ExoMol line lists - XXXII. The rovibronic spectrum of MgO

Line lists for magnesium oxide are computed and extensive comparisons are made with existing experimental spectra. The LiTY line lists cover all ro-vibration transitions within the five lowest-lying electronic states ($X\,{}^1\Sigma^+$, $a\,{}^3\Pi$, $A\,{}^1\Pi$, $B\,{}^1\Sigma^+$ and $b\,{}^3\Sigma^{+}$) and five isotopologues: $^{24}$Mg$^{16}$O, $^{25}$Mg$^{16}$O, $^{26}$Mg$^{16}$O, $^{24}$Mg$^{17}$O, $^{24}$Mg$^{18}$O, $^{24}$Mg$^{17}$O and $^{24}$Mg$^{18}$O. The calculation use potential energy cures, spin-orbit and electronic angular momentum couplings curves determined by fitting to empirical energy levels; these levels are reproduced to within 0.01 \cm\ in most cases. Computed nuclear-motion wavefunctions are combined with {\it ab initio} dipole moment curves to give transition intensities and excited state radiative lifetimes which are compared with laboraroty measurements. The $^{24}$Mg$^{16}$O line list comprises 186 842 ($J\le 320$) ro-vibronic states and 72 833 173 transitions with angular momenta, $J$, up to 300 and covering wavenumbers up to 33 000 cm$^{-1}$ ($\lambda > 0.3$ $\mu$m). The line lists are suitable for temperatures up to about 5000 K. They are relevant to astrophysical studies of exoplanet atmospheres, cool stars and brown dwarfs, and are made available in electronic form at the CDS and ExoMol databases

Controlled Sequential Monte Carlo

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; e.g. for inference in non-linear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their performance. We introduce here a class of controlled sequential Monte Carlo algorithms, where the proposal distributions are determined by approximating the solution to an associated optimal control problem using an iterative scheme. This method builds upon a number of existing algorithms in econometrics, physics, and statistics for inference in state space models, and generalizes these methods so as to accommodate complex static models. We provide a theoretical analysis concerning the fluctuation and stability of this methodology that also provides insight into the properties of related algorithms. We demonstrate significant gains over state-of-the-art methods at a fixed computational complexity on a variety of applications

A Multilevel Approach for Stochastic Nonlinear Optimal Control

We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many domains. Although the optimal control admits a path integral representation for this class of control problems, efficient computation of the associated path integrals remains a challenging Monte Carlo task. The focus of this article is to propose a new Monte Carlo approach that significantly improves upon existing methodology. Our proposed methodology first tackles the issue of exponential growth in variance with the time horizon by casting optimal control estimation as a smoothing problem for a state space model associated with the control problem, and applying smoothing algorithms based on particle Markov chain Monte Carlo. To further reduce computational cost, we then develop a multilevel Monte Carlo method which allows us to obtain an estimator of the optimal control with $\mathcal{O}(\epsilon^2)$ mean squared error with a computational cost of $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$. In contrast, a computational cost of $\mathcal{O}(\epsilon^{-3})$ is required for existing methodology to achieve the same mean squared error. Our approach is illustrated on two numerical examples, which validate our theory

The K\"ahler Potential of Abelian Higgs Vortices

We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in Liouville field theory. The K\"ahler potential on the moduli space of vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical reinterpretation of these vortices. Finally, we attempt to find the K\"ahler potential for vortices on \mathbbm{R}^{2} in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This approach does not give the correct result, and we offer a possible explanation for this.Comment: 25 page

Sticker systems over monoids

Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study

Constraining the Atmospheric Composition of the Day-Night Terminators of HD 189733b : Atmospheric Retrieval with Aerosols

A number of observations have shown that Rayleigh scattering by aerosols dominates the transmission spectrum of HD 189733b at wavelengths shortward of 1 $\mu$m. In this study, we retrieve a range of aerosol distributions consistent with transmission spectroscopy between 0.3-24 $\mu$m that were recently re-analyzed by Pont et al. (2013). To constrain the particle size and the optical depth of the aerosol layer, we investigate the degeneracies between aerosol composition, temperature, planetary radius, and molecular abundances that prevent unique solutions for transit spectroscopy. Assuming that the aerosol is composed of MgSiO$_3$, we suggest that a vertically uniform aerosol layer over all pressures with a monodisperse particle size smaller than about 0.1 $\mu$m and an optical depth in the range 0.002-0.02 at 1 $\mu$m provides statistically meaningful solutions for the day/night terminator regions of HD 189733b. Generally, we find that a uniform aerosol layer provide adequate fits to the data if the optical depth is less than 0.1 and the particle size is smaller than 0.1 $\mu$m, irrespective of the atmospheric temperature, planetary radius, aerosol composition, and gaseous molecules. Strong constraints on the aerosol properties are provided by spectra at wavelengths shortward of 1 $\mu$m as well as longward of 8 $\mu$m, if the aerosol material has absorption features in this region. We show that these are the optimal wavelengths for quantifying the effects of aerosols, which may guide the design of future space observations. The present investigation indicates that the current data offer sufficient information to constrain some of the aerosol properties of HD189733b, but the chemistry in the terminator regions remains uncertain.Comment: Transferred to ApJ and accepted. 11 pages, 10 figures, 1 tabl

Off-Diagonal Long-Range Order: Meissner Effect and Flux Quantization

There has been a proof by Sewell that the hypothesis of off-diagonal long-range order in the reduced density matrix $\rho _2$ implies the Meissner effect. We present in this note an elementary and straightforward proof that not only the Meissner effect but also the property of magnetic flux quantization follows from the hypothesis. It is explicitly shown that the two phenomena are closely related, and phase coherence is the origin for both.Comment: 11 pages, Latex fil

Profile for Aquatic Resources Management: Kdol Chrum, Bourei Cholsar and Sangkum Mean Chey Villages Kampong Krasaing Commune, Bourei Cholsar District, Takeo Province, Cambodia

This publication is part of a collection of three profiles covering nine aquatic resources-dependent villages in the provinces of Stung Treng, Takeo and Siem Reap. The profiles are important because in most, if not all, of the aquatic-resources villages of Cambodia, critical data and information useful for planning and management are not available in a documented form. The development of the village profiles is viewed as a basic requirement for planning and overall management. It is only an initial step to identify future programs and projects related to aquatic resources. The profiles depict the present state of the villages and their aquatic resources. In general, the villages have limited infrastructure and other physical resources. In the villages of Takeo and Siem Reap, total flooding occurs in the wet season and villagers must rely on transportation by boat. In Stung Treng villages, partial flooding is also a problem as it makes the few existing roads significantly impassable during the wet season.Botanical resources, Resource management, Fishery management, Cambodia,

Entanglement in a Valence-Bond-Solid State

We study entanglement in Valence-Bond-Solid state. It describes the ground state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model has a gap and open boundary conditions. We calculate an entropy of a subsystem (continuous block of spins). It quantifies the entanglement of this block with the rest of the ground state. We prove that the entanglement approaches a constant value exponentially fast as the size of the subsystem increases. Actually we proved that the density matrix of the continuous block of spins depends only on the length of the block, but not on the total size of the chain [distance to the ends also not essential]. We also study reduced density matrices of two spins both in the bulk and on the boundary. We evaluated concurrencies.Comment: 4pages, no figure

Stress-Energy Tensor Induced by Bulk Dirac Spinor in Randall-Sundrum Model

Motivated by the possible extension into a supersymmetric Randall-Sundrum (RS) model, we investigate the properties of the vacuum expectation value (VEV) of the stress-energy tensor for a quantized bulk Dirac spinor field in the RS geometry and compare it with that for a real scalar field. This is carried out via the Green function method based on first principles without invoking the degeneracy factor, whose validity in a warp geometry is a priori unassured. In addition, we investigate the local behavior of the Casimir energy near the two branes. One salient feature we found is that the surface divergences near the two branes have opposite signs. We argue that this is a generic feature of the fermionic Casimir energy density due to its parity transformation in the fifth dimension. Furthermore, we investigate the self-consistency of the RS metric under the quantum correction due to the stress-energy tensor. It is shown that the VEV of the stress-energy tensor and the classical one become comparable near the visible brane if k ~ M ~ M_Pl (the requirement of no hierarchy problem), where k is the curvature of the RS warped geometry and M the 5-dimensional Planck mass. In that case the self-consistency of RS model that includes bulk fields is in doubt. If, however, k <~ M, then an approximate self-consistency of the RS-type metric may still be satisfied.Comment: 7 pages with 2 figure