The Maintenance of Conservative Physical Laws Within Data Assimilation Systems

In many data assimilation applications, adding an error to represent forcing to certain dynamical equations may be physically unrealistic. Four-dimensional variational methods assume either an error in the dynamical equations of motion (weak constraint) or no error (strong constraint). The weak-constraint methodology proposes the errors to represent uncertainties in either forcing of the dynamical equations or parameterizations of dynamics. Dynamical equations that represent conservation of quantities (mass, entropy, momentum, etc.) may be cast in an analytical or control volume flux form containing minimal errors. The largest errors arise in determining the fluxes through control volume surfaces. Application of forcing errors to conservation formulas produces non-physical results (generation or destruction of mass or other properties), whereas application of corrections to the fluxes that contribute to the conservation formulas maintains the physically realistic conservation property while providing an ability to account for uncertainties in flux parameterizations. The results suggest that advanced assimilation systems must not be liberal in applying errors to conservative equations. Rather systems must carefully consider the points at which the errors exist and account for them correctly. Though careful accounting of error sources is certainly not an entirely new idea, this paper provides a focused examination of the problem and examines one possible solution within the 4D variational framework

A vortex description of the first-order phase transition in type-I superconductors

Using both analytical arguments and detailed numerical evidence we show that the first order transition in the type-I 2D Abelian Higgs model can be understood in terms of the statistical mechanics of vortices, which behave in this regime as an ensemble of attractive particles. The well-known instabilities of such ensembles are shown to be connected to the process of phase nucleation. By characterizing the equation of state for the vortex ensemble we show that the temperature for the onset of a clustering instability is in qualitative agreement with the critical temperature. Below this point the vortex ensemble collapses to a single cluster, which is a non-extensive phase, and disappears in the absence of net topological charge. The vortex description provides a detailed mechanism for the first order transition, which applies at arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic considerations, which rely on asymptotically large gauge coupling.Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some small corrections to the tex

Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field

Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral striped texture. Here, we investigate whether similar chiral modulations can occur in the induced molecular tilt of the smectic-A phase under an applied electric field. Using both continuum elastic theory and lattice simulations, we find that the state of uniform induced tilt can become unstable when the system approaches the smectic-A--smectic-C* transition, or when a high electric field is applied. Beyond that instability point, the system develops chiral stripes in the tilt, which induce corresponding ripples in the smectic layers. The modulation persists up to an upper critical electric field and then disappears. Furthermore, even in the uniform state, the system shows chiral fluctuations, including both incipient chiral stripes and localized chiral vortices. We compare these predictions with observed chiral modulations and fluctuations in smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and epsf.st

Alendroninezuur effectiever dan alfacalcidol voor preventie van osteoporose bij patiënten met een reumatische ziekte die starten met glucocorticoïdtherapie

OBJECTIVE: To compare the effects of alendronate and alfacalcidol in the prevention ofglucocorticoid-related osteoporosis in patients with a rheumatic disease. DESIGN: Randomised, double-blind, double-placebo clinical trial (www. clinicaltrials.gov; number: NCT00138983). METHODS: A total of 201 patients with rheumatic disease who were starting glucocorticoid treatment at a daily dose that was equivalent to at least 7.5 mg of prednisone were randomised to alendronate (10 mg) and a placebo capsule ofalfacalcidol daily (n = 100) or alfacalcidol (1 microg) and a placebo tablet ofalendronate daily (n = 101) for 18 months. Primary outcome was change in lumbar spine bone mineral density at 18 months. The main secondary outcome was the incidence of morphometrically confirmed vertebral deformities. RESULTS: Overall, 163 patients completed the study. The bone mineral density of the lumbar spine increased by 2.1% (95% CI: 1.1-3.1) in the alendronate group and decreased by 1.9% (95% CI: -3.I--0.7) in the alfacalcidol group. At 18 months the mean difference in change in bone mineral density between the two groups was 4.0% (95% CI: 2.4-5-5). Three patients in the alendronate group had a new vertebral deformity, compared with 8 patients in the alfacalcidol group, including 5 symptomatic vertebral fractures in 3 patients; the hazard ratio was 0.4 (95% CI: 0.1-1.4). CONCLUSION: Alendronate was more effective than alfacalcidol in preventing glucocorticoid-induced bone loss during this 18-month trial in patients with rheumatic diseases who were starting glucocorticoid treatment

Presenting symptoms and functional outcome of chronic subdural hematoma patients

Background Patients with chronic subdural hematoma (CSDH) can present with a variety of signs and symptoms. The relationship of these signs and symptoms with functional outcome is unknown. Knowledge of these associations might aid clinicians in the choice to initiate treatment and may allow them to better inform patients on expected outcomes. Objective To investigate if presenting signs and symptoms influence functional outcome in patients with CSDH. Methods We conducted a retrospective analysis of consecutive CSDH patients in three hospitals. Glasgow Outcome Scale Extended (GOS-E) scores were obtained from the first follow-up visit after treatment. An ordinal multivariable regression analysis was performed, to assess the relationship between the different signs and symptoms on the one hand and functional outcome on the other adjusted for potential confounders. Results We included 1,307 patients, of whom 958 (73%) were male and mean age was 74 (SD +/- 11) years. Cognitive complaints were associated with lower GOS-E scores at follow-up (aOR 0.7, 95% CI: 0.5 - 0.8) Headache and higher Glasgow Coma Scale (GCS) scores were associated with higher GOS-E scores. (aOR 1.9, 95% CI: 1.5-2.3 and aOR 1.3, 95% CI: 1.2-1.4). Conclusion Cognitive complaints are independently associated with worse functional outcome, whereas headache and higher GCS scores are associated with better outcome. The increased probability of unfavorable outcome in patients with CSDH who present with cognitive complaints favors a more prominent place of assessing cognitive status at diagnosis.Scientific Assessment and Innovation in Neurosurgical Treatment Strategie