The method of Glowinski and Pironneaufor the unsteady stokes problem

AbstractThe unsteady Stokes problem, i.e., the Stokes problem with a constant multiple of the velocity included in the velocity-pressure equation, is often central to methods used to solve the nonstationary Navier-Stokes equations and the equations governing viscoelastic flows. The Glowinski-Pironneau finite-element method for the Stokes problem decomposes the problem into a series of Poisson's equations, providing a potentially efficient approach for large problems in two or three dimensions. The goal of this paper is to present a complete development and analysis of the Glowinski-Pironneau method for the unsteady Stokes problem, along with numerical results which confirm the analytical estimates

Geodesics of Random Riemannian Metrics

We analyze the disordered Riemannian geometry resulting from random perturbations of the Euclidean metric. We focus on geodesics, the paths traced out by a particle traveling in this quenched random environment. By taking the point of the view of the particle, we show that the law of its observed environment is absolutely continuous with respect to the law of the random metric, and we provide an explicit form for its Radon-Nikodym derivative. We use this result to prove a "local Markov property" along an unbounded geodesic, demonstrating that it eventually encounters any type of geometric phenomenon. We also develop in this paper some general results on conditional Gaussian measures. Our Main Theorem states that a geodesic chosen with random initial conditions (chosen independently of the metric) is almost surely not minimizing. To demonstrate this, we show that a minimizing geodesic is guaranteed to eventually pass over a certain "bump surface," which locally has constant positive curvature. By using Jacobi fields, we show that this is sufficient to destabilize the minimizing property.Comment: 55 pages. Supplementary material at arXiv:1206.494

Fulminant immune-mediated necrotising myopathy (IMNM) mimicking myocardial infarction with non-obstructive coronary arteries (MINOCA)

A 74-year-old man, with inflammatory arthritis, recently commenced on adalimumab, presented with a 4-week history of left-sided chest pain, malaise and shortness of breath. Admission ECG showed age-indeterminate left bundle branch block. Troponin T was 4444 ng/L (normal range <15 ng/L) and acute coronary syndrome treatment was commenced. Catheter angiogram revealed mild-burden non-obstructive coronary disease. Cardiac magnetic resonance (CMR) was performed to refine the differential diagnosis and demonstrated no myocardial oedema or late gadolinium enhancement. Extracardiac review highlighted oedema and enhancement of the left shoulder girdle muscles consistent with acute myositis. Creatine kinase was subsequently measured and significantly elevated at 7386 IU/L (normal range 30–200 IU/L in men). Electrophoresis clarified that this was of predominantly skeletal muscle origin. Myositis protocol MRI revealed florid skeletal muscle oedema. The MR findings, together with positive anti-Scl-70 antibodies, suggested fulminant immune-mediated necrotising myopathy presenting as a rare mimic of myocardial infarction with non-obstructive coronary arteries, diagnosed by careful extracardiac CMR review

Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

Peculiarities of sub-barrier fusion with quantum diffusion approach

With the quantum diffusion approach the unexpected behavior of fusion cross section, angular momentum, and astrophysical S-factor at sub-barrier energies has been revealed. Out of the region of short-range nuclear interaction and action of friction at turning point the decrease rate of the cross section under the barrier becomes smaller. The calculated results for the reactions with spherical nuclei are in a good agreement with the existing experimental data.Comment: 11 pages, 5 figure

Childhood IQ and cardiovascular disease in adulthood: prospective observational study linking the Scottish Mental Survey 1932 and the Midspan studies

This study investigated the influence of childhood IQ on the relationships between risk factors and cardiovascular disease (CVD), coronary heart disease (CHD) and stroke in adulthood. Participants were from the Midspan prospective cohort studies which were conducted on adults in Scotland in the 1970s. Data on risk factors were collected from a questionnaire and at a screening examination, and participants were followed up for 25 years for hospital admissions and mortality. 938 Midspan participants were successfully matched with their age 11 IQ from the Scottish Mental Survey 1932, in which 1921-born children attending schools in Scotland took a cognitive ability test. Childhood IQ was negatively correlated with diastolic and systolic blood pressure, and positively correlated with height and respiratory function in adulthood. For each of CVD, CHD and stroke, defined as either a hospital admission or death, there was an increased relative rate per standard deviation decrease (15 points) in childhood IQ of 1.11 (95% confidence interval 1.01-1.23), 1.16 (1.03-1.32) and 1.10 (0.88-1.36) respectively. With events divided into those first occurring before and those first occurring after the age of 65, the relationships between childhood IQ and CVD, CHD and stroke were only seen before age 65 and not after age 65. Blood pressure, height, respiratory function and smoking were associated with CVD events. Relationships were stronger in the early compared to the later period for smoking and FEV1, and stronger in the later compared to the earlier period for blood pressure. Adjustment for childhood IQ had small attenuating effects on the risk factor-CVD relationship before age 65 and no effects after age 65. Adjustment for risk factors attenuated the childhood IQ-CVD relationship by a small amount before age 65. Childhood IQ was associated with CVD risk factors and events and can be considered an important new risk factor

Anderson-Yuval approach to the multichannel Kondo problem

We analyze the structure of the perturbation expansion of the general multichannel Kondo model with channel anisotropic exchange couplings and in the presence of an external magnetic field, generalizing to this case the Anderson-Yuval technique. For two channels, we are able to map the Kondo model onto a generalized resonant level model. Limiting cases in which the equivalent resonant level model is solvable are identified. The solution correctly captures the properties of the two channel Kondo model, and also allows an analytic description of the cross-over from the non Fermi liquid to the Fermi liquid behavior caused by the channel anisotropy.Comment: 23 pages, ReVTeX, 4 figures av. on reques

Multi-Channel Kondo Necklace

A multi--channel generalization of Doniach's Kondo necklace model is formulated, and its phase diagram studied in the mean--field approximation. Our intention is to introduce the possible simplest model which displays some of the features expected from the overscreened Kondo lattice. The $N$ conduction electron channels are represented by $N$ sets of pseudospins \vt_{j}, $j=1, ... , N$, which are all antiferromagnetically coupled to a periodic array of |\vs|=1/2 spins. Exploiting permutation symmetry in the channel index $j$ allows us to write down the self--consistency equation for general $N$. For $N>2$, we find that the critical temperature is rising with increasing Kondo interaction; we interpret this effect by pointing out that the Kondo coupling creates the composite pseudospin objects which undergo an ordering transition. The relevance of our findings to the underlying fermionic multi--channel problem is discussed.Comment: 29 pages (2 figures upon request from [email protected]), LATEX, submitted for publicatio

Anomalous heavy-fermion and ordered states in the filled skutterudite PrFe4P12

Specific heat and magnetization measurements have been performed on high-quality single crystals of filled-skutterudite PrFe_4P_{12} in order to study the high-field heavy-fermion state (HFS) and low-field ordered state (ODS). From a broad hump observed in C/T vs T in HFS for magnetic fields applied along the direction, the Kondo temperature of ~ 9 K and the existence of ferromagnetic Pr-Pr interactions are deduced. The {141}-Pr nuclear Schottky contribution, which works as a highly-sensitive on-site probe for the Pr magnetic moment, sets an upper bound for the ordered moment as ~ 0.03 \mu_B/Pr-ion. This fact strongly indicates that the primary order parameter in the ODS is nonmagnetic and most probably of quadrupolar origin, combined with other experimental facts. Significantly suppressed heavy-fermion behavior in the ODS suggests a possibility that the quadrupolar degrees of freedom is essential for the heavy quasiparticle band formation in the HFS. Possible crystalline-electric-field level schemes estimated from the anisotropy in the magnetization are consistent with this conjecture.Comment: 7 pages and 7 figures. Accepted for publication in Phys. Rev.