The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

Drying method influences the development of germinability, dessication tolerance and subsequent longevity of immature seeds of sumauma (Ceiba pentandra (L.) Gaertn. [Bombacaceae])

The ability to germinate, tolerate desiccation and survive in air-dry storage was investigated during early seed development in planta and subsequent ex planta maturation of sumauma (Ceiba pentandra). Immature fruits were collected on three different dates (i.e. from about 5 days before until 7 days after mass maturity). Immature fresh seeds were not able to germinate. Fruits or seeds were subjected immediately after each collection to three different drying treatments with progressively slower rates of dessication: (i) seeds were extracted from the fruits and dried immediately; (ii) fruits were dried in a thin layer; (iii) fruits were dried in a tied polyethylene bag (with 10 holes of 1cm diameter). Drying was in a room maintained at 25 degrees C +/- 3 degrees C and 65%+/- 5% r.h. For treatment (i) the seeds were dried for 6 days in order to reduce moisture content to around 13% ( +/- 2%) moisture content. For treatments (ii) and (iii) the fruits were subjected to different periods of drying depending upon collection date. The results of these post-collection treatments showed generally that the more immature the seeds the slower the rate of drying that is required to improve ability to germinate, ability to tolerate desiccation and potential longevity, but at the third harvest, 7 days after mass maturity, the intermediate drying rate treatment was the most beneficial. Thus post fruit collection treatments can be modified depending upon the stage of seed development in order to provide good to high quality seeds of sumauma when collection has to be made at a site with difficult access at less than ideal times. The results are relevant to seed collection practices for both forestry and ex situ plant biodiversity conservation.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

Are Cape floral clades the same age? Contemporaneous origins of two lineages in the genistoids s.l. (Fabaceae)

The hypothesis that the elements of the modern species-rich flora of the Cape Floristic Region (CFR), South Africa, originated more or less simultaneously at the Miocene/Pliocene boundary, in response to the development of a mediterranean climate, has been challenged by numerous molecular dating estimates of Cape floral clades. These studies reveal a more gradual emergence, with the oldest clades originating in the Eocene, but others appearing later, some as recently as the Pliocene. That there are factors which might affect the dates recovered, such as choice of calibration point, analysis method, sampling density and the delimitation of Cape floral clades, suggests a need for further critical evaluation of the age estimates presented to date. In this study, the dates of origin of two Cape floral clades (the legume Crotalarieae p.p. and Podalyrieae) are estimated, constrained by a shared calibration point in a single analysis using an rDNA ITS phylogeny in which 633 taxa are sampled. The results indicate that these two clades arose contemporaneously 44-46 mya, not at the Miocene/Pliocene boundary as had been previously supposed. The contemporaneous origin of these Cape floral clades suggests that additional more inclusive analyses are needed before rejecting the hypothesis that a. single environmental trigger explains the establishment of Cape floral clades. (c) 2007 Elsevier Inc. All rights reserved.

A time-domain probe method for three-dimensional rough surface reconstructions

The task of this paper is to develop a Time-Domain Probe Method for the reconstruction of impenetrable scatterers. The basic idea of the method is to use pulses in the time domain and the time-dependent response of the scatterer to reconstruct its location and shape. The method is based on the basic causality principle of timedependent scattering. The method is independent of the boundary condition and is applicable for limited aperture scattering data. In particular, we discuss the reconstruction of the shape of a rough surface in three dimensions from time-domain measurements of the scattered field. In practise, measurement data is collected where the incident field is given by a pulse. We formulate the time-domain fieeld reconstruction problem equivalently via frequency-domain integral equations or via a retarded boundary integral equation based on results of Bamberger, Ha-Duong, Lubich. In contrast to pure frequency domain methods here we use a time-domain characterization of the unknown shape for its reconstruction. Our paper will describe the Time-Domain Probe Method and relate it to previous frequency-domain approaches on sampling and probe methods by Colton, Kirsch, Ikehata, Potthast, Luke, Sylvester et al. The approach significantly extends recent work of Chandler-Wilde and Lines (2005) and Luke and Potthast (2006) on the timedomain point source method. We provide a complete convergence analysis for the method for the rough surface scattering case and provide numerical simulations and examples.

Memory for allergies and health foods: how younger and older adults strategically remember critical health information

Objectives. While older adults often display memory deficits, with practice they can sometimes selectively remember valuable information at the expense of less value information. We examined age-related differences and similarities in memory for health-related information under conditions where some information was critical to remember. Method. In Experiment 1, participants studied three lists of allergens, ranging in severity from 0 (not a health risk) to 10 (potentially fatal), with the instruction that it was particularly important to remember items to which a fictional relative was most severely allergic. After each list, participants received feedback regarding their recall of the high-value allergens. Experiment 2 examined memory for health benefits, presenting foods that were potentially beneficial to the relative’s immune system. Results. While younger adults exhibited better overall memory for the allergens, both age groups in Experiment 1 developed improved selectivity across the lists, with no evident age differences in severe allergen recall by List 2. Selectivity also developed in Experiment 2, although age differences for items of high health benefit were present. Discussion. The results have implications for models of selective memory in older age, and for how aging influences the ability to strategically remember important information within health-related contexts.

Melt brushes of diblock copolymer

Using self-consistent field theory (SCFT), we investigate the morphologies formed by a melt brush of AB diblock copolymers grafted to a flat substrate by their B ends. In addition to a laterally uniform morphology, SCFT predicts three ordered morphologies exhibiting different periodic patterns at the air surface: a hexagonal array of A-rich dots, an alternating sequence of A- and B-rich stripes, and a hexagonal pattern of B-rich dots. When the phase diagram of the tethered film is plotted as a function of A/B incompatibility, $\chi N$, and diblock composition, $f$, it resembles the bulk phase diagram with the periodic phases converging to a mean-field critical point at weak segregation. The periodic-phase region in the phase diagram shrinks with increasing grafting density and expands when the air surface acquires an affinity for the grafted B blocks.

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

The consolidation and bond strength of rafted sea ice

The consolidation and bond strength of rafted sea ice were investigated through a series of experiments undertaken in the Ice Physics Laboratory at the UCL. To simulate a section of rafted sea ice, blocks of laboratory grown saline ice were stacked in an insulated tank with spacers between adjacent blocks to allow saline water to flood in. The rate of consolidation was then monitored using a combination of temperature readings recorded in the ice and liquid layer, salinity measurements of the liquid layer, and cores taken at specific times of interest. Two states of consolidation were observed: thermodynamic consolidation where the ice blocks were physically bonded but the bond strength was weak, and mechanical consolidation where the bond had reached full strength. Results showed that the rafted ice had physically bonded in less than a day, however it took many more days (6 to 30 depending on the environmental conditions) for the bond to reach maximum strength. Increasing the thickness of the ice, the salinity of the water and the inter-block gap size all increased the consolidation time. Once consolidated, ice cores were taken and sheared using the asymmetric four-point bending method to measure the strength of the bond between the ice blocks. These were then compared to the shear strength of solid ice blocks simulating level sea ice. Our results show that the shear strength of the bond between the rafted ice blocks is about 30% weaker than that of level ice.

Glycogen synthase kinase 3 (GSK3) in the heart: a point of integration in hypertrophic signalling and a therapeutic target? A critical analysis

Glycogen synthase kinase 3 (GSK3, of which there are two isoforms, GSK3alpha and GSK3beta) was originally characterized in the context of regulation of glycogen metabolism, though it is now known to regulate many other cellular processes. Phosphorylation of GSK3alpha(Ser21) and GSK3beta(Ser9) inhibits their activity. In the heart, emphasis has been placed particularly on GSK3beta, rather than GSK3alpha. Importantly, catalytically-active GSK3 generally restrains gene expression and, in the heart, catalytically-active GSK3 has been implicated in anti-hypertrophic signalling. Inhibition of GSK3 results in changes in the activities of transcription and translation factors in the heart and promotes hypertrophic responses, and it is generally assumed that signal transduction from hypertrophic stimuli to GSK3 passes primarily through protein kinase B/Akt (PKB/Akt). However, recent data suggest that the situation is far more complex. We review evidence pertaining to the role of GSK3 in the myocardium and discuss effects of genetic manipulation of GSK3 activity in vivo. We also discuss the signalling pathways potentially regulating GSK3 activity and propose that, depending on the stimulus, phosphorylation of GSK3 is independent of PKB/Akt. Potential GSK3 substrates studied in relation to myocardial hypertrophy include nuclear factors of activated T cells, beta-catenin, GATA4, myocardin, CREB, and eukaryotic initiation factor 2Bvarepsilon. These and other transcription factor substrates putatively important in the heart are considered. We discuss whether cardiac pathologies could be treated by therapeutic intervention at the GSK3 level but conclude that any intervention would be premature without greater understanding of the precise role of GSK3 in cardiac processes.

Studying the contact point and interface moving in a sinusoidal tube with lattice Boltzmann method

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are nonwetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.