Gradient discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media with discontinuous pressures at the matrix fracture interfaces

We investigate the discretization of Darcy flow through fractured porous media on general meshes. We consider a hybrid dimensional model, invoking a complex network of planar fractures. The model accounts for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. The numerical analysis is performed in the general framework of gradient discretizations which is extended to the model under consideration. Two families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the Hybrid Finite Volume scheme (HFV) are detailed and shown to satisfy the gradient scheme framework, which yields, in particular, convergence. Numerical tests confirm the theoretical results. Gradient Discretization; Darcy Flow, Discrete Fracture Networks, Finite Volum

Effect of sampling rate and record length on the determination of stability and control derivatives

Flight data from five aircraft were used to assess the effects of sampling rate and record length reductions on estimates of stability and control derivatives produced by a maximum likelihood estimation method. Derivatives could be extracted from flight data with the maximum likelihood estimation method even if there were considerable reductions in sampling rate and/or record length. Small amplitude pulse maneuvers showed greater degradation of the derivative maneuvers than large amplitude pulse maneuvers when these reductions were made. Reducing the sampling rate was found to be more desirable than reducing the record length as a method of lessening the total computation time required without greatly degrading the quantity of the estimates

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $\lambda$ dependence of the shape and breaking rate.Comment: 4 pages, 3 figure

Multispace and Multilevel BDDC

BDDC method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl

High resolution Ge/Li/ spectrometer reduces rate-dependent distortions at high counting rates

Modified spectrometer system with a low-noise preamplifier reduces rate-dependent distortions at high counting rates, 25,000 counts per second. Pole-zero cancellation minimizes pulse undershoots due to multiple time constants, baseline restoration improves resolution and prevents spectral shifts

Independence day: Post-fledging movements and behavior of adult Eastern Towhees (\u3cem\u3ePipilo erythrophthalmus\u3c/em\u3e) in landscapes managed for American Woodcock (\u3cem\u3eScolopax minor\u3c/em\u3e)

Umbrella species management offers a potential solution to the financial and logistical challenges of managing for the many declining species in early-successional forests, a habitat that is also critical for many mature and young forest songbird species during the post-fledging and post-breeding period. We investigated the movements of adult Eastern Towhees (Pipilo erythrophthalmus) during the post-fledging period in 4 km2 landscapes managed for American Woodcock (Scolopax minor), a popular umbrella species candidate for young forest management. Home range size (mean = 2.8 ha, SE 0.33) did not differ during the post-fledging period between adult towhees inhabiting landscapes designated as high-likelihood (HL) or low-likelihood (LL) of woodcock use. Adults moved distances of ∼37–47 m per day during the first 3 weeks of the post-fledging period and this did not differ between the 2 landscapes. In contrast, once their young became independent, adults moved longer distances in HL compared to LL landscapes (49.5 m [SE 2.9] and 36.7 m [SE 3.6], respectively) and these distances increased with home range size and patch size. Landscape features within 100 m of the towhee home range best explained variation in towhee movement distance. Young forest habitat was also the predominant forest type used by adult towhees caring for fledglings throughout the post-fledging period. These results suggest that early successional forest management for woodcock can provide effective breeding habitat for towhees, but likely at a smaller spatial scale than typically managed for woodcock

Encapsulation of phosphorus dopants in silicon for the fabrication of a quantum computer

The incorporation of phosphorus in silicon is studied by analyzing phosphorus delta-doped layers using a combination of scanning tunneling microscopy, secondary ion mass spectrometry and Hall effect measurements. The samples are prepared by phosphine saturation dosing of a Si(100) surface at room temperature, a critical annealing step to incorporate phosphorus atoms, and subsequent epitaxial silicon overgrowth. We observe minimal dopant segregation (5 nm), complete electrical activation at a silicon growth temperature of 250 degrees C and a high two-dimensional electron mobility of 100 cm2/Vs at a temperature of 4.2 K. These results, along with preliminary studies aimed at further minimizing dopant diffusion, bode well for the fabrication of atomically precise dopant arrays in silicon such as those found in recent solid-state quantum computer architectures.Comment: 3 pages, 4 figure

Chemotactic Collapse and Mesenchymal Morphogenesis

We study the effect of chemotactic signaling among mesenchymal cells. We show that the particular physiology of the mesenchymal cells allows one-dimensional collapse in contrast to the case of bacteria, and that the mesenchymal morphogenesis represents thus a more complex type of pattern formation than those found in bacterial colonies. We finally compare our theoretical predictions with recent in vitro experiments

Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur