Semiclassical resolvent bounds for compactly supported radial potentials

We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator −h2Δ+V(|x|)−E in dimension n≥2, where h,E>0, and V:[0,∞)→ℝ is L∞ and compactly supported. We show that the weighted resolvent estimate grows no faster than exp(Ch−1), and prove an exterior weighted estimate which grows ∼h−1

Design of domestic photovoltaics manufacturing systems under global constraints and uncertainty

As global political discourse is taking place where the need for a cleaner energy mix is constantly highlighted, manufacturing strategies are becoming more relevant. Thus, the photovoltaics system design is a crucial aspect related with the overall sustainability. In fact, various countries are considering the potential to locally manufacture different elements of the photovoltaics (PV) value chain and the strategies to incentivize a local manufacturing base. This paper develops a mathematical programming approach for the optimal design of a PV manufacturing value chain considering diverse criteria linked to economic and environmental performance such as minimum sustainable price, transportation capacity, among others, and considering uncertainty. In addition, the proposed methodology involves the dependence over time of supply chain variables and economic parameters such as inflation, electricity cost, and weighted average cost of capital, to determine the manufacturing system topology under uncertain conditions. Our results highlight the importance of planning models to develop markets policies related to supply chains, production level changes and imposed tariffs all while involving uncertainty in economic parameters, which is an improvement compared to planning models that use deterministic formulations. Finally, the proposed methodology and results can encourage decision-making considering probable variations in different parameters

Cosmic Hydrogen Was Significantly Neutral a Billion Years After the Big Bang

The ionization fraction of cosmic hydrogen, left over from the big bang, provides crucial fossil evidence for when the first stars and quasar black holes formed in the infant universe. Spectra of the two most distant quasars known show nearly complete absorption of photons with wavelengths shorter than the Ly-alpha transition of neutral hydrogen, indicating that hydrogen in the intergalactic medium (IGM) had not been completely ionized at a redshift z~6.3, about a billion years after the big bang. Here we show that the radii of influence of ionizing radiation from these quasars imply that the surrounding IGM had a neutral hydrogen fraction of tens of percent prior to the quasar activity, much higher than previous lower limits of ~0.1%. When combined with the recent inference of a large cumulative optical depth to electron scattering after cosmological recombination from the WMAP data, our result suggests the existence of a second peak in the mean ionization history, potentially due to an early formation episode of the first stars.Comment: 14 Pages, 2 Figures. Accepted for publication in Nature. Press embargo until publishe

Why is there no queer international theory?

Over the last decade, Queer Studies have become Global Queer Studies, generating significant insights into key international political processes. Yet, the transformation from Queer to Global Queer has left the discipline of International Relations largely unaffected, which begs the question: if Queer Studies has gone global, why has the discipline of International Relations not gone somewhat queer? Or, to put it in Martin Wight’s provocative terms, why is there no Queer International Theory? This article claims that the presumed non-existence of Queer International Theory is an effect of how the discipline of International Relations combines homologization, figuration, and gentrification to code various types of theory as failures in order to manage the conduct of international theorizing in all its forms. This means there are generalizable lessons to be drawn from how the discipline categorizes Queer International Theory out of existence to bring a specific understanding of International Relations into existence

The Importance of PRI Therapy for the Pastoral Counsellor

It is not always easy for pastoral counsellors to help people change. Often people have become stuck in their ways. Recent developments in the field of brain research help explain why change is difficult. This article discusses Past Reality Integration Therapy (PRI), a psychotherapeutic method that integrates recent findings of brain research and offers an important addition to the work of (pastoral) counsellors and psychotherapists. The use of this approach with Dutch students in their pastoral training is presented. Furthermore the importance of this new method for counsellors themselves, their clients and their work is discussed and some overall conclusions about the method and its practical application are presented

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

A model of the Universe including Dark Energy accounted for by both a Quintessence Field and a (negative) Cosmological Constant

In this work we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a future collapsing universe (for a given region of the parameter space), which is necessary for a consistent formulation of string theory and quantum field theory. We have also reproduced the measurements of modulus distance from supernovae with good accuracy.Comment: 11 pages, 4 figures, only the results for the single exponential potential are preserved. One author added. Some changes in the reference section. Submitted to Physical Review

Accretion Disc Theory: From the Standard Model Until Advection

Accretion disc theory was first developed as a theory with the local heat balance, where the whole energy produced by a viscous heating was emitted to the sides of the disc. One of the most important new invention of this theory was a phenomenological treatment of the turbulent viscosity, known as ''alpha'' prescription, when the (r$\phi$) component of the stress tensor was approximated by ($\alpha$ P) with a unknown constant $\alpha$. This prescription played the role in the accretion disc theory as well important as the mixing-length theory of convection for stellar evolution. Sources of turbulence in the accretion disc are discussed, including nonlinear hydrodynamical turbulence, convection and magnetic field role. In parallel to the optically thick geometrically thin accretion disc models, a new branch of the optically thin accretion disc models was discovered, with a larger thickness for the same total luminosity. The choice between these solutions should be done of the base of a stability analysis. The ideas underlying the necessity to include advection into the accretion disc theory are presented and first models with advection are reviewed. The present status of the solution for a low-luminous optically thin accretion disc model with advection is discussed and the limits for an advection dominated accretion flows (ADAF) imposed by the presence of magnetic field are analysed.Comment: Roceeding of the Int. Workshop "Observational Evidence for Black Holes in the Universe". Calcutta, 11-17 January 1998. Kluwer Acad. Pu

Self-Organization, Layered Structure, and Aggregation Enhance Persistence of a Synthetic Biofilm Consortium

Microbial consortia constitute a majority of the earth’s biomass, but little is known about how these cooperating communities persist despite competition among community members. Theory suggests that non-random spatial structures contribute to the persistence of mixed communities; when particular structures form, they may provide associated community members with a growth advantage over unassociated members. If true, this has implications for the rise and persistence of multi-cellular organisms. However, this theory is difficult to study because we rarely observe initial instances of non-random physical structure in natural populations. Using two engineered strains of Escherichia coli that constitute a synthetic symbiotic microbial consortium, we fortuitously observed such spatial self-organization. This consortium forms a biofilm and, after several days, adopts a defined layered structure that is associated with two unexpected, measurable growth advantages. First, the consortium cannot successfully colonize a new, downstream environment until it selforganizes in the initial environment; in other words, the structure enhances the ability of the consortium to survive environmental disruptions. Second, when the layered structure forms in downstream environments the consortium accumulates significantly more biomass than it did in the initial environment; in other words, the structure enhances the global productivity of the consortium. We also observed that the layered structure only assembles in downstream environments that are colonized by aggregates from a previous, structured community. These results demonstrate roles for self-organization and aggregation in persistence of multi-cellular communities, and also illustrate a role for the techniques of synthetic biology in elucidating fundamental biological principles

Accretion Disks Around Black Holes: Twenty Five Years Later

We study the progress of the theory of accretion disks around black holes in last twenty five years and explain why advective disks are the best bet in explaining varied stationary and non-stationary observations from black hole candidates. We show also that the recently proposed advection dominated flows are incorrect.Comment: 30 Latex pages including figures. Kluwer Style files included. Appearing in `Observational Evidence for Black Holes in the Universe', ed. Sandip K. Chakrabarti, Kluwer Academic Publishers (DORDRECHT: Holland