655 research outputs found
Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set
In this paper we consider the submonoids ,
and of the dihedral inverse monoid
of all orientation-preserving, monotone and order-preserving
transformations, respectively. Our goal is to exhibit presentations for each of
these three monoids.Comment: arXiv admin note: text overlap with arXiv:2205.0219
On monoids of endomorphisms of a cycle graph
In this paper we consider endomorphisms of an undirected cycle graph from
Semigroup Theory perspective. Our main aim is to present a process to determine
sets of generators with minimal cardinality for the monoids and
of all weak endomorphisms and all endomorphisms of an undirected
cycle graph with vertices. We also describe Green's relations and
regularity of these monoids and calculate their cardinalities
Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole
Slice stretching effects such as slice sucking and slice wrapping arise when
foliating the extended Schwarzschild spacetime with maximal slices. For
arbitrary spatial coordinates these effects can be quantified in the context of
boundary conditions where the lapse arises as a linear combination of odd and
even lapse. Favorable boundary conditions are then derived which make the
overall slice stretching occur late in numerical simulations. Allowing the
lapse to become negative, this requirement leads to lapse functions which
approach at late times the odd lapse corresponding to the static Schwarzschild
metric. Demanding in addition that a numerically favorable lapse remains
non-negative, as result the average of odd and even lapse is obtained. At late
times the lapse with zero gradient at the puncture arising for the puncture
evolution is precisely of this form. Finally, analytic arguments are given on
how slice stretching effects can be avoided. Here the excision technique and
the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice
stretching can be avoided by using excision and/or shift
The use of mobile phones for skin tumor screening
A lot of importance is attributed to mobile telemedicine these days, a topic that encompasses a wide and ever growing range of applications. Small, handheld devices such as camera mobile phones have come into every day use providing technically sophisticated tasks on a user-friendly level and can therefore be easily used in various fields of telemedicine. Dermatology is a perfect candidate for the use of telemedicine tools in general, as well as mobile devices in particular. The unique aspect of mobile teledermatology is that this system represents a filtering, or triage system, allowing a sensitive approach for the management of patients with emergent skin diseases. In order to investigate the feasibility of teleconsultation using a new generation of cellular phones, a clinical study to evaluate the accuracy of online diagnosis of skin tumours was conducted. Teledermoscopy represents a recent development of teledermatology that might add up additional information in the diagnosis of pigmented skin lesions. Teledermatology, mobile as well as stationary, can advance the reliability of diagnosis by expert consultations without expensive and time-consuming relocations. Consequently, the quality of patient's care can be raised and the costs of the health care system can be reduced
Momentum constraint relaxation
Full relativistic simulations in three dimensions invariably develop runaway
modes that grow exponentially and are accompanied by violations of the
Hamiltonian and momentum constraints. Recently, we introduced a numerical
method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint
violation and helps improve the quality of the numerical model. We present here
a method that controls the violation of the momentum constraint. The method is
based on the addition of a longitudinal component to the traceless extrinsic
curvature generated by a vector potential w_i, as outlined by York. The
components of w_i are relaxed to solve approximately the momentum constraint
equations, pushing slowly the evolution toward the space of solutions of the
constraint equations. We test this method with simulations of binary neutron
stars in circular orbits and show that effectively controls the growth of the
aforementioned violations. We also show that a full numerical enforcement of
the constraints, as opposed to the gentle correction of the momentum relaxation
scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More
detailed description of the algorithms are provided. Final published versio
Getting a kick out of numerical relativity
Recent developments in numerical relativity have made it possible to follow
reliably the coalescence of two black holes from near the innermost stable
circular orbit to final ringdown. This opens up a wide variety of exciting
astrophysical applications of these simulations. Chief among these is the net
kick received when two unequal mass or spinning black holes merge. The
magnitude of this kick has bearing on the production and growth of supermassive
black holes during the epoch of structure formation, and on the retention of
black holes in stellar clusters. Here we report the first accurate numerical
calculation of this kick, for two nonspinning black holes in a 1.5:1 mass
ratio, which is expected based on analytic considerations to give a significant
fraction of the maximum possible recoil. We have performed multiple runs with
different initial separations, orbital angular momenta, resolutions, extraction
radii, and gauges. The full range of our kick speeds is 86--116 km s,
and the most reliable runs give kicks between 86 and 97 km s. This is
intermediate between the estimates from two recent post-Newtonian analyses and
suggests that at redshifts , halos with masses will have difficulty retaining coalesced black holes after major
mergers.Comment: Updated. Accepted by ApJ Letter
Recoil velocities from equal-mass binary black-hole mergers: a systematic investigation of spin-orbit aligned configurations
Binary black-hole systems with spins aligned with the orbital angular
momentum are of special interest, as studies indicate that this configuration
is preferred in nature. If the spins of the two bodies differ, there can be a
prominent beaming of the gravitational radiation during the late plunge,
causing a recoil of the final merged black hole. We perform an accurate and
systematic study of recoil velocities from a sequence of equal-mass black holes
whose spins are aligned with the orbital angular momentum, and whose individual
spins range from a = +0.584 to -0.584. In this way we extend and refine the
results of a previous study and arrive at a consistent maximum recoil of 448 +-
5 km/s for anti-aligned models as well as to a phenomenological expression for
the recoil velocity as a function of spin ratio. This relation highlights a
nonlinear behavior, not predicted by the PN estimates, and can be readily
employed in astrophysical studies on the evolution of binary black holes in
massive galaxies. An essential result of our analysis is the identification of
different stages in the waveform, including a transient due to lack of an
initial linear momentum in the initial data. Furthermore we are able to
identify a pair of terms which are largely responsible for the kick, indicating
that an accurate computation can be obtained from modes up to l=3. Finally, we
provide accurate measures of the radiated energy and angular momentum, finding
these to increase linearly with the spin ratio, and derive simple expressions
for the final spin and the radiated angular momentum which can be easily
implemented in N-body simulations of compact stellar systems. Our code is
calibrated with strict convergence tests and we verify the correctness of our
measurements by using multiple independent methods whenever possible.Comment: 24 pages, 15 figures, 5 table
Surface-near domain engineering in multi-domain x-cut lithium niobate tantalate mixed crystals
Lithium niobate and lithium tantalate are among the most widespread materials
for nonlinear, integrated photonics. Mixed crystals with arbitrary Nb-Ta ratios
provide a new degree of freedom to tune materials properties, such as the
birefringence, but also leverage the advantages of the singular compounds, for
example, by combining the thermal stability of lithium tantalate with the
larger nonlinear or piezoelectric constants of lithium niobate. Periodic poling
is the prerequisite for any nonlinear optical application. For mixed crystals
this has been challenging so far due to the lack of homogeneous, mono-domain
crystals, which severely inhibit domain growth and nucleation. In this work we
demonstrate that surface-near (~m depth) periodic poling on x-cut
lithium niobate tantalate mixed crystals can be achieved via electric field
poling and lithographically structured electrodes. We find that naturally
occurring head-to-head or tail-to-tail domain walls in the as-grown crystal
inhibit domain inversion at a larger scale. However, periodic poling is
possible, if the gap size between the poling electrodes is of the same order of
magnitude or smaller than the average size of naturally occurring domains. This
work provides the basis for the nonlinear optical application of lithium
niobate tantalate mixed crystals
Phenomenological template family for black-hole coalescence waveforms
Recent progress in numerical relativity has enabled us to model the
non-perturbative merger phase of the binary black-hole coalescence problem.
Based on these results, we propose a phenomenological family of waveforms which
can model the inspiral, merger, and ring-down stages of black hole coalescence.
We also construct a template bank using this family of waveforms and discuss
its implementation in the search for signatures of gravitational waves produced
by black-hole coalescences in the data of ground-based interferometers. This
template bank might enable us to extend the present inspiral searches to
higher-mass binary black-hole systems, i.e., systems with total mass greater
than about 80 solar masses, thereby increasing the reach of the current
generation of ground-based detectors.Comment: Minor changes, Submitted to Class. Quantum Grav. (Proc. GWDAW11
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