Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion-type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity.Comment: 29 page

Low temperature dephasing saturation from elastic magnetic spin disorder and interactions

We treat the question of the low temperature behavior of the dephasing rate of the electrons in the presence of elastic spin disorder scattering and interactions. In the frame of a self-consistent diagrammatic treatment, we obtain saturation of the dephasing rate in the limit of low temperature for magnetic scattering, in agreement with the non-interacting case. The magnitude of the dephasing rate is set by the strength of the magnetic scattering rate. We discuss the agreement of our results with relevant experiments.Comment: This paper supersedes cond-mat/021022

Optical conductivity in cluster dynamical mean field theory: formalism and application to high temperature superconductors

The optical conductivity of the one-band Hubbard model is calculated using the 'Dynamical Cluster Approximation' implementation of dynamical mean field theory for parameters appropriate to high temperature copper-oxide superconductors. The calculation includes vertex corrections and the result demonstrates their importance. At densities of one electron per site, an insulating state is found with gap value and above-gap absorption consistent with measurements. As carriers are added the above gap conductivity rapidly weakens and a three component structure emerges, with a low frequency 'Drude' peak, a mid-infrared absorption, and a remnant of the insulating gap. The mid-infrared feature obtained at intermediate dopings is shown to arise from a pseudogap structure in the density of states. On further doping the conductivity evolves to the Drude peak plus weakly frequency dependent tail structure expected for less strongly correlated metals.Comment: 5 pages, 3 figure

Development of learning objectives for neurology in a veterinary curriculum: part I: undergraduates

Background With an increasing caseload of veterinary neurology patients in first opinion practice, there is a requirement to establish relevant learning objectives for veterinary neurology encompassing knowledge, skills and attitudes for veterinary undergraduate students in Europe. With help of experts in veterinary neurology from the European College of Veterinary Neurology (ECVN) and the European Society of Veterinary Neurology (ESVN) a survey of veterinary neurologic learning objectives using a modified Delphi method was conducted. The first phase comprised the development of a draft job description and learning objectives by a working group established by the ECVN. In the second phase, a quantitative questionnaire (multiple choice, Likert scale and free text) covering 140 learning objectives and subdivided into 8 categories was sent to 341 ESVN and ECVN members and a return rate of 62% (n = 213/341) was achieved. Results Of these 140 learning objectives ECVN Diplomates and ESVN members considered 42 (30%) objectives as not necessary for standard clinical veterinary neurology training, 94 (67%) were graded to be learned at a beginner level and 4 (3%) at an advanced level. The following objectives were interpreted as the most important day one skills: interpret laboratory tests, perform a neurological examination and establish a neuroanatomical localization. In this survey the three most important diseases of the central nervous system included epilepsy, intervertebral disc disease and inflammatory diseases. The three most important diseases of the peripheral nervous system included polyradiculoneuritis, myasthenia gravis and toxic neuropathies. Conclusions The results of this study should help to reform the veterinary curriculum regarding neurology and may reduce the phenomenon of “Neurophobia”.</p

Lifshitz Transition in Underdoped Cuprates

Recent studies show that quantum oscillations thought to be associated with a density wave reconstructed Fermi surface disappear at a critical value of the doping for YBa2Cu3O6+y, and the cyclotron mass diverges as the critical value is approached from the high doping side. We argue that the phenomenon is due to a Lifshitz transition where the pockets giving rise to the quantum oscillations connect to form an open (quasi-1d) Fermi surface. The estimated critical doping is close to that found by experiment, and the theory predicts a logarithmic divergence of the cyclotron mass with a coefficient comparable to that observed in experiment.Comment: 4 pages, 4 figure

Empirical Determinations of Key Physical Parameters Related to Classical Double Radio Sources

Multi-frequency radio observations of the radio bridge of powerful classical double radio sources can be used to determine: the beam power of the jets emanating from the AGN; the total time the source will actively produce jets that power large-scale radio emission; the thermal pressure of the medium in the vicinity of the radio source; and the total mass, including dark matter, of the galaxy or cluster of galaxies traced by the ambient gas that surrounds the radio source. The theoretical constructs that allow a determination of each of these quantities using radio observations are presented and discussed. Empirical determinations of each of these quantities are obtained and analyzed. A sample of 14 radio galaxies and 8 radio loud quasars with redshifts between zero and two for which there is enough radio information to be able to determine the physical parameters listed above was studied in detail. (abridged)Comment: Submitted to ApJ, LaTex, 26 total pages of text which includes captions & two tables, plus 13 EPS figures & 1 tabl