40,132 research outputs found
Topological meaning of Z numbers in time reversal invariant systems
We show that the Z invariant, which classifies the topological properties
of time reversal invariant insulators, has deep relationship with the global
anomaly. Although the second Chern number is the basic topological invariant
characterizing time reversal systems, we show that the relative phase between
the Kramers doublet reduces the topological quantum number Z to Z.Comment: 4 pages, typos correcte
Neural-Network Vector Controller for Permanent-Magnet Synchronous Motor Drives: Simulated and Hardware-Validated Results
This paper focuses on current control in a permanentmagnet synchronous motor (PMSM). The paper has two main objectives: The first objective is to develop a neural-network (NN) vector controller to overcome the decoupling inaccuracy problem associated with conventional PI-based vector-control methods. The NN is developed using the full dynamic equation of a PMSM, and trained to implement optimal control based on approximate dynamic programming. The second objective is to evaluate the robust and adaptive performance of the NN controller against that of the conventional standard vector controller under motor parameter variation and dynamic control conditions by (a) simulating the behavior of a PMSM typically used in realistic electric vehicle applications and (b) building an experimental system for hardware validation as well as combined hardware and simulation evaluation. The results demonstrate that the NN controller outperforms conventional vector controllers in both simulation and hardware implementation
Phase Transformations in Binary Colloidal Monolayers
Phase transformations can be difficult to characterize at the microscopic
level due to the inability to directly observe individual atomic motions. Model
colloidal systems, by contrast, permit the direct observation of individual
particle dynamics and of collective rearrangements, which allows for real-space
characterization of phase transitions. Here, we study a quasi-two-dimensional,
binary colloidal alloy that exhibits liquid-solid and solid-solid phase
transitions, focusing on the kinetics of a diffusionless transformation between
two crystal phases. Experiments are conducted on a monolayer of magnetic and
nonmagnetic spheres suspended in a thin layer of ferrofluid and exposed to a
tunable magnetic field. A theoretical model of hard spheres with point dipoles
at their centers is used to guide the choice of experimental parameters and
characterize the underlying materials physics. When the applied field is normal
to the fluid layer, a checkerboard crystal forms; when the angle between the
field and the normal is sufficiently large, a striped crystal assembles. As the
field is slowly tilted away from the normal, we find that the transformation
pathway between the two phases depends strongly on crystal orientation, field
strength, and degree of confinement of the monolayer. In some cases, the
pathway occurs by smooth magnetostrictive shear, while in others it involves
the sudden formation of martensitic plates.Comment: 13 pages, 7 figures. Soft Matter Latex template was used. Published
online in Soft Matter, 201
Integral geometry of complex space forms
We show how Alesker's theory of valuations on manifolds gives rise to an
algebraic picture of the integral geometry of any Riemannian isotropic space.
We then apply this method to give a thorough account of the integral geometry
of the complex space forms, i.e. complex projective space, complex hyperbolic
space and complex euclidean space. In particular, we compute the family of
kinematic formulas for invariant valuations and invariant curvature measures in
these spaces. In addition to new and more efficient framings of the tube
formulas of Gray and the kinematic formulas of Shifrin, this approach yields a
new formula expressing the volumes of the tubes about a totally real
submanifold in terms of its intrinsic Riemannian structure. We also show by
direct calculation that the Lipschitz-Killing valuations stabilize the subspace
of invariant angular curvature measures, suggesting the possibility that a
similar phenomenon holds for all Riemannian manifolds. We conclude with a
number of open questions and conjectures.Comment: 68 pages; minor change
A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment
We present a preferential attachment growth model to obtain the distribution
of number of units in the classes which may represent business firms
or other socio-economic entities. We found that is described in its
central part by a power law with an exponent which depends on
the probability of entry of new classes, . In a particular problem of city
population this distribution is equivalent to the well known Zipf law. In the
absence of the new classes entry, the distribution is exponential. Using
analytical form of and assuming proportional growth for units, we derive
, the distribution of business firm growth rates. The model predicts that
has a Laplacian cusp in the central part and asymptotic power-law tails
with an exponent . We test the analytical expressions derived using
heuristic arguments by simulations. The model might also explain the
size-variance relationship of the firm growth rates.Comment: 19 pages 6 figures Applications of Physics in Financial Analysis,
APFA
The Growth of Business Firms: Theoretical Framework and Empirical Evidence
We introduce a model of proportional growth to explain the distribution of
business firm growth rates. The model predicts that the distribution is
exponential in the central part and depicts an asymptotic power-law behavior in
the tails with an exponent 3. Because of data limitations, previous studies in
this field have been focusing exclusively on the Laplace shape of the body of
the distribution. In this article, we test the model at different levels of
aggregation in the economy, from products to firms to countries, and we find
that the model's predictions agree with empirical growth distributions and
size-variance relationships.Comment: 22 pages, 5 Postscript figures, uses revtex4. to be published in
Proc. Natl. Acad. Sci. (2005
A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence
We introduce a model of proportional growth to explain the distribution
of business firm growth rates. The model predicts that is Laplace
in the central part and depicts an asymptotic power-law behavior in the tails
with an exponent . Because of data limitations, previous studies in
this field have been focusing exclusively on the Laplace shape of the body of
the distribution. We test the model at different levels of aggregation in the
economy, from products, to firms, to countries, and we find that the its
predictions are in good agreement with empirical evidence on both growth
distributions and size-variance relationships.Comment: 8 pages, 4 figure
States interpolating between number and coherent states and their interaction with atomic systems
Using the eigenvalue definition of binomial states we construct new
intermediate number-coherent states which reduce to number and coherent states
in two different limits. We reveal the connection of these intermediate states
with photon-added coherent states and investigate their non-classical
properties and quasi-probability distributions in detail. It is of interest to
note that these new states, which interpolate between coherent states and
number states, neither of which exhibit squeezing, are nevertheless squeezed
states. A scheme to produce these states is proposed. We also study the
interaction of these states with atomic systems in the framework of the
two-photon Jaynes-Cummings model, and describe the response of the atomic
system as it varies between the pure Rabi oscillation and the collapse-revival
mode and investigate field observables such as photon number distribution,
entropy and the Q-function.Comment: 26 pages, 29 EPS figures, Latex, Accepted for publication in J.Phys.
Scalar Meson Spectroscopy with Lattice Staggered Fermions
With sufficiently light up and down quarks the isovector () and
isosinglet () scalar meson propagators are dominated at large distance by
two-meson states. In the staggered fermion formulation of lattice quantum
chromodynamics, taste-symmetry breaking causes a proliferation of two-meson
states that further complicates the analysis of these channels. Many of them
are unphysical artifacts of the lattice approximation. They are expected to
disappear in the continuum limit. The staggered-fermion fourth-root procedure
has its purported counterpart in rooted staggered chiral perturbation theory
(rSXPT). Fortunately, the rooted theory provides a strict framework that
permits the analysis of scalar meson correlators in terms of only a small
number of low energy couplings. Thus the analysis of the point-to-point scalar
meson correlators in this context gives a useful consistency check of the
fourth-root procedure and its proposed chiral realization. Through numerical
simulation we have measured correlators for both the and channels
in the ``Asqtad'' improved staggered fermion formulation in a lattice ensemble
with lattice spacing fm. We analyze those correlators in the context
of rSXPT and obtain values of the low energy chiral couplings that are
reasonably consistent with previous determinations.Comment: 23 pp., 3 figs., submitted to Phys. Rev.
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