1,258 research outputs found
Wrinkling of a bilayer membrane
The buckling of elastic bodies is a common phenomenon in the mechanics of
solids. Wrinkling of membranes can often be interpreted as buckling under
constraints that prohibit large amplitude deformation. We present a combination
of analytic calculations, experiments, and simulations to understand wrinkling
patterns generated in a bilayer membrane. The model membrane is composed of a
flexible spherical shell that is under tension and that is circumscribed by a
stiff, essentially incompressible strip with bending modulus B. When the
tension is reduced sufficiently to a value \sigma, the strip forms wrinkles
with a uniform wavelength found theoretically and experimentally to be \lambda
= 2\pi(B/\sigma)^{1/3}. Defects in this pattern appear for rapid changes in
tension. Comparison between experiment and simulation further shows that, with
larger reduction of tension, a second generation of wrinkles with longer
wavelength appears only when B is sufficiently small.Comment: 9 pages, 5 color figure
Teaching forest stand dynamics or what happens when you thin your Marigold plantation
Teaching forestry students about forest stand dynamics can be an abstract activity. Very quickly concepts are reduced to mathematical formulae, graphs and diagrams, all with relatively complicated explanations. Alternatively, computer simulation and individual tree models can be used to demonstrate important concepts such as the \u273/2 Power law\u27 of self thinning. Students can also be taken to visit plantations to talk about practical issues of density management and perhaps produce a thinning prescription. However, no single teaching strategy enables students to have \u27hands on\u27 practice at manipulating a real plant population while being able to wait and see the results of their work
Nonlinear optical probe of tunable surface electrons on a topological insulator
We use ultrafast laser pulses to experimentally demonstrate that the
second-order optical response of bulk single crystals of the topological
insulator BiSe is sensitive to its surface electrons. By performing
surface doping dependence measurements as a function of photon polarization and
sample orientation we show that second harmonic generation can simultaneously
probe both the surface crystalline structure and the surface charge of
BiSe. Furthermore, we find that second harmonic generation using
circularly polarized photons reveals the time-reversal symmetry properties of
the system and is surprisingly robust against surface charging, which makes it
a promising tool for spectroscopic studies of topological surfaces and buried
interfaces
Microscopic theory for the light-induced anomalous Hall effect in graphene
We employ a quantum Liouville equation with relaxation to model the recently
observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of
circularly polarized light. In the weak-field regime, we demonstrate that the
Hall effect originates from an asymmetric population of photocarriers in the
Dirac bands. By contrast, in the strong-field regime, the system is driven into
a non-equilibrium steady state that is well-described by topologically
non-trivial Floquet-Bloch bands. Here, the anomalous Hall current originates
from the combination of a population imbalance in these dressed bands together
with a smaller anomalous velocity contribution arising from their Berry
curvature. This robust and general finding enables the simulation of electrical
transport from light-induced Floquet-Bloch bands in an experimentally relevant
parameter regime and creates a pathway to designing ultrafast quantum devices
with Floquet-engineered transport properties
Quantum Markov Channels for Qubits
We examine stochastic maps in the context of quantum optics. Making use of
the master equation, the damping basis, and the Bloch picture we calculate a
non-unital, completely positive, trace-preserving map with unequal damping
eigenvalues. This results in what we call the squeezed vacuum channel. A
geometrical picture of the effect of stochastic noise on the set of pure state
qubit density operators is provided. Finally, we study the capacity of the
squeezed vacuum channel to transmit quantum information and to distribute EPR
states.Comment: 18 pages, 4 figure
Theoretical and experimental study of second harmonic generation from the surface of the topological insulator Bi_2Se_3
We develop a theoretical model that describes the second harmonic generation of light from the surface of the topological insulator Bi_2Se_3 and experimentally demonstrate that the technique is sensitive to the surface electrons. By performing a crystal symmetry analysis of Bi_2Se_3 (111) we determine the nonlinear electric susceptibility tensor elements that give rise to second harmonic generation. Using these results, we present a phenomenological model that shows that the relative magnitudes of these tensor elements can be determined by measuring the polarization and intensity of the radiated second harmonic light as a function of the in-plane crystal orientation and incident laser polarization. We describe optical techniques capable of isolating second harmonic light and, using these techniques, we measure the first-order linear optical and second-order nonlinear optical responses as a function of crystal orientation and laser polarization on bulk single crystals of Bi_2Se_3 (111). The experimental results are consistent with our theoretical description. By comparing the data to our theoretical model we determine that a portion of the measured second harmonic light originates from the accumulation region of Bi_2Se_3 (111), which we confirm by performing surface doping-dependent studies. Our results show that second harmonic generation is a promising tool for spectroscopic studies of topological surfaces and buried interfaces
Nonequilibrium Quasiparticle Relaxation Dynamics in Single Crystals of Hole and Electron doped BaFeAs
We report on the nonequilibrium quasiparticle dynamics in BaFeAs on
both the hole doped (BaKFeAs) and electron doped
(BaFeCoAs) sides of the phase diagram using ultrafast
pump-probe spectroscopy. Below , measurements conducted at low
photoinjected quasiparticle densities in the optimally and overdoped
BaKFeAs samples reveal two distinct relaxation processes: a
fast component whose decay rate increases linearly with excitation density and
a slow component with an excitation density independent decay rate. We argue
that these two processes reflect the recombination of quasiparticles in the two
hole bands through intraband and interband processes. We also find that the
thermal recombination rate of quasiparticles increases quadratically with
temperature in these samples. The temperature and excitation density dependence
of the decays indicates fully gapped hole bands and nodal or very anisotropic
electron bands. At higher excitation densities and lower hole dopings, the
dependence of the dynamics on quasiparticle density disappears as the data are
more readily understood in terms of a model which accounts for the
quasiequilibrium temperature attained by the sample. In the
BaFeCoAs samples, dependence of the recombination rate on
quasiparticle density at low dopings (i.e., ) is suppressed upon
submergence of the inner hole band and quasiparticle relaxation occurs in a
slow, density independent manner.Comment: Accepted to Phys. Rev.
Bandgaps in the propagation and scattering of surface water waves over cylindrical steps
Here we investigate the propagation and scattering of surface water waves by
arrays of bottom-mounted cylindrical steps. Both periodic and random
arrangements of the steps are considered. The wave transmission through the
arrays is computed using the multiple scattering method based upon a recently
derived formulation. For the periodic case, the results are compared to the
band structure calculation. We demonstrate that complete band gaps can be
obtained in such a system. Furthermore, we show that the randomization of the
location of the steps can significantly reduce the transmission of water waves.
Comparison with other systems is also discussed.Comment: 4 pages, 3 figure
Finding polynomial loop invariants for probabilistic programs
Quantitative loop invariants are an essential element in the verification of
probabilistic programs. Recently, multivariate Lagrange interpolation has been
applied to synthesizing polynomial invariants. In this paper, we propose an
alternative approach. First, we fix a polynomial template as a candidate of a
loop invariant. Using Stengle's Positivstellensatz and a transformation to a
sum-of-squares problem, we find sufficient conditions on the coefficients.
Then, we solve a semidefinite programming feasibility problem to synthesize the
loop invariants. If the semidefinite program is unfeasible, we backtrack after
increasing the degree of the template. Our approach is semi-complete in the
sense that it will always lead us to a feasible solution if one exists and
numerical errors are small. Experimental results show the efficiency of our
approach.Comment: accompanies an ATVA 2017 submissio
- …