Characterizing Planetary Orbits and the Trajectories of Light

Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can be associated with different characteristics of the orbits. The boundaries for these regions are clearly defined. Observational data can be directly associated with points in the regions. A possible extension of these considerations with an additional parameter for the case of Kerr geometry is briefly discussed.Comment: 49 pages total with 11 tables and 10 figure

Comparing placentas from normal and abnormal pregnancies

This report describes work carried out at a Mathematics-in-Medicine Study Group. It is believed that placenta shape villous network characteristics are strongly linked to the placenta’s efficiency, and hence to pregnancy outcome. We were asked to consider mathematical ways to describe the shape and other characteristics of a placenta, as well as forming mathematical models for placenta development. In this report we propose a number of possible measure of placental shape, form, and efficiency, which can be computed from images already obtained. We also consider various models for the early development of placentas and the growth of the villous tree

Frontiers of Biogeography:Taking its place as a journal of choice for the publication of high quality biogeographical research articles

Through this editorial we seek your support and engagement as authors, readers and reviewers as we take the next steps in developing Frontiers of Biogeography as a leading international journal of biogeography and related subdisciplines. Here we make the case for submitting your next contribution to this journal: affordable, gold libre, open access, with the support of a disciplinarily-informed editorial and review team, which returns benefits to the biogeography community.Peer Reviewe

Statistical mechanics of an ideal Bose gas in a confined geometry

We study the behaviour of an ideal non-relativistic Bose gas in a three-dimensional space where one of the dimensions is compactified to form a circle. In this case there is no phase transition like that for the case of an infinite volume, nevertheless Bose-Einstein condensation signified by a sudden buildup of particles in the ground state can occur. We use the grand canonical ensemble to study this problem. In particular, the specific heat is evaluated numerically, as well as analytically in certain limits. We show analytically how the familiar result for the specific heat is recovered as we let the size of the circle become large so that the infinite volume limit is approached. We also examine in detail the behaviour of the chemical potential and establish the precise manner in which it approaches zero as the volume becomes large.Comment: 13 pages, 2 eps figures, revtex

Curvature-Induced Defect Unbinding in Toroidal Geometries

Toroidal templates such as vesicles with hexatic bond orientational order are discussed. The total energy including disclination charges is explicitly computed for hexatic order embedded in a toroidal geometry. Related results apply for tilt or nematic order on the torus in the one Frank constant approximation. Although there is no topological necessity for defects in the ground state, we find that excess disclination defects are nevertheless energetically favored for fat torii or moderate vesicle sizes. Some experimental consequences are discussed.Comment: 12 pages, 15 eps figure

New supersymmetric partners for the associated Lame potentials

We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The formalism of supersymmetric quantum mechanics is used to generate new exactly solvable potentials.Comment: 8 pages, 2 figures, submitted on 24 November 2004 to Phys. Lett.

Statistics of excitons in quantum dots and the resulting microcavity emission spectra

A theoretical investigation is presented of the statistics of excitons in quantum dots (QDs) of different sizes. A formalism is developed to build the exciton creation operator in a dot from the single exciton wavefunction and it is shown how this operator evolves from purely fermionic, in case of a small QD, to purely bosonic, in case of large QDs. Nonlinear optical emission spectra of semiconductor microcavities containing single QDs are found to exhibit a peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet in fermionic and bosonic limits, respectively.Comment: Extensively expanded revision, 14 pages, 12 figures, submitted to Phys. Rev.

The interaction of transmission intensity, mortality, and the economy: a retrospective analysis of the COVID-19 pandemic

The COVID-19 pandemic has caused over 6.4 million registered deaths to date, and has had a profound impact on economic activity. Here, we study the interaction of transmission, mortality, and the economy during the SARS-CoV-2 pandemic from January 2020 to December 2022 across 25 European countries. We adopt a Bayesian vector autoregressive model with both fixed and random effects. We find that increases in disease transmission intensity decreases Gross domestic product (GDP) and increases daily excess deaths, with a longer lasting impact on excess deaths in comparison to GDP, which recovers more rapidly. Broadly, our results reinforce the intuitive phenomenon that significant economic activity arises from diverse person-to-person interactions. We report on the effectiveness of non-pharmaceutical interventions (NPIs) on transmission intensity, excess deaths and changes in GDP, and resulting implications for policy makers. Our results highlight a complex cost-benefit trade off from individual NPIs. For example, banning international travel increases GDP however reduces excess deaths. We consider country random effects and their associations with excess changes in GDP and excess deaths. For example, more developed countries in Europe typically had more cautious approaches to the COVID-19 pandemic, prioritising healthcare and excess deaths over economic performance. Long term economic impairments are not fully captured by our model, as well as long term disease effects (Long Covid). Our results highlight that the impact of disease on a country is complex and multifaceted, and simple heuristic conclusions to extract the best outcome from the economy and disease burden are challenging