On the existence of infinitely many closed geodesics on orbifolds of revolution

Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S^2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with cone manifold structures.Comment: 21 pages, 4 figures; for a PDF version see http://www.calpoly.edu/~jborzell/Publications/publications.htm

A Lagrangian kinetic model for collisionless magnetic reconnection

A new fully kinetic system is proposed for modeling collisionless magnetic reconnection. The formulation relies on fundamental principles in Lagrangian dynamics, in which the inertia of the electron mean flow is neglected in the expression of the Lagrangian, rather then enforcing a zero electron mass in the equations of motion. This is done upon splitting the electron velocity into its mean and fluctuating parts, so that the latter naturally produce the corresponding pressure tensor. The model exhibits a new Coriolis force term, which emerges from a change of frame in the electron dynamics. Then, if the electron heat flux is neglected, the strong electron magnetization limit yields a hybrid model, in which the electron pressure tensor is frozen into the electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio

The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur

Shadow Pricing and Macroeconomic Analysis: Some Illustrations from Pakistan

Shadow prices are being used increasingly in the economic analysis of projects. The purpose of this paper, however, is to argue that shadow prices are equally relevant for certain types of analysis at the macro-economic level. In theory, macroeconomic issues can be properly analyzed, if at all, only in general equilibrium frame• work. Quantification then requires the solution of an appropriate model. But, estimable general equilibrium models can seldom include many variables, and the level of aggregation must remain high. They are general only in the very partial sense of simultaneous solution of a limited set of aggregated endogenous variables. On the other hand, some of the issues addressed by shadow pricing involve quite disaggregated variables, and, of course, project analysis itself often requires very detailed estimations

A simple interpretation of quantum mirages

In an interesting new experiment the electronic structure of a magnetic atom adsorbed on the surface of Cu(111), observed by STM, was projected into a remote location on the same surface. The purpose of the present paper is to interpret this experiment with a model Hamiltonian, using ellipses of the size of the experimental ones, containing about 2300 atoms. The charge distribution for the different wavefunctions is analyzed, in particular, for those with energy close to the Fermi energy of copper Ef. Some of them show two symmetric maxima located on the principal axis of the ellipse but not necessarily at the foci. If a Co atom is adsorbed at the site where the wavefunction with energy $E_F$ has a maximum and the interaction is small, the main effect of the adsorbed atom will be to split this particular wavefunction in two. The total charge density will remain the same but the local density of states will present a dip at Ef at any site where the charge density is large enough. We relate the presence of this dip to the observation of quantum mirages. Our interpretation suggests that other sites, apart from the foci of the ellipses, can be used for projecting atomic images and also indicates the conditions for other non magnetic adsorbates to produce mirages.Comment: 3 pages, 3 Fig

Narrating resistant citizenships through two pandemics

Covid has intensified inequalities in the UK, particularly for those already living with structural disadvantage, and despite community and popular resistance to those losses. Covid has also disproportionately affected people with HIV, especially those already living with multi-dimensional inequalities. However, many people with HIV have, as they have done before, made strong and often successful efforts to resist and to restore or reconstruct their citizenships, in opposition to dominant, dispossessing discourses during Covid times. A narrative approach offers a means of mapping these citizenly technologies. This article draws on a 2020 study conducted with 16 people living with HIV in the UK. The study explored, through telephone semi-structured interviews, the health, economic, and psychosocial resources with which these participants lived with HIV and how Covid has impacted those resources. Narrative analysis showed losses of HIV and other health resources, constituting reductions in health citizenship, resisted largely by reconstitutions of alternatives within the HIV sector; losses of economic citizenship, despite oppositional, anti-political attempts to retain it, and of psychosocial citizenship, in spite of family and friendship networks; resistant, ‘alter’ development of renewed HIV citizenships; and across fields, resistance by complaint. This study indicates that ‘de-citizening’ citizenship losses are likely to also affect other groups with long-term conditions, illnesses, and disabilities. Resistant ‘re-citizening’ technologies, while important, had limited effects. The study suggests potential future resistant effects of repeated ‘complaint’ about Covid-era citizenship losses, and the more general significance of histories of dissent for future effective resistance

Electoral Reforms, Membership Stability and the Existence of Committee Property Rights in American State Legislatures

One of the most creative theories advanced about legislative organization in recent years is Katz and Sala\u27s linkage of the development of committee property rights in the US House of Representatives to the introduction of the Australian ballot. Katz and Sala argue that the Australian ballot – a government-printed ballot cast in secret that replaced a party-produced ballot that was cast in public – gave members of the House an incentive to pursue personal constituency votes. This, in turn, led to the rise of committee property rights as members sought to keep their committee assignments from term to term because of the potential electoral benefits they derived from them. In this Note we use the state legislative committee membership dataset collected by Hamm and Hedlund and their colleagues to test whether committee property rights appeared in American state legislatures at roughly the same time as Katz and Sala find they emerged in the US House. State legislatures were, of course, exposed to the same electoral innovation at the same time. But, while in some ways state legislatures were much like Congress as organizations, in other ways they were very different. Our cross-sectional data and the variance in important institutional variables they provide allow us to test a critical proposition about the importance of membership stability rates in mediating the rise of committee property rights. We also go beyond Katz and Sala\u27s analysis by testing to see if differences in Australian ballot design (office column and party bloc) across the states influenced the behaviour of legislators in the way their theory suggests

Reflection-driven turbulence in the super-Alfv\'enic solar wind

In magnetized, stratified astrophysical environments such as the Sun's corona and solar wind, Alfv\'enic fluctuations ''reflect'' from background gradients, enabling nonlinear interactions and thus dissipation of their energy into heat. This process, termed ''reflection-driven turbulence,'' is thought to play a crucial role in coronal heating and solar-wind acceleration, explaining a range of observational correlations and constraints. Building on previous works focused on the inner heliosphere, here we study the basic physics of reflection-driven turbulence using reduced magnetohydrodynamics in an expanding box -- the simplest model that can capture the local turbulent plasma dynamics in the super-Alfv\'enic solar wind. Although idealized, our high-resolution simulations and simple theory reveal a rich phenomenology that is consistent with a diverse range of observations. Outwards-propagating fluctuations, which initially have high imbalance, decay nonlinearly to heat the plasma, becoming more balanced and magnetically dominated. Despite the high imbalance, the turbulence is strong because Els\"asser collisions are suppressed by reflection, leading to ''anomalous coherence'' between the two Els\"asser fields. This coherence, together with linear effects, causes the turbulence to anomalously grow the ''anastrophy'' (squared magnetic potential) as it decays, forcing the energy to rush to larger scales and forming a ''$1/f$-range'' energy spectrum as it does so. At late times, the expansion overcomes the nonlinear and Alfv\'enic physics, forming isolated, magnetically dominated ''Alfv\'en vortex'' structures that minimize their nonlinear dissipation. These results can plausibly explain the observed radial and wind-speed dependence of turbulence imbalance, residual energy, plasma heating, and fluctuation spectra, as well as making testable predictions for future observations

Evolution of large-amplitude Alfv\'en waves and generation of switchbacks in the expanding solar wind

Motivated by recent Parker Solar Probe (PSP) observations of "switchbacks" (abrupt, large-amplitude reversals in the radial magnetic field, which exhibit Alfv\'enic correlations) we examine the dynamics of large-amplitude Alfv\'en waves in the expanding solar wind. We develop an analytic model which makes several predictions: switchbacks should preferentially occur in regions where the solar wind plasma has undergone a greater expansion, the switchback fraction at radii comparable to PSP should be an increasing function of radius, and switchbacks should have their gradients preferentially perpendicular to the mean magnetic field direction. The expansion of the plasma generates small compressive components as part of the wave's nonlinear evolution: these are maximized when the normalized fluctuation amplitude is comparable to $\sin\theta$, where $\theta$ is the angle between the propagation direction and the mean magnetic field. These compressive components steepen the primary Alfv\'enic waveform, keeping the solution in a state of nearly constant magnetic field strength as its normalized amplitude $\delta B/B$ grows due to expansion. The small fluctuations in the magnetic-field-strength are minimized at a particular $\theta$-dependent value of $\beta$, usually of order unity, and the density and magnetic-field-strength fluctuations can be correlated or anticorrelated depending on $\beta$ and $\theta$. Example solutions of our dynamical equation are presented; some do indeed form magnetic-field reversals. Our predictions appear to match some previously unexplained phenomena in observations and numerical simulations, providing evidence that the observed switchbacks result from the nonlinear evolution of the initially small-amplitude Alfv\'en waves already known to be present at the coronal base.Comment: 20 pages, 1 table, 9 figures. Submitted to Ap