Considering the impact of situation-specific motivations and constraints in the design of naturally ventilated and hybrid buildings

A simple logical model of the interaction between a building and its occupants is presented based on the principle that if free to do so, people will adjust their posture, clothing or available building controls (windows, blinds, doors, fans, and thermostats) with the aim of achieving or restoring comfort and reducing discomfort. These adjustments are related to building design in two ways: first the freedom to adjust depends on the availability and ease-of-use of control options; second the use of controls affects building comfort and energy performance. Hence it is essential that these interactions are considered in the design process. The model captures occupant use of controls in response to thermal stimuli (too warm, too cold etc.) and non-thermal stimuli (e.g. desire for fresh air). The situation-specific motivations and constraints on control use are represented through trigger temperatures at which control actions occur, motivations are included as negative constraints and incorporated into a single constraint value describing the specifics of each situation. The values of constraints are quantified for a range of existing buildings in Europe and Pakistan. The integration of the model within a design flow is proposed and the impact of different levels of constraints demonstrated. It is proposed that to minimise energy use and maximise comfort in naturally ventilated and hybrid buildings the designer should take the following steps: 1. Provide unconstrained low energy adaptive control options where possible, 2. Avoid problems with indoor air quality which provide motivations for excessive ventilation rates, 3. Incorporate situation-specific adaptive behaviour of occupants in design simulations, 4. Analyse the robustness of designs against variations in patterns of use and climate, and 5. Incorporate appropriate comfort standards into the operational building controls (e.g. BEMS)

Two New LBV Candidates in the M33 Galaxy

We present two new luminous blue variable (LBV) candidate stars discovered in the M33 galaxy. We identified these stars (Valeev et al. 2010) as massive star candidates at the final stages of evolution, presumably with a notable interstellar extinction. The candidates were selected from the Massey et al. (2006) catalog based on the following criteria: emission in Halpha, V<18.5 and 0.35<(B-V)<1.2. The spectra of both stars reveal a broad and strong Halpha emission with extended wings (770 and 1000 km/s). Based on the spectra we estimated the main parameters of the stars. Object N45901 has a bolometric luminosity log(L/Lsun)=6.0-6.2 with the value of interstellar extinction Av=2.3+-0.1. The temperature of the star's photosphere is estimated as Tstar~13000-15000K its probable mass on the Zero Age Main Sequence is M~60-80Msun. The infrared excess in N45901 corresponds to the emission of warm dust with the temperature Twarm~1000K, and amounts to 0.1% of the bolometric luminosity. A comparison of stellar magnitude estimates from different catalogs points to the probable variability of the object N45901. Bolometric luminosity of the second object, N125093, is log(L/Lsun)=6.3-6.6, the value of interstellar extinction is Av=2.75+-0.15. We estimate its photosphere's temperature as Tstar~13000-16000K, the initial mass as M~90-120Msun. The infrared excess in N125093 amounts to 5-6% of the bolometric luminosity. Its spectral energy distribution reveals two thermal components with the temperatures Twarm~1000K and Tcold~480K. The [CaII] lines (7291A and 7323A), observed in LBV-like stars VarA and N93351 in M33, are also present in the spectrum of N125093. These lines indicate relatively recent gas eruptions and dust activity linked with them. High bolometric luminosity of these stars and broad Halpha emissions allow classifying the studied objects as LBV candidates.Comment: 14 pages, 4 figure

PT-symmetric deformations of Calogero models

We demonstrate that Coxeter groups allow for complex PT-symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems

Bounding the dimensions of rational cohomology groups

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field $\mathbb{F}_p$. In this paper we investigate situations where the dimension of a rational cohomology group for $G$ can be bounded by a constant times the dimension of the coefficient module. We then demonstrate how our results can be applied to obtain effective bounds on the first cohomology of the symmetric group. We also show how, for finite Chevalley groups, our methods permit significant improvements over previous estimates for the dimensions of second cohomology groups.Comment: 13 page

Matching Spherical Dust Solutions to Construct Cosmological Models

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaitre-Tolman-Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.Comment: 13 pages, Revtex; to appear Gen. Rel. Gra

The structure of quantum Lie algebras for the classical series B_l, C_l and D_l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys. A. Minor misprints in eqs. 5.11 and 5.12 correcte

On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Non-crystallographic reduction of generalized Calogero-Moser models

We apply a recently introduced reduction procedure based on the embedding of non-crystallographic Coxeter groups into crystallographic ones to Calogero–Moser systems. For rational potentials the familiar generalized Calogero Hamiltonian is recovered. For the Hamiltonians of trigonometric, hyperbolic and elliptic types, we obtain novel integrable dynamical systems with a second potential term which is rescaled by the golden ratio. We explicitly show for the simplest of these non-crystallographic models, how the corresponding classical equations of motion can be derived from a Lie algebraic Lax pair based on the larger, crystallographic Coxeter group

Crossing the `Yellow Void' -- Spatially Resolved Spectroscopy of the Post- Red Supergiant IRC+10420 and Its Circumstellar Ejecta

IRC +10420 is one of the extreme hypergiant stars that define the empirical upper luminosity boundary in the HR diagram. During their post--RSG evolution, these massive stars enter a temperature range (6000-9000 K) of increased dynamical instability, high mass loss, and increasing opacity, a semi--forbidden region, that de Jager and his collaborators have called the `yellow void'. We report HST/STIS spatially resolved spectroscopy of IRC +10420 and its reflection nebula with some surprising results. Long slit spectroscopy of the reflected spectrum allows us to effectively view the star from different directions. Measurements of the double--peaked Halpha emission profile show a uniform outflow of gas in a nearly spherical distribution, contrary to previous models with an equatorial disk or bipolar outflow. Based on the temperature and mass loss rate estimates that are usually quoted for this object, the wind is optically thick to the continuum at some and possibly all wavelengths. Consequently the observed variations in apparent spectral type and inferred temperature are changes in the wind and do not necessarily mean that the underlying stellar radius and interior structure are evolving on such a short timescale. To explain the evidence for simultaneous outflow and infall of material near the star, we propose a `rain' model in which blobs of gas condense in regions of lowered opacity outside the dense wind. With the apparent warming of its wind, the recent appearance of strong emission, and a decline in the mass loss rate, IRC +10420 may be about to shed its opaque wind, cross the `yellow void', and emerge as a hotter star.Comment: To appear in the Astronomical Journal, August 200