Structure parameters in rotating Couette-Poiseuille channel flow

It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing

A selection principle in Benard-type convection

In a Benard-type convection problem, the stationary flows of an infinite layer of fluid lying between two rigid horizontal walls and heated uniformly from below are determined. As the temperature difference across the layer increases beyond a certain value, other convective motions appear. These motions areoften cellular in character in that their streamlines are confined to certain well-defined cells having, for example, the shape of rolls or hexagons. A selection principle that explains why hexagonal cells seem to be preferred for certain ranges of the parameters is formulated. An operator-theoretical formulation of one generalized Bernard problem is given. The infinite dimensional problem is reduced to one of solving a finite dimensional system of equations, namely, the selection equations. These equations are solved and a linearized stability analysis of the resultant stationary flows is presented

The maximum principle and sign changing solutions of the hyperbolic equation with the Higgs potential

In this article we discuss the maximum principle for the linear equation and the sign changing solutions of the semilinear equation with the Higgs potential. Numerical simulations indicate that the bubbles for the semilinear Klein-Gordon equation in the de Sitter spacetime are created and apparently exist for all times

Students as co-creators of teaching approaches, course design and curricula: implications for academic developers

Within higher education, students’ voices are frequently overlooked in the design of teaching approaches, courses and curricula. In this paper we outline the theoretical background to arguments for including students as partners in pedagogical planning processes. We present examples where students have worked collaboratively in design processes along with the beneficial outcomes of these examples. Finally we focus on some of the implications and opportunities for academic developers of proposing collaborative approaches to pedagogical planning

Electroweak Baryogenesis and Standard Model CP Violation

We analyze the mechanism of electroweak baryogenesis proposed by Farrar and Shaposhnikov in which the phase of the CKM mixing matrix is the only source of $CP$ violation. This mechanism is based on a phase separation of baryons via the scattering of quasiparticles by the wall of an expanding bubble produced at the electroweak phase transition. In agreement with the recent work of Gavela, Hern\'andez, Orloff and P\`ene, we conclude that QCD damping effects reduce the asymmetry produced to a negligible amount. We interpret the damping as quantum decoherence. We compute the asymmetry analytically. Our analysis reflects the observation that only a thin, outer layer of the bubble contributes to the coherent scattering of the quasiparticles. The generality of our arguments rules out any mechanism of electroweak baryogenesis that does not make use of a new source of $CP$ violation.Comment: 36 pages, in LaTeX, one LaTeX figure included, 5 others available upon request, SLAC-PUB-647

Launching a Journal About and Through Students as Partners

Editorial of first issue of the International Journal for Student as Partners

Flavor and Charge Symmetry in the Parton Distributions of the Nucleon

Recent calculations of charge symmetry violation(CSV) in the valence quark distributions of the nucleon have revealed that the dominant symmetry breaking contribution comes from the mass associated with the spectator quark system.Assuming that the change in the spectator mass can be treated perturbatively, we derive a model independent expression for the shift in the parton distributions of the nucleon. This result is used to derive a relation between the charge and flavor asymmetric contributions to the valence quark distributions in the proton, and to calculate CSV contributions to the nucleon sea. The CSV contribution to the Gottfried sum rule is also estimated, and found to be small

Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two

Charge symmetry violation in the parton distributions of the nucleon

We point out that charge symmetry violation in both the valence and sea quark distributions of the nucleon has a non-perturbative source. We calculate this non-perturbative charge symmetry violation using the meson cloud model, which has earlier been successfully applied to both the study of SU(2) flavour asymmetry in the nucleon sea and quark-antiquark asymmetry in the nucleon. We find that the charge symmetry violation in the valence quark distribution is well below 1%, which is consistent with most low energy tests but significantly smaller than the quark model prediction about 5%-10%. Our prediction for the charge symmetry violation in the sea quark distribution is also much smaller than the quark model calculation.Comment: RevTex, 26 pages, 6 PostScript figure