23,771 research outputs found
A note on dispersing particles on a line
We consider a synchronous dispersion process introduced in \cite{CRRS} and we
show that on the infinite line the final set of occupied sites takes up
space, where is the number of particles involved
Soil Particle Size Distribution Protocol
The purpose of this resource is to sure the distribution of different sizes of soil particles in each horizon of a soil profile. Using dry, sieved soil from a horizon, students mix the soil with water and a dispersing solution to completely separate the particles from each other. Students shake the mixture to fully suspend the soil in the water. The soil particles are then allowed to settle out of suspension, and the specific gravity and temperature of the suspension are measured using a hydrometer and thermometer. These measurements are taken after 2 minutes and 24 hours. Educational levels: Middle school, High school
Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states
We determine the local density of states (LDOS) for spin-gapped
one-dimensional charge density wave (CDW) states and Mott insulators in the
presence of a hard-wall boundary. We calculate the boundary contribution to the
single-particle Green function in the low-energy limit using field theory
techniques and analyze it in terms of its Fourier transform in both time and
space. The boundary LDOS in the CDW case exhibits a singularity at momentum
2kF, which is indicative of the pinning of the CDW order at the impurity. We
further observe several dispersing features at frequencies above the spin gap,
which provide a characteristic signature of spin-charge separation. This
demonstrates that the boundary LDOS can be used to infer properties of the
underlying bulk system. In presence of a boundary magnetic field mid-gap states
localized at the boundary emerge. We investigate the signature of such bound
states in the LDOS. We discuss implications of our results on STM experiments
on quasi-1D systems such as two-leg ladder materials like Sr14Cu24O41. By
exchanging the roles of charge and spin sectors, all our results directly carry
over to the case of one-dimensional Mott insulators.Comment: 28 page
Recent advances in open billiards with some open problems
Much recent interest has focused on "open" dynamical systems, in which a
classical map or flow is considered only until the trajectory reaches a "hole",
at which the dynamics is no longer considered. Here we consider questions
pertaining to the survival probability as a function of time, given an initial
measure on phase space. We focus on the case of billiard dynamics, namely that
of a point particle moving with constant velocity except for mirror-like
reflections at the boundary, and give a number of recent results, physical
applications and open problems.Comment: 16 pages, 1 figure in six parts. To appear in Frontiers in the study
of chaotic dynamical systems with open problems (Ed. Z. Elhadj and J. C.
Sprott, World Scientific
Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks
How do the topology and geometry of a tubular network affect the spread of
particles within fluid flows? We investigate patterns of effective dispersion
in the hierarchical, biological transport network formed by Physarum
polycephalum. We demonstrate that a change in topology - pruning in the
foraging state - causes a large increase in effective dispersion throughout the
network. By comparison, changes in the hierarchy of tube radii result in
smaller and more localized differences. Pruned networks capitalize on Taylor
dispersion to increase the dispersion capability.Comment: 5 pages, 4 figures, 11 pages supplemental materia
Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards
The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives
sufficient conditions under which a phase point has an open neighborhood that
belongs (mod 0) to one ergodic component. This theorem is a key ingredient of
many proofs of ergodicity for billiards and, more generally, for smooth
hyperbolic maps with singularities. However the proof of that theorem relies
upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check
for some physically relevant models, including gases of hard balls. Here we
give a proof of the Local Ergodic Theorem for two dimensional billiards without
using the Ansatz.Comment: 17 pages, 2 figure
Local density of states of 1D Mott insulators and CDW states with a boundary
We determine the local density of states (LDOS) of one-dimensional
incommensurate charge density wave (CDW) states in the presence of a strong
impurity potential, which is modeled by a boundary. We find that the CDW gets
pinned at the impurity, which results in a singularity in the Fourier transform
of the LDOS at momentum 2k_F. At energies above the spin gap we observe
dispersing features associated with the spin and charge degrees of freedom
respectively. In the presence of an impurity magnetic field we observe the
formation of a bound state localized at the impurity. All of our results carry
over to the case of one dimensional Mott insulators by exchanging the roles of
spin and charge degrees of freedom. We discuss the implications of our result
for scanning tunneling microscopy experiments on spin-gap systems such as
two-leg ladder cuprates and 1D Mott insulators
Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity
A formalism for studying spontaneous decay of an excited two-level atom in
the presence of dispersing and absorbing dielectric bodies is developed. An
integral equation, which is suitable for numerical solution, is derived for the
atomic upper-state-probability amplitude. The emission pattern and the power
spectrum of the emitted light are expressed in terms of the Green tensor of the
dielectric-matter formation including absorption and dispersion. The theory is
applied to the spontaneous decay of an excited atom at the center of a
three-layered spherical cavity, with the cavity wall being modeled by a
band-gap dielectric of Lorentz type. Both weak coupling and strong coupling are
studied, the latter with special emphasis on the cases where the atomic
transition is (i) in the normal-dispersion zone near the medium resonance and
(ii) in the anomalous-dispersion zone associated with the band gap. In a
single-resonance approximation, conditions of the appearance of Rabi
oscillations and closed solutions to the evolution of the atomic state
population are derived, which are in good agreement with the exact numerical
results.Comment: 12 pages, 6 figures, typos fixed, 1 figure adde
On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas
We analyse the process of energy exchanges generated by the elastic
collisions between a point-particle, confined to a two-dimensional cell with
convex boundaries, and a `piston', i.e. a line-segment, which moves back and
forth along a one-dimensional interval partially intersecting the cell. This
model can be considered as the elementary building block of a spatially
extended high-dimensional billiard modeling heat transport in a class of hybrid
materials exhibiting the kinetics of gases and spatial structure of solids.
Using heuristic arguments and numerical analysis, we argue that, in a regime of
rare interactions, the billiard process converges to a Markov jump process for
the energy exchanges and obtain the expression of its generator.Comment: 23 pages, 6 figure
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