Parity-induced Selmer growth for symplectic, ordinary families

Let p be an odd prime, and let K/K₀ be a quadratic extension of number fields. Denote by K_± the maximal Zp-power extensions of K that are Galois over K₀, with K₊ abelian over K₀ and K₋ dihedral over K₀. In this paper we show that for a Galois representation over K₀ satisfying certain hypotheses, if it has odd Selmer rank over K then for one of K_± its Selmer rank over L is bounded below by [L:K] for L ranging over the finite subextensions of K in K_±. Our method of proof generalizes a method of Mazur and Rubin, building upon results of Neková?, and applies to abelian varieties of arbitrary dimension, (self-dual twists of) modular forms of even weight, and (twisted) Hida families.     

In situ studies of the active sites for the water gas shift reaction over Cu-CeO2 catalysts: complex interaction between metallic copper and oxygen vacancies of ceria

New information about the active sites for the water gas shift (WGS) reaction over Cu-CeO2 systems was obtained using in-situ, time-resolved X-ray diffraction (TR-XRD), X-ray absorption spectroscopy (TR-XAS, Cu K and Ce L3 edges), and infrared spectroscopy (DRIFTS). Cu-CeO2 nanoparticles prepared by a novel reversed microemulsion method (doped Ce1-xCuxO2 sample) and an impregnation method (impregnated CuOx/CeO2 sample) were studied. The results from all of the samples indicate that both metallic copper and oxygen vacancies in ceria were involved in the generation of active sites for the WGS reaction. Evidence was found for a synergistic Cu-Ovacancy interaction. This interaction enhances the chemical activity of Cu, and the presence of Cu facilitates the formation of O vacancies in ceria under reaction conditions. Water dissociation occurred on the Ovacancy sites or the Cu-Ovacancy interface. No significant amounts of formate were formed on the catalysts during the WGS reaction. The presence of strongly bound carbonates is an important factor for the deactivation of the catalysts at high temperatures. This work identifies for the first time the active sites for the WGS reaction on Cu-CeO2 catalysts and illustrates the importance of in situ structural studies for heterogeneous catalytic reactions.     

Anomalous Richtmyer-Meshkov fingering in dissipative particle systems

We study the fingering instability induced by a shock that propagates across a perturbed interface that separates two types of discrete particles. If collisions between particles conserve energy, then the relative sizes and growth rates of the fingers are similar to those in the analogous shock-induced fingering instability in fluids. However, we show that energy loss during particle collisions, even when very small, causes the qualitative features of the finger growth to be completely opposite to the fluid case. The fingers formed by light particles grow faster and become longer and narrower than the fingers formed by heavy particles. In addition, the finger composed of light particles collapses into an extremely compact, tortuous filament, and diffusive mixing between particle types at the particle scale is heavily suppressed.     

Improved Decay for Solutions to the Linear Wave Equation on a Schwarzschild Black Hole

We prove that sufficiently regular solutions to the wave equation ${\square_g\phi=0}We prove that sufficiently regular solutions to the wave equation \square_gf = 0{\square_g\phi=0} on the exterior of the Schwarzschild black hole obey the estimates |f| ￡ C_d v₊^-\frac32+d{|\phi|\leq C_\delta v_+^{-\frac{3}{2}+\delta}} and |?_tf| ￡ C_d v₊^-2+d{|\partial_t\phi|\leq C_{\delta} v_+^{-2+\delta}} on a compact region of r, including inside the black hole region. This is proved with the help of a new vector field commutator that is analogous to the scaling vector field on Minkowski spacetime. This result improves the known decay rates in the region of finite r and along the event horizon.     

A generalized approach to the calculation of ro-vibrational spectra of triatomic molecules

A generalization of the well known atom-diatom scattering hamiltonian to a coordinate system of two lengths and an angle is derived, another special case of which is a previously known bond angle-bond length hamiltonian. Different axis embeddings are also considered. The formalism is applied to the ro-vibrational levels of D₂H⁺, CH⁺ ₂ and HDHe (A ¹ A′) and the advantage of a judicious choice of coordinates demonstrated. The vibrational band origins for HDHe*, the first predictions for this system for which previous calculations had failed, are obtained using a new geometrically defined coordinate system. It is suggested that these coordinates might be used to represent isotopically substituted van der Waals complexes.     

The Zero-Divisor Graph Associated to a Semigroup

The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zero-divisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on the number of edges necessary to guarantee a graph is a zero-divisor graph. In addition, the removal or addition of vertices to a zero-divisor graph is investigated by using equivalence relations and quotient sets. We also prove necessary and sufficient conditions for determining when regular graphs and complete graphs with more than two triangles attached are zero-divisor graphs. Lastly, we classify several graph structures that satisfy all known necessary conditions but are not zero-divisor graphs.     

Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations

A variety of numerical methods are available for determining the stability of a given solution of a partial differential equation. However for a family of solutions, calculation of boundaries in parameter space between stable and unstable solutions remains a major challenge. This paper describes an algorithm for the calculation of such stability boundaries, for the case of periodic travelling wave solutions of spatially extended local dynamical systems. The algorithm is based on numerical continuation of the spectrum. It is implemented in a fully automated way by the software package wavetrain, and two examples of its use are presented. One example is the Klausmeier model for banded vegetation in semi-arid environments, for which the change in stability is of Eckhaus (sideband) type; the other is the two-component Oregonator model for the photosensitive Belousov–Zhabotinskii reaction, for which the change in stability is of Hopf type.