Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

The heat shock protein 90 inhibitor, 17-allylamino-17- demethoxygeldanamycin, enhances osteoclast formation and potentiates bone metastasis of a human breast cancer cell line

Breast cancer metastasis to the bone occurs frequently, causing numerous complications including severe pain, fracture, hypercalcemia, and paralysis. Despite its prevalence and severity, few effective therapies exist. To address this, we examined whether the heat shock protein 90 (Hsp90) inhibitor, 17-allylamino-17-demethoxygeldanamycin (17-AAG), would be efficacious in inhibiting breast cancer metastasis to bone. Utilizing the human breast cancer subline, MDA-MB-231SA, previously in vivo selected for its enhanced ability to generate osteolytic bone lesions, we determined that 17-AAG potently inhibited its in vitro proliferation and migration. Moreover, 17-AAG significantly reduced MDA-MB-231SA tumor growth in the mammary-fat pad of nude mice. Despite these findings, 17-AAG enhanced the incidence of bone metastasis and osteolytic lesions following intracardiac inoculation in the nude mouse. Consistent with these findings, 17-AAG enhanced osteoclast formation 2- to 4-fold in mouse bone marrow/osteoblast cocultures, receptor activator of nuclear factor κB ligand (BANKL)-stimulated bone marrow, and RAW264.7 cell models of in vitro osteoclastogenesis. Moreover, the drug enhanced osteoclastogenesis in human cord blood progenitor cells, demonstrating that its effects were not limited to mouse models. In addition to 17-AAG, other Hsp90 inhibitors, such as radicicol and herbimycin A, also enhanced osteoclastogenesis. A pro-osteolytic action of 17-AAG independent of tumor presence was also determined in vivo, in which 17-AAG-treated tumor-naive mice had reduced trabecular bone volume with an associated increase in osteoclast number. Thus, HSP90 inhibitors can stimulate osteoclast formation, which may underlie the increased incidence of osteolysis and skeletal tumor incidence causedby 17-AAG in vivo. These data suggest an important contraindication to the Hsp90 targeted cancer therapy currently undergoing clinical trial.

Use of genetic decompositions to scaffold the development of a structurally sequenced curriculum for mathematics acceleration

The authors have collaboratively used a graphical language to describe their shared knowledge of a small domain of mathematics, which has in turn scaffolded their re-development of a related curriculum for mathematics acceleration. This collaborative use of the graphical language is reported as a simple descriptive case study. This leads to an evaluation of the graphical language’s usefulness as a tool to support the articulation of the structure of mathematics knowledge. In turn, implications are drawn for how the graphical language may be utilised as the detail of the curriculum is further elaborated and communicated to teachers.

Fractional models in space for diffusive processes in heterogeneous media with applications in cell motility and electrical signal propagation

This work addresses fundamental issues in the mathematical modelling of the diffusive motion of particles in biological and physiological settings. New mathematical results are proved and implemented in computer models for the colonisation of the embryonic gut by neural cells and the propagation of electrical waves in the heart, offering new insights into the relationships between structure and function. In particular, the thesis focuses on the use of non-local differential operators of non-integer order to capture the main features of diffusion processes occurring in complex spatial structures characterised by high levels of heterogeneity.

A preliminary investigation into adrenal responsiveness and outcomes in patients with cardiogenic shock after acute myocardial infarction

PURPOSE: This study investigated the significance of baseline cortisol levels and adrenal response to corticotropin in shocked patients after acute myocardial infarction (AMI). METHODS: A short corticotropin stimulation test was performed in 35 patients with cardiogenic shock after AMI by intravenously injecting of 250 μg of tetracosactrin (Synacthen). Blood samples were obtained at baseline (T0) before and at 30 (T30) and 60 (T60) minutes after the test to determine plasma total cortisol (TC) and free cortisol concentrations. The main outcome measure was in-hospital mortality and its association with T0 TC and maximum response to corticotropin (maximum difference [Δ max] in cortisol levels between T0 and the highest value between T30 and T60). RESULTS: The in-hospital mortality was 37%, and the median time to death was 4 days (interquartile range, 3-9 days). There was some evidence of an increased mortality in patients with T0 TC concentrations greater than 34 μg/dL (P=.07). Maximum difference by itself was not an independent predictor of death. Patients with a T0 TC 34 μg/dL or less and Δ max greater than 9 μg/dL appeared to have the most favorable survival (91%) when compared with the other 2 groups: T0 34 μg/dL or less and Δ max 9 μg/dL or less or T0 34 μg/dL or higher and Δ max greater than 9 μg/dL (75%; P=.8) and T0 greater than 34 μg/dL and Δ max 9 μg/dL or less (60%; P=.02). Corticosteroid therapy was associated with an increased mortality (P=.03). There was a strong correlation between plasma TC and free cortisol (r=0.85). CONCLUSIONS: A high baseline plasma TC was associated with a trend toward increased mortality in patients with cardiogenic shock post-AMI. Patients with lower baseline TC, but with an inducible adrenal response, appeared to have a survival benefit. A prognostic system based on basal TC and Δ max similar to that described in septic shock appears feasible in this cohort. Corticosteroid therapy was associated with adverse outcomes. These findings require further validation in larger studies.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Shock propagation in gas dynamics: explicit form of higher order compatibility conditions

With the use of tensor analysis and the method of singular surfaces, an infinite system of equations can be derived to study the propagation of curved shocks of arbitrary strength in gas dynamics. The first three of these have been explicitly given here. This system is further reduced to one involving scalars only. The choice of dependent variables in the infinite system is quite important, it leads to coefficients free from singularities for all values of the shock strength.

Thermal shock characteristics of plasma sprayed mullite coatings

Commercially available mullite (3Al(2)O(3). 2SiO(2)) powders containing oxides of calcium and iron as impurities, have been made suitable for plasma spraying by using an organic binder. Stainless steel substrates covered with Ni-22Cr-10Al-1.0Y bond coat were spray coated with mullite, The 425 mu m thick coatings were subjected to thermal shock cycling under burner rig conditions between 1000 and 1200 degrees C and less than 200 degrees C with holding times of 1, 5, and 30 min. While the coatings withstood as high as 1000 shock cycles without failure between 1000 and 200 degrees C, spallation occurred early at 120 cycles when shocked from 1200 degrees C, The coatings appeared to go through a process of self erosion at high temperatures resulting in loss of material. Also observed were changes attributable to melting of the silicate grains, which smooth down the surface. Oxidation of the bond coat did not appear to influence the failure, These observations were supported by detailed scanning electron microscopy and quantitative chemical composition analysis, differential thermal analysis, and surface roughness measurements.

Heat shock protein 70 on Neuro2a cells is a putative receptor for Japanese encephalitis virus

Japanese encephalitis virus (JEV) envelope (E) protein has been shown to play a critical role in attachment to cells. However, the receptor interacting with envelope protein has not been conclusively identified. Using mouse neuroblastoma (Neuro2a) cells and purified JEV-E protein in `Virus Overlay Protein Binding Assay' followed by MALDI-TOF analysis, we identified `heat shock protein 70' (Hsp70) as a possible receptor for JEV. Indirect immunofluorescence and flow-cytometry analysis demonstrated localization of Hsp70 on Neuro2a cell surface. Co-immunoprecipitation followed by Western blot analysis reconfirmed the interaction between Hsp70 and JEV-E protein. Further, anti-Hsp70 polyclonal-antibodies were able to block JEV entry into Neuro2a cells. Additionally, using the bioinformatic tool - FTDOCK, clocking between the proteins was performed. Amongst six interacting structural poses studied one pose involving RGD motif on JEV-E and leucine(539) on Hsp70 displayed stable interaction. These observations indicate that Hsp70 serves as putative receptor for JEV in Neuro2A cells.

Extrapolation and series acceleration procedures: Hard spheres and discs as illustrations

Three new procedures - in the context of estimation of virial coefficients and summation of the partial virial series for hard discs and hard spheres - are proposed. They are based on the parametrised Euler transformation, a novel resummation, identity and the ε-convergence methods respectively. A comparison with other estimates (molecular dynamics, graph theory and empirical methods) reveals satisfactory agreement.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.

Velocity and acceleration analysis of complex mechanisms by graphical iteration

A simple graphical method is presented for velocity and acceleration analysis of complex mechanisms possessing low or high degree of complexity. The method is iterative in character and generally yields the solution within a few iterations. Several examples have been worked out to illustrate the method.