3,990 research outputs found
Creation and Growth of Components in a Random Hypergraph Process
Denote by an -component a connected -uniform hypergraph with
edges and vertices. We prove that the expected number of
creations of -component during a random hypergraph process tends to 1 as
and tend to with the total number of vertices such that
. Under the same conditions, we also show that
the expected number of vertices that ever belong to an -component is
approximately . As an immediate
consequence, it follows that with high probability the largest -component
during the process is of size . Our results
give insight about the size of giant components inside the phase transition of
random hypergraphs.Comment: R\'{e}sum\'{e} \'{e}tend
Crystal water induced switching of magnetically active orbitals in CuCl2
The dehydration of CuCl2*2(H2O) to CuCl2 leads to a dramatic change in
magnetic behavior and ground state. Combining density functional electronic
structure and model calculations with thermodynamical measurements we reveal
the microscopic origin of this unexpected incident -- a crystal water driven
switching of the magnetically active orbitals. This switching results in a
fundamental change of the coupling regime from a three-dimensional
antiferromagnet to a quasi one-dimensional behavior. CuCl2 can be well
described as a frustrated J1-J2 Heisenberg chain with ferromagnetic exchange J1
and J2/J1 ~ -1.5 for which a helical ground state is predicted.Comment: 6 pages, 5 figures, 1 table (PRB, accepted
AKLT Models with Quantum Spin Glass Ground States
We study AKLT models on locally tree-like lattices of fixed connectivity and
find that they exhibit a variety of ground states depending upon the spin,
coordination and global (graph) topology. We find a) quantum paramagnetic or
valence bond solid ground states, b) critical and ordered N\'eel states on
bipartite infinite Cayley trees and c) critical and ordered quantum vector spin
glass states on random graphs of fixed connectivity. We argue, in consonance
with a previous analysis, that all phases are characterized by gaps to local
excitations. The spin glass states we report arise from random long ranged
loops which frustrate N\'eel ordering despite the lack of randomness in the
coupling strengths.Comment: 10 pages, 1 figur
Magnetism of CuX2 frustrated chains (X = F, Cl, Br): the role of covalency
Periodic and cluster density-functional theory (DFT) calculations, including
DFT+U and hybrid functionals, are applied to study magnetostructural
correlations in spin-1/2 frustrated chain compounds CuX2: CuCl2, CuBr2, and a
fictitious chain structure of CuF2. The nearest-neighbor and second-neighbor
exchange integrals, J1 and J2, are evaluated as a function of the Cu-X-Cu
bridging angle, theta, in the physically relevant range 80-110deg. In the ionic
CuF2, J1 is ferromagnetic for theta smaller 100deg. For larger angles, the
antiferromagnetic superexchange contribution becomes dominant, in accord with
the Goodenough-Kanamori-Anderson rules. However, both CuCl2 and CuBr2 feature
ferromagnetic J1 in the whole angular range studied. This surprising behavior
is ascribed to the increased covalency in the Cl and Br compounds, which
amplifies the contribution from Hund's exchange on the ligand atoms and renders
J1 ferromagnetic. At the same time, the larger spatial extent of X orbitals
enhances the antiferromagnetic J2, which is realized via the long-range
Cu-X-X-Cu paths. Both, periodic and cluster approaches supply a consistent
description of the magnetic behavior which is in good agreement with the
experimental data for CuCl2 and CuBr2. Thus, owing to their simplicity, cluster
calculations have excellent potential to study magnetic correlations in more
involved spin lattices and facilitate application of quantum-chemical methods
Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
We introduce an alternative definition of the relative height h^\kappa(x) of
a one-dimensional fluctuating interface indexed by a continuously varying real
paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to
the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the
spatially averaged height for \kappa = 1. We compute exactly the distribution
P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of
finite size L and periodic boundary conditions. One finds that it takes the
scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the
scaling function f^\kappa(x) interpolates between the Rayleigh distribution for
\kappa=0 and the Airy distribution for \kappa=1, the latter being the
probability distribution of the area under a Brownian excursion over the unit
interval. For arbitrary \kappa, one finds that it is related to, albeit
different from, the distribution of the area restricted to the interval [0,
\kappa] under a Brownian excursion over the unit interval.Comment: 25 pages, 4 figure
Microscopic magnetic modeling for the =1/2 alternating chain compounds NaCuSbO and NaCuTeO
The spin-1/2 alternating Heisenberg chain system NaCuSbO features
two relevant exchange couplings: within the structural CuO
dimers and between the dimers. Motivated by the controversially
discussed nature of , we perform extensive density-functional-theory
(DFT) calculations, including DFT+ and hybrid functionals. Fits to the
experimental magnetic susceptibility using high-temperature series expansions
and quantum Monte Carlo simulations yield the optimal parameters =
217 K and = 174 K with the alternation ratio 1.25. For the closely related system
NaCuTeO, DFT yields substantially enhanced , but weaker
. The comparative analysis renders the buckling of the chains as the
key parameter altering the magnetic coupling regime. Numerical simulation of
the dispersion relations of the alternating chain model clarify why both
antiferromagnetic and ferrromagnetic can reproduce the experimental
magnetic susceptibility data.Comment: published version: 11 pages, 8 figures, 5 tables + Supplemental
materia
On the identification of Ti-Ta-Nb-oxides in “wiikites” from Karelia
Purpose. With respect to the nature of Ti-Ta-Nb-oxides, which are included in the mineral associations that have historically gone by the now outdated name of “wiikites”, there is no unanimity of opinion. The main difficulty in identifying them is associated with the complexity of their chemical composition, their metamict structure and the substantial changes in their initial mineral form due to the effects of natural weathering. The aim of this work is the development of methodology to identify Ti-Ta-Nb-oxides corresponding to the mineral formulas AB2O6 and A2B2O7.
Methods. The methodology developed in the work includes two experimental approaches: 1) electron probe microanalysis of phases revealed through use of the SEM-BSE method. Based on the resulting data, a hypothesis about the nature of the Ti-Ta-Nb-oxides in a number of wiikite samples is proposed. 2) XRD analysis of those phases that are formed in the course of thermal annealing of samples from 200 to 1000°C. Based on the resulting data here, the previous hypotheses are either accepted or rejected for each sample.
Findings. Using this methodology, three “wiikite” samples were analyzed (the experimental codes were Wk-2, Wk-3 and Wk-7). The Ti-Ta-Nb-oxides in two of these wiikites (Wk-2 and Wk-3) were preliminarily determined to be hydroxyyttropyrochlore and hydroxycalciobetafite, respectively. In the third sample (Wk-7), the Ti-Ta-Nb-oxide was classified as polycrase. The results of XRD phase analysis of the annealed samples were compatible with the primary hypotheses that hydroxycalciobetafite and polycrase were the initial minerals in “wiikites” 3 and 7, respectively.
Originality. The paper considers the issue of the chemical conditions necessary for the recovery of the original
Ti-Ta-Nb-oxide during recrystallization of the metamict structures. This is a problem that has not been substantively addressed in the literature. Also for the first time experimentally proved the existence of the polycrase in “wiikites”.
Practical implications. Completed work expands our knowledge of the mineral composition of the granitic pegmatites of the Baltic shield and the possibility of their use both for research purposes and for needs of national economy.Мета. Розробка методології ідентифікації Ti-Ta-Nb-оксидів складного хімічного складу з метаміктною структурою, що відповідають мінеральним формулами АВ2О6 та А2В2О7.
Методика. Для розробки методології ідентифікації у роботі використано два експериментальних підходи: 1) рентген-спектральний мікроаналіз фаз, виявлених методом скануючої електронної мікроскопії зразків у назад відображених електронах. На основі отриманих результатів висунута гіпотеза щодо природи Ti-Ta-Nb-оксидів. 2) рентген-дифракційний аналіз фаз, що утворюються в процесі термічного відпалу зразків від 200 до 1000°С. На основі отриманих результатів для кожного зразка первинна гіпотеза приймалася або відкидалася.
Результати. З використанням даної методики були вивчені три зразки “віікітів” (шифри зразків: Wk-2, Wk-3 і Wk-7). Наявність Ti-Ta-Nb-оксидів попередньо визначено e двох зразках (Wk-2 і Wk-3) відповідно, як гідроксііттропірохлор та гідроксікальціобетафіт. У третьому зразку (Wk-7) Ti-Ta-Nb діагностований як полікраз. Результати рентген-дифракційного аналізу відпалених зразків підтвердили гіпотези про те, що початковими мінералами у Wk-3 і Wk-7 були гідроксікальціобетафіт і полікраз відповідно.
Наукова новизна. Визначено хімічні умови, необхідні для утворення початкового Тi-Ta-Nb під час рекристалізації метаміктної структури, що раніше не розглядалось у відповідній тематичній науковій літературі. Вперше експериментально виявлено присутність у “віікітах” полікраза.
Практична значимість. Отримані результати розширюють й доповнюють знання щодо мінерального складу гранітних пегматитів Балтійського щита та надають можливість їх використання в дослідницьких цілях і потребах народного господарства.Цель. Разработка методологии идентификации Ti-Ta-Nb-оксидов сложного химического состава с метамиктной структурой, соответствующих минеральным формулам АВ2О6 и А2В2О7.
Методика. Для разработки методологии идентификации в работе использовано два экспериментальных подхода: 1) рентген-спектральный микроанализ фаз, выявленных методом сканирующей электронной микроскопии образцов в обратно отраженных электронах. На основе полученных результатов выдвинута гипотеза о природе Ti-Ta-Nb-оксидов. 2) рентген-дифракционный анализ фаз, образующихся в процессе термического отжига образцов от 200 до 1000°С. На основе полученных результатов для каждого образца первоначальная гипотеза принималась или отвергалась.
Результаты. С использованием данной методики были изучены три образца “виикитов” (шифры образцов: Wk-2, Wk-3 и Wk-7). Наличие Ti-Ta-Nb-оксидов предварительно определено в двух образцах (Wk-2 и Wk-3) соответственно, как гидроксииттропирохлор и гидроксикальциобетафит. В третьем образце (Wk-7)
Ti-Ta-Nb диагностирован как поликраз. Результаты рентген-дифракционного анализа отожженных образцов подтвердили гипотезы о том, что первоначальными минералами в Wk-3 и Wk-7 были гидроксикальциобетафит и поликраз соответственно.
Научная новизна. Определены химические условия, необходимые для образования первоначального Тi-Ta-Nb во время рекристаллизации метамиктной структуры, что ранее не рассматривалось в соответствующих тематических научных литературе. Впервые экспериментально выявлено присутствие в “виикитах” поликраза.
Практическая значимость. Полученные результаты расширяют и дополняют знания о минеральном составе гранитных пегматитов Балтийского щита и дают возможности их использования в исследовательских целях и нуждах народного хозяйства.The study was conducted using equipment of the Center of X-ray Diffraction Studies and the Center for Microscopy and Microanalysis of the Research Park at Saint Petersburg State University, as well as the analytical laboratory of OJSC MMC Norilsk Nickel in Saint Petersburg
Quicksort with unreliable comparisons: a probabilistic analysis
We provide a probabilistic analysis of the output of Quicksort when
comparisons can err.Comment: 29 pages, 3 figure
Discovery of a stellar companion to the nearby solar-analogue HD 104304
Sun-like stars are promising candidates to host exoplanets and are often
included in exoplanet surveys by radial velocity (RV) and direct imaging. In
this paper we report on the detection of a stellar companion to the nearby
solar-analogue star HD 104304, which previously was considered to host a
planetary mass or brown dwarf companion. We searched for close stellar and
substellar companions around extrasolar planet host stars with high angular
resolution imaging to characterize planet formation environments. The detection
of the stellar companion was achieved by high angular resolution measurements,
using the "Lucky Imaging" technique at the ESO NTT 3.5m with the AstraLux Sur
instrument. We combined the results with VLT/NACO archive data, where the
companion could also be detected. The results were compared to precise RV
measurements of HD 104304, obtained at the Lick and Keck observatories from
2001-2010.
We confirmed common proper motion of the binary system. A spectral type of
M4V of the companion and a mass of 0.21 M_Sun was derived. Due to comparison of
the data with RV measurements of the unconfirmed planet candidate listed in the
Extrasolar Planets Encyclopaedia, we suggest that the discovered companion is
the origin of the RV trend and that the inclination of the orbit of
approximately 35 degrees explains the relatively small RV signal.Comment: 4 pages, 4 PNG figures, use aa.cls, accepted for publication in
Astronomy & Astrophysic
Localization Transition of Biased Random Walks on Random Networks
We study random walks on large random graphs that are biased towards a
randomly chosen but fixed target node. We show that a critical bias strength
b_c exists such that most walks find the target within a finite time when
b>b_c. For b<b_c, a finite fraction of walks drifts off to infinity before
hitting the target. The phase transition at b=b_c is second order, but finite
size behavior is complex and does not obey the usual finite size scaling
ansatz. By extending rigorous results for biased walks on Galton-Watson trees,
we give the exact analytical value for b_c and verify it by large scale
simulations.Comment: 4 pages, includes 4 figure
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