4,409 research outputs found
Solving the time-dependent Schr\"odinger equation with absorbing boundary conditions and source terms in Mathematica 6.0
In recent decades a lot of research has been done on the numerical solution
of the time-dependent Schr\"odinger equation. On the one hand, some of the
proposed numerical methods do not need any kind of matrix inversion, but source
terms cannot be easily implemented into this schemes; on the other, some
methods involving matrix inversion can implement source terms in a natural way,
but are not easy to implement into some computational software programs widely
used by non-experts in programming (e.g. Mathematica). We present a simple
method to solve the time-dependent Schr\"odinger equation by using a standard
Crank-Nicholson method together with a Cayley's form for the finite-difference
representation of evolution operator. Here, such standard numerical scheme has
been simplified by inverting analytically the matrix of the evolution operator
in position representation. The analytical inversion of the N x N matrix let us
easily and fully implement the numerical method, with or without source terms,
into Mathematica or even into any numerical computing language or computational
software used for scientific computing.Comment: 15 pages, 7 figure
Role of material properties and mesostructure on dynamic deformation and shear instability in Al-W granular composites
Dynamic experiments with Al-W granular/porous composites revealed
qualitatively different behavior with respect to shear localization depending
on bonding between Al particles. Two-dimensional numerical modeling was used to
explore the mesomechanics of the large strain dynamic deformation in Al-W
granular/porous composites and explain the experimentally observed differences
in shear localization between composites with various mesostructures.
Specifically, the bonding between the Al particles, the porosity, the roles of
the relative particle sizes of Al and W, the arrangements of the W particles,
and the material properties of Al were investigated using numerical
calculations. It was demonstrated in simulations that the bonding between the
"soft" Al particles facilitated shear localization as seen in the experiments.
Numerical calculations and experiments revealed that the mechanism of the shear
localization in granular composites is mainly due to the local high strain flow
of "soft" Al around the "rigid" W particles causing localized damage
accumulation and subsequent growth of the meso/macro shear bands/cracks. The
"rigid" W particles were the major geometrical factor determining the
initiation and propagation of "kinked" shear bands in the matrix of "soft" Al
particles, leaving some areas free of extensive plastic deformation as observed
in experiments and numerical calculations.Comment: 10 pages, 14 figures, submitted to Journal of Applied Physic
Modeling the plasma near-wakes
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76834/1/AIAA-7721-514.pd
First Penning-trap mass measurement in the millisecond half-life range: the exotic halo nucleus 11Li
In this letter, we report a new mass for Li using the trapping
experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived
nuclide, , for which a mass measurement has ever been
performed with a Penning trap. Combined with our mass measurements of
Li we derive a new two-neutron separation energy of 369.15(65) keV: a
factor of seven more precise than the best previous value. This new value is a
critical ingredient for the determination of the halo charge radius from
isotope-shift measurements. We also report results from state-of-the-art
atomic-physics calculations using the new mass and extract a new charge radius
for Li. This result is a remarkable confluence of nuclear and atomic
physics.Comment: Formatted for submission to PR
Spin transport theory in ferromagnet/semiconductor systems with non-collinear magnetization configurations
We present a comprehensive theory of spin transport in a non-degenerate
semiconductor that is in contact with multiple ferromagnetic terminals. The
spin dynamics in the semiconductor is studied during a perturbation of a
general, non-collinear magnetization configuration and a method is shown to
identify the various configurations from current signals. The conventional
Landauer-B\"{u}ttiker description for spin transport across Schottky contacts
is generalized by the use of a non-linearized I-V relation, and it is extended
by taking into account non-coherent transport mechanisms. The theory is used to
analyze a three terminal lateral structure where a significant difference in
the spin accumulation profile is found when comparing the results of this model
with the conventional model.Comment: 17 pages, 10 figure
Symmetry-preserving discrete schemes for some heat transfer equations
Lie group analysis of differential equations is a generally recognized
method, which provides invariant solutions, integrability, conservation laws
etc. In this paper we present three characteristic examples of the construction
of invariant difference equations and meshes, where the original continuous
symmetries are preserved in discrete models. Conservation of symmetries in
difference modeling helps to retain qualitative properties of the differential
equations in their difference counterparts.Comment: 21 pages, 4 ps figure
Semianalytic theory of self-similar optical propagation and mode locking using a shape-adaptive model pulse
A semianalytic theory for the pulse dynamics in similariton amplifiers and
lasers is presented, based on a model pulse with adaptive shape. By changing a
single parameter, this test function can be continuously tweaked between a pure
Gaussian and a pure parabolic profile and can even represent sech-like pulses,
the shape of a soliton. This approach allows us to describe the pulse evolution
in the self-similar and other regimes of optical propagation. Employing the
method of moments, the evolution equations for the characteristic pulse
parameters are derived from the governing nonlinear Schr\"odinger or
Ginzburg-Landau equation. Due to its greatly reduced complexity, this
description allows for extensive parameter optimization, and can aid intuitive
understanding of the dynamics. As an application of this approach, we model a
soliton-similariton laser and validate the results against numerical
simulations. This constitutes a semianalytic model of the soliton-similariton
laser. Due to the versatility of the model pulse, it can also prove useful in
other application areas
Loop Quantum Cosmology IV: Discrete Time Evolution
Using general features of recent quantizations of the Hamiltonian constraint
in loop quantum gravity and loop quantum cosmology, a dynamical interpretation
of the constraint equation as evolution equation is presented. This involves a
transformation from the connection to a dreibein representation and the
selection of an internal time variable. Due to the discrete nature of
geometrical quantities in loop quantum gravity also time turns out to be
discrete leading to a difference rather than differential evolution equation.
Furthermore, evolving observables are discussed in this framework which enables
an investigation of physical spectra of geometrical quantities. In particular,
the physical volume spectrum is proven to equal the discrete kinematical volume
spectrum in loop quantum cosmology.Comment: 21 page
Interplay of chiral and helical states in a Quantum Spin Hall Insulator lateral junction
We study the electronic transport across an electrostatically-gated lateral
junction in a HgTe quantum well, a canonical 2D topological insulator, with and
without applied magnetic field. We control carrier density inside and outside a
junction region independently and hence tune the number and nature of 1D edge
modes propagating in each of those regions. Outside the 2D gap, magnetic field
drives the system to the quantum Hall regime, and chiral states propagate at
the edge. In this regime, we observe fractional plateaus which reflect the
equilibration between 1D chiral modes across the junction. As carrier density
approaches zero in the central region and at moderate fields, we observe
oscillations in resistance that we attribute to Fabry-Perot interference in the
helical states, enabled by the broken time reversal symmetry. At higher fields,
those oscillations disappear, in agreement with the expected absence of helical
states when band inversion is lifted.Comment: 5 pages, 4 figures, supp. ma
Non-classical symmetries and the singular manifold method: A further two examples
This paper discusses two equations with the conditional Painleve property.
The usefulness of the singular manifold method as a tool for determining the
non-classical symmetries that reduce the equations to ordinary differential
equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics
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