Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM

© EDP Sciences, SMAI 2011This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in Rn (n ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ωc := Rn\￣Ω. The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping (NtD) given in terms of boundary integral operators. The resulting variational formulation becomes a variational inequality with a linear operator. Then we treat the corresponding numerical scheme and discuss an approximation of the NtD mapping with an appropriate discretization of the inverse Poincar´e-Steklov operator. In particular, assuming some abstract approximation properties and a discrete inf-sup condition, we show unique solvability of the discrete scheme and obtain the corresponding a-priori error estimate. Next, we prove that these assumptions are satisfied with Raviart- Thomas elements and piecewise constants in Ω, and continuous piecewise linear functions on Γ. We suggest a solver based on a modified Uzawa algorithm and show convergence. Finally we present some numerical results illustrating our theory

Benefit Plan Design and Prescription Drug Utilization Among Asthmatics: Do Patient Copayments Matter?

Objective: The ratio of controller to reliever medication use has been proposed as a measure of treatment quality for asthma patients. In this study we examine the effects of plan level mean out-of-pocket asthma medication patient copayments and other features of benefit plan design on the use of controller medications alone, controller and reliever medications (combination therapy), and reliever medications alone. Methods: 1995-2000 MarketScan claims data were used to construct plan-level out-of-pocket copayment and physician/practice prescriber preference variables for asthma medications. Separate multinomial logit models were estimated for patients in fee-for-service (FFS) and non-FFS plans relating benefit plan design features, physician/practice prescribing preferences, patient demographics, patient comorbidities and county-level income variables to patient-level asthma treatment patterns. Results: We find that the controller reliever ratio rose steadily over 1995-2000, along with out-of-pocket payments for asthma medications, which rose more for controllers than for relievers. However, after controlling for other variables, plan level mean out-of-pocket copayments were not found to have a statistically significant influence upon patient-level asthma treatment patterns. On the other hand, physician practice prescribing patterns strongly influenced patient level treatment patterns. Conclusions: There is no strong statistical evidence that higher levels of out-of-pocket copayments for prescription drugs influence asthma treatment patterns. However, physician/practice prescribing preferences influence patient treatment.

Granular gases under extreme driving

We study inelastic gases in two dimensions using event-driven molecular dynamics simulations. Our focus is the nature of the stationary state attained by rare injection of large amounts of energy to balance the dissipation due to collisions. We find that under such extreme driving, with the injection rate much smaller than the collision rate, the velocity distribution has a power-law high energy tail. The numerically measured exponent characterizing this tail is in excellent agreement with predictions of kinetic theory over a wide range of system parameters. We conclude that driving by rare but powerful energy injection leads to a well-mixed gas and constitutes an alternative mechanism for agitating granular matter. In this distinct nonequilibrium steady-state, energy cascades from large to small scales. Our simulations also show that when the injection rate is comparable with the collision rate, the velocity distribution has a stretched exponential tail.Comment: 6 pages, 7 figures; new version contains 2 new figures and text describing cascade

Equatorial symmetry/antisymmetry of stationary axisymmetric electrovac spacetimes

Two theorems are proved concerning how stationary axisymmetric electrovac spacetimes that are equatorially symmetric or equatorially antisymmetric can be characterized correctly in terms of the Ernst potentials \E and $\Phi$ or in terms of axis-data.Comment: 8 page

On the problem of mass-dependence of the two-point function of the real scalar free massive field on the light cone

We investigate the generally assumed inconsistency in light cone quantum field theory that the restriction of a massive, real, scalar, free field to the nullplane $\Sigma=\{x^0+x^3=0\}$ is independent of mass \cite{LKS}, but the restriction of the two-point function depends on it (see, e.g., \cite{NakYam77, Yam97}). We resolve this inconsistency by showing that the two-point function has no canonical restriction to $\Sigma$ in the sense of distribution theory. Only the so-called tame restriction of the two-point function exists which we have introduced in \cite{Ull04sub}. Furthermore, we show that this tame restriction is indeed independent of mass. Hence the inconsistency appears only by the erroneous assumption that the two-point function would have a (canonical) restriction to $\Sigma$.Comment: 10 pages, 2 figure

Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic and conservative interactions

We present a generalization of the Green-Kubo expressions for thermal transport coefficients $\mu$ in complex fluids of the generic form, $\mu= \mu_\infty +\int^\infty_0 dt V^{-1} _0$, i.e. a sum of an instantaneous transport coefficient $\mu_\infty$, and a time integral over a time correlation function in a state of thermal equilibrium between a current $J$ and a transformed current $J_\epsilon$. The streaming operator $\exp(t{\cal L})$ generates the trajectory of a dynamical variable $J(t) =\exp(t{\cal L}) J$ when used inside the thermal average $_0$. These formulas are valid for conservative, impulsive (hard spheres), stochastic and dissipative forces (Langevin fluids), provided the system approaches a thermal equilibrium state. In general $\mu_\infty \neq 0$ and $J_\epsilon \neq J$, except for the case of conservative forces, where the equality signs apply. The most important application in the present paper is the hard sphere fluid.Comment: 14 pages, no figures. Version 2: expanded Introduction and section II specifying the classes of fluids covered by this theory. Some references added and typos correcte

Magnetic properties of single-crystalline CeCuGa3

The magnetic behavior of single-crystalline CeCuGa3 has been investigated. The compound forms in a tetragonal BaAl4-type structure consisting of rare-earth planes separated by Cu-Ga layers. If the Cu-Ga site disorder is reduced, CeCuGa3 adopts the related, likewise tetragonal BaNiSn3-type structure, in which the Ce ion are surrounded by different Cu and Ga layers and the inversion symmetry is lost. In the literature conflicting reports about the magnetic order of CeCuGa3 have been published. Single crystals with the centrosymmetric structure variant exhibit ferromagnetic order below approx. 4 K with a strong planar anisotropy. The magnetic behavior above the transition temperature can be well understood by the crystal-field splitting of the 4f Hund's rule ground-state multiplet of the Ce ions

Contracts in Practice

Contracts are a form of lightweight formal specification embedded in the program text. Being executable parts of the code, they encourage programmers to devote proper attention to specifications, and help maintain consistency between specification and implementation as the program evolves. The present study investigates how contracts are used in the practice of software development. Based on an extensive empirical analysis of 21 contract-equipped Eiffel, C#, and Java projects totaling more than 260 million lines of code over 7700 revisions, it explores, among other questions: 1) which kinds of contract elements (preconditions, postconditions, class invariants) are used more often; 2) how contracts evolve over time; 3) the relationship between implementation changes and contract changes; and 4) the role of inheritance in the process. It has found, among other results, that: the percentage of program elements that include contracts is above 33% for most projects and tends to be stable over time; there is no strong preference for a certain type of contract element; contracts are quite stable compared to implementations; and inheritance does not significantly affect qualitative trends of contract usage