666 research outputs found
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Binary particle coagulation can be modelled as the repeated random process of
the combination of two particles to form a third. The kinetics can be
represented by population rate equations based on a mean field assumption,
according to which the rate of aggregation is taken to be proportional to the
product of the mean populations of the two participants. This can be a poor
approximation when the mean populations are small. However, using the Poisson
representation it is possible to derive a set of rate equations that go beyond
mean field theory, describing pseudo-populations that are continuous, noisy and
complex, but where averaging over the noise and initial conditions gives the
mean of the physical population. Such an approach is explored for the simple
case of a size-independent rate of coagulation between particles. Analytical
results are compared with numerical computations and with results derived by
other means. In the numerical work we encounter instabilities that can be
eliminated using a suitable 'gauge' transformation of the problem [P. D.
Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the
application of the Cameron-Martin-Girsanov formula describing a shift in a
probability measure. The cost of such a procedure is to introduce additional
statistical noise into the numerical results, but we identify an optimised
gauge transformation where this difficulty is minimal for the main properties
of interest. For more complicated systems, such an approach is likely to be
computationally cheaper than Monte Carlo simulation
Manufactured Solutions for Verification of a Coupled Flow and Material Response Code
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106457/1/AIAA2013-2646.pd
New Renormalization Group Equations and the Naturalness Problem
Looking for an observable manifestation of the so-called unnaturalness of
scalar fields we introduce a seemingly new set of differential equations for
connected Green functions. These equations describe the momentum dependence of
the Green functions and are close relatives to the previously known
renormalization group equations. Applying the new equations to the theory of
scalar field with interaction we identify a relation between the
four-point Green function and the propagator which expresses the unnaturalness
of the scalar field. Possible manifestations of the unnaturalness at low
momenta are briefly discussed.Comment: 12 revtex pages; a coefficient has been corrected in eq. (34), four
new references added; final version to appear in Phys. Rev.
Generating Functional for Strong and Nonleptonic Weak Interactions
The generating functional for Green functions of quark currents is given in
closed form to next-to-leading order in the low-energy expansion for chiral
SU(3), including one-loop amplitudes with up to three meson propagators. Matrix
elements and form factors for strong and nonleptonic weak processes with at
most six external states can be extracted from this functional by performing
three-dimensional flavour traces. To implement this procedure, a Mathematica
program is provided that evaluates amplitudes with at most six external mesons,
photons (real or virtual) and virtual W (semileptonic form factors). The
program is illustrated with several examples that can be compared with existing
calculations.Comment: 26 pages; references added, comparison with other programs added,
small changes in the text, version to appear in JHE
Single particle multipole expansions from Micromagnetic Tomography
Micromagnetic tomography aims at reconstructing large numbers of individual
magnetizations of magnetic particles from combining high-resolution magnetic
scanning techniques with micro X-ray computed tomography (microCT). Previous
work demonstrated that dipole moments can be robustly inferred, and
mathematical analysis showed that the potential field of each particle is
uniquely determined. Here, we describe a mathematical procedure to recover
higher orders of the magnetic potential of the individual magnetic particles in
terms of their spherical harmonic expansions (SHE). We test this approach on
data from scanning superconducting quantum interference device microscopy and
microCT of a reference sample. For particles with high signal-to-noise ratio of
the magnetic scan we demonstrate that SHE up to order can be robustly
recovered. This additional level of detail restricts the possible internal
magnetization structures of the particles and provides valuable rock magnetic
information with respect to their stability and reliability as paleomagnetic
remanence carriers. Micromagnetic tomography therefore enables a new approach
for detailed rock magnetic studies on large ensembles of individual particles.Comment: 21 pages, 4 Figures, 3 Tables. For Supplemental Material see
"Ancillary files" in this arxiv websit
Wind-induced ground motion: dynamic model and non-uniform structure for ground
Wind-induced ground vibrations are a source of noise in seismic surveys. In a previous study, a wind-ground coupling theory was developed to predict the power spectral density (PSD) of ground motions caused by wind perturbations on the ground surface. The prediction was developed using a superposition of the point source response of an elastic isotropic homogeneous medium deforming quasi-statically with the statistical description of the wind-induced pressure fluctuations on the ground. Model predictions and field measurements were in agreement for the normal component of the displacement but under predicted the horizontal component. In this paper, two generalizations are investigated to see if they lead to increased horizontal displacement predictions: 1. First, the dynamic point source response is calculated and incorporated in the ground displacement calculation. Measured ground responses are used to incorporate losses into the dynamic calculation. 2. The quasi-static response function for three different types of non-uniform grounds are calculated and used in the seismic wind noise superposition. The dynamic point source response and the three more realistic ground models result in larger horizontal displacements for the point source at distances on the order of 1 m or greater from the source. However, the superposition to predict the seismic wind noise is dominated by the displacements very close to the point source where the prediction is unchanged. This research indicates that the modeling of the wind-induced pressure source distribution must be improved to predict the observed equivalency of the vertical and horizontal displacements
The exact equivalence of the two-flavour strong coupling lattice Schwinger model with Wilson fermions to a vertex model
In this paper a method previously employed by Salmhofer to establish an exact
equivalence of the one-flavour strong coupling lattice Schwinger model with
Wilson fermions to some 8-vertex model is applied to the case with two
flavours. As this method is fairly general and can be applied to strong
coupling QED and purely fermionic models with any (sufficiently small) number
of Wilson fermions in any dimension the purpose of the present study is mainly
a methodical one in order to gain some further experience with it. In the paper
the vertex model equivalent to the two-flavour strong coupling lattice
Schwinger model with Wilson fermions is found. It turns out to be some modified
3-state 20-vertex model on the square lattice, which can also be understood as
a regular 6-state vertex model. In analogy with the one- flavour case, this
model can be viewed as some loop model.Comment: 22 pages LaTe
Heisenberg XXZ Model and Quantum Galilei Group
The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed in
terms of the symmetry given by the quantum Galilei group Gamma_q(1). We show
that the magnon excitations and the s=1/2, n-magnon bound states are determined
by the algebra. Thus the Gamma_q(1) symmetry provides a description that
naturally induces the Bethe Ansatz. The recurrence relations determined by
Gamma_q(1) permit to express the energy of the n-magnon bound states in a
closed form in terms of Tchebischeff polynomials.Comment: (pag. 10
Quantum repeaters and quantum key distribution: analysis of secret key rates
We analyze various prominent quantum repeater protocols in the context of
long-distance quantum key distribution. These protocols are the original
quantum repeater proposal by Briegel, D\"ur, Cirac and Zoller, the so-called
hybrid quantum repeater using optical coherent states dispersively interacting
with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using
atomic ensembles together with linear optics and, in its most recent extension,
heralded qubit amplifiers. For our analysis, we investigate the most important
experimental parameters of every repeater component and find their minimally
required values for obtaining a nonzero secret key. Additionally, we examine in
detail the impact of device imperfections on the final secret key rate and on
the optimal number of rounds of distillation when the entangled states are
purified right after their initial distribution.Comment: Published versio
Speed and entropy of an interacting continuous time quantum walk
We present some dynamic and entropic considerations about the evolution of a
continuous time quantum walk implementing the clock of an autonomous machine.
On a simple model, we study in quite explicit terms the Lindblad evolution of
the clocked subsystem, relating the evolution of its entropy to the spreading
of the wave packet of the clock. We explore possible ways of reducing the
generation of entropy in the clocked subsystem, as it amounts to a deficit in
the probability of finding the target state of the computation. We are thus
lead to examine the benefits of abandoning some classical prejudice about how a
clocking mechanism should operate.Comment: 25 pages, 14 figure
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