Sum Uncertainty Relation in Quantum Theory

We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the quantum mechanical uncertainty in any observable is a convex function. We prove that if we have a finite number $N$ of identically prepared quantum systems, then a joint measurement of any observable gives an error $\sqrt N$ less than that of the individual measurements. This has application in quantum metrology that aims to give better precision in the parameter estimation. Furthermore, this proves that a quantum system evolves slowly under the action of a sum Hamiltonian than the sum of individuals, even if they are non-commuting.Comment: LaTeX file, no figure, 4 page

Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh

Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equations and has been realized in the AREPO code both in 2D and 3D. We propose a new approach to compute accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a finite volume solver of the Navier-Stokes equations. Through a number of test problems, including circular Couette flow and flow past a cylindrical obstacle, we show that our new scheme combines good accuracy with geometric flexibility, and hence promises to be competitive with other highly refined Eulerian methods. This will in particular allow astrophysical applications of the AREPO code where physical viscosity is important, such as in the hot plasma in galaxy clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA

Interpolation of Linear Operators on Orlicz and BMO function spaces

This thesis is concerned with the study of interpolation theorems involving certain Orlicz spaces and spaces of functions of Bounded Mean Oscillation. In addition, we consider the Orlicz spaces in a weighted sense by applying weight functions satisfying certain growth conditions.Master of Science (MS

Ab initio study of the modification of elastic properties of alpha-iron by hydrostatic strain and by hydrogen interstitials

The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of $\alpha$-iron is investigated using \textit{ab initio} density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic elastic shear moduli. For the key slip planes in $\alpha$-iron, $[1\bar{1}0]$ and $[11\bar{2}]$, we find a shear modulus reduction of approximately 1.6% per at.% H.Comment: Updated first part of 1009.378

Heisenberg's Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum feature of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson-antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.Comment: 17 page

Evaluating Soil Surface Properties in Two Contrasting Tillage Systems

Soil properties are affected by tillage practices. Tillage practices that provides an adequate growing environment for crops and maintains good soil structure is crucial. The objective of this study was to compare selected soil properties collected from no-till (NT) and conventional tillage (CT) systems in Kentucky, Indiana, and Illinois. Three undisturbed and three disturbed soil samples were taken from the topsoil at the depth of 0 to 7.5 cm. The samples were analyzed for bulk density (BD), water holding capacity (WHC), field capacity (FC), soil pH, soil organic matter (SOM), and compaction. Bulk density, WHC, and FC of the soil was determined from the undisturbed soil samples. Disturbed soil samples were used to determine soil pH and SOM levels. In addition, a penetrometer was used to measure compaction levels in the soil. Statistical analysis was performed to test the significant effect of tillage practices on soil properties in questions. The soils had average bulk density of 1.24 g/cm3 in the no-till fields compared to 1.33 g/cm3 in conventionally tilled fields in both the Indiana and Kentucky sites, while no-till was 1.32 g/cm3 in Illinois. Conventional tillage fields had a higher average of 45.28% of soil water holding capacity compared to no-till which was 44.33%. Soil water holding capacity for no-till fields in Perry County (42.64%) and Henderson County (49.06%) were higher than the conventionally tilled fields at these sites. There was a significant difference between two tillage systems in SOM content at the Kentucky site which displayed 3.8% SOM in conventional till and 4.7% SOM for no-till. However, there was no significant effect of tillage systems on soil pH in Kentucky and Illinois. The average of soil pH of Indiana’s conventional tillage site was 8.8, while no-till was 6.6. Compaction results varied between the three sites: Kentucky had the highest compaction rating at 280 psi at no-till fields at 30 cm. However, the Kentucky site also had the lowest compaction at conventional tillage from 15 cm which was 136.6 psi. The Indiana site displayed a very small significant difference between either conventional or no-till tillage systems from 15 or 30 cm. For Illinois, both no-till depths had less compaction than either of the conventional tillage depths. Macroporosity showed no significant difference among the three sites. For the ratio macroporosity over microporosity, the Indiana and Illinois sites showed similar results (4.55%) and (4.27%), respectively, for conventional tillage. For no-till, Indiana and Illinois were (3.22%) and (3.26%), respectively. In general, the aeration for all fields are considered good for crops as indicated by macroporosity, bulk density and compaction level. These findings show that implementing no-till systems into the farming operations has improved soil quality indicators which eventually reduces soil erosion rate and thus maintains the crop production sustainability. The results of this study would help farmers justify whether implementing a no-till or conventional tillage practices can improve soil properties indicators to promote crop production and sustainability. Keywords: Bulk Density, Compaction, Macroporosity, Organic Matter, Water Holding Capacit

Supporting lifestyle risk reduction: promoting men’s health through professional football

For men, unhealthy lifestyle behaviours including physical inactivity, a poor diet, smoking and excess alcohol represent major, modifiable causes of non-communicable disease worldwide. Innovative approaches that seek to overcome the barriers that men experience when attempting to deploy more self-care to manage these behaviours are required. This study assessed the outcomes of a 12-week men’s health promotion intervention delivered in and by professional football clubs. Data comprised self-reports from 1667 men aged 18–75 years from 16 English Premier League and Championship football clubs. A multinomial logistic regression model estimated the probability of self-reporting a number of baseline lifestyle risk factors compared to a reference group with none. Wilcoxon signed-rank tests assessed differences in lifestyle risk profiles. Over 85% of participants presented with multiple risk factors. Men aged ≥35 years were least likely to present all four risk factors (OR: 0.45, 95% CI: 0.23–0.88), whereas unemployed men (OR: 3.64, 95% CI: 1.78–7.51) and those with no social support network (OR: 5.10, 95% CI: 2.44–10.50) were most likely to self-report all four lifestyle risks. The prevalence of risk factors was significantly reduced post-intervention (z = −7.488, p < 0.001, r = −0.13), indicating a positive effect, and potential public health significance. Findings show that men can respond positively to behaviourally-focused interventions delivered in familiar and local settings, like professional football clubs

The genomes of two key bumblebee species with primitive eusocial organization

Background: The shift from solitary to social behavior is one of the major evolutionary transitions. Primitively eusocial bumblebees are uniquely placed to illuminate the evolution of highly eusocial insect societies. Bumblebees are also invaluable natural and agricultural pollinators, and there is widespread concern over recent population declines in some species. High-quality genomic data will inform key aspects of bumblebee biology, including susceptibility to implicated population viability threats. Results: We report the high quality draft genome sequences of Bombus terrestris and Bombus impatiens, two ecologically dominant bumblebees and widely utilized study species. Comparing these new genomes to those of the highly eusocial honeybee Apis mellifera and other Hymenoptera, we identify deeply conserved similarities, as well as novelties key to the biology of these organisms. Some honeybee genome features thought to underpin advanced eusociality are also present in bumblebees, indicating an earlier evolution in the bee lineage. Xenobiotic detoxification and immune genes are similarly depauperate in bumblebees and honeybees, and multiple categories of genes linked to social organization, including development and behavior, show high conservation. Key differences identified include a bias in bumblebee chemoreception towards gustation from olfaction, and striking differences in microRNAs, potentially responsible for gene regulation underlying social and other traits. Conclusions: These two bumblebee genomes provide a foundation for post-genomic research on these key pollinators and insect societies. Overall, gene repertoires suggest that the route to advanced eusociality in bees was mediated by many small changes in many genes and processes, and not by notable expansion or depauperation