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 $k$ 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 $q$-state Potts model to non-integer values $q>1$. 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 $q$, 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 $z_{\rm exp} =0.07 (1), 0.521 (7)$, and $1.007 (9)$ for $q=2, 3$, and 4 respectively. For non-integer $q$, 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 $K_{\rm nn}$, next-nearest-neighbor couplings $K_{\rm nnn}>0$, and a magnetic field $H$. 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 $K_{\rm nn}<0$, but we also explore the ferromagnetic regime $K_{\rm nn}\ge 0$ for H=0. For $K_{\rm nn}<0$ and H=0 we locate a critical phase presumably covering the whole range $-\infty < K_{\rm nn}<0$. For $K_{\rm nn}<0$, $H\neq 0$ we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit $H \to \infty$ this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential

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

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