3,839 research outputs found
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
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 ''-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
, where 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 grows due to
expansion. The small fluctuations in the magnetic-field-strength are minimized
at a particular -dependent value of , usually of order unity,
and the density and magnetic-field-strength fluctuations can be correlated or
anticorrelated depending on and . 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
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