title
stringlengths 1
382
| abstract
stringlengths 6
6.09k
⌀ |
|---|---|
Calculation of prompt diphoton production cross sections at Tevatron and
LHC energies | A fully differential calculation in perturbative quantum chromodynamics is
presented for the production of massive photon pairs at hadron colliders. All
next-to-leading order perturbative contributions from quark-antiquark,
gluon-(anti)quark, and gluon-gluon subprocesses are included, as well as
all-orders resummation of initial-state gluon radiation valid at
next-to-next-to-leading logarithmic accuracy. The region of phase space is
specified in which the calculation is most reliable. Good agreement is
demonstrated with data from the Fermilab Tevatron, and predictions are made for
more detailed tests with CDF and DO data. Predictions are shown for
distributions of diphoton pairs produced at the energy of the Large Hadron
Collider (LHC). Distributions of the diphoton pairs from the decay of a Higgs
boson are contrasted with those produced from QCD processes at the LHC, showing
that enhanced sensitivity to the signal can be obtained with judicious
selection of events.
|
Sparsity-certifying Graph Decompositions | We describe a new algorithm, the $(k,\ell)$-pebble game with colors, and use
it obtain a characterization of the family of $(k,\ell)$-sparse graphs and
algorithmic solutions to a family of problems concerning tree decompositions of
graphs. Special instances of sparse graphs appear in rigidity theory and have
received increased attention in recent years. In particular, our colored
pebbles generalize and strengthen the previous results of Lee and Streinu and
give a new proof of the Tutte-Nash-Williams characterization of arboricity. We
also present a new decomposition that certifies sparsity based on the
$(k,\ell)$-pebble game with colors. Our work also exposes connections between
pebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and
Westermann and Hendrickson.
|
The evolution of the Earth-Moon system based on the dark matter field
fluid model | The evolution of Earth-Moon system is described by the dark matter field
fluid model proposed in the Meeting of Division of Particle and Field 2004,
American Physical Society. The current behavior of the Earth-Moon system agrees
with this model very well and the general pattern of the evolution of the
Moon-Earth system described by this model agrees with geological and fossil
evidence. The closest distance of the Moon to Earth was about 259000 km at 4.5
billion years ago, which is far beyond the Roche's limit. The result suggests
that the tidal friction may not be the primary cause for the evolution of the
Earth-Moon system. The average dark matter field fluid constant derived from
Earth-Moon system data is 4.39 x 10^(-22) s^(-1)m^(-1). This model predicts
that the Mars's rotation is also slowing with the angular acceleration rate
about -4.38 x 10^(-22) rad s^(-2).
|
A determinant of Stirling cycle numbers counts unlabeled acyclic
single-source automata | We show that a determinant of Stirling cycle numbers counts unlabeled acyclic
single-source automata. The proof involves a bijection from these automata to
certain marked lattice paths and a sign-reversing involution to evaluate the
determinant.
|
From dyadic $\Lambda_{\alpha}$ to $\Lambda_{\alpha}$ | In this paper we show how to compute the $\Lambda_{\alpha}$ norm, $\alpha\ge
0$, using the dyadic grid. This result is a consequence of the description of
the Hardy spaces $H^p(R^N)$ in terms of dyadic and special atoms.
|
Bosonic characters of atomic Cooper pairs across resonance | We study the two-particle wave function of paired atoms in a Fermi gas with
tunable interaction strengths controlled by Feshbach resonance. The Cooper pair
wave function is examined for its bosonic characters, which is quantified by
the correction of Bose enhancement factor associated with the creation and
annihilation composite particle operators. An example is given for a
three-dimensional uniform gas. Two definitions of Cooper pair wave function are
examined. One of which is chosen to reflect the off-diagonal long range order
(ODLRO). Another one corresponds to a pair projection of a BCS state. On the
side with negative scattering length, we found that paired atoms described by
ODLRO are more bosonic than the pair projected definition. It is also found
that at $(k_F a)^{-1} \ge 1$, both definitions give similar results, where more
than 90% of the atoms occupy the corresponding molecular condensates.
|
Polymer Quantum Mechanics and its Continuum Limit | A rather non-standard quantum representation of the canonical commutation
relations of quantum mechanics systems, known as the polymer representation has
gained some attention in recent years, due to its possible relation with Planck
scale physics. In particular, this approach has been followed in a symmetric
sector of loop quantum gravity known as loop quantum cosmology. Here we explore
different aspects of the relation between the ordinary Schroedinger theory and
the polymer description. The paper has two parts. In the first one, we derive
the polymer quantum mechanics starting from the ordinary Schroedinger theory
and show that the polymer description arises as an appropriate limit. In the
second part we consider the continuum limit of this theory, namely, the reverse
process in which one starts from the discrete theory and tries to recover back
the ordinary Schroedinger quantum mechanics. We consider several examples of
interest, including the harmonic oscillator, the free particle and a simple
cosmological model.
|
Numerical solution of shock and ramp compression for general material
properties | A general formulation was developed to represent material models for
applications in dynamic loading. Numerical methods were devised to calculate
response to shock and ramp compression, and ramp decompression, generalizing
previous solutions for scalar equations of state. The numerical methods were
found to be flexible and robust, and matched analytic results to a high
accuracy. The basic ramp and shock solution methods were coupled to solve for
composite deformation paths, such as shock-induced impacts, and shock
interactions with a planar interface between different materials. These
calculations capture much of the physics of typical material dynamics
experiments, without requiring spatially-resolving simulations. Example
calculations were made of loading histories in metals, illustrating the effects
of plastic work on the temperatures induced in quasi-isentropic and
shock-release experiments, and the effect of a phase transition.
|
The Spitzer c2d Survey of Large, Nearby, Insterstellar Clouds. IX. The
Serpens YSO Population As Observed With IRAC and MIPS | We discuss the results from the combined IRAC and MIPS c2d Spitzer Legacy
observations of the Serpens star-forming region. In particular we present a set
of criteria for isolating bona fide young stellar objects, YSO's, from the
extensive background contamination by extra-galactic objects. We then discuss
the properties of the resulting high confidence set of YSO's. We find 235 such
objects in the 0.85 deg^2 field that was covered with both IRAC and MIPS. An
additional set of 51 lower confidence YSO's outside this area is identified
from the MIPS data combined with 2MASS photometry. We describe two sets of
results, color-color diagrams to compare our observed source properties with
those of theoretical models for star/disk/envelope systems and our own modeling
of the subset of our objects that appear to be star+disks. These objects
exhibit a very wide range of disk properties, from many that can be fit with
actively accreting disks to some with both passive disks and even possibly
debris disks. We find that the luminosity function of YSO's in Serpens extends
down to at least a few x .001 Lsun or lower for an assumed distance of 260 pc.
The lower limit may be set by our inability to distinguish YSO's from
extra-galactic sources more than by the lack of YSO's at very low luminosities.
A spatial clustering analysis shows that the nominally less-evolved YSO's are
more highly clustered than the later stages and that the background
extra-galactic population can be fit by the same two-point correlation function
as seen in other extra-galactic studies. We also present a table of matches
between several previous infrared and X-ray studies of the Serpens YSO
population and our Spitzer data set.
|
Partial cubes: structures, characterizations, and constructions | Partial cubes are isometric subgraphs of hypercubes. Structures on a graph
defined by means of semicubes, and Djokovi\'{c}'s and Winkler's relations play
an important role in the theory of partial cubes. These structures are employed
in the paper to characterize bipartite graphs and partial cubes of arbitrary
dimension. New characterizations are established and new proofs of some known
results are given.
The operations of Cartesian product and pasting, and expansion and
contraction processes are utilized in the paper to construct new partial cubes
from old ones. In particular, the isometric and lattice dimensions of finite
partial cubes obtained by means of these operations are calculated.
|
Computing genus 2 Hilbert-Siegel modular forms over $\Q(\sqrt{5})$ via
the Jacquet-Langlands correspondence | In this paper we present an algorithm for computing Hecke eigensystems of
Hilbert-Siegel cusp forms over real quadratic fields of narrow class number
one. We give some illustrative examples using the quadratic field
$\Q(\sqrt{5})$. In those examples, we identify Hilbert-Siegel eigenforms that
are possible lifts from Hilbert eigenforms.
|
Distribution of integral Fourier Coefficients of a Modular Form of Half
Integral Weight Modulo Primes | Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty}
a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N),\chi)\cap \mathbb{Z}[[q]]$ that does
not satisfy a certain distribution property for modulo odd primes $p$. In this
paper, using Rankin-Cohen Bracket, we extend this result to modular forms of
half integral weight for primes $p \geq 5$. As applications of our main theorem
we derive distribution properties, for modulo primes $p\geq5$, of traces of
singular moduli and Hurwitz class number. We also study an analogue of Newman's
conjecture for overpartitions.
|
$p$-adic Limit of Weakly Holomorphic Modular Forms of Half Integral
Weight | Serre obtained the p-adic limit of the integral Fourier coefficient of
modular forms on $SL_2(\mathbb{Z})$ for $p=2,3,5,7$. In this paper, we extend
the result of Serre to weakly holomorphic modular forms of half integral weight
on $\Gamma_{0}(4N)$ for $N=1,2,4$. A proof is based on linear relations among
Fourier coefficients of modular forms of half integral weight. As applications
we obtain congruences of Borcherds exponents, congruences of quotient of
Eisentein series and congruences of values of $L$-functions at a certain point
are also studied. Furthermore, the congruences of the Fourier coefficients of
Siegel modular forms on Maass Space are obtained using Ikeda lifting.
|
Iterated integral and the loop product | In this article we discuss a relation between the string topology and
differential forms based on the theory of Chen's iterated integrals and the
cyclic bar complex.
|
Fermionic superstring loop amplitudes in the pure spinor formalism | The pure spinor formulation of the ten-dimensional superstring leads to
manifestly supersymmetric loop amplitudes, expressed as integrals in pure
spinor superspace. This paper explores different methods to evaluate these
integrals and then uses them to calculate the kinematic factors of the one-loop
and two-loop massless four-point amplitudes involving two and four Ramond
states.
|
Lifetime of doubly charmed baryons | In this work, we evaluate the lifetimes of the doubly charmed baryons
$\Xi_{cc}^{+}$, $\Xi_{cc}^{++}$ and $\Omega_{cc}^{+}$. We carefully calculate
the non-spectator contributions at the quark level where the Cabibbo-suppressed
diagrams are also included. The hadronic matrix elements are evaluated in the
simple non-relativistic harmonic oscillator model. Our numerical results are
generally consistent with that obtained by other authors who used the diquark
model. However, all the theoretical predictions on the lifetimes are one order
larger than the upper limit set by the recent SELEX measurement. This
discrepancy would be clarified by the future experiment, if more accurate
experiment still confirms the value of the SELEX collaboration, there must be
some unknown mechanism to be explored.
|
Spectroscopic Observations of the Intermediate Polar EX Hydrae in
Quiescence | Results from spectroscopic observations of the Intermediate Polar (IP) EX Hya
in quiescence during 1991 and 2001 are presented. Spin-modulated radial
velocities consistent with an outer disc origin were detected for the first
time in an IP. The spin pulsation was modulated with velocities near ~500-600
km/s. These velocities are consistent with those of material circulating at the
outer edge of the accretion disc, suggesting corotation of the accretion
curtain with material near the Roche lobe radius. Furthermore, spin Doppler
tomograms have revealed evidence of the accretion curtain emission extending
from velocities of ~500 km/s to ~1000 km/s. These findings have confirmed the
theoretical model predictions of King & Wynn (1999), Belle et al. (2002) and
Norton et al. (2004) for EX Hya, which predict large accretion curtains that
extend to a distance close to the Roche lobe radius in this system. Evidence
for overflow stream of material falling onto the magnetosphere was observed,
confirming the result of Belle et al. (2005) that disc overflow in EX Hya is
present during quiescence as well as outburst. It appears that the hbeta and
hgamma spin radial velocities originated from the rotation of the funnel at the
outer disc edge, while those of halpha were produced due to the flow of
material along the field lines far from the white dwarf (narrow component) and
close to the white dwarf (broad-base component), in agreement with the
accretion curtain model.
|
In quest of a generalized Callias index theorem | We give a prescription for how to compute the Callias index, using as
regulator an exponential function. We find agreement with old results in all
odd dimensions. We show that the problem of computing the dimension of the
moduli space of self-dual strings can be formulated as an index problem in
even-dimensional (loop-)space. We think that the regulator used in this Letter
can be applied to this index problem.
|
Approximation for extinction probability of the contact process based on
the Gr\"obner basis | In this note we give a new method for getting a series of approximations for
the extinction probability of the one-dimensional contact process by using the
Gr\"obner basis.
|
Measurement of the Hadronic Form Factor in D0 --> K- e+ nue Decays | The shape of the hadronic form factor f+(q2) in the decay D0 --> K- e+ nue
has been measured in a model independent analysis and compared with theoretical
calculations. We use 75 fb(-1) of data recorded by the BABAR detector at the
PEPII electron-positron collider. The corresponding decay branching fraction,
relative to the decay D0 --> K- pi+, has also been measured to be RD = BR(D0
--> K- e+ nue)/BR(D0 --> K- pi+) = 0.927 +/- 0.007 +/- 0.012. From these
results, and using the present world average value for BR(D0 --> K- pi+), the
normalization of the form factor at q2=0 is determined to be f+(0)=0.727 +/-
0.007 +/- 0.005 +/- 0.007 where the uncertainties are statistical, systematic,
and from external inputs, respectively.
|
Molecular Synchronization Waves in Arrays of Allosterically Regulated
Enzymes | Spatiotemporal pattern formation in a product-activated enzymic reaction at
high enzyme concentrations is investigated. Stochastic simulations show that
catalytic turnover cycles of individual enzymes can become coherent and that
complex wave patterns of molecular synchronization can develop. The analysis
based on the mean-field approximation indicates that the observed patterns
result from the presence of Hopf and wave bifurcations in the considered
system.
|
Stochastic Lie group integrators | We present Lie group integrators for nonlinear stochastic differential
equations with non-commutative vector fields whose solution evolves on a smooth
finite dimensional manifold. Given a Lie group action that generates transport
along the manifold, we pull back the stochastic flow on the manifold to the Lie
group via the action, and subsequently pull back the flow to the corresponding
Lie algebra via the exponential map. We construct an approximation to the
stochastic flow in the Lie algebra via closed operations and then push back to
the Lie group and then to the manifold, thus ensuring our approximation lies in
the manifold. We call such schemes stochastic Munthe-Kaas methods after their
deterministic counterparts. We also present stochastic Lie group integration
schemes based on Castell--Gaines methods. These involve using an underlying
ordinary differential integrator to approximate the flow generated by a
truncated stochastic exponential Lie series. They become stochastic Lie group
integrator schemes if we use Munthe-Kaas methods as the underlying ordinary
differential integrator. Further, we show that some Castell--Gaines methods are
uniformly more accurate than the corresponding stochastic Taylor schemes.
Lastly we demonstrate our methods by simulating the dynamics of a free rigid
body such as a satellite and an autonomous underwater vehicle both perturbed by
two independent multiplicative stochastic noise processes.
|
ALMA as the ideal probe of the solar chromosphere | The very nature of the solar chromosphere, its structuring and dynamics,
remains far from being properly understood, in spite of intensive research.
Here we point out the potential of chromospheric observations at millimeter
wavelengths to resolve this long-standing problem. Computations carried out
with a sophisticated dynamic model of the solar chromosphere due to Carlsson
and Stein demonstrate that millimeter emission is extremely sensitive to
dynamic processes in the chromosphere and the appropriate wavelengths to look
for dynamic signatures are in the range 0.8-5.0 mm. The model also suggests
that high resolution observations at mm wavelengths, as will be provided by
ALMA, will have the unique property of reacting to both the hot and the cool
gas, and thus will have the potential of distinguishing between rival models of
the solar atmosphere. Thus, initial results obtained from the observations of
the quiet Sun at 3.5 mm with the BIMA array (resolution of 12 arcsec) reveal
significant oscillations with amplitudes of 50-150 K and frequencies of 1.5-8
mHz with a tendency toward short-period oscillations in internetwork and longer
periods in network regions. However higher spatial resolution, such as that
provided by ALMA, is required for a clean separation between the features
within the solar atmosphere and for an adequate comparison with the output of
the comprehensive dynamic simulations.
|
Formation of quasi-solitons in transverse confined ferromagnetic film
media | The formation of quasi-2D spin-wave waveforms in longitudinally magnetized
stripes of ferrimagnetic film was observed by using time- and space-resolved
Brillouin light scattering technique. In the linear regime it was found that
the confinement decreases the amplitude of dynamic magnetization near the
lateral stripe edges. Thus, the so-called effective dipolar pinning of dynamic
magnetization takes place at the edges.
In the nonlinear regime a new stable spin wave packet propagating along a
waveguide structure, for which both transversal instability and interaction
with the side walls of the waveguide are important was observed. The
experiments and a numerical simulation of the pulse evolution show that the
shape of the formed waveforms and their behavior are strongly influenced by the
confinement.
|
Spectroscopic Properties of Polarons in Strongly Correlated Systems by
Exact Diagrammatic Monte Carlo Method | We present recent advances in understanding of the ground and excited states
of the electron-phonon coupled systems obtained by novel methods of
Diagrammatic Monte Carlo and Stochastic Optimization, which enable the
approximation-free calculation of Matsubara Green function in imaginary times
and perform unbiased analytic continuation to real frequencies. We present
exact numeric results on the ground state properties, Lehmann spectral function
and optical conductivity of different strongly correlated systems: Frohlich
polaron, Rashba-Pekar exciton-polaron, pseudo Jahn-Teller polaron, exciton, and
interacting with phonons hole in the t-J model.
|
Placeholder Substructures II: Meta-Fractals, Made of Box-Kites, Fill
Infinite-Dimensional Skies | Zero-divisors (ZDs) derived by Cayley-Dickson Process (CDP) from
N-dimensional hypercomplex numbers (N a power of 2, at least 4) can represent
singularities and, as N approaches infinite, fractals -- and thereby,scale-free
networks. Any integer greater than 8 and not a power of 2 generates a
meta-fractal or "Sky" when it is interpreted as the "strut constant" (S) of an
ensemble of octahedral vertex figures called "Box-Kites" (the fundamental
building blocks of ZDs). Remarkably simple bit-manipulation rules or "recipes"
provide tools for transforming one fractal genus into others within the context
of Wolfram's Class 4 complexity.
|
Filling-Factor-Dependent Magnetophonon Resonance in Graphene | We describe a peculiar fine structure acquired by the in-plane optical phonon
at the Gamma-point in graphene when it is brought into resonance with one of
the inter-Landau-level transitions in this material. The effect is most
pronounced when this lattice mode (associated with the G-band in graphene Raman
spectrum) is in resonance with inter-Landau-level transitions 0 -> (+,1) and
(-,1) -> 0, at a magnetic field B_0 ~ 30 T. It can be used to measure the
strength of the electron-phonon coupling directly, and its filling-factor
dependence can be used experimentally to detect circularly polarized lattice
modes.
|
Pfaffians, hafnians and products of real linear functionals | We prove pfaffian and hafnian versions of Lieb's inequalities on determinants
and permanents of positive semi-definite matrices. We use the hafnian
inequality to improve the lower bound of R\'ev\'esz and Sarantopoulos on the
norm of a product of linear functionals on a real Euclidean space (this subject
is sometimes called the `real linear polarization constant' problem).
|
Understanding the Flavor Symmetry Breaking and Nucleon Flavor-Spin
Structure within Chiral Quark Model | In $\XQM$, a quark can emit Goldstone bosons. The flavor symmetry breaking in
the Goldstone boson emission process is used to intepret the nucleon
flavor-spin structure. In this paper, we study the inner structure of
constituent quarks implied in $\XQM$ caused by the Goldstone boson emission
process in nucleon. From a simplified model Hamiltonian derived from $\XQM$,
the intrinsic wave functions of constituent quarks are determined. Then the
obtained transition probabilities of the emission of Goldstone boson from a
quark can give a reasonable interpretation to the flavor symmetry breaking in
nucleon flavor-spin structure.
|
Tuning correlation effects with electron-phonon interactions | We investigate the effect of tuning the phonon energy on the correlation
effects in models of electron-phonon interactions using DMFT. In the regime
where itinerant electrons, instantaneous electron-phonon driven correlations
and static distortions compete on similar energy scales, we find several
interesting results including (1) A crossover from band to Mott behavior in the
spectral function, leading to hybrid band/Mott features in the spectral
function for phonon frequencies slightly larger than the band width. (2) Since
the optical conductivity depends sensitively on the form of the spectral
function, we show that such a regime should be observable through the low
frequency form of the optical conductivity. (3) The resistivity has a double
kondo peak arrangement
|
Crystal channeling of LHC forward protons with preserved distribution in
phase space | We show that crystal can trap a broad (x, x', y, y', E) distribution of
particles and channel it preserved with a high precision. This sampled-and-hold
distribution can be steered by a bent crystal for analysis downstream. In
simulations for the 7 TeV Large Hadron Collider, a crystal adapted to the
accelerator lattice traps 90% of diffractively scattered protons emerging from
the interaction point with a divergence 100 times the critical angle. We set
the criterion for crystal adaptation improving efficiency ~100-fold. Proton
angles are preserved in crystal transmission with accuracy down to 0.1
microrad. This makes feasible a crystal application for measuring very forward
protons at the LHC.
|
Probing non-standard neutrino interactions with supernova neutrinos | We analyze the possibility of probing non-standard neutrino interactions
(NSI, for short) through the detection of neutrinos produced in a future
galactic supernova (SN).We consider the effect of NSI on the neutrino
propagation through the SN envelope within a three-neutrino framework, paying
special attention to the inclusion of NSI-induced resonant conversions, which
may take place in the most deleptonised inner layers. We study the possibility
of detecting NSI effects in a Megaton water Cherenkov detector, either through
modulation effects in the $\bar\nu_e$ spectrum due to (i) the passage of shock
waves through the SN envelope, (ii) the time dependence of the electron
fraction and (iii) the Earth matter effects; or, finally, through the possible
detectability of the neutronization $\nu_e$ burst. We find that the $\bar\nu_e$
spectrum can exhibit dramatic features due to the internal NSI-induced resonant
conversion. This occurs for non-universal NSI strengths of a few %, and for
very small flavor-changing NSI above a few$\times 10^{-5}$.
|
Convergence of the discrete dipole approximation. I. Theoretical
analysis | We performed a rigorous theoretical convergence analysis of the discrete
dipole approximation (DDA). We prove that errors in any measured quantity are
bounded by a sum of a linear and quadratic term in the size of a dipole d, when
the latter is in the range of DDA applicability. Moreover, the linear term is
significantly smaller for cubically than for non-cubically shaped scatterers.
Therefore, for small d errors for cubically shaped particles are much smaller
than for non-cubically shaped. The relative importance of the linear term
decreases with increasing size, hence convergence of DDA for large enough
scatterers is quadratic in the common range of d. Extensive numerical
simulations were carried out for a wide range of d. Finally we discuss a number
of new developments in DDA and their consequences for convergence.
|
Origin of adaptive mutants: a quantum measurement? | This is a supplement to the paper arXiv:q-bio/0701050, containing the text of
correspondence sent to Nature in 1990.
|
Convergence of the discrete dipole approximation. II. An extrapolation
technique to increase the accuracy | We propose an extrapolation technique that allows accuracy improvement of the
discrete dipole approximation computations. The performance of this technique
was studied empirically based on extensive simulations for 5 test cases using
many different discretizations. The quality of the extrapolation improves with
refining discretization reaching extraordinary performance especially for
cubically shaped particles. A two order of magnitude decrease of error was
demonstrated. We also propose estimates of the extrapolation error, which were
proven to be reliable. Finally we propose a simple method to directly separate
shape and discretization errors and illustrated this for one test case.
|
A remark on the number of steady states in a multiple futile cycle | The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly
used in cell signaling. This motif itself can generate a variety of dynamic
behaviors like bistability and ultrasensitivity without direct positive
feedbacks. In this paper, we study the number of positive steady states of a
general multisite phosphorylation-dephosphorylation cycle, and how the number
of positive steady states varies by changing the biological parameters. We show
analytically that (1) for some parameter ranges, there are at least n+1 (if n
is even) or n (if n is odd) steady states; (2) there never are more than 2n-1
steady states (in particular, this implies that for n=2, including single
levels of MAPK cascades, there are at most three steady states); (3) for
parameters near the standard Michaelis-Menten quasi-steady state conditions,
there are at most n+1 steady states; and (4) for parameters far from the
standard Michaelis-Menten quasi-steady state conditions, there is at most one
steady state.
|
The discrete dipole approximation for simulation of light scattering by
particles much larger than the wavelength | In this manuscript we investigate the capabilities of the Discrete Dipole
Approximation (DDA) to simulate scattering from particles that are much larger
than the wavelength of the incident light, and describe an optimized publicly
available DDA computer program that processes the large number of dipoles
required for such simulations. Numerical simulations of light scattering by
spheres with size parameters x up to 160 and 40 for refractive index m=1.05 and
2 respectively are presented and compared with exact results of the Mie theory.
Errors of both integral and angle-resolved scattering quantities generally
increase with m and show no systematic dependence on x. Computational times
increase steeply with both x and m, reaching values of more than 2 weeks on a
cluster of 64 processors. The main distinctive feature of the computer program
is the ability to parallelize a single DDA simulation over a cluster of
computers, which allows it to simulate light scattering by very large
particles, like the ones that are considered in this manuscript. Current
limitations and possible ways for improvement are discussed.
|
The discrete dipole approximation: an overview and recent developments | We present a review of the discrete dipole approximation (DDA), which is a
general method to simulate light scattering by arbitrarily shaped particles. We
put the method in historical context and discuss recent developments, taking
the viewpoint of a general framework based on the integral equations for the
electric field. We review both the theory of the DDA and its numerical aspects,
the latter being of critical importance for any practical application of the
method. Finally, the position of the DDA among other methods of light
scattering simulation is shown and possible future developments are discussed.
|
Scalar radius of the pion and zeros in the form factor | The quadratic pion scalar radius, \la r^2\ra^\pi_s, plays an important role
for present precise determinations of \pi\pi scattering. Recently, Yndur\'ain,
using an Omn\`es representation of the null isospin(I) non-strange pion scalar
form factor, obtains \la r^2\ra^\pi_s=0.75\pm 0.07 fm^2. This value is larger
than the one calculated by solving the corresponding Muskhelishvili-Omn\`es
equations, \la r^2\ra^\pi_s=0.61\pm 0.04 fm^2. A large discrepancy between both
values, given the precision, then results. We reanalyze Yndur\'ain's method and
show that by imposing continuity of the resulting pion scalar form factor under
tiny changes in the input \pi\pi phase shifts, a zero in the form factor for
some S-wave I=0 T-matrices is then required. Once this is accounted for, the
resulting value is \la r^2\ra_s^\pi=0.65\pm 0.05 fm^2. The main source of error
in our determination is present experimental uncertainties in low energy S-wave
I=0 \pi\pi phase shifts. Another important contribution to our error is the not
yet settled asymptotic behaviour of the phase of the scalar form factor from
QCD.
|
Multilinear function series in conditionally free probability with
amalgamation | As in the cases of freeness and monotonic independence, the notion of
conditional freeness is meaningful when complex-valued states are replaced by
positive conditional expectations. In this framework, the paper presents
several positivity results, a version of the central limit theorem and an
analogue of the conditionally free R-transform constructed by means of
multilinear function series.
|
Quantum Group of Isometries in Classical and Noncommutative Geometry | We formulate a quantum generalization of the notion of the group of
Riemannian isometries for a compact Riemannian manifold, by introducing a
natural notion of smooth and isometric action by a compact quantum group on a
classical or noncommutative manifold described by spectral triples, and then
proving the existence of a universal object (called the quantum isometry group)
in the category of compact quantum groups acting smoothly and isometrically on
a given (possibly noncommutative) manifold satisfying certain regularity
assumptions. In fact, we identify the quantum isometry group with the universal
object in a bigger category, namely the category of `quantum families of smooth
isometries', defined along the line of Woronowicz and Soltan. We also construct
a spectral triple on the Hilbert space of forms on a noncommutative manifold
which is equivariant with respect to a natural unitary representation of the
quantum isometry group. We give explicit description of quantum isometry groups
of commutative and noncommutative tori, and in this context, obtain the quantum
double torus defined in \cite{hajac} as the universal quantum group of
holomorphic isometries of the noncommutative torus.
|
General System theory, Like-Quantum Semantics and Fuzzy Sets | It is outlined the possibility to extend the quantum formalism in relation to
the requirements of the general systems theory. It can be done by using a
quantum semantics arising from the deep logical structure of quantum theory. It
is so possible taking into account the logical openness relationship between
observer and system. We are going to show how considering the truth-values of
quantum propositions within the context of the fuzzy sets is here more useful
for systemics . In conclusion we propose an example of formal quantum
coherence.
|
Nonequilibrium entropy limiters in lattice Boltzmann methods | We construct a system of nonequilibrium entropy limiters for the lattice
Boltzmann methods (LBM). These limiters erase spurious oscillations without
blurring of shocks, and do not affect smooth solutions. In general, they do the
same work for LBM as flux limiters do for finite differences, finite volumes
and finite elements methods, but for LBM the main idea behind the construction
of nonequilibrium entropy limiter schemes is to transform a field of a scalar
quantity - nonequilibrium entropy. There are two families of limiters: (i)
based on restriction of nonequilibrium entropy (entropy "trimming") and (ii)
based on filtering of nonequilibrium entropy (entropy filtering). The physical
properties of LBM provide some additional benefits: the control of entropy
production and accurate estimate of introduced artificial dissipation are
possible. The constructed limiters are tested on classical numerical examples:
1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven
cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100*100 grid.
All limiter constructions are applicable for both entropic and non-entropic
quasiequilibria.
|
Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in
magnetized weakly collisional plasmas | We present a theoretical framework for plasma turbulence in astrophysical
plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks).
The key assumptions are that the turbulence is anisotropic with respect to the
mean magnetic field and frequencies are low compared to the ion cyclotron
frequency. The energy injected at the outer scale scale has to be converted
into heat, which ultimately cannot be done without collisions. A KINETIC
CASCADE develops that brings the energy to collisional scales both in space and
velocity. Its nature depends on the physics of plasma fluctuations. In each of
the physically distinct scale ranges, the kinetic problem is systematically
reduced to a more tractable set of equations. In the "inertial range" above the
ion gyroscale, the kinetic cascade splits into a cascade of Alfvenic
fluctuations, which are governed by the RMHD equations at both the collisional
and collisionless scales, and a passive cascade of compressive fluctuations,
which obey a linear kinetic equation along the moving field lines associated
with the Alfvenic component. In the "dissipation range" between the ion and
electron gyroscales, there are again two cascades: the kinetic-Alfven-wave
(KAW) cascade governed by two fluid-like Electron RMHD equations and a passive
phase-space cascade of ion entropy fluctuations. The latter cascade brings the
energy of the inertial-range fluctuations that was damped by collisionless
wave-particle interaction at the ion gyroscale to collisional scales in the
phase space and leads to ion heating. The KAW energy is similarly damped at the
electron gyroscale and converted into electron heat. Kolmogorov-style scaling
relations are derived for these cascades. Astrophysical and space-physical
applications are discussed in detail.
|
Evolution of solitary waves and undular bores in shallow-water flows
over a gradual slope with bottom friction | This paper considers the propagation of shallow-water solitary and nonlinear
periodic waves over a gradual slope with bottom friction in the framework of a
variable-coefficient Korteweg-de Vries equation. We use the Whitham averaging
method, using a recent development of this theory for perturbed integrable
equations. This general approach enables us not only to improve known results
on the adiabatic evolution of isolated solitary waves and periodic wave trains
in the presence of variable topography and bottom friction, modeled by the
Chezy law, but also importantly, to study the effects of these factors on the
propagation of undular bores, which are essentially unsteady in the system
under consideration. In particular, it is shown that the combined action of
variable topography and bottom friction generally imposes certain global
restrictions on the undular bore propagation so that the evolution of the
leading solitary wave can be substantially different from that of an isolated
solitary wave with the same initial amplitude. This non-local effect is due to
nonlinear wave interactions within the undular bore and can lead to an
additional solitary wave amplitude growth, which cannot be predicted in the
framework of the traditional adiabatic approach to the propagation of solitary
waves in slowly varying media.
|
A limit relation for entropy and channel capacity per unit cost | In a quantum mechanical model, Diosi, Feldmann and Kosloff arrived at a
conjecture stating that the limit of the entropy of certain mixtures is the
relative entropy as system size goes to infinity. The conjecture is proven in
this paper for density matrices. The first proof is analytic and uses the
quantum law of large numbers. The second one clarifies the relation to channel
capacity per unit cost for classical-quantum channels. Both proofs lead to
generalization of the conjecture.
|
Intelligent location of simultaneously active acoustic emission sources:
Part I | The intelligent acoustic emission locator is described in Part I, while Part
II discusses blind source separation, time delay estimation and location of two
simultaneously active continuous acoustic emission sources.
The location of acoustic emission on complicated aircraft frame structures is
a difficult problem of non-destructive testing. This article describes an
intelligent acoustic emission source locator. The intelligent locator comprises
a sensor antenna and a general regression neural network, which solves the
location problem based on learning from examples. Locator performance was
tested on different test specimens. Tests have shown that the accuracy of
location depends on sound velocity and attenuation in the specimen, the
dimensions of the tested area, and the properties of stored data. The location
accuracy achieved by the intelligent locator is comparable to that obtained by
the conventional triangulation method, while the applicability of the
intelligent locator is more general since analysis of sonic ray paths is
avoided. This is a promising method for non-destructive testing of aircraft
frame structures by the acoustic emission method.
|
Inference on white dwarf binary systems using the first round Mock LISA
Data Challenges data sets | We report on the analysis of selected single source data sets from the first
round of the Mock LISA Data Challenges (MLDC) for white dwarf binaries. We
implemented an end-to-end pipeline consisting of a grid-based coherent
pre-processing unit for signal detection, and an automatic Markov Chain Monte
Carlo post-processing unit for signal evaluation. We demonstrate that signal
detection with our coherent approach is secure and accurate, and is increased
in accuracy and supplemented with additional information on the signal
parameters by our Markov Chain Monte Carlo approach. We also demonstrate that
the Markov Chain Monte Carlo routine is additionally able to determine
accurately the noise level in the frequency window of interest.
|
An algorithm for the classification of smooth Fano polytopes | We present an algorithm that produces the classification list of smooth Fano
d-polytopes for any given d. The input of the algorithm is a single number,
namely the positive integer d. The algorithm has been used to classify smooth
Fano d-polytopes for d<=7. There are 7622 isomorphism classes of smooth Fano
6-polytopes and 72256 isomorphism classes of smooth Fano 7-polytopes.
|
Intelligent location of simultaneously active acoustic emission sources:
Part II | Part I describes an intelligent acoustic emission locator, while Part II
discusses blind source separation, time delay estimation and location of two
continuous acoustic emission sources.
Acoustic emission (AE) analysis is used for characterization and location of
developing defects in materials. AE sources often generate a mixture of various
statistically independent signals. A difficult problem of AE analysis is
separation and characterization of signal components when the signals from
various sources and the mode of mixing are unknown. Recently, blind source
separation (BSS) by independent component analysis (ICA) has been used to solve
these problems. The purpose of this paper is to demonstrate the applicability
of ICA to locate two independent simultaneously active acoustic emission
sources on an aluminum band specimen. The method is promising for
non-destructive testing of aircraft frame structures by acoustic emission
analysis.
|
Visualizing Teleportation | A novel way of picturing the processing of quantum information is described,
allowing a direct visualization of teleportation of quantum states and
providing a simple and intuitive understanding of this fascinating phenomenon.
The discussion is aimed at providing physicists a method of explaining
teleportation to non-scientists. The basic ideas of quantum physics are first
explained in lay terms, after which these ideas are used with a graphical
description, out of which teleportation arises naturally.
|
Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries | We study space-time symmetries in scalar quantum field theory (including
interacting theories) on static space-times. We first consider Euclidean
quantum field theory on a static Riemannian manifold, and show that the
isometry group is generated by one-parameter subgroups which have either
self-adjoint or unitary quantizations. We analytically continue the
self-adjoint semigroups to one-parameter unitary groups, and thus construct a
unitary representation of the isometry group of the associated Lorentzian
manifold. The method is illustrated for the example of hyperbolic space, whose
Lorentzian continuation is Anti-de Sitter space.
|
A Global Approach to the Theory of Special Finsler Manifolds | The aim of the present paper is to provide a global presentation of the
theory of special Finsler manifolds. We introduce and investigate globally (or
intrinsically, free from local coordinates) many of the most important and most
commonly used special Finsler manifolds: locally Minkowskian, Berwald,
Landesberg, general Landesberg, $P$-reducible, $C$-reducible,
semi-$C$-reducible, quasi-$C$-reducible, $P^{*}$-Finsler, $C^{h}$-recurrent,
$C^{v}$-recurrent, $C^{0}$-recurrent, $S^{v}$-recurrent, $S^{v}$-recurrent of
the second order, $C_{2}$-like, $S_{3}$-like, $S_{4}$-like, $P_{2}$-like,
$R_{3}$-like, $P$-symmetric, $h$-isotropic, of scalar curvature, of constant
curvature, of $p$-scalar curvature, of $s$-$ps$-curvature. The global
definitions of these special Finsler manifolds are introduced. Various
relationships between the different types of the considered special Finsler
manifolds are found. Many local results, known in the literature, are proved
globally and several new results are obtained. As a by-product, interesting
identities and properties concerning the torsion tensor fields and the
curvature tensor fields are deduced. Although our investigation is entirely
global, we provide; for comparison reasons, an appendix presenting a local
counterpart of our global approach and the local definitions of the special
Finsler spaces considered.
|
The Hardy-Lorentz Spaces $H^{p,q}(R^n)$ | In this paper we consider the Hardy-Lorentz spaces $H^{p,q}(R^n)$, with
$0<p\le 1$, $0<q\le \infty$. We discuss the atomic decomposition of the
elements in these spaces, their interpolation properties, and the behavior of
singular integrals and other operators acting on them.
|
Potassium intercalation in graphite: A van der Waals density-functional
study | Potassium intercalation in graphite is investigated by first-principles
theory. The bonding in the potassium-graphite compound is reasonably well
accounted for by traditional semilocal density functional theory (DFT)
calculations. However, to investigate the intercalate formation energy from
pure potassium atoms and graphite requires use of a description of the graphite
interlayer binding and thus a consistent account of the nonlocal dispersive
interactions. This is included seamlessly with ordinary DFT by a van der Waals
density functional (vdW-DF) approach [Phys. Rev. Lett. 92, 246401 (2004)]. The
use of the vdW-DF is found to stabilize the graphite crystal, with crystal
parameters in fair agreement with experiments. For graphite and
potassium-intercalated graphite structural parameters such as binding
separation, layer binding energy, formation energy, and bulk modulus are
reported. Also the adsorption and sub-surface potassium absorption energies are
reported. The vdW-DF description, compared with the traditional semilocal
approach, is found to weakly soften the elastic response.
|
Phase diagram of Gaussian-core nematics | We study a simple model of a nematic liquid crystal made of parallel
ellipsoidal particles interacting via a repulsive Gaussian law. After
identifying the relevant solid phases of the system through a careful
zero-temperature scrutiny of as many as eleven candidate crystal structures, we
determine the melting temperature for various pressure values, also with the
help of exact free energy calculations. Among the prominent features of this
model are pressure-driven reentrant melting and the stabilization of a columnar
phase for intermediate temperatures.
|
High-spin to low-spin and orbital polarization transitions in
multiorbital Mott systems | We study the interplay of crystal field splitting and Hund coupling in a
two-orbital model which captures the essential physics of systems with two
electrons or holes in the e_g shell. We use single site dynamical mean field
theory with a recently developed impurity solver which is able to access strong
couplings and low temperatures. The fillings of the orbitals and the location
of phase boundaries are computed as a function of Coulomb repulsion, exchange
coupling and crystal field splitting. We find that the Hund coupling can drive
the system into a novel Mott insulating phase with vanishing orbital
susceptibility. Away from half-filling, the crystal field splitting can induce
an orbital selective Mott state.
|
Intelligent Life in Cosmology | I shall present three arguments for the proposition that intelligent life is
very rare in the universe. First, I shall summarize the consensus opinion of
the founders of the Modern Synthesis (Simpson, Dobzhanski, and Mayr) that the
evolution of intelligent life is exceedingly improbable. Second, I shall
develop the Fermi Paradox: if they existed they'd be here. Third, I shall show
that if intelligent life were too common, it would use up all available
resources and die out. But I shall show that the quantum mechanical principle
of unitarity (actually a form of teleology!) requires intelligent life to
survive to the end of time. Finally, I shall argue that, if the universe is
indeed accelerating, then survival to the end of time requires that intelligent
life, though rare, to have evolved several times in the visible universe. I
shall argue that the acceleration is a consequence of the excess of matter over
antimatter in the universe. I shall suggest experiments to test these claims.
|
The Mass and Radius of the Unseen M-Dwarf Companion in the Single-Lined
Eclipsing Binary HAT-TR-205-013 | We derive masses and radii for both components in the single-lined eclipsing
binary HAT-TR-205-013, which consists of a F7V primary and a late M-dwarf
secondary. The system's period is short, $P=2.230736 \pm 0.000010$ days, with
an orbit indistinguishable from circular, $e=0.012 \pm 0.021$. We demonstrate
generally that the surface gravity of the secondary star in a single-lined
binary undergoing total eclipses can be derived from characteristics of the
light curve and spectroscopic orbit. This constrains the secondary to a unique
line in the mass-radius diagram with $M/R^2$ = constant. For HAT-TR-205-013, we
assume the orbit has been tidally circularized, and that the primary's rotation
has been synchronized and aligned with the orbital axis. Our observed line
broadening, $V_{\rm rot} \sin i_{\rm rot} = 28.9 \pm 1.0$ \kms, gives a primary
radius of $R_{\rm A} = 1.28 \pm 0.04$ \rsun. Our light curve analysis leads to
the radius of the secondary, $R_{\rm B} = 0.167 \pm 0.006$ \rsun, and the
semimajor axis of the orbit, $a = 7.54 \pm 0.30 \rsun = 0.0351 \pm 0.0014$ AU.
Our single-lined spectroscopic orbit and the semimajor axis then yield the
individual masses, $M_{\rm B} = 0.124 \pm 0.010$ \msun and $M_{\rm A} = 1.04
\pm 0.13$ \msun. Our result for HAT-TR-205-013 B lies above the theoretical
mass-radius models from the Lyon group, consistent with results from
double-lined eclipsing binaries. The method we describe offers the opportunity
to study the very low end of the stellar mass-radius relation.
|
Coulomb excitation of unstable nuclei at intermediate energies | We investigate the Coulomb excitation of low-lying states of unstable nuclei
in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is
shown that the cross sections for the $E1$ and $E2$ transitions are larger at
lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb
distortion are found to be both relevant for energies as low as 10 MeV/nucleon
and as high as 500 MeV/nucleon. Implications for studies at radioactive beam
facilities are discussed.
|
Intersection Bodies and Generalized Cosine Transforms | Intersection bodies represent a remarkable class of geometric objects
associated with sections of star bodies and invoking
Radon transforms, generalized cosine transforms, and the relevant Fourier
analysis. The main focus of this article is interrelation between generalized
cosine transforms of different kinds in the context of their application to
investigation of a certain family of intersection bodies, which we call
$\lam$-intersection bodies. The latter include $k$-intersection bodies (in the
sense of A. Koldobsky) and unit balls of finite-dimensional subspaces of
$L_p$-spaces. In particular, we show that restrictions onto lower dimensional
subspaces of the spherical Radon transforms and the generalized cosine
transforms preserve their integral-geometric structure. We apply this result to
the study of sections of $\lam$-intersection bodies. New characterizations of
this class of bodies are obtained and examples are given. We also review some
known facts and give them new proofs.
|
On-line Viterbi Algorithm and Its Relationship to Random Walks | In this paper, we introduce the on-line Viterbi algorithm for decoding hidden
Markov models (HMMs) in much smaller than linear space. Our analysis on
two-state HMMs suggests that the expected maximum memory used to decode
sequence of length $n$ with $m$-state HMM can be as low as $\Theta(m\log n)$,
without a significant slow-down compared to the classical Viterbi algorithm.
Classical Viterbi algorithm requires $O(mn)$ space, which is impractical for
analysis of long DNA sequences (such as complete human genome chromosomes) and
for continuous data streams. We also experimentally demonstrate the performance
of the on-line Viterbi algorithm on a simple HMM for gene finding on both
simulated and real DNA sequences.
|
Experimental efforts in search of 76Ge Neutrinoless Double Beta Decay | Neutrinoless double beta decay is one of the most sensitive approaches in
non-accelerator particle physics to take us into a regime of physics beyond the
standard model. This article is a brief review of the experiments in search of
neutrinoless double beta decay from 76Ge. Following a brief introduction of the
process of double beta decay from 76Ge, the results of the very first
experiments IGEX and Heidelberg-Moscow which give indications of the existence
of possible neutrinoless double beta decay mode has been reviewed. Then ongoing
efforts to substantiate the early findings are presented and the Majorana
experiment as a future experimental approach which will allow a very detailed
study of the neutrinoless decay mode is discussed.
|
Nilpotent symmetry invariance in the superfield formulation: the
(non-)Abelian 1-form gauge theories | We capture the off-shell as well as the on-shell nilpotent
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the
Lagrangian densities of the four (3 + 1)-dimensional (4D) (non-)Abelian 1-form
gauge theories within the framework of the superfield formalism. In particular,
we provide the geometrical interpretations for (i) the above nilpotent symmetry
invariance, and (ii) the above Lagrangian densities, in the language of the
specific quantities defined in the domain of the above superfield formalism.
Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge
theories, are clarified within the framework of the above superfield formalism
where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional
supermanifold parametrized by the four spacetime coordinates x^\mu (with \mu =
0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta. One of
the key results of our present investigation is a great deal of simplification
in the geometrical understanding of the nilpotent (anti-)BRST symmetry
invariance.
|
Littlewood-Richardson polynomials | We introduce a family of rings of symmetric functions depending on an
infinite sequence of parameters. A distinguished basis of such a ring is
comprised by analogues of the Schur functions. The corresponding structure
coefficients are polynomials in the parameters which we call the
Littlewood-Richardson polynomials. We give a combinatorial rule for their
calculation by modifying an earlier result of B. Sagan and the author. The new
rule provides a formula for these polynomials which is manifestly positive in
the sense of W. Graham. We apply this formula for the calculation of the
product of equivariant Schubert classes on Grassmannians which implies a
stability property of the structure coefficients. The first manifestly positive
formula for such an expansion was given by A. Knutson and T. Tao by using
combinatorics of puzzles while the stability property was not apparent from
that formula. We also use the Littlewood-Richardson polynomials to describe the
multiplication rule in the algebra of the Casimir elements for the general
linear Lie algebra in the basis of the quantum immanants constructed by A.
Okounkov and G. Olshanski.
|
Lagrangian quantum field theory in momentum picture. IV. Commutation
relations for free fields | Possible (algebraic) commutation relations in the Lagrangian quantum theory
of free (scalar, spinor and vector) fields are considered from mathematical
view-point. As sources of these relations are employed the Heisenberg
equations/relations for the dynamical variables and a specific condition for
uniqueness of the operators of the dynamical variables (with respect to some
class of Lagrangians). The paracommutation relations or some their
generalizations are pointed as the most general ones that entail the validity
of all Heisenberg equations. The simultaneous fulfillment of the Heisenberg
equations and the uniqueness requirement turn to be impossible. This problem is
solved via a redefinition of the dynamical variables, similar to the normal
ordering procedure and containing it as a special case. That implies
corresponding changes in the admissible commutation relations. The introduction
of the concept of the vacuum makes narrow the class of the possible commutation
relations; in particular, the mentioned redefinition of the dynamical variables
is reduced to normal ordering. As a last restriction on that class is imposed
the requirement for existing of an effective procedure for calculating vacuum
mean values. The standard bilinear commutation relations are pointed as the
only known ones that satisfy all of the mentioned conditions and do not
contradict to the existing data.
|
Order of Epitaxial Self-Assembled Quantum Dots: Linear Analysis | Epitaxial self-assembled quantum dots (SAQDs) are of interest for
nanostructured optoelectronic and electronic devices such as lasers,
photodetectors and nanoscale logic. Spatial order and size order of SAQDs are
important to the development of usable devices. It is likely that these two
types of order are strongly linked; thus, a study of spatial order will also
have strong implications for size order. Here a study of spatial order is
undertaken using a linear analysis of a commonly used model of SAQD formation
based on surface diffusion. Analytic formulas for film-height correlation
functions are found that characterize quantum dot spatial order and
corresponding correlation lengths that quantify order. Initial atomic-scale
random fluctuations result in relatively small correlation lengths (about two
dots) when the effect of a wetting potential is negligible; however, the
correlation lengths diverge when SAQDs are allowed to form at a near-critical
film height. The present work reinforces previous findings about anisotropy and
SAQD order and presents as explicit and transparent mechanism for ordering with
corresponding analytic equations. In addition, SAQD formation is by its nature
a stochastic process, and various mathematical aspects regarding statistical
analysis of SAQD formation and order are presented.
|
A Note About the {Ki(z)} Functions | In the article [Petojevic 2006], A. Petojevi\' c verified useful properties
of the $K_{i}(z)$ functions which generalize Kurepa's [Kurepa 1971] left
factorial function. In this note, we present simplified proofs of two of these
results and we answer the open question stated in [Petojevic 2006]. Finally, we
discuss the differential transcendency of the $K_{i}(z)$ functions.
|
Dynamical Objects for Cohomologically Expanding Maps | The goal of this paper is to construct invariant dynamical objects for a (not
necessarily invertible) smooth self map of a compact manifold. We prove a
result that takes advantage of differences in rates of expansion in the terms
of a sheaf cohomological long exact sequence to create unique lifts of finite
dimensional invariant subspaces of one term of the sequence to invariant
subspaces of the preceding term. This allows us to take invariant cohomological
classes and under the right circumstances construct unique currents of a given
type, including unique measures of a given type, that represent those classes
and are invariant under pullback. A dynamically interesting self map may have a
plethora of invariant measures, so the uniquess of the constructed currents is
important. It means that if local growth is not too big compared to the growth
rate of the cohomological class then the expanding cohomological class gives
sufficient "marching orders" to the system to prohibit the formation of any
other such invariant current of the same type (say from some local dynamical
subsystem). Because we use subsheaves of the sheaf of currents we give
conditions under which a subsheaf will have the same cohomology as the sheaf
containing it. Using a smoothing argument this allows us to show that the sheaf
cohomology of the currents under consideration can be canonically identified
with the deRham cohomology groups. Our main theorem can be applied in both the
smooth and holomorphic setting.
|
Coincidence of the oscillations in the dipole transition and in the
persistent current of narrow quantum rings with two electrons | The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings with
two electrons has been studied and has been explained in an analytical way, the
evolution of the period and amplitudes against the magnetic field can be
exactly described. Furthermore, the dipole transition of the ground state was
found to have essentially two frequencies, their difference appears as an
oscillation matching the oscillation of the persistent current exactly. A
number of equalities relating the observables and dynamical parameters have
been found.
|
Pairwise comparisons of typological profiles (of languages) | No abstract given; compares pairs of languages from World Atlas of Language
Structures.
|
The decomposition method and Maple procedure for finding first integrals
of nonlinear PDEs of any order with any number of independent variables | In present paper we propose seemingly new method for finding solutions of
some types of nonlinear PDEs in closed form. The method is based on
decomposition of nonlinear operators on sequence of operators of lower orders.
It is shown that decomposition process can be done by iterative procedure(s),
each step of which is reduced to solution of some auxiliary PDEs system(s) for
one dependent variable. Moreover, we find on this way the explicit expression
of the first-order PDE(s) for first integral of decomposable initial PDE.
Remarkably that this first-order PDE is linear if initial PDE is linear in its
highest derivatives.
The developed method is implemented in Maple procedure, which can really
solve many of different order PDEs with different number of independent
variables. Examples of PDEs with calculated their general solutions demonstrate
a potential of the method for automatic solving of nonlinear PDEs.
|
A transcendental approach to Koll\'ar's injectivity theorem | We treat Koll\'ar's injectivity theorem from the analytic (or differential
geometric) viewpoint. More precisely, we give a curvature condition which
implies Koll\'ar type cohomology injectivity theorems. Our main theorem is
formulated for a compact K\"ahler manifold, but the proof uses the space of
harmonic forms on a Zariski open set with a suitable complete K\"ahler metric.
We need neither covering tricks, desingularizations, nor Leray's spectral
sequence.
|
Injective Morita contexts (revisited) | This paper is an exposition of the so-called injective Morita contexts (in
which the connecting bimodule morphisms are injective) and Morita
$\alpha$contexts (in which the connecting bimodules enjoy some local
projectivity in the sense of Zimmermann-Huisgen). Motivated by situations in
which only one trace ideal is in action, or the compatibility between the
bimodule morphisms is not needed, we introduce the notions of Morita
semi-contexts and Morita data, and investigate them. Injective Morita data will
be used (with the help of static and adstatic modules) to establish
equivalences between some intersecting subcategories related to subcategories
of modules that are localized or colocalized by trace ideals of a Morita datum.
We end up with applications of Morita $\alpha$-contexts to $\ast$-modules and
injective right wide Morita contexts.
|
Strong decays of charmed baryons | There has been important experimental progress in the sector of heavy baryons
in the past several years. We study the strong decays of the S-wave, P-wave,
D-wave and radially excited charmed baryons using the $^3P_0$ model. After
comparing the calculated decay pattern and total width with the available data,
we discuss the possible internal structure and quantum numbers of those charmed
baryons observed recently.
|
CP violation in beauty decays | Precision tests of the Kobayashi-Maskawa model of CP violation are discussed,
pointing out possible signatures for other sources of CP violation and for new
flavor-changing operators. The current status of the most accurate tests is
summarized.
|
Universal Forces and the Dark Energy Problem | The Dark Energy problem is forcing us to re-examine our models and our
understanding of relativity and space-time. Here a novel idea of Fundamental
Forces is introduced. This allows us to perceive the General Theory of
Relativity and Einstein's Equation from a new pesrpective. In addition to
providing us with an improved understanding of space and time, it will be shown
how it leads to a resolution of the Dark Energy problem.
|
Linear perturbations of matched spacetimes: the gauge problem and
background symmetries | We present a critical review about the study of linear perturbations of
matched spacetimes including gauge problems. We analyse the freedom introduced
in the perturbed matching by the presence of background symmetries and revisit
the particular case of spherically symmetry in n-dimensions. This analysis
includes settings with boundary layers such as brane world models and shell
cosmologies.
|
Operator algebras associated with unitary commutation relations | We define nonselfadjoint operator algebras with generators $L_{e_1},...,
L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of
the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=
(u_{i,j,k,l})$ is an $nm \times nm$ unitary matrix. These algebras, which
generalise the analytic Toeplitz algebras of rank 2 graphs with a single
vertex, are classified up to isometric isomorphism in terms of the matrix $u$.
|
Shaping the Globular Cluster Mass Function by Stellar-Dynamical
Evaporation | We show that the globular cluster mass function (GCMF) in the Milky Way
depends on cluster half-mass density (rho_h) in the sense that the turnover
mass M_TO increases with rho_h while the width of the GCMF decreases. We argue
that this is the expected signature of the slow erosion of a mass function that
initially rose towards low masses, predominantly through cluster evaporation
driven by internal two-body relaxation. We find excellent agreement between the
observed GCMF -- including its dependence on internal density rho_h, central
concentration c, and Galactocentric distance r_gc -- and a simple model in
which the relaxation-driven mass-loss rates of clusters are approximated by
-dM/dt = mu_ev ~ rho_h^{1/2}. In particular, we recover the well-known
insensitivity of M_TO to r_gc. This feature does not derive from a literal
``universality'' of the GCMF turnover mass, but rather from a significant
variation of M_TO with rho_h -- the expected outcome of relaxation-driven
cluster disruption -- plus significant scatter in rho_h as a function of r_gc.
Our conclusions are the same if the evaporation rates are assumed to depend
instead on the mean volume or surface densities of clusters inside their tidal
radii, as mu_ev ~ rho_t^{1/2} or mu_ev ~ Sigma_t^{3/4} -- alternative
prescriptions that are physically motivated but involve cluster properties
(rho_t and Sigma_t) that are not as well defined or as readily observable as
rho_h. In all cases, the normalization of mu_ev required to fit the GCMF
implies cluster lifetimes that are within the range of standard values
(although falling towards the low end of this range). Our analysis does not
depend on any assumptions or information about velocity anisotropy in the
globular cluster system.
|
Quantum Deformations of Relativistic Symmetries | We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In
the case of Poincare algebra it is shown that almost all classical r-matrices
of S. Zakrzewski classification correspond to twisted deformations of Abelian
and Jordanian types. A part of twists corresponding to the r-matrices of
Zakrzewski classification are given in explicit form.
|
Matter-Wave Bright Solitons with a Finite Background in Spinor
Bose-Einstein Condensates | We investigate dynamical properties of bright solitons with a finite
background in the F=1 spinor Bose-Einstein condensate (BEC), based on an
integrable spinor model which is equivalent to the matrix nonlinear
Schr\"{o}dinger equation with a self-focusing nonlineality. We apply the
inverse scattering method formulated for nonvanishing boundary conditions. The
resulting soliton solutions can be regarded as a generalization of those under
vanishing boundary conditions. One-soliton solutions are derived in an explicit
manner. According to the behaviors at the infinity, they are classified into
two kinds, domain-wall (DW) type and phase-shift (PS) type. The DW-type implies
the ferromagnetic state with nonzero total spin and the PS-type implies the
polar state, where the total spin amounts to zero. We also discuss two-soliton
collisions. In particular, the spin-mixing phenomenon is confirmed in a
collision involving the DW-type. The results are consistent with those of the
previous studies for bright solitons under vanishing boundary conditions and
dark solitons. As a result, we establish the robustness and the usefulness of
the multiple matter-wave solitons in the spinor BECs.
|
Why there is something rather than nothing (out of everything)? | The path integral over Euclidean geometries for the recently suggested
density matrix of the Universe is shown to describe a microcanonical ensemble
in quantum cosmology. This ensemble corresponds to a uniform (weight one)
distribution in phase space of true physical variables, but in terms of the
observable spacetime geometry it is peaked about complex saddle-points of the
{\em Lorentzian} path integral. They are represented by the recently obtained
cosmological instantons limited to a bounded range of the cosmological
constant. Inflationary cosmologies generated by these instantons at late stages
of expansion undergo acceleration whose low-energy scale can be attained within
the concept of dynamically evolving extra dimensions. Thus, together with the
bounded range of the early cosmological constant, this cosmological ensemble
suggests the mechanism of constraining the landscape of string vacua and,
simultaneously, a possible solution to the dark energy problem in the form of
the quasi-equilibrium decay of the microcanonical state of the Universe.
|
Formation of density singularities in ideal hydrodynamics of freely
cooling inelastic gases: a family of exact solutions | We employ granular hydrodynamics to investigate a paradigmatic problem of
clustering of particles in a freely cooling dilute granular gas. We consider
large-scale hydrodynamic motions where the viscosity and heat conduction can be
neglected, and one arrives at the equations of ideal gas dynamics with an
additional term describing bulk energy losses due to inelastic collisions. We
employ Lagrangian coordinates and derive a broad family of exact non-stationary
analytical solutions that depend only on one spatial coordinate. These
solutions exhibit a new type of singularity, where the gas density blows up in
a finite time when starting from smooth initial conditions. The density blowups
signal formation of close-packed clusters of particles. As the density blow-up
time $t_c$ is approached, the maximum density exhibits a power law $\sim
(t_c-t)^{-2}$. The velocity gradient blows up as $\sim - (t_c-t)^{-1}$ while
the velocity itself remains continuous and develops a cusp (rather than a shock
discontinuity) at the singularity. The gas temperature vanishes at the
singularity, and the singularity follows the isobaric scenario: the gas
pressure remains finite and approximately uniform in space and constant in time
close to the singularity. An additional exact solution shows that the density
blowup, of the same type, may coexist with an "ordinary" shock, at which the
hydrodynamic fields are discontinuous but finite. We confirm stability of the
exact solutions with respect to small one-dimensional perturbations by solving
the ideal hydrodynamic equations numerically. Furthermore, numerical solutions
show that the local features of the density blowup hold universally,
independently of details of the initial and boundary conditions.
|
A Universality in PP-Waves | We discuss a universality property of any covariant field theory in
space-time expanded around pp-wave backgrounds. According to this property the
space-time lagrangian density evaluated on a restricted set of field
configurations, called universal sector, turns out to be same around all the
pp-waves, even off-shell, with same transverse space and same profiles for the
background scalars. In this paper we restrict our discussion to tensorial
fields only. In the context of bosonic string theory we consider on-shell
pp-waves and argue that universality requires the existence of a universal
sector of world-sheet operators whose correlation functions are insensitive to
the pp-wave nature of the metric and the background gauge flux. Such results
can also be reproduced using the world-sheet conformal field theory. We also
study such pp-waves in non-polynomial closed string field theory (CSFT). In
particular, we argue that for an off-shell pp-wave ansatz with flat transverse
space and dilaton independent of transverse coordinates the field redefinition
relating the low energy effective field theory and CSFT with all the massive
modes integrated out is at most quadratic in fields. Because of this
simplification it is expected that the off-shell pp-waves can be identified on
the two sides. Furthermore, given the massless pp-wave field configurations, an
iterative method for computing the higher massive modes using the CSFT
equations of motion has been discussed. All our bosonic string theory analyses
can be generalised to the common Neveu-Schwarz sector of superstrings.
|
Clustering in a stochastic model of one-dimensional gas | We give a quantitative analysis of clustering in a stochastic model of
one-dimensional gas. At time zero, the gas consists of $n$ identical particles
that are randomly distributed on the real line and have zero initial speeds.
Particles begin to move under the forces of mutual attraction. When particles
collide, they stick together forming a new particle, called cluster, whose mass
and speed are defined by the laws of conservation. We are interested in the
asymptotic behavior of $K_n(t)$ as $n\to \infty$, where $K_n(t)$ denotes the
number of clusters at time $t$ in the system with $n$ initial particles. Our
main result is a functional limit theorem for $K_n(t)$. Its proof is based on
the discovered localization property of the aggregation process, which states
that the behavior of each particle is essentially defined by the motion of
neighbor particles.
|
Approximate solutions to the Dirichlet problem for harmonic maps between
hyperbolic spaces | Our main result in this paper is the following: Given $H^m, H^n$ hyperbolic
spaces of dimensional $m$ and $n$ corresponding, and given a Holder function
$f=(s^1,...,f^{n-1}):\partial H^m\to \partial H^n$ between geometric boundaries
of $H^m$ and $H^n$. Then for each $\epsilon >0$ there exists a harmonic map
$u:H^m\to H^n$ which is continuous up to the boundary (in the sense of
Euclidean) and $u|_{\partial H^m}=(f^1,...,f^{n-1},\epsilon)$.
|
Some new experimental photonic flame effect features | The results of the spectral, energetical and temporal characteristics of
radiation in the presence of the photonic flame effect are presented.
Artificial opal posed on Cu plate at the temperature of liquid nitrogen boiling
point (77 K) being irradiated by nanosecond ruby laser pulse produces long-
term luminiscence with a duration till ten seconds with a finely structured
spectrum in the the antistocks part of the spectrum. Analogous visible
luminescence manifesting time delay appeared in other samples of the artificial
opals posed on the same plate. In the case of the opal infiltrated with
different nonlinear liquids the threshold of the luminiscence is reduced and
the spatial disribution of the bright emmiting area on the opal surface is
being changed. In the case of the putting the frozen nonlinear liquids on the
Cu plate long-term blue bright luminiscence took place in the frozen species of
the liquids. Temporal characteristics of this luminiscence are nearly the same
as in opal matrixes.
|
A general approach to statistical modeling of physical laws:
nonparametric regression | Statistical modeling of experimental physical laws is based on the
probability density function of measured variables. It is expressed by
experimental data via a kernel estimator. The kernel is determined objectively
by the scattering of data during calibration of experimental setup. A physical
law, which relates measured variables, is optimally extracted from experimental
data by the conditional average estimator. It is derived directly from the
kernel estimator and corresponds to a general nonparametric regression. The
proposed method is demonstrated by the modeling of a return map of noisy
chaotic data. In this example, the nonparametric regression is used to predict
a future value of chaotic time series from the present one. The mean predictor
error is used in the definition of predictor quality, while the redundancy is
expressed by the mean square distance between data points. Both statistics are
used in a new definition of predictor cost function. From the minimum of the
predictor cost function, a proper number of data in the model is estimated.
|
Real Options for Project Schedules (ROPS) | Real Options for Project Schedules (ROPS) has three recursive
sampling/optimization shells. An outer Adaptive Simulated Annealing (ASA)
optimization shell optimizes parameters of strategic Plans containing multiple
Projects containing ordered Tasks. A middle shell samples probability
distributions of durations of Tasks. An inner shell samples probability
distributions of costs of Tasks. PATHTREE is used to develop options on
schedules.. Algorithms used for Trading in Risk Dimensions (TRD) are applied to
develop a relative risk analysis among projects.
|
Groups with finitely many conjugacy classes and their automorphisms | We combine classical methods of combinatorial group theory with the theory of
small cancellations over relatively hyperbolic groups to construct finitely
generated torsion-free groups that have only finitely many classes of conjugate
elements. Moreover, we present several results concerning embeddings into such
groups.
As another application of these techniques, we prove that every countable
group $C$ can be realized as a group of outer automorphisms of a group $N$,
where $N$ is a finitely generated group having Kazhdan's property (T) and
containing exactly two conjugacy classes.
|
Energy density for chiral lattice fermions with chemical potential | We study a recently proposed formulation of overlap fermions at finite
density. In particular we compute the energy density as a function of the
chemical potential and the temperature. It is shown that overlap fermions with
chemical potential reproduce the correct continuum behavior.
|
Aspects of Electron-Phonon Self-Energy Revealed from Angle-Resolved
Photoemission Spectroscopy | Lattice contribution to the electronic self-energy in complex correlated
oxides is a fascinating subject that has lately stimulated lively discussions.
Expectations of electron-phonon self-energy effects for simpler materials, such
as Pd and Al, have resulted in several misconceptions in strongly correlated
oxides. Here we analyze a number of arguments claiming that phonons cannot be
the origin of certain self-energy effects seen in high-$T_c$ cuprate
superconductors via angle resolved photoemission experiments (ARPES), including
the temperature dependence, doping dependence of the renormalization effects,
the inter-band scattering in the bilayer systems, and impurity substitution. We
show that in light of experimental evidences and detailed simulations, these
arguments are not well founded.
|
Timing and Lensing of the Colliding Bullet Clusters: barely enough time
and gravity to accelerate the bullet | We present semi-analytical constraint on the amount of dark matter in the
merging bullet galaxy cluster using the classical Local Group timing arguments.
We consider particle orbits in potential models which fit the lensing data.
{\it Marginally consistent} CDM models in Newtonian gravity are found with a
total mass M_{CDM} = 1 x 10^{15}Msun of Cold DM: the bullet subhalo can move
with V_{DM}=3000km/s, and the "bullet" X-ray gas can move with
V_{gas}=4200km/s. These are nearly the {\it maximum speeds} that are
accelerable by the gravity of two truncated CDM halos in a Hubble time even
without the ram pressure. Consistency breaks down if one adopts higher end of
the error bars for the bullet gas speed (5000-5400km/s), and the bullet gas
would not be bound by the sub-cluster halo for the Hubble time. Models with
V_{DM}~ 4500km/s ~ V_{gas} would invoke unrealistic large amount M_{CDM}=7x
10^{15}Msun of CDM for a cluster containing only ~ 10^{14}Msun of gas. Our
results are generalisable beyond General Relativity, e.g., a speed of
$4500\kms$ is easily obtained in the relativistic MONDian lensing model of
Angus et al. (2007). However, MONDian model with little hot dark matter
$M_{HDM} \le 0.6\times 10^{15}\msun$ and CDM model with a small halo mass $\le
1\times 10^{15}\msun$ are barely consistent with lensing and velocity data.
|
Geometry of Locally Compact Groups of Polynomial Growth and Shape of
Large Balls | We get asymptotics for the volume of large balls in an arbitrary locally
compact group G with polynomial growth. This is done via a study of the
geometry of G and a generalization of P. Pansu's thesis. In particular, we show
that any such G is weakly commensurable to some simply connected solvable Lie
group S, the Lie shadow of G. We also show that large balls in G have an
asymptotic shape, i.e. after a suitable renormalization, they converge to a
limiting compact set which can be interpreted geometrically. We then discuss
the speed of convergence, treat some examples and give an application to
ergodic theory. We also answer a question of Burago about left invariant
metrics and recover some results of Stoll on the irrationality of growth series
of nilpotent groups.
|
Much ado about 248 | In this note we present three representations of a 248-dimensional Lie
algebra, namely the algebra of Lie point symmetries admitted by a system of
five trivial ordinary differential equations each of order forty-four, that
admitted by a system of seven trivial ordinary differential equations each of
order twenty-eight and that admitted by one trivial ordinary differential
equation of order two hundred and forty-four.
|
Conformal Field Theory and Operator Algebras | We review recent progress in operator algebraic approach to conformal quantum
field theory. Our emphasis is on use of representation theory in classification
theory. This is based on a series of joint works with R. Longo.
|
Sparsely-spread CDMA - a statistical mechanics based analysis | Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA
method in which the spreading (signature) matrix contains only a relatively
small number of non-zero elements, is presented and analysed using methods of
statistical physics. The analysis provides results on the performance of
maximum likelihood decoding for sparse spreading codes in the large system
limit. We present results for both cases of regular and irregular spreading
matrices for the binary additive white Gaussian noise channel (BIAWGN) with a
comparison to the canonical (dense) random spreading code.
|
On Ando's inequalities for convex and concave functions | For positive semidefinite matrices $A$ and $B$, Ando and Zhan proved the
inequalities $||| f(A)+f(B) ||| \ge ||| f(A+B) |||$ and $||| g(A)+g(B) ||| \le
||| g(A+B) |||$, for any unitarily invariant norm, and for any non-negative
operator monotone $f$ on $[0,\infty)$ with inverse function $g$. These
inequalities have very recently been generalised to non-negative concave
functions $f$ and non-negative convex functions $g$, by Bourin and Uchiyama,
and Kosem, respectively.
In this paper we consider the related question whether the inequalities $|||
f(A)-f(B) ||| \le ||| f(|A-B|) |||$, and $||| g(A)-g(B) ||| \ge ||| g(|A-B|)
|||$, obtained by Ando, for operator monotone $f$ with inverse $g$, also have a
similar generalisation to non-negative concave $f$ and convex $g$. We answer
exactly this question, in the negative for general matrices, and affirmatively
in the special case when $A\ge ||B||$.
In the course of this work, we introduce the novel notion of $Y$-dominated
majorisation between the spectra of two Hermitian matrices, where $Y$ is itself
a Hermitian matrix, and prove a certain property of this relation that allows
to strengthen the results of Bourin-Uchiyama and Kosem, mentioned above.
|
Topology Change of Black Holes | The topological structure of the event horizon has been investigated in terms
of the Morse theory. The elementary process of topological evolution can be
understood as a handle attachment. It has been found that there are certain
constraints on the nature of black hole topological evolution: (i) There are n
kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii)
Handles are further classified as either of black or white type, and only black
handles appear in real black hole space-times. (iii) The spatial section of an
exterior of the black hole region is always connected. As a corollary, it is
shown that the formation of a black hole with an S**(n-2) x S**1 horizon from
that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat
space-times.
|