4,932 research outputs found
A variant of Horn's problem and derivative principle
Identifying the spectrum of the sum of two given Hermitian matrices with
fixed eigenvalues is the famous Horn's problem.In this note, we investigate a
variant of Horn's problem, i.e., we identify the probability density function
(abbr. pdf) of the diagonals of the sum of two random Hermitian matrices with
given spectra. We then use it to re-derive the pdf of the eigenvalues of the
sum of two random Hermitian matrices with given eigenvalues via
\emph{derivative principle}, a powerful tool used to get the exact probability
distribution by reducing to the corresponding distribution of diagonal
entries.We can recover Jean-Bernard Zuber's recent results on the pdf of the
eigenvalues of two random Hermitian matrices with given eigenvalues. Moreover,
as an illustration, we derive the analytical expressions of eigenvalues of the
sum of two random Hermitian matrices from \rG\rU\rE(n) or Wishart ensemble by
derivative principle, respectively.We also investigate the statistics of
exponential of random matrices and connect them with Golden-Thompson
inequality, and partly answer a question proposed by Forrester. Some potential
applications in quantum information theory, such as uniform average quantum
Jensen-Shannon divergence and average coherence of uniform mixture of two
orbits,are discussed.Comment: 24 pages, LaTeX; a new result, i.e., Theorem 3.7, is added and
several references are include
Research of the active reflector antenna using laser angle metrology system
Active reflector is one of the key technologies for constructing large
telescopes, especially for the millimeter/sub-millimeter radio telescopes. This
article introduces a new efficient laser angle metrology system for the active
reflector antenna of the large radio telescopes, with a plenty of active
reflector experiments mainly about the detecting precisions and the maintaining
of the surface shape in real time, on the 65-meter radio telescope prototype
constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT).
The test results indicate that the accuracy of the surface shape segmenting and
maintaining is up to micron dimension, and the time-response can be of the
order of minutes. Therefore, it is proved to be workable for the sub-millimeter
radio telescopes.Comment: 10 pages, 15 figure
High cycle fatigue and ratcheting interaction of laser powder bed fusion stainless steel 316L:Fracture behaviour and stress-based modelling
Variations in the physical and mechanical properties of parts made by laser power bed fusion (L-PBF) could be affected by the choice of processing or post-processing strategies. This work examined the influence of build orientation and post-processing treatments (annealing or hot isostatic pressing) on the fatigue and fracture behaviours of L-PBF stainless steel 316L in the high cycle fatigue region, i.e. 104 – 106 cycles. Experimental results show that both factors introduce significant changes in the plastic deformation properties, which affect fatigue strength via the mechanism of fatigue-ratcheting interaction. Cyclic plasticity is characterised by hardening, which promotes mean stress insensitivity and improved fatigue resistance. Fatigue activities, involving the initiation of crack at defects and microstructural heterogeneities, are of greater relevance to the longer life region where the global deformation mode is elastic. As the simultaneous actions of ratcheting and fatigue generate complex nonlinear interactions between the alternating stress amplitude and mean stress, the fatigue properties could not be effectively predicted using traditional stress-based models. A modification to the Goodman relation was proposed to account for the added effects of cyclic plasticity and was demonstrated to produce good agreement with experimental results for both cyclic hardening and softening materials.EDB (Economic Devt. Board, S’pore)Accepted versio
Unifying ultrafast demagnetization and intrinsic Gilbert damping in Co/Ni bilayers with electronic relaxation near the Fermi surface
The ability to controllably manipulate the laser-induced ultrafast magnetic
dynamics is a prerequisite for future high speed spintronic devices. The
optimization of devices requires the controllability of the ultrafast
demagnetization time, , and intrinsic Gilbert damping, . In previous attempts
to establish the relationship between and , the rare-earth doping of a
permalloy film with two different demagnetization mechanism is not a suitable
candidate. Here, we choose Co/Ni bilayers to investigate the relations between
and by means of time-resolved magneto-optical Kerr effect (TRMOKE) via
adjusting the thickness of the Ni layers, and obtain an approximately
proportional relation between these two parameters. The remarkable agreement
between TRMOKE experiment and the prediction of breathing Fermi-surface model
confirms that a large Elliott-Yafet spin-mixing parameter is relevant to the
strong spin-orbital coupling at the Co/Ni interface. More importantly, a
proportional relation between and in such metallic films or heterostructures
with electronic relaxation near Fermi surface suggests the local spin-flip
scattering domains the mechanism of ultrafast demagnetization, otherwise the
spin-current mechanism domains. It is an effective method to distinguish the
dominant contributions to ultrafast magnetic quenching in metallic
heterostructures by investigating both the ultrafast demagnetization time and
Gilbert damping simultaneously. Our work can open a novel avenue to manipulate
the magnitude and efficiency of Terahertz emission in metallic heterostructures
such as the perpendicular magnetic anisotropic Ta/Pt/Co/Ni/Pt/Ta multilayers,
and then it has an immediate implication of the design of high frequency
spintronic devices
2-{2,6-Bis[bis(4-fluorophenyl)methyl]-4-chlorophenylimino} -3-aryliminobutylnickel(II) bromide complexes: Synthesis, characterization, and investigation of their catalytic behavior
The series of 2-{2,6-bis[di(4-fluorophenyl)methyl]-4-chlorophenylimino}-3- aryliminobutane derivatives (L1-L5) and their nickel(II) dibromide complexes (Ni1-Ni5) were synthesized, and all organic compounds were fully characterized by the Fourier transform infrared (FT-IR) and nuclear magnetic resonance (NMR) spectroscopy and by elemental analysis, while the nickel complexes were characterized by FT-IR spectroscopy, elemental analysis, as well as by single-crystal X-ray diffraction for two representative examples, namely Ni1 and Ni4. A distorted tetrahedral geometry was observed for these four-coordinate nickel complexes. Upon the activation with either Methylaluminoxane or modified methylaluminoxane as co-catalyst, all nickel complex precatalysts showed very high activity toward ethylene polymerization with activities of up to 10 7 g(PE)·mol -1 (Ni)·h -1 , and afforded highly branched polyethylene with a bimodal distribution. © 2014 Elsevier B.V
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