2,021 research outputs found
Raman signatures of classical and quantum phases in coupled dots: A theoretical prediction
We study electron molecules in realistic vertically coupled quantum dots in a
strong magnetic field. Computing the energy spectrum, pair correlation
functions, and dynamical form factor as a function of inter-dot coupling via
diagonalization of the many-body Hamiltonian, we identify structural
transitions between different phases, some of which do not have a classical
counterpart. The calculated Raman cross section shows how such phases can be
experimentally singled out.Comment: 9 pages, 2 postscript figures, 1 colour postscript figure, Latex 2e,
Europhysics Letters style and epsfig macros. Submitted to Europhysics Letter
A model for shock wave chaos
We propose the following model equation:
that predicts chaotic shock waves.
It is given on the half-line and the shock is located at for any
. Here is the shock state and the source term is assumed
to satisfy certain integrability constraints as explained in the main text. We
demonstrate that this simple equation reproduces many of the properties of
detonations in gaseous mixtures, which one finds by solving the reactive Euler
equations: existence of steady traveling-wave solutions and their instability,
a cascade of period-doubling bifurcations, onset of chaos, and shock formation
in the reaction zone.Comment: 4 pages, 4 figure
Constraint and gauge shocks in one-dimensional numerical relativity
We study how different types of blow-ups can occur in systems of hyperbolic
evolution equations of the type found in general relativity. In particular, we
discuss two independent criteria that can be used to determine when such
blow-ups can be expected. One criteria is related with the so-called geometric
blow-up leading to gradient catastrophes, while the other is based upon the
ODE-mechanism leading to blow-ups within finite time. We show how both
mechanisms work in the case of a simple one-dimensional wave equation with a
dynamic wave speed and sources, and later explore how those blow-ups can appear
in one-dimensional numerical relativity. In the latter case we recover the well
known ``gauge shocks'' associated with Bona-Masso type slicing conditions.
However, a crucial result of this study has been the identification of a second
family of blow-ups associated with the way in which the constraints have been
used to construct a hyperbolic formulation. We call these blow-ups ``constraint
shocks'' and show that they are formulation specific, and that choices can be
made to eliminate them or at least make them less severe.Comment: 19 pages, 8 figures and 1 table, revised version including several
amendments suggested by the refere
Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
In this paper, we investigate the performance of pseudo-spectral methods in
computing nearly singular solutions of fluid dynamics equations. We consider
two different ways of removing the aliasing errors in a pseudo-spectral method.
The first one is the traditional 2/3 dealiasing rule. The second one is a high
(36th) order Fourier smoothing which keeps a significant portion of the Fourier
modes beyond the 2/3 cut-off point in the Fourier spectrum for the 2/3
dealiasing method. Both the 1D Burgers equation and the 3D incompressible Euler
equations are considered. We demonstrate that the pseudo-spectral method with
the high order Fourier smoothing gives a much better performance than the
pseudo-spectral method with the 2/3 dealiasing rule. Moreover, we show that the
high order Fourier smoothing method captures about more effective
Fourier modes in each dimension than the 2/3 dealiasing method. For the 3D
Euler equations, the gain in the effective Fourier codes for the high order
Fourier smoothing method can be as large as 20% over the 2/3 dealiasing method.
Another interesting observation is that the error produced by the high order
Fourier smoothing method is highly localized near the region where the solution
is most singular, while the 2/3 dealiasing method tends to produce oscillations
in the entire domain. The high order Fourier smoothing method is also found be
very stable dynamically. No high frequency instability has been observed.Comment: 26 pages, 23 figure
A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations
We discuss the scalable parallel solution of the Poisson equation within a
Particle-In-Cell (PIC) code for the simulation of electron beams in particle
accelerators of irregular shape. The problem is discretized by Finite
Differences. Depending on the treatment of the Dirichlet boundary the resulting
system of equations is symmetric or `mildly' nonsymmetric positive definite. In
all cases, the system is solved by the preconditioned conjugate gradient
algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG)
preconditioning. We investigate variants of the implementation of SA-AMG that
lead to considerable improvements in the execution times. We demonstrate good
scalability of the solver on distributed memory parallel processor with up to
2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver
that is more commonly used for applications in beam dynamics
Numerical evolution of multiple black holes with accurate initial data
We present numerical evolutions of three equal-mass black holes using the
moving puncture approach. We calculate puncture initial data for three black
holes solving the constraint equations by means of a high-order multigrid
elliptic solver. Using these initial data, we show the results for three black
hole evolutions with sixth-order waveform convergence. We compare results
obtained with the BAM and AMSS-NCKU codes with previous results. The
approximate analytic solution to the Hamiltonian constraint used in previous
simulations of three black holes leads to different dynamics and waveforms. We
present some numerical experiments showing the evolution of four black holes
and the resulting gravitational waveform.Comment: Published in PR
First order hyperbolic formalism for Numerical Relativity
The causal structure of Einstein's evolution equations is considered. We show
that in general they can be written as a first order system of balance laws for
any choice of slicing or shift. We also show how certain terms in the evolution
equations, that can lead to numerical inaccuracies, can be eliminated by using
the Hamiltonian constraint. Furthermore, we show that the entire system is
hyperbolic when the time coordinate is chosen in an invariant algebraic way,
and for any fixed choice of the shift. This is achieved by using the momentum
constraints in such as way that no additional space or time derivatives of the
equations need to be computed. The slicings that allow hyperbolicity in this
formulation belong to a large class, including harmonic, maximal, and many
others that have been commonly used in numerical relativity. We provide details
of some of the advanced numerical methods that this formulation of the
equations allows, and we also discuss certain advantages that a hyperbolic
formulation provides when treating boundary conditions.Comment: To appear in Phys. Rev.
Projected SO(5) Hamiltonian for Cuprates and Its Applications
The projected SO(5) (pSO(5)) Hamiltonian incorporates the quantum spin and
superconducting fluctuations of underdoped cuprates in terms of four bosons
moving on a coarse grained lattice. A simple mean field approximation can
explain some key feautures of the experimental phase diagram: (i) The Mott
transition between antiferromagnet and superconductor, (ii) The increase of T_c
and superfluid stiffness with hole concentration x and (iii) The increase of
antiferromagnetic resonance energy as sqrt{x-x_c} in the superconducting phase.
We apply this theory to explain the ``two gaps'' problem found in underdoped
cuprate Superconductor-Normal- Superconductor junctions. In particular we
explain the sharp subgap Andreev peaks of the differential resistance, as
signatures of the antiferromagnetic resonance (the magnon mass gap). A critical
test of this theory is proposed. The tunneling charge, as measured by shot
noise, should change by increments of Delta Q= 2e at the Andreev peaks, rather
than by Delta Q=e as in conventional superconductors.Comment: 3 EPS figure
Macro-Architectures in Spinal Cord Scaffold Implants Influence Regeneration
Abstract Biomaterial scaffold architecture has not been investigated as a tunable source of influence on spinal cord regeneration. This study compared regeneration in a transected spinal cord within various designed-macro-architecture scaffolds to determine if these architectures alone could enhance regeneration. Three-dimensional (3-D) designs were created and molds were built on a 3-D printer. Salt-leached porous poly(ε-caprolactone) was cast in five different macro-architectures: cylinder, tube, channel, open-path with core, and open-path without core. The two open-path designs were created in this experiment to compare different supportive aspects of architecture provided by scaffolds and their influence on regeneration. Rats received T8 transections and implanted scaffolds for 1 and 3 months. Overall morphology and orientation of sections were characterized by H&E, luxol fast blue, and cresyl violet staining. Borders between intact gray matter and non-regenerated defect were observed from GFAP immunolabeling. Nerve fibers and regenerating axons were identified with Tuj-1 immunolabeling. The open-path designs allowed extension of myelinated fibers along the length of the defect both exterior to and inside the scaffolds and maintained their original defect length up to 3 months. In contrast, the cylinder, tube, and channel implants had a doubling of defect length from secondary damage and large scar and cyst formation with no neural tissue bridging. The open-path scaffold architectures enhanced spinal cord regeneration compared to the three other designs without the use of biological factors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63279/1/neu.2007.0473.pd
First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
We prescribe a choice of 18 variables in all that casts the equations of the
fully nonlinear characteristic formulation of general relativity in
first--order quasi-linear canonical form. At the analytical level, a
formulation of this type allows us to make concrete statements about existence
of solutions. In addition, it offers concrete advantages for numerical
applications as it now becomes possible to incorporate advanced numerical
techniques for first order systems, which had thus far not been applicable to
the characteristic problem of the Einstein equations, as well as in providing a
framework for a unified treatment of the vacuum and matter problems. This is of
relevance to the accurate simulation of gravitational waves emitted in
astrophysical scenarios such as stellar core collapse.Comment: revtex4, 7 pages, text and references added, typos corrected, to
appear in Phys. Rev.
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