816 research outputs found
Measurements of Solid Spheres Bouncing Off Flat Plates
Recent years have seen a substantial increase of interest in the flows of granular materials whose rheology is dominated by the physical contact between particles and between particles and the containing walls. Considerable advances in the theoretical understanding of rapid granular material flows have been made by the application of the statistical methods of molecular gas dynamics (e.g., Jenkins and Savage (1983), Lun et al. (1984)) and by the use of computers simulations of these flows (e.g., Campbell and Brennen (1985), Walton (1984)). Experimental studies aimed at measurements of the fundamental rheology properties are much less numerous and are understandably limited by the great difficulties involved in trying to measure velocity profiles, solid fraction profiles, and fluctuating velocities within a flowing granular material. Nevertheless, it has become clear that one of the most severe problems encountered when trying to compare experimental data with the theoretical models is the uncertainty in the material properties governing particle/particle or particle/wall collisions. Many of the theoretical models and computer simulations assume a constant coefficient of restitution (and, in some cases, a coefficient of friction).
The purpose of the present project was to provide some documentation for particle/wall collisions by means of a set of relatively simple experiments in which solid spheres of various diameters and materials were bounced off plates of various thickness and material. The objective was to provide the kind of information on individual particle/wall collisions needed for the theoretical rheological models and computer simulations of granular material flows: in particular, to help resolve some of the issues associated with the boundary condition at a solid wall. For discussion of the complex issues associated with dynamic elastic or inelastic impact, reference is made to Goldsmith (1960) and the recent text by Johnson (1985)
Direct Numerical Simulation of a Temporally Evolving Incompressible Plane Wake: Effect of Initial Conditions on Evolution and Topology
Direct numerical simulations have been used to examine the effect of the initial disturbance field on the development of three-dimensionality and the transition to turbulence in the incompressible plane wake. The simulations were performed using a new numerical method for solving the time-dependent, three-dimensional, incompressible Navier-Stokes equations in flows with one infinite and two periodic directions. The method uses standard Fast Fourier Transforms and is applicable to cases where the vorticity field is compact in the infinite direction. Initial disturbances fields examined were combinations of two-dimensional waves and symmetric pairs of 60 deg oblique waves at the fundamental, subharmonic, and sub-subharmonic wavelengths. The results of these simulations indicate that the presence of 60 deg disturbances at the subharmonic streamwise wavelength results in the development of strong coherent three-dimensional structures. The resulting strong three-dimensional rate-of-strain triggers the growth of intense fine scale motions. Wakes initiated with 60 deg disturbances at the fundamental streamwise wavelength develop weak coherent streamwise structures, and do not develop significant fine scale motions, even at high Reynolds numbers. The wakes which develop strong three-dimensional structures exhibit growth rates on par with experimentally observed turbulent plane wakes. Wakes which develop only weak three-dimensional structures exhibit significantly lower late time growth rates. Preliminary studies of wakes initiated with an oblique fundamental and a two-dimensional subharmonic, which develop asymmetric coherent oblique structures at the subharmonic wavelength, indicate that significant fine scale motions only develop if the resulting oblique structures are above an angle of approximately 45 deg
Collision of One-Dimensional Nonlinear Chains
We investigate one-dimensional collisions of unharmonic chains and a rigid
wall. We find that the coefficient of restitution (COR) is strongly dependent
on the velocity of colliding chains and has a minimum value at a certain
velocity. The relationship between COR and collision velocity is derived for
low-velocity collisions using perturbation methods. We found that the velocity
dependence is characterized by the exponent of the lowest unharmonic term of
interparticle potential energy
The impact of two-dimensional elastic disk
The impact of a two-dimensional elastic disk with a wall is numerically
studied. It is clarified that the coefficient of restitution (COR) decreases
with the impact velocity. The result is not consistent with the recent
quasi-static theory of inelastic collisions even for very slow impact. The
abrupt drop of COR is found due to the plastic deformation of the disk, which
is assisted by the initial internal motion.(to be published in J. Phys. Soc.
Jpn.)Comment: 6 Pages,2 figure
A study of the fine scale motions of incompressible time-developing mixing layers
This work is an extension of a project conducted at the previous CTR summer program and was reported by Chen et al. (1990). In that program, the geometry and topology of the dissipating motions in a variety of shear flows was examined. All data was produced by direct numerical simulations (DNS). The partial derivatives of the velocity field were determined at every grid point in the flow and various invariants and related quantities were computed from the velocity gradient tensor. Motions characterized by high rates of kinetic energy dissipation and high enstrophy were of particular interest. Scatter diagrams of the invariants were mapped out and interesting and unexpected patterns were seen. Each type of shear layer produced its own characteristic scatter plot. In the present project, attention is focused on the incompressible plane mixing layer, and the scatter diagrams are replaced with more useful joint probability density contours. Comparison of the topology of the dissipating motions of flows at different Reynolds numbers are made. Also, plane mixing layers at the same Reynolds number but with different initial conditions are compared
A model for inter-module analysis and optimizing compilation
Recent research into the implementation of logic programming
languages has demonstrated that global program analysis can be used to speed up execution by an order of magnitude. However, currently such global program analysis requires the program to be analysed as a whole: sepárate compilation of modules is not supported. We describe and empirically evalúate a simple model for extending global program
analysis to support sepárate compilation of modules. Importantly, our model supports context-sensitive program analysis and multi-variant specialization of procedures in the modules
Monodromy--like Relations for Finite Loop Amplitudes
We investigate the existence of relations for finite one-loop amplitudes in
Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection
between tree and loop level, we deduce sequences of amplitude relations for any
number of external legs.Comment: 24 pages, 6 figures, v2 typos corrected, reference adde
Simulation for the oblique impact of a lattice system
The oblique collision between an elastic disk and an elastic wall is
numerically studied.
We investigate the dependency of the tangential coefficient of restitution on
the incident angle of impact.
From the results of simulation, our model reproduces experimental results and
can be explained by a phenomenological theory of the oblique impact.Comment: 30 pages, 9 figures, submitted to J. Phys. Soc. Japa
Multigluon tree amplitudes with a pair of massive fermions
We consider the calculation of n-point multigluon tree amplitudes with a pair
of massive fermions in QCD. We give the explicit transformation rules of this
kind of massive fermion-pair amplitudes with respect to different reference
momenta and check the correctness of them by SUSY Ward identities. Using these
rules and onshell BCFW recursion relation, we calculate the analytic results of
several n-point multigluon amplitudes.Comment: 15page
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