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

Origin of stabilization of macrotwin boundaries in martensites

The origin of stabilization of complex microstructures along macrotwin boundaries in martensites is explained by comparing two models based on Ginzburg-Landau theory. The first model incorporates a geometrically nonlinear strain tensor to ensure that the Landau energy is invariant under rigid body rotations, while the second model uses a linearized strain tensor under the assumption that deformations and rotations are small. We show that the approximation in the second model does not always hold for martensites and that the experimental observations along macrotwin boundaries can only be reproduced by the geometrically nonlinear (exact) theory

On the modified nonlinear Schr\"odinger equation in the semiclassical limit: supersonic, subsonic, and transsonic behavior

The purpose of this paper is to present a comparison between the modified nonlinear Schr\"odinger (MNLS) equation and the focusing and defocusing variants of the (unmodified) nonlinear Schr\"odinger (NLS) equation in the semiclassical limit. We describe aspects of the limiting dynamics and discuss how the nature of the dynamics is evident theoretically through inverse-scattering and noncommutative steepest descent methods. The main message is that, depending on initial data, the MNLS equation can behave either like the defocusing NLS equation, like the focusing NLS equation (in both cases the analogy is asymptotically accurate in the semiclassical limit when the NLS equation is posed with appropriately modified initial data), or like an interesting mixture of the two. In the latter case, we identify a feature of the dynamics analogous to a sonic line in gas dynamics, a free boundary separating subsonic flow from supersonic flow.Comment: 30 pages, 2 figures. Submitted to Acta Mathematica Scientia (special issue in honor of Peter Lax's 85th birthday

Silo Music and Silo Quake: Granular Flow Induced Vibration

Acceleration and sound measurements during granular discharge from silos are used to show that silo music is a sound resonance produced by silo quake. The latter is produced by stick-slip friction between the wall and the granular material in tall narrow silos. For the discharge rates studied, the occurrence and frequency of flow pulsations are determined primarily by the surface properties of the granular material and the silo wall. The measurements show that the pulsating motion of the granular material drives the oscillatory motion of the silo and the occurrence of silo quake does not require a resonant interaction between the silo and the granular material.Comment: 16 pages, submitted to Powder Technolog

Solving the Klein-Gordon equation using Fourier spectral methods: A benchmark test for computer performance

The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of the code is examined on thirteen different machines for a problem size of 512^3. The results are useful in assessing likely performance of other parallel fast Fourier transform based programs for solving partial differential equations. The problem is chosen to be large enough to solve on a workstation, yet also of interest to solve quickly on a supercomputer, in particular for parametric studies. Unlike other high performance computing benchmarks, for this problem size, the time to solution will not be improved by simply building a bigger supercomputer.Comment: 10 page