168,204 research outputs found
On the enumeration of closures and environments with an application to random generation
Environments and closures are two of the main ingredients of evaluation in
lambda-calculus. A closure is a pair consisting of a lambda-term and an
environment, whereas an environment is a list of lambda-terms assigned to free
variables. In this paper we investigate some dynamic aspects of evaluation in
lambda-calculus considering the quantitative, combinatorial properties of
environments and closures. Focusing on two classes of environments and
closures, namely the so-called plain and closed ones, we consider the problem
of their asymptotic counting and effective random generation. We provide an
asymptotic approximation of the number of both plain environments and closures
of size . Using the associated generating functions, we construct effective
samplers for both classes of combinatorial structures. Finally, we discuss the
related problem of asymptotic counting and random generation of closed
environemnts and closures
Hamiltonian closures for fluid models with four moments by dimensional analysis
Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the
Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian
closures using the first four moments of the Vlasov distribution are obtained,
and all closures provided by a dimensional analysis procedure for satisfying
the Jacobi identity are identified. Two Hamiltonian models emerge, for which
the explicit closures are given, along with their Poisson brackets and Casimir
invariants
Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence
Turbulence in compressible plasma plays a key role in many areas of
astrophysics and engineering. The extreme plasma parameters in these
environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows,
however, make direct numerical simulations computationally intractable even for
the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem
one can use subgrid-scale (SGS) closures -- models for the influence of
unresolved, subgrid-scales on the resolved ones. In this work we propose and
validate a set of constant coefficient closures for the resolved, compressible,
ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like
equilibrium closures. The turbulent stresses and the electromotive force (EMF)
are described by expressions that are nonlinear in terms of large scale
velocity and magnetic field gradients. To verify the closures we conduct a
priori tests over 137 simulation snapshots from two different codes with
varying ratios of thermal to magnetic pressure () and sonic Mach numbers (). Furthermore, we make a
comparison to traditional, phenomenological eddy-viscosity and
closures. We find only mediocre performance of the
kinetic eddy-viscosity and closures, and that the
magnetic eddy-viscosity closure is poorly correlated with the simulation data.
Moreover, three of five coefficients of the traditional closures exhibit a
significant spread in values. In contrast, our new closures demonstrate
consistently high correlation and constant coefficient values over time and and
over the wide range of parameters tested. Important aspects in compressible MHD
turbulence such as the bi-directional energy cascade, turbulent magnetic
pressure and proper alignment of the EMF are well described by our new
closures.Comment: 15 pages, 6 figures; to be published in New Journal of Physic
Demographics, Fiscal Health, and School Quality: Shedding Light on School Closure Decisions
In our current challenging budgetary environment, school closures remain a potentially attractive choice. With a large panel of Illinois schools from 1991 to 2005, I investigate which factors contribute to school closures. Among elementary schools, declining enrolments and rural locations coincide with closures. However, schools with higher per-pupil spending are ceteris paribus less likely to close. Furthermore, better test scores also yield lower probabilities. High expenditures contribute to junior high closure, but the most significant predictors are the proportions of black and low income students. Administrators may claim that low enrolments and high spending motivate school closures, but in Illinois, that is not the whole story.education finance, education administration, school closures, tax policy
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