1,187 research outputs found
Analytical Solutions of Singular Isothermal Quadrupole Lens
Using analytical method, we study the Singular Isothermal Quadrupole (SIQ)
lens system, which is the simplest lens model that can produce four images. In
this case, the radial mass distribution is in accord with the profile of the
Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given
by adding a quadrupole on the monopole component. The basic properties of the
SIQ lens have been studied in this paper, including deflection potential,
deflection angle, magnification, critical curve, caustic, pseudo-caustic and
transition locus. Analytical solutions of the image positions and
magnifications for the source on axes are derived. As have been found, naked
cusps will appear when the relative intensity of quadrupole to monopole is
larger than 0.6. According to the magnification invariant theory of the SIQ
lens, the sum of the signed magnifications of the four images should be equal
to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed
magnification of the left three images is smaller than the invariant 1. With
this simple lens system, we study the situations that a point source infinitely
approaches a cusp or a fold. The sum of magnifications of cusp image triplet is
usually not equal to 0, and it is usually positive for major cusp while
negative for minor cusp. Similarly, the sum of magnifications of fold image
pair is usually neither equal to 0. Nevertheless, the cusp and fold relations
are still equal to 0, in that the sum values are divided by infinite absolute
magnifications by definition.Comment: 12 pages, 2 figures, accepted for publication in ApJ
Single-cluster dynamics for the random-cluster model
We formulate a single-cluster Monte Carlo algorithm for the simulation of the
random-cluster model. This algorithm is a generalization of the Wolff
single-cluster method for the -state Potts model to non-integer values
. Its results for static quantities are in a satisfactory agreement with
those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which
involves a full cluster decomposition of random-cluster configurations. We
explore the critical dynamics of this algorithm for several two-dimensional
Potts and random-cluster models. For integer , the single-cluster algorithm
can be reduced to the Wolff algorithm, for which case we find that the
autocorrelation functions decay almost purely exponentially, with dynamic
exponents , and for , and
4 respectively. For non-integer , the dynamical behavior of the
single-cluster algorithm appears to be very dissimilar to that of the SWCM
algorithm. For large critical systems, the autocorrelation function displays a
range of power-law behavior as a function of time. The dynamic exponents are
relatively large. We provide an explanation for this peculiar dynamic behavior.Comment: 7 figures, 4 table
A QM/MM equation-of-motion coupled-cluster approach for predicting semiconductor color-center structure and emission frequencies
Valence excitation spectra are computed for all deep-center silicon-vacancy
defect types in 3C, 4H, and 6H silicon carbide (SiC) and comparisons are made
with literature photoluminescence measurements. Nuclear geometries surrounding
the defect centers are optimized within a Gaussian basis-set framework using
many-body perturbation theory or density functional theory (DFT) methods, with
computational expenses minimized by a QM/MM technique called SIMOMM. Vertical
excitation energies are subsequently obtained by applying excitation-energy,
electron-attached, and ionized equation-of-motion coupled-cluster (EOMCC)
methods, where appropriate, as well as time-dependent (TD) DFT, to small models
including only a few atoms adjacent to the defect center. We consider the
relative quality of various EOMCC and TD-DFT methods for (i) energy-ordering
potential ground states differing incrementally in charge and multiplicity,
(ii) accurately reproducing experimentally measured photoluminescence peaks,
and (iii) energy-ordering defects of different types occurring within a given
polytype. The extensibility of this approach to transition-metal defects is
also tested by applying it to silicon-substitutional chromium defects in SiC
and comparing with measurements. It is demonstrated that, when used in
conjunction with SIMOMM-optimized geometries, EOMCC-based methods can provide a
reliable prediction of the ground-state charge and multiplicity, while also
giving a quantitative description of the photoluminescence spectra, accurate to
within 0.1 eV of measurement in all cases considered.Comment: 13 pages, 4 figures, 6 tables, 5 equations, 100 reference
Decentralized Event-Triggered Consensus of Linear Multi-agent Systems under Directed Graphs
An event-triggered control technique for consensus of multi-agent systems
with general linear dynamics is presented. This paper extends previous work to
consider agents that are connected using directed graphs. Additionally, the
approach shown here provides asymptotic consensus with guaranteed positive
inter-event time intervals. This event-triggered control method is also used in
the case where communication delays are present. For the communication delay
case we also show that the agents achieve consensus asymptotically and that,
for every agent, the time intervals between consecutive transmissions is
lower-bounded by a positive constant.Comment: 9 pages, 5 figures, A preliminary version of this manuscript has been
submitted to the 2015 American Control Conferenc
The triangular Ising model with nearest- and next-nearest-neighbor couplings in a field
We study the Ising model on the triangular lattice with nearest-neighbor
couplings , next-nearest-neighbor couplings , and a
magnetic field . This work is done by means of finite-size scaling of
numerical results of transfer matrix calculations, and Monte Carlo simulations.
We determine the phase diagram and confirm the character of the critical
manifolds. The emphasis of this work is on the antiferromagnetic case , but we also explore the ferromagnetic regime for H=0.
For and H=0 we locate a critical phase presumably covering the
whole range . For , we locate a
plane of phase transitions containing a line of tricritical three-state Potts
transitions. In the limit this line leads to a tricritical model
of hard hexagons with an attractive next-nearest-neighbor potential
The closo-Si\u3csub\u3e12\u3c/sub\u3eC\u3csub\u3e12\u3c/sub\u3e Molecule from Cluster to Crystal: A Theoretical Prediction
The structure of closo-Si12C12 is unique among stable SinCm isomers (n, m \u3e 4) because of its high symmetry, π–π stacking of C6 rings and unsaturated silicon atoms at symmetrical peripheral positions. Dimerization potential surfaces reveal various dimerization reactions that form between two closo-Si12C12 molecules through Si–Si bonds at unsaturated Si atoms. As a result the closo-Si12C12 molecule is capable of polymerization to form stable 1D polymer chains, 2D crystal layers, and 3D crystals. 2D crystal structures formed by side-side polymerization satisfy eight Si valences on each monomer without large distortion of the monomer structure. 3D crystals are formed by stacking 2D structures in the Z direction, preserving registry of C6 rings in monomer moiety
Bi(111) thin film with insulating interior but metallic surfaces
The electrical conductance of molecular beam epitaxial Bi on BaF2(111) was
measured as a function of both film thickness (4-540 nm) and temperature (5-300
K). Unlike bulk Bi as a prototype semimetal, the Bi thin films up to 90 nm are
found to be insulating in the interiors but metallic on the surfaces. This
result has not only resolved unambiguously the long controversy about the
existence of semimetal-semiconductor transition in Bi thin film but also
provided a straightforward interpretation for the long-puzzled temperature
dependence of the resistivity of Bi thin films, which in turn might suggest
some potential applications in spintronics
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