, works with the hint for embedding the message only on the image edges alone. If the hacker knows that the system uses LSB technique also, it cannot decrypt correct message. To make my system robust and secure, we added cryptography algorithm as Vigenere square. Whereas the message is transmitted in cipher text and its added advantage to the proposed system. The standard Vigenere square algorithm works with either lower case or upper case. The proposed cryptography algorithm is Vigenere square with extension of numbers also. We can keep the crypto key with combination of characters and numbers. So by using these modifications and updating in this existing algorithm and combination of cryptography and steganography method we develop a secure and strong watermarking method. Performance of this watermarking scheme has been analyzed by evaluating the robustness of the algorithm with PSNR (Peak Signal to Noise Ratio) and MSE (Mean Square Error) against the quality of the image for large amount of data. While coming to see results of the proposed encryption, higher value of 89dB of PSNR with small value of MSE is 0.0017. Then it seems the proposed watermarking system is secure and robust for hiding secure information in any digital system, because this system collect the properties of both steganography and cryptography sciences.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)