59,569 research outputs found
Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems
We discuss the statistical mechanics of granular matter and derive several
significant results. First, we show that, contrary to common belief, the volume
and stress ensembles are inter-dependent, necessitating the use of both. We use
the combined ensemble to calculate explicitly expectation values of structural
and stress-related quantities for two-dimensional systems. We thence
demonstrate that structural properties may depend on the angoricity tensor and
that stress-based quantities may depend on the compactivity. This calls into
question previous statistical mechanical analyses of static granular systems
and related derivations of expectation values. Second, we establish the
existence of an intriguing equipartition principle - the total volume is shared
equally amongst both structural and stress-related degrees of freedom. Third,
we derive an expression for the compactivity that makes it possible to quantify
it from macroscopic measurements.Comment: 5 pages, including 2 figures, To appear in Phys. Rev. Let
Statistical Mechanics of Vibration-Induced Compaction of Powders
We propose a theory which describes the density relaxation of loosely packed,
cohesionless granular material under mechanical tapping. Using the compactivity
concept we develope a formalism of statistical mechanics which allows us to
calculate the density of a powder as a function of time and compactivity. A
simple fluctuation-dissipation relation which relates compactivity to the
amplitude and frequency of a tapping is proposed. Experimental data of
E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of
initially deposited in a fluffy state powder evolves under carefully controlled
tapping towards a random close packing (RCP) density. Ramping the vibration
amplitude repeatedly up and back down again reveals the existence of reversible
and irreversible branches in the response. In the framework of our approach the
reversible branch (along which the RCP density is obtained) corresponds to the
steady state solution of the Fokker-Planck equation whereas the irreversible
one is represented by a superposition of "excited states" eigenfunctions. These
two regimes of response are analyzed theoretically and a qualitative
explanation of the hysteresis curve is offered.Comment: 11 pages, 2 figures, Latex. Revised tex
Dynamic mechanical response of polymer networks
The dynamic-mechanical response of flexible polymer networks is studied in
the framework of tube model, in the limit of small affine deformations, using
the approach based on Rayleighian dissipation function. The dynamic complex
modulus G* is calculated from the analysis of a network strand relaxation to
the new equilibrium conformation around the distorted primitive path. Chain
equilibration is achieved via a sliding motion of polymer segments along the
tube, eliminating the inhomogeneity of the polymer density caused by the
deformation. The characteristic relaxation time of this motion separates
the low-frequency limit of the complex modulus from the high-frequency one,
where the main role is played by chain entanglements, analogous to the rubber
plateau in melts. The dependence of storage and loss moduli, G' and G'', on
crosslink and entanglement densities gives an interpolation between polymer
melts and crosslinked networks. We discuss the experimental implications of the
rather short relaxation time and the slow square-root variation of the moduli
and the loss factor tan at higher frequencies.Comment: Journal of Chemical Physics (Oct-2000); Lates, 4 EPS figures include
Multiple wavemode scanning for near and far-side defect characterisation
The combination of ultrasonic inspections using different wavemodes can give more information than is available with single mode inspection. In this work, the response of shear and Rayleigh waves to surface-breaking defects propagating on the near-side and far-side of a sample is investigated. The directivity of shear waves generated by a racetrack coil electromagnetic acoustic transducer (EMAT) is identified and used to set an ideal separation for a pair of transmit-receive EMATs. Defects are indicated by a reduction in the transmitted Rayleigh wave amplitude, and by blocking of the shear wave. Used together, these can identify features in the bulk wave behaviour which are due to near-face surface-breaking defects, and give a full picture of both surfaces. By using a combination of the two wavemodes, the angle of propagation and length of any near-side defects can additionally be identified. A scanning method for samples is proposed
An Economics Capstone Course from Creation to Presentation
This paper details a methodology used to construct a capstone course for the economics major. The capstone course should require students to utilize key concepts that they have learned. The lack of a meaningful topic, however, detracts from a showcase for student understanding. The author details the use of Michael Porter's (1998) location quotients and competitive cluster theory in a capstone course. Applying these concepts increases student understanding of state industries as well as exposing them to an alternative theory of competition not necessarily included in intermediate microeconomic theory.
Lamb wave near field enhancements for surface breaking defects in plates
Near field surface wave ultrasonic enhancements have previously been used to detect surface breaking defects in thick samples using Rayleigh waves. Here, we present analogous surface wave enhancements for Lamb waves propagating in plates. By tracking frequency intensities in selected regions of time-frequency representations, we observe frequency enhancement in the near field, due to constructive interference of the incident wave mode with those reflected and mode converted at the defect. This is explained using two test models; a square based notch and an opening crack, which are used to predict the contribution to the out-of-plane displacement from the reflected and mode converted waves. This method has the potential to provide a reliable method for the near field identification and characterisation of surface breaking defects in plates
An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems
In the context of analyzing a new model for nonlinear diffusion in polymers, an
unusual condition appears at the moving interface between the glassy and rubbery phases of the
polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our
equations, has received very little attention in the mathematical literature. Due to the unusual form
of the moving-boundary condition, further study is needed as to the existence and uniqueness of
solutions satisfying such a condition. The moving boundary condition which results is not solvable
by similarity solutions, but can be solved by integral equation techniques. A solution process is
outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic
of a dissolving polymer
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