The effects of a counter-current interstitial flow on a discharging hourglass

This work experimentally investigates the effects of an interstitial fluid on the discharge of granular material within an hourglass. The experiments include observations of the flow patterns, measurements of the discharge rates, and pressure variations for a range of different fluid viscosities, particle densities and diameters, and hourglass geometries. The results are classified into three regimes: (i) granular flows with negligible interstitial fluid effects; (ii) flows affected by the presence of the interstitial fluid; and (iii) a no-flow region in which particles arch across the orifice and do not discharge. Within the fluid-affected region, the flows were visually classified as lubricated and air-coupled flows, oscillatory flows, channeling flows in which the flow preferentially rises along the sidewalls, and fluidized flows in which the upward flow suspends the particles. The discharge rates depends on the Archimedes number, the ratio of the effective hopper diameter to the particle diameter, and hourglass geometry. The hopper-discharge experiments, as well as experiments found in the literature, demonstrate that the presence of the interstitial fluid is important when the nondimensional ratio (N) of the single-particle terminal velocity to the hopper discharge velocity is less than 10. Flow ceased in all experiments in which the particle diameter was greater than 25% of the effective hopper diameter regardless of the interstitial fluid

On the Interpretation of the Redshift in a Static Gravitational Field

The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: on the one hand the phenomenon is explained through the behaviour of clocks which run the faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency of the clock. On the other hand the phenomenon is alternatively discussed (even in some authoritative texts) in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. This second approach operates with notions such as the "gravitational mass" or the "potential energy" of a photon and we assert that it is misleading. We do not claim to present any original ideas or to give a comprehensive review of the subject, our goal being essentially a pedagogical one.Comment: latex, 16 pages, to be published in American Journal of Physic

Supersymmetry for disordered systems with interaction

Considering disordered electron systems we suggest a scheme that allows us to include an electron-electron interaction into a supermatrix sigma-model. The method is based on replacing the initial model of interacting electons by a fully supersymmetric model. Although this replacement is not exact, it is a good approximation for a weak short range interaction and arbitrary disorder. The replacement makes the averaging over disorder and further manipulations straightforward and we come to a supermatrix sigma-model containing an interaction term. The structure of the model is rather similar to the replica one, although the interaction term has a different form. We study the model making perturbation theory and renormalization group calculations. We check the renormalizability of the model in the first loop approximation and in the first order in the interaction. In this limit we reproduce the renormalization group equations known from earlier works. We hope that the new supermatrix sigma-model may become a new tool for non-perturbative calculations for disordered systems with interaction.Comment: 18 pages, 8 figures, published version with minor change

Testing post-Newtonian theory with gravitational wave observations

The Laser Interferometric Space Antenna (LISA) will observe supermassive black hole binary mergers with amplitude signal-to-noise ratio of several thousands. We investigate the extent to which such observations afford high-precision tests of Einstein's gravity. We show that LISA provides a unique opportunity to probe the non-linear structure of post-Newtonian theory both in the context of general relativity and its alternatives.Comment: 9 pages, 2 figure

Aerodynamic design and analysis of the AST-204, AST-205, and AST-206 blended wing-fuse large supersonic transport configuration concepts

The aerodynamic design and analysis of three blended wing-fuselage supersonic cruise configurations providing four, five, and six abreast seating was conducted using a previously designed supersonic cruise configuration as the baseline. The five abreast configuration was optimized for wave drag at a Mach number of 2.7. The four and six abreast configurations were also optimized at Mach 2.7, but with the added constraint that the majority of their structure be common with the five abreast configuration. Analysis of the three configurations indicated an improvement of 6.0, 7.5, and 7.7 percent in cruise lift-to-drag ratio over the baseline configuration for the four, five, and six abreast configurations, respectively

Aerodynamic design and analysis of the AST-200 supersonic transport configuration concept

The design and analysis of a supersonic transport configuration was conducted using linear theory methods in conjunction with appropriate constraints. Wing optimization centered on the determination of the required twist and camber and proper integration of the wing and fuselage. Also included in the design are aerodynamic refinements to the baseline wing thickness distribution and nacelle shape. Analysis to the baseline and revised configurations indicated an improvement in lift-to-drag ratio of 0.36 at the Mach 2.7 cruise condition. Validation of the design is planned through supersonic wing tunnel tests

Fan-spine topology formation through two-step reconnection driven by twisted flux emergence

We address the formation of 3D nullpoint topologies in the solar corona by combining Hinode/XRT observations of a small dynamic limb event, which occurred beside a non-erupting prominence cavity, with a 3D zero-beta MHD simulation. To this end, we model the boundary-driven kinematic emergence of a compact, intense, and uniformly twisted flux tube into a potential field arcade that overlies a weakly twisted coronal flux rope. The expansion of the emerging flux in the corona gives rise to the formation of a nullpoint at the interface of the emerging and the pre-existing fields. We unveil a two-step reconnection process at the nullpoint that eventually yields the formation of a broad 3D fan-spine configuration above the emerging bipole. The first reconnection involves emerging fields and a set of large-scale arcade field lines. It results in the launch of a torsional MHD wave that propagates along the arcades, and in the formation of a sheared loop system on one side of the emerging flux. The second reconnection occurs between these newly formed loops and remote arcade fields, and yields the formation of a second loop system on the opposite side of the emerging flux. The two loop systems collectively display an anenome pattern that is located below the fan surface. The flux that surrounds the inner spine field line of the nullpoint retains a fraction of the emerged twist, while the remaining twist is evacuated along the reconnected arcades. The nature and timing of the features which occur in the simulation do qualititatively reproduce those observed by XRT in the particular event studied in this paper. Moreover, the two-step reconnection process suggests a new consistent and generic model for the formation of anemone regions in the solar corona.Comment: Accepted for publication in ApJ, 11 pages and 5 figure