On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f_0. We prove that for each f_0 there is an arbitrarily small delta f_0' in W^{1,1}(R) such that f_0+delta f_0$is unstable. When$f_0$ is perturbed by an area preserving rearrangement, f_0 will always be stable if the continuous spectrum is only of positive signature, where the signature of the continuous spectrum is defined as in previous work. If there is a signature change, then there is a rearrangement of f_0 that is unstable and arbitrarily close to f_0 with f_0' in W^{1,1}. This result is analogous to Krein's theorem for the continuous spectrum. We prove that if a discrete mode embedded in the continuous spectrum is surrounded by the opposite signature there is an infinitesimal perturbation in C^n norm that makes f_0 unstable. If f_0 is stable we prove that the signature of every discrete mode is the opposite of the continuum surrounding it.Comment: Submitted to the journal Transport Theory and Statistical Physics. 36 pages, 12 figure

Penrose Limits of Orbifolds and Orientifolds

We study the Penrose limit of various AdS_p X S^q orbifolds. The limiting spaces are waves with parallel rays and singular wave fronts. In particular, we consider the orbifolds AdS_3 X S^3/\Gamma, AdS_5 X S^5/\Gamma and AdS_{4,7} X S^{7,4}/\Gamma where \Gamma acts on the sphere and/or the AdS factor. In the pp-wave limit, the wave fronts are the orbifolds C^2/\Gamma, C^4/\Gamma and R XC^4/\Gamma, respectively. When desingularization is possible, we get asymptotically locally pp-wave backgrounds (ALpp). The Penrose limit of orientifolds are also discussed. In the AdS_5 X RP^5 case, the limiting singularity can be resolved by an Eguchi-Hanson gravitational instanton. The pp-wave limit of D3-branes near singularities in F-theory is also presented. Finally, we give the embedding of D-dimensional pp-waves in flat M^{2,D} space.Comment: 20 pages, references adde

Construction of a deep shaft for Crossrail

An 8·2 m diameter, 37·5 m deep shaft has been successfully constructed from within the basement of a new development, Moorhouse, near Moorgate in the City of London. Programme constraints led to the shaft being constructed after completion of the foundations, basements and most of the superstructure for the development. At its closest point the shaft is less than 2 m from the large-diameter piles that support Moorhouse, and the presence of these foundations placed tight constraints on acceptable ground movements associated with construction of the shaft. The depth of the shaft is such that it penetrates through stiff London Clay and is founded at the bottom of the Lambeth Group. The paper describes the contingency measures to deal with potentially difficult ground conditions, including the water-bearing layers of the Lambeth Group. The construction processes included a complex temporary works dewatering system around the shaft, with the option to carry out additional dewatering from within the shaft during excavation. Provision was also made for radial grouting to ‘restress’ the ground, to prevent long-term settlement of the Moorhouse piles, should the need arise. The success of the project was due, in no small part, to the detailed planning and consideration of contingency measures to deal with perceived risk

The Stark effect in linear potentials

We examine the Stark effect (the second-order shift in the energy spectrum due to an external constant force) for two 1-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z>0 and V(z) infinite for z<0) and the symmetric linear potential (given by V(z) = F|z|). We show how straightforward use of the most obvious properties of the Airy function solutions and simple Taylor expansions give closed form results for the Stark shifts in both systems. These exact results are then compared to other approximation techniques, such as perturbation theory and WKB methods. These expressions add to the small number of closed-form descriptions available for the Stark effect in model quantum mechanical systems.Comment: 15 pages. To appear in Eur. J. Phys. Needs Institute of Physics (iopart) style file

Mapping 6D N = 1 supergravities to F-theory

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the gauge group; each block depends only on the group factor and the matter charged under it. All 6D chiral supergravity models can be constructed by gluing such blocks together in accordance with constraints from anomalies. Associating a geometric structure to each block gives a dictionary for translating a supergravity model into a set of topological data for an F-theory construction. We construct the dictionary of F-theory divisors explicitly for some simple gauge group factors and associated matter representations. Using these building blocks we analyze a variety of models. We identify some 6D supergravity models which do not map to integral F-theory divisors, possibly indicating quantum inconsistency of these 6D theories.Comment: 37 pages, no figures; v2: references added, minor typos corrected; v3: minor corrections to DOF counting in section

Experimental evidence on promotion of electric and improved biomass cookstoves.

Improved cookstoves (ICS) can deliver "triple wins" by improving household health, local environments, and global climate. Yet their potential is in doubt because of low and slow diffusion, likely because of constraints imposed by differences in culture, geography, institutions, and missing markets. We offer insights about this challenge based on a multiyear, multiphase study with nearly 1,000 households in the Indian Himalayas. In phase I, we combined desk reviews, simulations, and focus groups to diagnose barriers to ICS adoption. In phase II, we implemented a set of pilots to simulate a mature market and designed an intervention that upgraded the supply chain (combining marketing and home delivery), provided rebates and financing to lower income and liquidity constraints, and allowed households a choice among ICS. In phase III, we used findings from these pilots to implement a field experiment to rigorously test whether this combination of upgraded supply and demand promotion stimulates adoption. The experiment showed that, compared with zero purchase in control villages, over half of intervention households bought an ICS, although demand was highly price-sensitive. Demand was at least twice as high for electric stoves relative to biomass ICS. Even among households that received a negligible price discount, the upgraded supply chain alone induced a 28 percentage-point increase in ICS ownership. Although the bundled intervention is resource-intensive, the full costs are lower than the social benefits of ICS promotion. Our findings suggest that market analysis, robust supply chains, and price discounts are critical for ICS diffusion

Thermal infrared observations of near-Earth asteroid 2002 NY40

We obtained N-band observations of the Apollo asteroid 2002 NY40 during its close Earth fly-by in August 2002 with TIMMI2 at the ESO 3.6 m telescope. The photometric measurement allowed us to derive a radiometric diameter of 0.28+/-0.03 km and an albedo of 0.34+/-0.06 through the near-Earth asteroid thermal model (NEATM) and a thermophysical model (TPM). The values are in agreement with results from radar data, visual and near-IR observations. In this first comparison between these two model approaches we found that the empirical NEATM beaming parameter $\eta$=1.0 corresponds to a thermal inertia values of about 100 $\mathrm{J m^{-2} s^{-0.5} K^{-1}}$ for a typical range of surface roughness, assuming an equator-on viewing angle. Our TPM analysis indicated that the surface of 2002 NY40 consists of rocky material with a thin or no dust regolith. The asteroid very likely has a prograde sense of rotation with a cold terminator at the time of our observations. Although both model approaches can fit the thermal spectra taken at phase angles of 22$^{\circ}$ and 59$^{\circ}$, we did not find a consistent model solution that describes all pieces of photometric and spectroscopic data. In addition to the 2002 NY40 analysis, we discuss the possibilities to distinguish between different models with only very few photometric and/or spectroscopic measurements spread over a range of phase angles.Comment: 6 pages, 4 figures, A&A accepte

Strengthening impact assessment: a call for integration and focus

We suggest that the impact assessment community has lost its way based on our observation that impact assessment is under attack because of a perceived lack of efficiency. Specifically, we contend that the proliferation of different impact assessment types creates separate silos of expertise and feeds arguments for not only a lack of efficiency but also a lack of effectiveness of the process through excessive specialisation and a lack of interdisciplinary practice. We propose that the solution is a return to the basics of impact assessment with a call for increased integration around the goal of sustainable development and focus through better scoping. We rehearse and rebut counter arguments covering silo-based expertise, advocacy, democracy, sustainability understanding and communication. We call on the impact assessment community to rise to the challenge of increasing integration and focus, and to engage in the debate about the means of strengthening impact assessment

Geometric invariant theory of syzygies, with applications to moduli spaces

We define syzygy points of projective schemes, and introduce a program of studying their GIT stability. Then we describe two cases where we have managed to make some progress in this program, that of polarized K3 surfaces of odd genus, and of genus six canonical curves. Applications of our results include effectivity statements for divisor classes on the moduli space of odd genus K3 surfaces, and a new construction in the Hassett-Keel program for the moduli space of genus six curves.Comment: v1: 23 pages, submitted to the Proceedings of the Abel Symposium 2017, v2: final version, corrects a sign error and resulting divisor class calculations on the moduli space of K3 surfaces in Section 5, other minor changes, In: Christophersen J., Ranestad K. (eds) Geometry of Moduli. Abelsymposium 2017. Abel Symposia, vol 14. Springer, Cha