14,053 research outputs found
Rear-surface integral method for calculating thermal diffusivity from laser flash experiments
The laser flash method for measuring thermal diffusivity of solids involves
subjecting the front face of a small sample to a heat pulse of radiant energy
and recording the resulting temperature rise on the opposite (rear) surface.
For the adiabatic case, the widely-used standard approach estimates the thermal
diffusivity from the rear-surface temperature rise history by calculating the
half rise time: the time required for the temperature rise to reach one half of
its maximum value. In this article, we develop a novel alternative approach by
expressing the thermal diffusivity exactly in terms of the area enclosed by the
rear-surface temperature rise curve and the steady-state temperature over time.
Approximating this integral numerically leads to a simple formula for the
thermal diffusivity involving the rear-surface temperature rise history. Using
synthetic experimental data we demonstrate that the new formula produces
estimates of the thermal diffusivity - for a typical test case - that are more
accurate and less variable than the standard approach. The article concludes by
briefly commenting on extension of the new method to account for heat losses
from the sample.Comment: 7 pages, 1 figure, accepted versio
Accurate and efficient calculation of response times for groundwater flow
We study measures of the amount of time required for transient flow in
heterogeneous porous media to effectively reach steady state, also known as the
response time. Here, we develop a new approach that extends the concept of mean
action time. Previous applications of the theory of mean action time to
estimate the response time use the first two central moments of the probability
density function associated with the transition from the initial condition, at
, to the steady state condition that arises in the long time limit, as . This previous approach leads to a computationally convenient
estimation of the response time, but the accuracy can be poor. Here, we outline
a powerful extension using the first raw moments, showing how to produce an
extremely accurate estimate by making use of asymptotic properties of the
cumulative distribution function. Results are validated using an existing
laboratory-scale data set describing flow in a homogeneous porous medium. In
addition, we demonstrate how the results also apply to flow in heterogeneous
porous media. Overall, the new method is: (i) extremely accurate; and (ii)
computationally inexpensive. In fact, the computational cost of the new method
is orders of magnitude less than the computational effort required to study the
response time by solving the transient flow equation. Furthermore, the approach
provides a rigorous mathematical connection with the heuristic argument that
the response time for flow in a homogeneous porous medium is proportional to
, where is a relevant length scale, and is the aquifer
diffusivity. Here, we extend such heuristic arguments by providing a clear
mathematical definition of the proportionality constant.Comment: 22 pages, 3 figures, accepted version of paper published in Journal
of Hydrolog
New homogenization approaches for stochastic transport through heterogeneous media
The diffusion of molecules in complex intracellular environments can be
strongly influenced by spatial heterogeneity and stochasticity. A key challenge
when modelling such processes using stochastic random walk frameworks is that
negative jump coefficients can arise when transport operators are discretized
on heterogeneous domains. Often this is dealt with through homogenization
approximations by replacing the heterogeneous medium with an
homogeneous medium. In this work, we present a new class
of homogenization approximations by considering a stochastic diffusive
transport model on a one-dimensional domain containing an arbitrary number of
layers with different jump rates. We derive closed form solutions for the th
moment of particle lifetime, carefully explaining how to deal with the internal
interfaces between layers. These general tools allow us to derive simple
formulae for the effective transport coefficients, leading to significant
generalisations of previous homogenization approaches. Here, we find that
different jump rates in the layers gives rise to a net bias, leading to a
non-zero advection, for the entire homogenized system. Example calculations
show that our generalized approach can lead to very different outcomes than
traditional approaches, thereby having the potential to significantly affect
simulation studies that use homogenization approximations.Comment: 9 pages, 2 figures, accepted version of paper published in The
Journal of Chemical Physic
Rear-surface integral method for calculating thermal diffusivity: finite pulse time correction and two-layer samples
We study methods for calculating the thermal diffusivity of solids from laser
flash experiments. This experiment involves subjecting the front surface of a
small sample of the material to a heat pulse and recording the resulting
temperature rise on the opposite (rear) surface. Recently, a method was
developed for calculating the thermal diffusivity from the rear-surface
temperature rise, which was shown to produce improved estimates compared with
the commonly used half-time approach. This so-called rear-surface integral
method produced a formula for calculating the thermal diffusivity of
homogeneous samples under the assumption that the heat pulse is instantaneously
absorbed uniformly into a thin layer at the front surface. In this paper, we
show how the rear-surface integral method can be applied to a more physically
realistic heat flow model involving the actual heat pulse shape from the laser
flash experiment. New thermal diffusivity formulas are derived for handling
arbitrary pulse shapes for either a homogeneous sample or a heterogeneous
sample comprising two layers of different materials. Presented numerical
experiments confirm the accuracy of the new formulas and demonstrate how they
can be applied to the kinds of experimental data arising from the laser flash
experiment.Comment: 10 pages, 3 figures, accepted versio
Drug delivery from microcapsules: how can we estimate the release time?
Predicting the release performance of a drug delivery device is an important
challenge in pharmaceutics and biomedical science. In this paper, we consider a
multi-layer diffusion model of drug release from a composite spherical
microcapsule into an external surrounding medium. Based on this model, we
present two approaches that provide useful indicators of the release time, i.e.
the time required for the drug-filled capsule to be depleted. Both approaches
make use of temporal moments of the drug concentration versus time curve at the
centre of the capsule, which provide useful insight into the timescale of the
process and can be computed exactly without explicit calculation of the full
transient solution of the multi-layer diffusion model. The first approach,
which uses the zeroth and first temporal moments only, provides simple
algebraic expressions involving the various parameters in the model (e.g. layer
diffusivities, mass transfer coefficients, partition coefficients) to
characterize the release time while the second approach yields an asymptotic
estimate of the release time that depends on consecutive higher moments.
Through several test cases, we show that both approaches provide a
computationally-cheap and useful measure to compare \textit{a priori} the
release time of different composite microcapsule configurations.Comment: 15 pages, 4 figures, submitte
Putting a Price Tag on the Common Core: How Much Will Smart Implementation Cost?
The Common Core State Standards (CCSS) for English language arts and mathematics represent a sea change in standards-based reform and their implementation is the movement's next -- and greatest -- challenge. Yet, while most states have now set forth implementation plans, these tomes seldom address the crucial matter of cost. Putting a Price Tag on the Common Core: How Much Will Smart Implementation Cost? estimates the implementation cost for each of the forty-five states (and the District of Columbia) that have adopted the Common Core State Standards and shows that costs naturally depend on how states approach implementation. Authors Patrick J. Murphy of the University of San Francisco and Elliot Regenstein of EducationCounsel LLC illustrate this with three models
Raman scattering in a Heisenberg {\boldmath } antiferromagnet on the triangular lattice
We investigate two-magnon Raman scattering from the Heisenberg
antiferromagnet on the triangular lattice, considering both the effect of
renormalization of the one-magnon spectrum by 1/S corrections and final-state
magnon-magnon interactions. The bare Raman intensity displays two peaks related
to one-magnon van-Hove singularities. We find that 1/S self-energy corrections
to the one-magnon spectrum strongly modify this intensity profile. The central
Raman-peak is significantly enhanced due to plateaus in the magnon dispersion,
the high frequency peak is suppressed due to magnon damping, and the overall
spectral support narrows considerably. Additionally we investigate final-state
interactions by solving the Bethe-Salpeter equation to . In contrast to
collinear antiferromagnets, the non-collinear nature of the magnetic ground
state leads to an irreducible magnon scattering which is retarded and
non-separable already to lowest order. We show that final-state interactions
lead to a rather broad Raman-continuum centered around approximately twice the
'roton'-energy. We also discuss the dependence on the scattering geometry.Comment: 7 pages, 5 figure
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