The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Nuclear magnetic resonance structure shows that the severe acute respiratory syndrome coronavirus-unique domain contains a macrodomain fold

The nuclear magnetic resonance (NMR) structure of a central segment of the previously annotated severe acute respiratory syndrome (SARS)-unique domain (SUD-M, for "middle of the SARS-unique domain") in SARS coronavirus (SARS-CoV) nonstructural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3 residues 528 to 648, and there is a flexibly extended N-terminal tail with the residues 513 to 527 and a C-terminal flexible tail of residues 649 to 651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527 to 651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly(A) and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In a further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1 ''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows three-dimensional structure homology with several helicases and nucleoside triphosphate-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.

NMR structure shows that the SARS-unique domain contains a macrodomain fold

The NMR structure of a central segment of the previously annotated "SARS-unique domain" (SUD-M; "middle of the SARS-unique domain") in the SARS coronavirus (SARS-CoV) non-structural protein 3 (nsp3) has been determined. SUD-M(513-651) exhibits a macrodomain fold containing the nsp3-residues 528-648, and there is a flexibly extended N-terminal tail with the residues 513-527 and a C-terminal flexible tail of residues 649-651. As a follow-up to this initial result, we also solved the structure of a construct representing only the globular domain of residues 527-651 [SUD-M(527-651)]. NMR chemical shift perturbation experiments showed that SUD-M(527-651) binds single-stranded poly-A and identified the contact area with this RNA on the protein surface, and electrophoretic mobility shift assays then confirmed that SUD-M has higher affinity for purine bases than for pyrimidine bases. In further search for clues to the function, we found that SUD-M(527-651) has the closest three-dimensional structure homology with another domain of nsp3, the ADP-ribose-1''-phosphatase nsp3b, although the two proteins share only 5% sequence identity in the homologous sequence regions. SUD-M(527-651) also shows 3D structure homology with several helicases and NTP-binding proteins, but it does not contain the motifs of catalytic residues found in these structural homologues. The combined results from NMR screening of potential substrates and the structure-based homology studies now form a basis for more focused investigations on the role of the SARS-unique domain in viral infection.

SARS coronavirus unique domain: three-domain molecular architecture in solution and RNA binding

Nonstructural protein 3 of the severe acute respiratory syndrome (SARS) coronavirus includes a "SARS-unique domain" (SUD) consisting of three globular domains separated by short linker peptide segments. This work reports NMR structure determinations of the C-terminal domain (SUD-C) and a two-domain construct (SUD-MC) containing the middle domain (SUD-M) and the C-terminal domain, and NMR data on the conformational states of the N-terminal domain (SUD-N) and the SUD-NM two-domain construct. Both SUD-N and SUD-NM are monomeric and globular in solution; in SUD-NM, there is high mobility in the two-residue interdomain linking sequence, with no preferred relative orientation of the two domains. SUD-C adopts a frataxin like fold and has structural similarity to DNA-binding domains of DNA-modifying enzymes. The structures of both SUD-M (previously determined) and SUD-C (from the present study) are maintained in SUD-MC, where the two domains are flexibly linked. Gel-shift experiments showed that both SUD-C and SUD-MC bind to single-stranded RNA and recognize purine bases more strongly than pyrimidine bases, whereby SUD-MC binds to a more restricted set of purine-containing RNA sequences than SUD-M. NMR chemical shift perturbation experiments with observations of (15)N-labeled proteins further resulted in delineation of RNA binding sites (i.e., in SUD-M, a positively charged surface area with a pronounced cavity, and in SUD-C, several residues of an anti-parallel beta-sheet). Overall, the present data provide evidence for molecular mechanisms involving the concerted actions of SUD-M and SUD-C, which result in specific RNA binding that might be unique to the SUD and, thus, to the SARS coronavirus.

Perturbation growth at the convective scale for CSIP IOP18

The Met Office Unified Model is run for a case observed during Intensive Observation Period 18 (IOP18) of the Convective Storms Initiation Project (CSIP). The aims are to identify the physical processes that lead to perturbation growth at the convective scale in response to model-state perturbations and to determine their sensitivity to the character of the perturbations. The case is strongly upper-level forced but with detailed mesoscale/convective-scale evolution that is dependent on smaller-scale processes. Potential temperature is perturbed within the boundary layer. The effects on perturbation growth of both the amplitude and typical scalelength of the perturbations are investigated and perturbations are applied either sequentially (every 30 min throughout the simulation) or at specific times. The direct effects (within one timestep) of the perturbations are to generate propagating Lamb and acoustic waves and produce generally small changes in cloud parameters and convective instability. In exceptional cases a perturbation at a specific gridpoint leads to switching of the diagnosed boundary-layer type or discontinuous changes in convective instability, through the generation or removal of a lid. The indirect effects (during the entire simulation) are changes in the intensity and location of precipitation and in the cloud size distribution. Qualitatively different behaviour is found for strong (1K amplitude) and weak (0.01K amplitude) perturbations, with faster growth after sunrise found only for the weaker perturbations. However, the overall perturbation growth (as measured by the root-mean-square error of accumulated precipitation) reaches similar values at saturation, regardless of the perturbation characterisation.

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 effect of a large freshwater perturbation on the glacial north Atlantic Ocean using a coupled general circulation model

The commonly held view of the conditions in the North Atlantic at the last glacial maximum, based on the interpretation of proxy records, is of large-scale cooling compared to today, limited deep convection, and extensive sea ice, all associated with a southward displaced and weakened overturning thermohaline circulation (THC) in the North Atlantic. Not all studies support that view; in particular, the "strength of the overturning circulation" is contentious and is a quantity that is difficult to determine even for the present day. Quasi-equilibrium simulations with coupled climate models forced by glacial boundary conditions have produced differing results, as have inferences made from proxy records. Most studies suggest the weaker circulation, some suggest little or no change, and a few suggest a stronger circulation. Here results are presented from a three-dimensional climate model, the Hadley Centre Coupled Model version 3 (HadCM3), of the coupled atmosphere - ocean - sea ice system suggesting, in a qualitative sense, that these diverging views could all have occurred at different times during the last glacial period, with different modes existing at different times. One mode might have been characterized by an active THC associated with moderate temperatures in the North Atlantic and a modest expanse of sea ice. The other mode, perhaps forced by large inputs of meltwater from the continental ice sheets into the northern North Atlantic, might have been characterized by a sluggish THC associated with very cold conditions around the North Atlantic and a large areal cover of sea ice. The authors' model simulation of such a mode, forced by a large input of freshwater, bears several of the characteristics of the Climate: Long-range Investigation, Mapping, and Prediction (CLIMAP) Project's reconstruction of glacial sea surface temperature and sea ice extent.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

Vibrational perturbation theory

Expressions are derived for the Jacobian of the coriolis ζ interaction constants and the centrifugal stretching constants (DJ, DJK, etc.) with respect to the force constants in a vibrating-rotating molecule.

Characterisation of an s-type low molecular weight glutenin subunit of wheat and its proline and glutamine-rich repetitive domain

The low molecular weight glutenin subunits (LMW-GS) are major components of the glutenin polymers which determine the elastomeric properties of wheat (Triticum aestivum L.) gluten and dough. They comprise a complex mixture of components and have proved to be difficult to purify for detailed characterisation. The mature LMW subunit proteins comprise two structural domains, with one domain consisting of repeated sequences based on short peptide motifs. DNA sequences encoding this domain and a whole subunit were expressed in Escherichia coli and the recombinant proteins purified. Detailed comparisons by spectroscopy (CD, FT-IR) and dynamic light scattering indicated that the repetitive and non-repetitive domains of the proteins formed different structures with the former having an extended conformation with an equilibrium between poly-L-proline II-like structure and type II’ b-turns, and the latter a more compact globular structure rich in a-helix. Although the structures of these two domains appear to form independently, dynamic light scattering of the whole subunit dissolved in trifluoroethanol(TFE) suggested that they interact, leading to a more compact conformation. These observations may have relevance to the role of the LMW-GS in gluten structure and functionality.

Cost-benefit analysis model of badger (Meles meles) culling to reduce cattle herd tuberculosis breakdowns in Britain, with particular reference to badger perturbation

Bovine tuberculosis (TB)is an important economic disease. Badgers (Meles meles) are the wildlife source implicated in many cattle outbreaks of TB in Britain, and extensive badger control is a controversial option to reduce the disease. A badger and cattle population model was developed, simulating TB epidemiology; badger ecology, including postcull social perturbation; and TB-related farm management. An economic cost-benefit module was integrated into the model to assess whether badger control offers economic benefits. Model results strongly indicate that although, if perturbation were restricted, extensive badger culling could reduce rates in cattle, overall an economic loss would be more likely than a benefit. Perturbation of the badger population was a key factor determining success or failure of control. The model highlighted some important knowledge gaps regarding both the spatial and temporal characteristics of perturbation that warrant further research.