Singular Casimir Elements of the Euler Equation and Equilibrium Points

The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations describing ideal fluid and plasma dynamics, is addressed in the context of the Euler equation for an incompressible inviscid fluid. The problem is traced to a Casimir deficit, where Casimir elements constitute the center of the Lie-Poisson algebra underlying the Hamiltonian formulation, and this leads to a study of the symplectic operator defining the Poisson bracket. The kernel of the symplectic operator, for this typical example of an infinite-dimensional Hamiltonian system for media in terms of Eulerian variables, is analyzed. For two-dimensional flows, a rigorously solvable system is formulated. The nonlinearity of the Euler equation makes the symplectic operator inhomogeneous on phase space (the function space of the state variable), and it is seen that this creates a singularity where the nullity of the symplectic operator (the "dimension" of the center) changes. Singular Casimir elements stemming from this singularity are unearthed using a generalization of the functional derivative that occurs in the Poisson bracket

Solubility, Light Output and Energy Resolution Studies of Molybdenum-Loaded Liquid Scintillators

The search for neutrinoless double-beta decay is an important part of the global neutrino physics program. One double-beta decay isotope currently under investigation is 100Mo. In this article, we discuss the results of a feasibility study investigating the use of molybdenum-loaded liquid scintillator. A large, molybdenum-loaded liquid scintillator detector is one potential design for a low-background, internal-source neutrinoless double-beta decay search with 100Mo. The program outlined in this article included the selection of a solute containing molybdenum, a scintillating solvent and the evaluation of the mixture's performance as a radiation detector.Comment: 8 pages, 3 figure

Classification and Casimir Invariants of Lie-Poisson Brackets

We classify Lie-Poisson brackets that are formed from Lie algebra extensions. The problem is relevant because many physical systems owe their Hamiltonian structure to such brackets. A classification involves reducing all brackets to a set of normal forms, and is achieved partially through the use of Lie algebra cohomology. For extensions of order less than five, the number of normal forms is small and they involve no free parameters. We derive a general method of finding Casimir invariants of Lie-Poisson bracket extensions. The Casimir invariants of all low-order brackets are explicitly computed. We treat in detail a four field model of compressible reduced magnetohydrodynamics.Comment: 59 pages, Elsevier macros. To be published in Physica

The market of biopharmaceutical medicines: A snapshot of a diverse industrial landscape

Background: Biopharmaceutical medicines represent a growing share of the global pharmaceutical market, and with many of these biopharmaceutical products facing loss of exclusivity rights, also biosimilars may now enter the biopharmaceutical market. Objectives: This study aims to identify and document which investment and development strategies are adopted by industrial players in the global biopharmaceutical market. Methods: A descriptive analysis was undertaken of the investment and development strategies of the top 25 pharmaceutical companies according to 2015 worldwide prescription drug sales. Strategies were documented by collecting data on manufacturing plans, development programs, acquisition and collaboration agreements, the portfolio and pipeline of biosimilar, originator and next-generation biopharmaceutical products. Data were extracted from publicly available sources. Results: Various investment and development strategies can be identified in the global biopharmaceutical market: (a) development of originator biopharmaceuticals, (b) investment in biotechnology, (c) development of next-generation biopharmaceuticals, (d) development of biosimilars, (e) investment in emerging countries, and (f) collaboration between companies. In the top 25 pharmaceutical companies almost every company invests in originator biopharmaceuticals and in biotechnology in general, but only half of them develops next-generation biopharmaceuticals. Furthermore, only half of them invest in development of biosimilars. The companies' biosimilar pipeline is mainly focused on development of biosimilar monoclonal antibodies and to some extent on biosimilar insulins. A common strategy is collaboration between companies and investment in emerging countries. Conclusions: A snapshot of investment and development strategies used by industrial players in the global biopharmaceutical market shows that all top 25 pharmaceutical companies are engaged in the biopharmaceutical market and that this industrial landscape is diverse. Companies do not focus on a single strategy, but are involved in multiple investment and development strategies. A common strategy to market biopharmaceuticals is collaboration between companies. These collaborations can as well be used to gain access in regions the company has less experience with. With patents expiring for some of the highest selling monoclonal antibodies, this snapshot highlights the interest of companies to invest in the development of these molecules and/or enter into collaborations to create access to these molecules

Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.Comment: 8 pages, 3 figures, to appear in Phys. Lett.

A biomechanical analysis of prognathous and orthognathous insect head capsules: evidence for a many‐to‐one mapping of form to function

Insect head shapes are remarkably variable, but the influences of these changes on biomechanical performance are unclear. Among ‘basal’ winged insects, such as dragonflies, mayflies, earwigs and stoneflies, some of the most prominent anatomical changes are the general mouthpart orientation, eye size and the connection of the endoskeleton to the head. Here, we assess these variations as well as differing ridge and sclerite configurations using modern engineering methods including multibody dynamics modelling and finite element analysis in order to quantify and compare the influence of anatomical changes on strain in particular head regions and the whole head. We show that a range of peculiar structures such as the genal/subgenal, epistomal and circumocular areas are consistently highly loaded in all species, despite drastically differing morphologies in species with forward‐projecting (prognathous) and downward‐projecting (orthognathous) mouthparts. Sensitivity analyses show that the presence of eyes has a negligible influence on head capsule strain if a circumocular ridge is present. In contrast, the connection of the dorsal endoskeletal arms to the head capsule especially affects overall head loading in species with downward‐projecting mouthparts. Analysis of the relative strains between species for each head region reveals that concerted changes in head substructures such as the subgenal area, the endoskeleton and the epistomal area lead to a consistent relative loading for the whole head capsule and vulnerable structures such as the eyes. It appears that biting‐chewing loads are managed by a system of strengthening ridges on the head capsule irrespective of the general mouthpart and head orientation. Concerted changes in ridge and endoskeleton configuration might allow for more radical anatomical changes such as the general mouthpart orientation, which could be an explanation for the variability of this trait among insects. In an evolutionary context, many‐to‐one mapping of strain patterns onto a relatively similar overall head loading indeed could have fostered the dynamic diversification processes seen in insects

Radiation dose reduction in pediatric great vessel stent computed tomography using iterative reconstruction: A phantom study

Background To study dose reduction using iterative reconstruction (IR) for pediatric great vessel stent computed tomography (CT). Methods Five different great vessel stents were separately placed in a gel-containing plastic holder within an anthropomorphic chest phantom. The stent lumen was filled with diluted contrast gel. CT acquisitions were performed at routine dose, 52% and 81% reduced dose and reconstructed with filtered back projection (FBP) and IR. Objective image quality in terms of noise, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) as well as subjective image quality were evaluated. Results Noise, SNR and CNR were improved with IR at routine and 52% reduced dose, compared to FBP at routine dose. The lowest dose level resulted in decreased objective image quality with both FBP and IR. Subjective image quality was excellent at all dose levels. Conclusion IR resulted in improved objective image quality at routine dose and 52% reduced dose, while objective image quality deteriorated at 81% reduced dose. Subjective image quality was not affected by dose reduction

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Considerations in relation to off-site emergency procedures and response for nuclear accidents

The operation of nuclear facilities has, fortunately, not led to many accidents with off-site consequences. However, it is well-recognised that should a large release of radioactivity occur, the effects in the surrounding area and population will be significant. These effects can be mitigated by developing emergency preparedness and response plans prior to the operation of the nuclear facility that can be exercised regularly and implemented if an accident occurs. This review paper details the various stages of a nuclear accident and the corresponding aspects of an emergency preparedness plan that are relevant to these stages, both from a UK and international perspective. The paper also details how certain aspects of emergency preparedness have been affected by the accident at Fukushima Dai-ichi and as a point of comparison how emergency management plans were implemented following the accidents at Three Mile Island 2 and Chernobyl. In addition, the UK’s economic costing model for nuclear accidents COCO-2, and the UK’s Level-3 Probabilistic Safety Assessment code “PACE” are introduced. Finally, the factors that affect the economic impact of a nuclear accident, especially from a UK standpoint, are described

Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure