Temperature relaxation and the Kapitza boundary resistance paradox

The calculation of the Kapitza boundary resistance between dissimilar harmonic solids has since long (Little [Can. J. Phys. 37, 334 (1959)]) suffered from a paradox: this resistance erroneously tends to a finite value in the limit of identical solids. We resolve this paradox by calculating temperature differences in the final heat-transporting state, rather than with respect to the initial state of local equilibrium. For a one-dimensional model we thus derive an exact, paradox-free formula for the boundary resistance. The analogy to ballistic electron transport is explained.Comment: 10 p., REVTeX 3.0 with LaTeX 2.09, ITFA-94-2

Spacetime Encodings II - Pictures of Integrability

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a two degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about two degree of freedom systems. Evidence is given, in the form of orbit-crossing structure, that geodesics in SAV spacetimes might admit, a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic).Comment: 11 pages, 10 figure

Three-body model calculations for 16C nucleus

We apply a three-body model consisting of two valence neutrons and the core nucleus $^{14}$C in order to investigate the ground state properties and the electronic quadrupole transition of the $^{16}$C nucleus. The discretized continuum spectrum within a large box is taken into account by using a single-particle basis obtained from a Woods-Saxon potential. The calculated B(E2) value from the first 2$^+$ state to the ground state shows good agreement with the observed data with the core polarization charge which reproduces the experimental B(E2) value for $^{15}$C. We also show that the present calculation well accounts for the longitudinal momentum distribution of $^{15}$C fragment from the breakup of $^{16}$C nucleus. We point out that the dominant ($d_{5/2})^2$ configuration in the ground state of $^{16}$C plays a crucial role for these agreement.Comment: 5 pages, 3 figures, 3 table

Counterterms in Gravity in the Light-Front Formulation and a D=2 Conformal-like Symmetry in Gravity

In this paper we discuss gravity in the light-front formulation (light-cone gauge) and show how possible counterterms arise. We find that Poincare invariance is not enough to find the three-point counterterms uniquely. Higher-spin fields can intrude and mimic three-point higher derivative gravity terms. To select the correct term we have to use the remaining reparametrization invariance that exists after the gauge choice. We finally sketch how the corresponding programme for N=8 Supergravity should work.Comment: 26 pages, references added, published versio

Alpha-cluster structure and density wave in oblate nuclei

Pentagon and triangle shapes in Si-28 and C-12 are discussed in relation with nuclear density wave. In the antisymmetrized molecular dynamics calculations, the $K^\pi=5^-$ band in Si-28 and the $K^\pi=3^-$ band in C-12 are described by the pentagon and triangle shapes, respectively. These negative-parity bands can be interpreted as the parity partners of the $K^\pi=0^+$ ground bands and they are constructed from the parity-asymmetric-intrinsic states. The pentagon and the triangle shapes originate in 7alpha and 3alpha cluster structures, respectively. In a mean-field picture, they are described also by the static one-dimensional density wave at the edge of the oblate states. In analysis with ideal alpha cluster models using Brink-Bloch cluster wave functions and that with a simplified model, we show that the static edge density wave for the pentagon and triangle shapes can be understood by spontaneous breaking of axial symmetry, i.e., the instability of the oblate states with respect to the edge density wave. The density wave is enhanced in the Z=N nuclei due to the proton-neutron coherent density waves, while it is suppressed in Z\ne N nuclei.Comment: 23 pages, 8 figure

Island-trapped waves with stratification, topography, mean flow and bottom friction in Matlab

This set of Matlab mfiles (all having names that begin with “bigi”) can be used to calculate island-trapped wave modal structures and dispersion curves under very general circumstances for a circular island. A complex frequency is allowed, so that instability and damping can be accounted for directly. Modal structures and energy diagnostics are provided. For most applications, the code is only useful for subinertial wave frequencies (i.e., the real part of wave frequency is smaller than the Coriolis parameter). For interpreting the model results, see Brink (1999), which deals with the case with no mean flow or finite bottom friction. The present code was developed independently of the Fortran code used in that publication

Continental shelf baroclinic instability. Part I : relaxation from upwelling or downwelling

Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 551-568, doi:10.1175/JPO-D-15-0047.1.There exists a good deal of indirect evidence, from several locations around the world, that there is a substantial eddy field over continental shelves. These eddies appear to have typical swirl velocities of a few centimeters per second and have horizontal scales of perhaps 5–10 km. These eddies are weak compared to typical, wind-driven, alongshore flows but often seem to dominate middepth cross-shelf flows. The idea that motivates the present contribution is that the alongshore wind stress ultimately energizes these eddies by means of baroclinic instabilities, even in cases where obvious intense fronts do not exist. The proposed sequence is that alongshore winds over a stratified ocean cause upwelling or downwelling, and the resulting horizontal density gradients are strong enough to fuel baroclinic instabilities of the requisite energy levels. This idea is explored here by means of a sequence of idealized primitive equation numerical model studies, each driven by a modest, nearly steady, alongshore wind stress applied for about 5–10 days. Different runs vary wind forcing, stratification, bottom slope, bottom friction, and Coriolis parameter. All runs, both upwelling and downwelling, are found to be baroclinically unstable and to have scales compatible with the underlying hypothesis. The model results, combined with physically based scalings, show that eddy kinetic energy generally increases with bottom slope, stratification, wind impulse (time integral of the wind stress), and inverse Coriolis parameter. The dominant length scale of the eddies is found to increase with increasing eddy kinetic energy and to decrease with Coriolis parameter.This work was supported by the Woods Hole Oceanographic Institution and by the National Science Foundation, Physical Oceanography section through Grant OCE-1433953.2016-06-0

Cross-shelf exchange

Author Posting. © The Author(s), 2015. This is the author's version of the work. It is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Marine Science 8 (2016): 59-78, doi:10.1146/annurev-marine-010814-015717.Cross-shelf exchange dominates the pathways and rates by which nutrients, biota and materials on the continental shelf are delivered and removed. These transports are limited by Earth’s rotation, which inhibits flow from crossing isobaths. Thus, cross-shelf transports are generally weak compared to alongshore flows, and this leads to interesting observational issues. Cross-shelf flows are enabled by turbulent mixing processes, by nonlinear processes (such as momentum advection), and by time-dependence. Thus, there is a wide range of possible effects that can allow these critical transports, and different natural settings are often governed by differing mixes of processes. Examples of representative transport mechanisms are discussed, and possible observational and theoretical paths to future progress are explored.Support from the National Science Foundation Physical Oceanography program, through grant OCE-1433953, and the Biological Oceanography program through grant OCE-125866