Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Entropic Origin of the Growth of Relaxation Times in Simple Glassy Liquids

Transitions between ``glassy'' local minima of a model free-energy functional for a dense hard-sphere system are studied numerically using a ``microcanonical'' Monte Carlo method that enables us to obtain the transition probability as a function of the free energy and the Monte Carlo ``time''. The growth of the height of the effective free energy barrier with density is found to be consistent with a Vogel-Fulcher law. The dependence of the transition probability on time indicates that this growth is primarily due to entropic effects arising from the difficulty of finding low-free-energy saddle points connecting glassy minima.Comment: Four pages, plus three postscript figure

Continuous Melting of a "Partially Pinned" Two-Dimensional Vortex Lattice in a Square Array of Pinning Centers

The structure and equilibrium properties of a two-dimensional system of superconducting vortices in a periodic pinning potential with square symmetry are studied numerically. For a range of the strength of the pinning potential, the low-temperature crystalline state exhibits only one of the two basic periodicities (in the $x$- and $y$-directions) of the pinning potential. This ``partially pinned'' solid undergoes a continuous melting transition to a weakly modulated liquid as the temperature is increased. A spin model, constructed using symmetry arguments, is shown to reproduce the critical behavior at this transition.Comment: 5 pages, 4 figure

Structure and Magnetization of Two-Dimensional Vortex Arrays in the Presence of Periodic Pinning

Ground-state properties of a two-dimensional system of superconducting vortices in the presence of a periodic array of strong pinning centers are studied analytically and numerically. The ground states of the vortex system at different filling ratios are found using a simple geometric argument under the assumption that the penetration depth is much smaller than the spacing of the pin lattice. The results of this calculation are confirmed by numerical studies in which simulated annealing is used to locate the ground states of the vortex system. The zero-temperature equilibrium magnetization as a function of the applied field is obtained by numerically calculating the energy of the ground state for a large number of closely spaced filling ratios. The results show interesting commensurability effects such as plateaus in the B-H diagram at simple fractional filling ratios.Comment: 12 pages, 19 figures, submitted for publicatio

Phase Diagram Of A Hard-sphere System In A Quenched Random Potential: A Numerical Study

We report numerical results for the phase diagram in the density-disorder plane of a hard sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.Comment: 14 pages, 10 postscript figures (included), submitted to Phys. Rev.

Free Energy Landscape Of Simple Liquids Near The Glass Transition

Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local minima of the free energy are located and the distribution of an appropriately defined ``overlap'' between minima is calculated. The process of transition from the basin of attraction of a minimum to that of another one is studied using a new ``microcanonical'' Monte Carlo procedure, leading to a determination of the effective height of free energy barriers that separate different glassy minima. The general appearance of the free energy landscape resembles that of a putting green: deep minima separated by a fairly flat structure. The growth of the effective free-energy barriers with increasing density is consistent with the Vogel-Fulcher law, and this growth is primarily driven by an entropic mechanism.Comment: 10 pages, 6 postscript figures, uses iopart.cls and iopart10.clo (included). Invited talk at the ICTP Trieste Conference on "Unifying Concepts in Glass Physics", September 1999. To be published in J. Phys. Cond. Ma

Time Scales for transitions between free energy minima of a hard sphere system

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E, March 1996 or s

Impact of varying degrees of renal dysfunction on transcatheter and surgical aortic valve replacement

BackgroundRenal impairment portends adverse outcomes in patients undergoing valvular heart surgery. The relationship between renal dysfunction in patients undergoing transcatheter aortic valve replacement (TAVR) is incompletely understood.MethodsA retrospective review of 1336 patients undergoing surgical aortic valve replacement (SAVR; 2002-2012) and 321 patients undergoing TAVR (2007-2012) was performed. Patients were divided into 3 glomerular filtration rate (GFR) groups: GFR greater than 60 mL/min, GFR 31 to 60 mL/min, and GFR 30 mL/min or less. Logistic and linear regression analysis was performed to estimate the TAVR effect on outcomes. Risk adjustments were made using the Society for Thoracic Surgeons (STS) predicted risk of mortality (PROM).ResultsTAVR patients were older (82 vs 65 years; P < .001), had a poorer ejection fraction (48% vs 53%; P < .001), were more likely female (45% vs 41%; P = .23), and had a higher STS PROM (11.9% vs 4.6%; P < .001). In-hospital mortality rates for TAVR and SAVR were 3.5% and 4.1%, respectively (P = .60), a result that marginally favors TAVR after risk adjustment (adjusted odds ratio = .52, P = .06). In SAVR patients, worsening preoperative renal failure was associated with increased in-hospital mortality (P = .004) and hospital (P < .001) and intensive care unit (ICU) (P < .001) lengths of stay. In contrast, worsening renal function did not influence in-hospital mortality (P = .78) and hospital (P < .23) and ICU (P = .88) lengths of stay in TAVR patients.ConclusionsWorsening renal function was associated with increased in-hospital mortality, hospital length of stay, and ICU length of stay in SAVR patients, but not in TAVR patients. This unexpected finding may have important clinical implications in patients with aortic stenosis and preoperative renal dysfunction