796 research outputs found
Determination of diffusion coefficients from viscosity measurements : effect of higher Chapman-Enskog approximations
"Reprinted from The Journal of Chemical Physics, Vol. 45, No. 10, November, 1966.""Numerical calculations based on the higher Chapman-Enskog approximations show that mutual diffusion coefficients calculated from binary mixture viscosity data agree within experimental uncertainty with the measured D12 values at compositions corresponding to a trace of the heavy component."--Page 3752
Fracturing rock with ultra high pressure water
Modelling issues are considered for the process of cracking rock in mines using ultra high pressure water. The elevated pressures are caused by the ignition of a propellant and may be as large as 1000MPa. We first consider time, length and pressure scales and then derive a model for the propagation of a two-dimensional crack. A number of aspects of this model are considered and similarity solutions and behaviour near the crack tip are investigated. Consideration is given to a simplified model where the elastic component of the interaction between the rock and the fluid is handled using an elementary closure law: in this case much progress may be made and closed-form solutions may be determined. Conditions are also identified where a model based on “impulsive” lubrication theory is appropriate. However, this leads to a very challenging problem. Finally, some other ways of extending the model to include (for example) fluid leak-off into the rock are discussed
Noticing for Equity to Sustain Multilingual Literacies
This department explores how teachers can sustain students’ multilingual literacies and reimagine literacy learning across multiple contexts in conversation with researchers, practitioners, and communities
Mapping the Sensitive Volume of an Ion-Counting Nanodosimeter
We present two methods of independently mapping the dimensions of the
sensitive volume in an ion-counting nanodosimeter. The first method is based on
a calculational approach simulating the extraction of ions from the sensitive
volume, and the second method on probing the sensitive volume with 250 MeV
protons. Sensitive-volume maps obtained with both methods are compared and
systematic errors inherent in both methods are quantified.Comment: 27 pages, 8 figures. Submitted to JINST, Jan. 16 200
Modulated Amplitude Waves in Bose-Einstein Condensates
We analyze spatio-temporal structures in the Gross-Pitaevskii equation to
study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs)
with mean-field interactions. A coherent structure ansatz yields a
parametrically forced nonlinear oscillator, to which we apply Lindstedt's
method and multiple-scale perturbation theory to determine the dependence of
the intensity of periodic orbits (``modulated amplitude waves'') on their wave
number. We explore BEC band structure in detail using Hamiltonian perturbation
theory and supporting numerical simulations.Comment: 5 pages, 4 figs, revtex, final form of paper, to appear in PRE
(forgot to include \bibliography command in last update, so this is a
correction of that; the bibliography is hence present again
Confined granular packings: structure, stress, and forces
The structure and stresses of static granular packs in cylindrical containers
are studied using large-scale discrete element molecular dynamics simulations
in three dimensions. We generate packings by both pouring and sedimentation and
examine how the final state depends on the method of construction. The vertical
stress becomes depth-independent for deep piles and we compare these stress
depth-profiles to the classical Janssen theory. The majority of the tangential
forces for particle-wall contacts are found to be close to the Coulomb failure
criterion, in agreement with the theory of Janssen, while particle-particle
contacts in the bulk are far from the Coulomb criterion. In addition, we show
that a linear hydrostatic-like region at the top of the packings unexplained by
the Janssen theory arises because most of the particle-wall tangential forces
in this region are far from the Coulomb yield criterion. The distributions of
particle-particle and particle-wall contact forces exhibit
exponential-like decay at large forces in agreement with previous studies.Comment: 11 pages, 11 figures, submitted to PRE (v2) added new references,
fixed typo
Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property
The integrability (solvability via an associated single-valued linear
problem) of a differential equation is closely related to the singularity
structure of its solutions. In particular, there is strong evidence that all
integrable equations have the Painlev\'e property, that is, all solutions are
single-valued around all movable singularities. In this expository article, we
review methods for analysing such singularity structure. In particular, we
describe well known techniques of nonlinear regular-singular-type analysis,
i.e. the Painlev\'e tests for ordinary and partial differential equations. Then
we discuss methods of obtaining sufficiency conditions for the Painlev\'e
property. Recently, extensions of \textit{irregular} singularity analysis to
nonlinear equations have been achieved. Also, new asymptotic limits of
differential equations preserving the Painlev\'e property have been found. We
discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer
School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B.
Grammaticos and K. Tamizhman
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.
Bending bad—testing caramel wafer bars (#TestATunnocks)
During the coronavirus pandemic, there have been significant challenges in the remote teaching and demonstration of experiments, especially those that require laboratory testing equipment. With a desire to give students a feel for our materials laboratory on open days and allow them to gain a deeper understanding of what materials science and engineering is about, we have designed an experiment focused on composite materials that can be performed remotely and without specialist equipment. This enabled students to experience a bend test sensorily through seeing, hearing and feeling it, creating a strong link to then being able to relate it to the pre-prepared experimental data taken in the laboratory. This fun, easy-to-run and engaging experiment allowed a shared experience and encouraged a discussion about students' observations, differences in results and implications of the bend strength of sandwich composites. We have found it not only works well universally by all ages but can be used with younger children to think about words such as 'stronger', 'stiffer' and 'flexible' and how materials can be different in different directions
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