Operator splitting for the Benjamin-Ono equation

In this paper we analyze operator splitting for the Benjamin-Ono equation, u_t = uu_x + Hu_xx, where H denotes the Hilbert transform. If the initial data are sufficiently regular, we show the convergence of both Godunov and Strang splitting.Comment: 18 Page

The structure of triphenylgermanium hydroxide

C18H~6GeO, Mr = 320.9, triclinic, Pi, a = 15.408 (6), b = 19.974 (7), c = 23.264 (11) A, a = 107.78 (4), 13 = 1.03.54 (4), y= 101.51 (3) °, V = 6338 (5)/~3, Z = 16, Dx = 1.34 g cm -3, a(Mo Ka) = 0.71073A, /z = 19.1cm-1, F(000)=2624, T= 293 K, R = 0.055 for 6846 observed reflections. The eight independent molecules in the asymmetric unit form two independent O--H...O hydrogen-bonded tetramers with the O atoms in a flattened tetrahedral arrangement [hydrogen-bond distances in the range 2.609 (11) to 2.657 (11)A]. The Ge atoms are tetrahedrally coordinated with mean Gc O 1.791 (7) and Gc C 1.931 (8) A

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system

The Camassa-Holm equation and its two-component Camassa-Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the original equation given in Eulerian coordinates, into a system of ordinary differential equations in Lagrangian coordinates. It is of considerable interest to study the stability of solutions and how this is manifested in Eulerian and Lagrangian variables. We identify criteria of convergence, such that convergence in Eulerian coordinates is equivalent to convergence in Lagrangian coordinates. In addition, we show how one can approximate global conservative solutions of the scalar Camassa-Holm equation by smooth solutions of the two-component Camassa-Holm system that do not experience wave breaking

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

EVIDENCE OF SUPPRESSOR CELL ACTIVITY IN SPLEENS OF MICE BEARING PRIMARY TUMORS INDUCED BY MOLONEY SARCOMA VIRUS

Spleens from Moloney sarcoma virus (MSV) tumor-bearing C57BL/6N mice contained four times the normal number of mononuclear cells and displayed a markedly elevated "spontaneous" (mitogen-independent) DNA synthesis on a per cell basis. The number of macrophages were increased three-fold while there was a slight reduction in the percentage of T lymphocytes. The phytohemagglutinin (PHA) response on a per cell basis of spleens from tumor-bearing mice was decreased about 90% when compared with normal control mice. The primary in vitro immune response to sheep red blood cells was also suppressed to levels of less than 10% of normals. The PHA response could be restored by purification of MSV spleen cells by rayon adherence columns and by removal of phagocytic cells by an iron/magnet technique. The activity of suppressor cells in MSV spleens was demonstrated in mixtures with syngeneic normal spleen cells where a marked impairment of the PHA response was observed. Spleen cells from tumor-free nude mice and normal spleen cells treated by anti-θ serum plus guinea pig complement (C'), both totally unreactive to PHA, had no such effect. The inhibitor cell in MSV spleens was shown to be insensitive to inactivation by anti-θ plus C', but could be removed by the adherence columns and the iron/magnet technique. These data suggest that this suppressor cell is a cell of the monocyte/macrophage series. Suggestive evidence was also presented that the suppressor cells belong to a proliferating population in MSV spleens. Similar suppressor cells have been previously demonstrated in spleens of mice during a variety of immune responses. Our data show, that a tumor, although stimulating the immune system, nevertheless may be suppressive on certain immune functions through the activation of suppressor cells

Modeling Intake of Grazing Cows Fed Complementary Feeds

A model suitable for predicting intake for grazing or non-grazing dairy cows is presented. The model integrates the potentially intake limiting factors of physical fill, physiological energy demand, wet mass, herbage availability, herbage cover, and grazing time. Integration of these factors with a simple set of linear ration balancing constraints yields a model suitable for predicting supplemental feed requirements as well as potential animal production from a grazed land. The model is semi-theoretical, being descriptive in structure, but containing empirical relationships

The Galaxy Population of Cluster RXJ0848+4453 at z=1.27

We present a study of the galaxy population in the cluster RXJ0848+4453 at z=1.27, using deep HST NICMOS and WFPC2 images. We morphologically classify all galaxies to K_s=20.6 that are covered by the HST imaging, and determine photometric redshifts using deep ground based BRIzJK_s photometry. Of 22 likely cluster members with morphological classifications, eleven (50%) are classified as early-type galaxies, nine (41%) as spiral galaxies, and two (9%) as ``merger/peculiar''. At HST resolution the second brightest cluster galaxy is resolved into a spectacular merger between three red galaxies of similar luminosity, separated from each other by ~6 kpc, with an integrated magnitude K=17.6 (~3 L* at z=1.27). The two most luminous early-type galaxies also show evidence for recent or ongoing interactions. Mergers and interactions between galaxies are possible because RXJ0848+4453 is not yet relaxed. The fraction of early-type galaxies in our sample is similar to that in clusters at 0.5<z<1, and consistent with a gradual decrease of the number of early-type galaxies in clusters from z=0 to z=1.3. We find evidence that the color-magnitude relation of the early-type galaxies is less steep than in the nearby Coma cluster. This may indicate that the brightest early-type galaxies have young stellar populations at z=1.27, but is also consistent with predictions of single age ``monolithic'' models with a galactic wind. The scatter in the color-magnitude relation is ~0.04 in rest frame U-V, similar to that in clusters at 0<z<1. Taken together, these results show that luminous early-type galaxies exist in clusters at z~1.3, but that their number density may be smaller than in the local Universe. Additional observations are needed to determine whether the brightest early-type galaxies harbor young stellar populations.Comment: Accepted for publication in The Astrophysical Journal Letter