Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points"

Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy predictions for the decayed, late-time state. Both formulations define an entropy through a somewhat ad hoc discretization of vorticity to the "particles" of which statistical mechanical methods are employed to define an entropy, before passing to a mean-field limit. In one case, the particles are delta-function parallel "line" vortices ("points" in two dimensions), and in the other, they are finite-area, mutually-exclusive convected "patches" of vorticity which in the limit of zero area become "points." We use time-dependent, spectral-method direct numerical simulation of the Navier-Stokes equations to see if initial conditions which should relax to different late-time states under the two formulations actually do so.Comment: 21 pages, 24 figures: submitted to "Physics of Fluids

Symmetry Reduction of Optimal Control Systems and Principal Connections

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to obtain explicit expressions of the reduced system by exploiting the geometry. In particular, we show how to obtain a principal connection to be used in the reduction for various choices of symmetry groups, as opposed to assuming such a principal connection is given or choosing a particular symmetry group to simplify the setting. Our result synthesizes some previous works on symmetry reduction of nonlinear control and optimal control systems. Affine and kinematic optimal control systems are of particular interest: We explicitly work out the details for such systems and also show a few examples of symmetry reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure

Apparent suppression of turbulent magnetic dynamo action by a dc magnetic field

Numerical studies of the effect of a dc magnetic field on dynamo action (development of magnetic fields with large spatial scales), due to helically-driven magnetohydrodynamic turbulence, are reported. The apparent effect of the dc magnetic field is to suppress the dynamo action, above a relatively low threshold. However, the possibility that the suppression results from an improper combination of rectangular triply spatially-periodic boundary conditions and a uniform dc magnetic field is addressed: heretofore a common and convenient computational convention in turbulence investigations. Physical reasons for the observed suppression are suggested. Other geometries and boundary conditions are offered for which the dynamo action is expected not to be suppressed by the presence of a dc magnetic field component.Comment: To appear in Physics of Plasma

Anisotropy in MHD turbulence due to a mean magnetic field

The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers

The Centennial Celebration of the Town of Penobscot, Hancock County, Maine, 1887

A transcript of an address delivered by J. H. Montgomery for the Centennial Celebration of the town of Penobscot, Maine, in 1887

All-cause mortality following a cancer diagnosis amongst multiple sclerosis patients: A Swedish population-based cohort study

Background and purpose: A reduced cancer risk amongst patients with multiple sclerosis (MS) has been reported. Theoretically, this could represent a genuine reduction in risk or, alternatively, 'diagnostic neglect', where cancer is undiagnosed when symptoms are misattributed to MS. Objective: Assess all-cause mortality risk following a cancer diagnosis in patients with MS compared with a cohort without MS. Patients: A cohort of MS patients (n = 19 364) and a cohort of the general population (n = 192 519) were extracted from national Swedish registers from 1969 to 2005. All-cause mortality after cancer in MS was compared with the general population. Poisson regression analysis was conducted in the MS and non-MS cohorts separately. The models were adjusted for follow-up duration, year at entry, sex, region and socioeconomic index. The two cohorts were combined and differences in mortality risk were assessed using interaction testing. Results: The adjusted relative risk (and 95 confidence interval) for all-cause mortality following a cancer diagnosis in MS patients (compared with MS patients without cancer) is 3.06 (2.86-3.27; n = 1768) and amongst those without MS 5.73 (5.62-5.85; n = 24 965). This lower magnitude mortality risk in the MS patients was confirmed by multiplicative interaction testing (P < 0.001). Conclusions: A consistent pattern of lower magnitude of all-cause mortality risk following cancer in MS patients for a range of organ-specific cancer types was found. It suggests that cancer diagnoses tend not to be delayed in MS and diagnostic neglect is unlikely to account for the reduced cancer risk associated with MS. The lower magnitude cancer risk in MS may be due to disease-associated characteristics or exposures. © 2015 EAN