13,268 research outputs found
Perturbation theory for the effective diffusion constant in a medium of random scatterer
We develop perturbation theory and physically motivated resummations of the
perturbation theory for the problem of a tracer particle diffusing in a random
media. The random media contains point scatterers of density uniformly
distributed through out the material. The tracer is a Langevin particle
subjected to the quenched random force generated by the scatterers. Via our
perturbative analysis we determine when the random potential can be
approximated by a Gaussian random potential. We also develop a self-similar
renormalisation group approach based on thinning out the scatterers, this
scheme is similar to that used with success for diffusion in Gaussian random
potentials and agrees with known exact results. To assess the accuracy of this
approximation scheme its predictions are confronted with results obtained by
numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style
Effective diffusion constant in a two dimensional medium of charged point scatterers
We obtain exact results for the effective diffusion constant of a two
dimensional Langevin tracer particle in the force field generated by charged
point scatterers with quenched positions. We show that if the point scatterers
have a screened Coulomb (Yukawa) potential and are uniformly and independently
distributed then the effective diffusion constant obeys the
Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained
for pure Coulomb scatterers frozen in an equilibrium configuration of the same
temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure
Superfluidity and excitations at unitarity
We present lattice results for spin-1/2 fermions at unitarity, where the
effective range of the interaction is zero and the scattering length is
infinite. We measure the spatial coherence of difermion pairs for a system of
6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a
periodic cube. Using Euclidean time projection, we analyze ground state
properties and transient behavior due to low-energy excitations. At
asymptotically large values of t we see long-range order consistent with
spontaneously broken U(1) fermion-number symmetry and a superfluid ground
state. At intermediate times we see exponential decay in the t-dependent signal
due to an unknown low-energy excitation. We probe this low-energy excitation
further by calculating two-particle correlation functions. We find that the
excitation has the properties of a chain of particles extending across the
periodic lattice.Comment: 40 pages, 19 figures, revised version includes new data on
two-particle density correlation
Visibility Representations of Boxes in 2.5 Dimensions
We initiate the study of 2.5D box visibility representations (2.5D-BR) where
vertices are mapped to 3D boxes having the bottom face in the plane and
edges are unobstructed lines of sight parallel to the - or -axis. We
prove that: Every complete bipartite graph admits a 2.5D-BR; The
complete graph admits a 2.5D-BR if and only if ; Every
graph with pathwidth at most admits a 2.5D-BR, which can be computed in
linear time. We then turn our attention to 2.5D grid box representations
(2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit
square at integer coordinates. We show that an -vertex graph that admits a
2.5D-GBR has at most edges and this bound is tight. Finally,
we prove that deciding whether a given graph admits a 2.5D-GBR with a given
footprint is NP-complete. The footprint of a 2.5D-BR is the set of
bottom faces of the boxes in .Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Blowing Off STE(A)M: The Value of the Creative Arts for Gifted STEM Students (IAGC 2017)
The following is a collection of teaching documents, including classroom activities and assignment prompts, used in the Illinois Mathematics and Science Academyâs Graphic Novels, Creative Writing, and Modern Theater classes. These materials are easily included in courses with broader topical focuses, however, either as single-day activities or units of study. The specific materials included here are especially beneficial as means of encouraging student creativity, building up a variety of communication skills, rewarding experimental work, and providing new outlets for critical thinking and social-emotional development
Imaging Polarimeter Arrays for Near-Millimeter Waves
An integrated-circuit antenna array has been developed that images both polarization and intensity. The array consists of a row of antennas that lean alternately left and right, creating two interlaced sub-arrays that respond to different polarizations. The arrays and the bismuth bolometer detectors are made by a photoresist shadowing technique that requires only one photolithographic mask. The array has measured polarization at a wavelength of 800 ”m with an absolute accuracy of 0.8° and a relative precision of 7 arc min. and has demonstrated nearly diffraction-Iimited resolutiort of a 20° step in polarization
Continuum Derrida Approach to Drift and Diffusivity in Random Media
By means of rather general arguments, based on an approach due to Derrida
that makes use of samples of finite size, we analyse the effective diffusivity
and drift tensors in certain types of random medium in which the motion of the
particles is controlled by molecular diffusion and a local flow field with
known statistical properties. The power of the Derrida method is that it uses
the equilibrium probability distribution, that exists for each {\em finite}
sample, to compute asymptotic behaviour at large times in the {\em infinite}
medium. In certain cases, where this equilibrium situation is associated with a
vanishing microcurrent, our results demonstrate the equality of the
renormalization processes for the effective drift and diffusivity tensors. This
establishes, for those cases, a Ward identity previously verified only to
two-loop order in perturbation theory in certain models. The technique can be
applied also to media in which the diffusivity exhibits spatial fluctuations.
We derive a simple relationship between the effective diffusivity in this case
and that for an associated gradient drift problem that provides an interesting
constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8
Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
The fractional quantum Hall effect is observed at low field, in a regime
where the cyclotron energy is smaller than the Coulomb interaction. The nu=5/2
excitation gap is measured to be 262+/-15 mK at ~2.6 T, in good agreement with
previous measurements performed on samples with similar mobility, but with
electronic density larger by a factor of two. The role of disorder on the
nu=5/2 gap is examined. Comparison between experiment and theory indicates that
a large discrepancy remains for the intrinsic gap extrapolated from the
infinite mobility (zero disorder) limit. In contrast, no such large discrepancy
is found for the nu=1/3 Laughlin state. The observation of the nu=5/2 state in
the low-field regime implies that inclusion of non-perturbative Landau level
mixing may be necessary to better understand the energetics of half-filled
fractional quantum hall liquids.Comment: 5 pages, 4 figures; typo corrected, comment expande
A Model for the Propagation of Sound in Granular Materials
This paper presents a simple ball-and-spring model for the propagation of
small amplitude vibrations in a granular material. In this model, the
positional disorder in the sample is ignored and the particles are placed on
the vertices of a square lattice. The inter-particle forces are modeled as
linear springs, with the only disorder in the system coming from a random
distribution of spring constants. Despite its apparent simplicity, this model
is able to reproduce the complex frequency response seen in measurements of
sound propagation in a granular system. In order to understand this behavior,
the role of the resonance modes of the system is investigated. Finally, this
simple model is generalized to include relaxation behavior in the force network
-- a behavior which is also seen in real granular materials. This model gives
quantitative agreement with experimental observations of relaxation.Comment: 21 pages, requires Harvard macros (9/91), 12 postscript figures not
included, HLRZ preprint 6/93, (replacement has proper references included
Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field
Using a tilted field geometry, the effect of an in-plane magnetic field on
the even denominator nu = 5/2 fractional quantum Hall state is studied. The
energy gap of the nu = 5/2 state is found to collapse linearly with the
in-plane magnetic field above ~0.5 T. In contrast, a strong enhancement of the
gap is observed for the nu = 7/3 state. The radically distinct tilted-field
behaviour between the two states is discussed in terms of Zeeman and
magneto-orbital coupling within the context of the proposed Moore-Read pfaffian
wavefunction for the 5/2 fractional quantum Hall effect
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