11,672 research outputs found
Weakly nonparaxial effects on the propagation of (1+1)D spatial solitons in inhomogeneous Kerr media
The widely-used approach to study the beam propagation in Kerr media is based on the slowly varying envelope approximation (SVEA) which is also known as the paraxial approximation. Within this approximation, the beam evolution is described by the nonlinear Schrödinger (NLS) equation. In this paper, we extend the NLS equation by including higher-order terms to study the effects of nonparaxiality on the soliton propagation in inhomogeneous Kerr media. The result is still a one-way wave equation which means that all back-reflections are neglected. The accuracy of this approximation exceeds the standard SVEA. By performing several numerical simulations, we show that the NLS equation produces reasonably good predictions for relatively small degrees of nonparaxiality, as expected. However, in the regions where the envelope beam is changing rapidly as in the breakup of a multisoliton bound state, the nonparaxiality plays an important role
Effect of Bilayer Thickness on Membrane Bending Rigidity
The bending rigidity of bilayer vesicles self-assembled from
amphiphilic diblock copolymers has been measured using single and
dual-micropipet techniques. These copolymers are nearly a factor of 5 greater
in hydrophobic membrane thickness than their lipid counterparts, and an
order of magnitude larger in molecular weight . The macromolecular
structure of these amphiphiles lends insight into and extends relationships for
traditional surfactant behavior. We find the scaling of with thickness to
be nearly quadratic, in agreement with existing theories for bilayer membranes.
The results here are key to understanding and designing soft interfaces such as
biomembrane mimetics
Helmholtz solver with transparent influx boundary conditions and nonuniform exterior
Boundary conditions for a 2D finite element Helmholtz solver are derived, which allow scattered light to leave the calculation domain in the presence of outgoing waveguides. Influx of light, through a waveguide or otherwise, can be prescribed at any boundary
A combination of Dirichlet to Neumann operators and perfectly matched layers as boundary conditions for optical finite element simulations
By combining Dirichlet to Neumann (DtN) operators and Perfectly Matched Layers (PML’s) as boundary conditions on a rectangular domain on which the Helmholtz equation is solved, the disadvantages of both methods are greatly diminished. Due to the DtN operators, light may be accurately fluxed into the domain, while the PML’s absorb light that is reflected from the corners of the domain when only DtN boundaries are used
Signatures of few-body resonances in finite volume
We study systems of bosons and fermions in finite periodic boxes and show how
the existence and properties of few-body resonances can be extracted from
studying the volume dependence of the calculated energy spectra. Using a
plane-wave-based discrete variable representation to conveniently implement
periodic boundary conditions, we establish that avoided level crossings occur
in the spectra of up to four particles and can be linked to the existence of
multi-body resonances. To benchmark our method we use two-body calculations,
where resonance properties can be determined with other methods, as well as a
three-boson model interaction known to generate a three-boson resonance state.
Finding good agreement for these cases, we then predict three-body and
four-body resonances for models using a shifted Gaussian potential. Our results
establish few-body finite-volume calculations as a new tool to study few-body
resonances. In particular, the approach can be used to study few-neutron
systems, where such states have been conjectured to exist.Comment: 13 pages, 10 figures, 2 tables, published versio
Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?
We present quantum Monte Carlo calculations of few-neutron systems confined
in external potentials based on local chiral interactions at
next-to-next-to-leading order in chiral effective field theory. The energy and
radial densities for these systems are calculated in different external
Woods-Saxon potentials. We assume that their extrapolation to zero
external-potential depth provides a quantitative estimate of three- and
four-neutron resonances. The validity of this assumption is demonstrated by
benchmarking with an exact diagonalization in the two-body case. We find that
the extrapolated trineutron resonance, as well as the energy for shallow well
depths, is lower than the tetraneutron resonance energy. This suggests that a
three-neutron resonance exists below a four-neutron resonance in nature and is
potentially measurable. To confirm that the relative ordering of three- and
four-neutron resonances is not an artifact of the external confinement, we test
that the odd-even staggering in the helium isotopic chain is reproduced within
this approach. Finally, we discuss similarities between our results and
ultracold Fermi gases.Comment: 6 pages, 5 figures, version compatible with published lette
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The economics of health
This report presents results from the Economics of Health project funded by the East Midlands Development Agency. The work was undertaken between November 2007 and February 2008. The main aim of the project was to examine the relationship between mental and physical health and employability, labour market participation and economic performance, with specific attention given to the direction of causal relationships
Molecular Weight Dependence of Polymersome Membrane Elasticity and Stability
Vesicles prepared in water from a series of diblock copolymers and termed
"polymersomes" are physically characterized. With increasing molecular weight
, the hydrophobic core thickness for the self-assembled bilayers
of polyethyleneoxide - polybutadiene (PEO-PBD) increases up to 20 -
considerably greater than any previously studied lipid system. The mechanical
responses of these membranes, specifically, the area elastic modulus and
maximal areal strain are measured by micromanipulation. As expected
for interface-dominated elasticity, ( 100 ) is found to be
independent of . Related mean-field ideas also predict a limiting
value for which is universal and about 10-fold above that typical of
lipids. Experiments indeed show generally increases with
, coming close to the theoretical limit before stress relaxation is
opposed by what might be chain entanglements at the highest . The
results highlight the interfacial limits of self-assemblies at the nano-scale.Comment: 16 pages, 5 figures, and 1 tabl
Flight Gate Assignment with a Quantum Annealer
Optimal flight gate assignment is a highly relevant optimization problem from
airport management. Among others, an important goal is the minimization of the
total transit time of the passengers. The corresponding objective function is
quadratic in the binary decision variables encoding the flight-to-gate
assignment. Hence, it is a quadratic assignment problem being hard to solve in
general. In this work we investigate the solvability of this problem with a
D-Wave quantum annealer. These machines are optimizers for quadratic
unconstrained optimization problems (QUBO). Therefore the flight gate
assignment problem seems to be well suited for these machines. We use real
world data from a mid-sized German airport as well as simulation based data to
extract typical instances small enough to be amenable to the D-Wave machine. In
order to mitigate precision problems, we employ bin packing on the passenger
numbers to reduce the precision requirements of the extracted instances. We
find that, for the instances we investigated, the bin packing has little effect
on the solution quality. Hence, we were able to solve small problem instances
extracted from real data with the D-Wave 2000Q quantum annealer.Comment: Updated figure
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