Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

Many operational weather forecasting centres use semi-implicit time-stepping schemes because of their good efficiency. However, as computers become ever more parallel, horizontally explicit solutions of the equations of atmospheric motion might become an attractive alternative due to the additional inter-processor communication of implicit methods. Implicit and explicit (IMEX) time-stepping schemes have long been combined in models of the atmosphere using semi-implicit, split-explicit or HEVI splitting. However, most studies of the accuracy and stability of IMEX schemes have been limited to the parabolic case of advection–diffusion equations. We demonstrate how a number of Runge–Kutta IMEX schemes can be used to solve hyperbolic wave equations either semi-implicitly or HEVI. A new form of HEVI splitting is proposed, UfPreb, which dramatically improves accuracy and stability of simulations of gravity waves in stratified flow. As a consequence it is found that there are HEVI schemes that do not lose accuracy in comparison to semi-implicit ones. The stability limits of a number of variations of trapezoidal implicit and some Runge–Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge–Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.

Sea level extremes at the coasts of China

Hourly sea level records from 1954 to 2012 at 20 tide gauges at and adjacent to the Chinese coasts are used to analyze extremes in sea level and in tidal residual. Tides and tropical cyclones determine the spatial distribution of sea level maxima. Tidal residual maxima are predominantly determined by tropical cyclones. The 50 year return level is found to be sensitive to the number of extreme events used in the estimation. This is caused by the small number of tropical cyclone events happening each year which lead to other local storm events included thus significantly affecting the estimates. Significant increase in sea level extremes is found with trends in the range between 2.0 and 14.1 mm yr−1. The trends are primarily driven by changes in median sea level but also linked with increases in tidal amplitudes at three stations. Tropical cyclones cause significant interannual variations in the extremes. The interannual variability in the sea level extremes is also influenced by the changes in median sea level at the north and by the 18.6 year nodal cycle at the South China Sea. Neither of PDO and ENSO is found to be an indicator of changes in the size of extremes, but ENSO appears to regulate the number of tropical cyclones that reach the Chinese coasts. Global mean atmospheric temperature appears to be a good descriptor of the interannual variability of tidal residual extremes induced by tropical cyclones but the trend in global temperature is inconsistent with the lack of trend in the residuals.

The partial oxidation of methane over Pd/Al2O3 catalyst nanoparticles studied in-situ by near ambient-pressure x-ray photoelectron spectroscopy

Near ambient-pressure X-ray photoelectron spectroscopy (NAP-XPS) is used to study the chemical state of methane oxidation catalysts in-situ. Al2O3{supported Pd catalysts are prepared with different particle sizes ranging from 4 nm to 10 nm. These catalysts were exposed to conditions similar to those used in the partial oxidation of methane (POM) to syn-gas and simultaneously monitored by NAP-XPS and mass spectrometry. NAP-XPS data show changes in the oxidation state of the palladium as the temperature in- creases, from metallic Pd0 to PdO, and back to Pd0. Mass spectrometry shows an increase in CO production whilst the Pd is in the oxide phase, and the metal is reduced back under presence of newly formed H2. A particle size effect is observed, such that CH4 conversion starts at lower temperatures with larger sized particles from 6 nm to 10 nm. We find that all nanoparticles begin CH4 conversion at lower temperatures than polycrystalline Pd foil.

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Biorefinery development through utilization of biodiesel industry by-products as sole fermentation feedstock for 1,3-propanediol production

Rapeseed meal (RSM) hydrolysate was evaluated as substitute for commercial nutrient supplements in 1,3-propanediol (PDO) fermentation using the strain Clostridium butyricum VPI 1718. RSM was enzymatically converted into a generic fermentation feedstock, enriched in amino acids, peptides and various micro-nutrients, using crude enzyme consortia produced via solid state fermentation by a fungal strain of Aspergillus oryzae. Initial free amino nitrogen concentration influenced PDO production in batch cultures. RSM hydrolysates were compared with commercial nutrient supplements regarding PDO production in fed-batch cultures carried out in a bench-scale bioreactor. The utilization of RSM hydrolysates in repeated batch cultivation resulted in a PDO concentration of 65.5 g/L with an overall productivity of 1.15 g/L/h that was almost 2 times higher than the productivity achieved when yeast extract was used as nutrient supplement.

Comparing detection and location performance of perpendicular and parallel broadside GPR antenna orientations

GPR (Ground Penetrating Radar) results are shown for perpendicular broadside and parallel broadside antenna orientations. Performance in detection and localization of concrete tubes and steel tanks is compared as a function of acquisition configuration. The comparison is done using 100 MHz and 200 MHz center frequency antennas. All tubes and tanks are buried at the geophysical test site of IAG/USP in Sao Paulo city, Brazil. The results show that the long steel pipe with a 38-mm diameter was well detected with the perpendicular broadside configuration. The concrete tubes were better detected with the parallel broadside configuration, clearly showing hyperbolic diffraction events from all targets up to 2-m depth. Steel tanks were detected with the two configurations. However, the parallel broadside configuration was generated to a much lesser extent an apparent hyperbolic reflection corresponding to constructive interference of diffraction hyperbolas of adjacent targets placed at the same depth. Vertical concrete tubes and steel tanks were better contained with parallel broadside antennas, where the apexes of the diffraction hyperbolas better corresponded to the horizontal location of the buried target disposition. The two configurations provide details about buried targets emphasizing how GPR multi-component configurations have the potential to improve the subsurface image quality as well as to discriminate different buried targets. It is judged that they hold some applicability in geotechnical and geoscientific studies. (C) 2009 Elsevier B.V. All rights reserved.

(65)Zn(2+) transport by isolated gill epithelial cells of the American lobster, Homarus americanus

Gills are the first site of impact by metal ions in contaminated waters. Work on whole gill cells and metal uptake has not been reported before in crustaceans. In this study, gill filaments of the American lobster, Homarus americanus, were dissociated in physiological saline and separated into several cell types on a 30, 40, 50, and 80% sucrose gradient. Cells from each sucrose solution were separately resuspended in physiological saline and incubated in (65)Zn(2+) in order to assess the nature of metal uptake by each cell type. Characteristics of zinc accumulation by each kind of cell were investigated in the presence and absence of 10 mM calcium, variable NaCl concentrations and pH values, and 100 mu M verapamil, nifedipine, and the calcium ionophore A23187. (65)Zn(2+) influxes were hyperbolic functions of zinc concentration (1-1,000 mu M) and followed Michaelis-Menten kinetics. Calcium reduced both apparent zinc binding affinity (K (m)) and maximal transport velocity (J (max)) for 30% sucrose cells, but doubled the apparent maximal transport velocity for 80% sucrose cells. Results suggest that calcium, sodium, and protons enter gill epithelial cells by an endogenous broad-specificity cation channel and trans-stimulate metal uptake by a plasma membrane carrier system. Differences in zinc transport observed between gill epithelial cell types appear related to apparent affinity differences of the transporters in each kind of cell. Low affinity cells from 30% sucrose were inhibited by calcium, while high affinity cells from 80% sucrose were stimulated. (65)Zn(2+) transport was also studied by isolated, intact, gill filament tips. These intact gill fragments generally displayed the same transport properties as did cells from 80% sucrose and provided support for metal uptake processes being an apical phenomenon. A working model for zinc transport by lobster gill cells is presented.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions.

Continuity of the dynamics in a localized large diffusion problem with nonlinear boundary conditions

This paper is concerned with singular perturbations in parabolic problems subjected to nonlinear Neumann boundary conditions. We consider the case for which the diffusion coefficient blows up in a subregion Omega(0) which is interior to the physical domain Omega subset of R(n). We prove, under natural assumptions, that the associated attractors behave continuously as the diffusion coefficient blows up locally uniformly in Omega(0) and converges uniformly to a continuous and positive function in Omega(1) = (Omega) over bar\Omega(0). (C) 2009 Elsevier Inc. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are Upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in L(p) and H(1) norms. (C) 2008 Elsevier Inc. All rights reserved.

A thermoelastic system of memory type in noncylindrical domains

In this paper, we consider a hyperbolic thermoelastic system of memory type in domains with moving boundary. The problem models vibrations of an elastic bar under thermal effects according to the heat conduction law of Gurtin and Pipkin. Global existence is proved by using the penalty method of Lions. (c) 2007 Elsevier Inc. All rights reserved.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Real map germs and higher open book structures

The paper focusses on the existence of higher open book structures defined by real map germs psi : (R(m), 0) -> (R(p), 0) such that Sing psi boolean AND psi(-1)(0) subset of {0}. A general existence criterion is proved, with view to weighted-homogeneous maps.