Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Establishing a connection between knowledge transfer and innovation diffusion

Successful innovation diffusion process may well take the form of knowledge transfer process. Therefore, the primary objectives of this paper include: first, to evaluate the interrelations between transfer of knowledge and diffusion of innovation; and second to develop a model to establish a connection between the two. This has been achieved using a four-step approach. The first step of the approach is to assess and discuss the theories relating to knowledge transfer (KT) and innovation diffusion (ID). The second step focuses on developing basic models for KT and ID, based on the key theories surrounding these areas. A considerable amount of literature has been written on the association between knowledge management and innovation, the respective fields of KT and ID. The next step, therefore, explores the relationship between innovation and knowledge management in order to identify the connections between the latter, i.e. KT and ID. Finally, step four proposes and develops an integrated model for KT and ID. As the developed model suggests the sub-processes of knowledge transfer can be connected to the innovation diffusion process in several instances as discussed and illustrated in the paper.

Quasilimiting behavior for one-dimensional diffusions with killing

This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285–1234], which found conditions for convergence of a killed one-dimensional diffusion conditioned on survival, to a quasistationary distribution whose density is given by the principal eigenfunction of the generator. Under the assumption that the limit of the killing at infinity differs from the principal eigenvalue we prove that convergence to quasistationarity occurs if and only if the principal eigenfunction is integrable. When the killing at ∞ is larger than the principal eigenvalue, then the eigenfunction is always integrable. When the killing at ∞ is smaller, the eigenfunction is integrable only when the unkilled process is recurrent; otherwise, the process conditioned on survival converges to 0 density on any bounded interval.

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.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

K-T transition in Deccan traps of central India marks major marine seaway across India.

Deccan intertrappean sediments in central India are generally considered as terrestrial deposits of Maastrichtian age, but the Cretaceous–Tertiary (K–T) position is still unknown. Here we report the discovery of the K–T transition, a marine incursion and environmental changes preserved within the intertrappean sediments at Jhilmili, Chhindwara District, Madhya Pradesh. Integrative biostratigraphic, sedimentologic, mineralogic and chemostratigraphic analyses reveal the basal Danian in the intertrappean sediments between lower and upper trap basalts that regionally correspond to C29r and the C29R/C29N transition, respectively. Intertrappean deposition occurred in predominantly terrestrial semi-humid to arid environments. But a short aquatic interval of fresh water ponds and lakes followed by shallow coastal marine conditions with brackish marine ostracods and early Danian zone P1a planktic foraminifera mark this interval very close to the K–T boundary. This marine incursion marks the existence of a nearby seaway, probably extending inland from the west through the Narmada and Tapti rift valleys. The Jhilmili results thus identify the K–T boundary near the end of the main phase of Deccan eruptions and indicate that a major seaway extended at least 800 km across India.

Balitskiǐ-Fadin-Kuraev-Lipatov equation versus data from DESY HERA

The BFKL equation and the kT-factorization theorem are used to obtain predictions for F2 in the small Bjo/rken-x region over a wide range of Q2. The dependence on the parameters, especially on those concerning the infrared region, is discussed. After a background fit to recent experimental data obtained at DESY HERA and at Fermilab (E665 experiment) we find that the predicted, almost Q2 independent BFKL slope λ≳0.5 appears to be too steep at lower Q2 values. Thus there seems to be a chance that future HERA data can distinguish between pure BFKL and conventional field theoretic renormalization group approaches. © 1995 The American Physical Society.

Cesium toxicity in Arabidopsis

Cesium (Cs) is chemically similar to potassium (K). However, although K is an essential element, Cs is toxic to plants. Two contrasting hypotheses to explain Cs toxicity have been proposed: (1) extracellular Cs+ prevents K+ uptake and, thereby, induces K starvation; and (2) intracellular Cs+ interacts with vital K+-binding sites in proteins, either competitively or noncompetitively, impairing their activities. We tested these hypotheses with Arabidopsis (Arabidopsis thaliana). Increasing the Cs concentration in the agar (Cs(agar)) on which Arabidopsis were grown reduced shoot growth. Increasing the K concentration in the agar (K(agad)) increased the Cs(agar) at which Cs toxicity was observed. However, although increasing Cs(agar) reduced shoot K concentration (K(shoot)), the decrease in shoot growth appeared unrelated to K(shoot) per se. Furthermore, the changes in gene expression in Cs-intoxicated plants differed from those of K-starved plants, suggesting that Cs intoxication was not perceived genetically solely as K starvation. In addition to reducing K(shoot) increasing Cs(agar) also increased shoot Cs concentration (Cs(shoot)), but shoot growth appeared unrelated to Cs(shoot) per se. The relationship between shoot growth and Cs(shoot)/Kt(shoot) suggested that, at a nontoxic Cs(shoot) growth was determined by K(shoot) but that the growth of Cs-intoxicated plants was related to the Cs(shoot)/K(shoot) quotient. This is consistent with Cs intoxication resulting from competition between K+ and Cs+ for K+-binding sites on essential proteins.

The sources of phosphorus in the waters of Great Britain

Total phosphorus (TP) and soluble reactive phosphorus (SRP) loads to watercourses of the River Basin Districts (RBDs) of Great Britain (GB) were estimated using inventories of industrial P loads and estimates of P loads from sewage treatment works and diffuse P loads calculated using region-specific export coefficients for particular land cover classes combined with census data for agricultural stocking densities and human populations. The TP load to GB waters was estimated to be 60 kt yr(-1), of which households contributed 73, agriculture contributed 20, industry contributed 3, and 4 came from background sources. The SRP load to GB waters was estimated to be 47 kt yr(-1), of which households contributed 78, agriculture contributed 13, industry contributed 4, and 6 came from background Sources. The 'average' area-normalized TP and SRP loads to GB waters approximated 2.4 kg ha(-1) yr(-1) and 1.8 kg ha(-1) yr(-1), respectively. A consideration of uncertainties in the data contributing to these estimates suggested that the TP load to GB waters might lie between 33 and 68 kt yr(-1), with agriculture contributing between 10 and 28 of the TP load. These estimates are consistent with recent appraisals of annual TP and SRP loads to GB coastal waters and area-normalized TP loads from their catchments. Estimates of the contributions of RBDs to these P loads were consistent with the geographical distribution of P concentrations in GB rivers and recent assessments of surface waters at risk from P Pollution.

Self-assembly of palmitoyl lipopeptides used in skin care products

The self-assembly of three cosmetically active peptide amphiphiles C16-GHK, C16-KT, and C16-KTTKS (C16 denotes a hexadecyl, palmitoyl chain) used in commercial skin care products is examined. A range of spectroscopic, microscopic, and X-ray scattering methods is used to probe the secondary structure, aggregate morphology, and the nanostructure. Peptide amphiphile (PA) C16-KTTKS forms flat tapes and extended fibrillar structures with high β-sheet content. In contrast, C16-KT and C16-GHK exhibit crystal-like aggregates with, in the case of the latter PA, lower β-sheet content. All three PA samples show spacings from bilayer structures in small-angle X-ray scattering profiles, and all three have similar critical aggregation concentrations, this being governed by the lipid chain length. However, only C16-KTTKS is stained by Congo red, a diagnostic dye used to detect amyloid formation, and this PA also shows a highly aligned cross-β X-ray diffraction pattern consistent with the high β-sheet content in the self-assembled aggregates. These findings may provide important insights relevant to the role of self-assembled aggregates on the reported collagen-stimulating properties of these PAs.

A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.

Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.