Three-dimensional black holes from deformed anti-de Sitter

We present new exact three-dimensional black-string backgrounds, which contain both NS--NS and electromagnetic fields, and generalize the BTZ black holes and the black string studied by Horne and Horowitz. They are obtained as deformations of the Sl(2,R) WZW model. Black holes resulting from purely continuous deformations possess true curvature singularities. When discrete identifications are introduced, extra chronological singularities appear, which under certain circumstances turn out to be naked. The backgrounds at hand appear in the moduli space of the Sl(2,R) WZW model. Hence, they provide exact string backgrounds and allow for a more algebraical CFT description. This makes possible the determination of the spectrum of primaries.Comment: JHEP style, 33 pages, 1 figur

The classical origin of quantum affine algebra in squashed sigma models

We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.Comment: 25 pages, 2 figure

Fracture Propagation Driven by Fluid Outflow from a Low-permeability Aquifer

Deep saline aquifers are promising geological reservoirs for CO2 sequestration if they do not leak. The absence of leakage is provided by the caprock integrity. However, CO2 injection operations may change the geomechanical stresses and cause fracturing of the caprock. We present a model for the propagation of a fracture in the caprock driven by the outflow of fluid from a low-permeability aquifer. We show that to describe the fracture propagation, it is necessary to solve the pressure diffusion problem in the aquifer. We solve the problem numerically for the two-dimensional domain and show that, after a relatively short time, the solution is close to that of one-dimensional problem, which can be solved analytically. We use the relations derived in the hydraulic fracture literature to relate the the width of the fracture to its length and the flux into it, which allows us to obtain an analytical expression for the fracture length as a function of time. Using these results we predict the propagation of a hypothetical fracture at the In Salah CO2 injection site to be as fast as a typical hydraulic fracture. We also show that the hydrostatic and geostatic effects cause the increase of the driving force for the fracture propagation and, therefore, our solution serves as an estimate from below. Numerical estimates show that if a fracture appears, it is likely that it will become a pathway for CO2 leakage.Comment: 21 page

Cost-Effectiveness of Web-Based Patient-Reported Outcome Surveillance in Patients With Lung Cancer

INTRODUCTION: A multicenter randomized clinical trial in France found an overall survival benefit of web-based patient-reported outcome (PRO)-based surveillance after initial treatment for lung cancer compared with conventional surveillance. The aim of this study was to assess the cost-effectiveness of this PRO-based surveillance in lung cancer patients. METHODS: This medico-economic analysis used data from the clinical trial, augmented by abstracted chart data and costs of consultations, imaging, transportations, information technology, and treatments. Costs were calculated based on actual reimbursement rates in France, and health utilities were estimated based on scientific literature review. Willingness-to-pay thresholds of €30,000 per quality-adjusted life year (QALY) and €90,000 per QALY were used to define a very cost-effective and cost-effective strategy, respectively. Average annual costs of experimental and control surveillance approaches were calculated. The incremental cost-effectiveness ratio was expressed as cost per life-year gained and QALY gained, from the health insurance payer perspective. One-way and multivariate probabilistic sensitivity analyses were performed. RESULTS: Average annual cost of surveillance follow-up was €362 lower per patient in the PRO arm (€941/year/patient) compared to control (€1,304/year/patient). The PRO approach presented an incremental cost-effectiveness ratio of €12,127 per life-year gained and €20,912 per QALY gained. The probabilities that the experimental strategy is very cost-effective and cost-effective were 97% and 100%, respectively. CONCLUSIONS: Surveillance of lung cancer patients using web-based PRO reduced the follow-up costs. Compared to conventional monitoring, this surveillance modality represents a cost-effective strategy and should be considered in cancer care delivery

Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

All stationary axi-symmetric local solutions of topologically massive gravity

We classify all stationary axi-symmetric solutions of topologically massive gravity into Einstein, Schr\"odinger, warped and generic solutions. We construct explicitly all local solutions in the first three sectors and present an algorithm for the numerical construction of all local solutions in the generic sector. The only input for this algorithm is the value of one constant of motion if the solution has an analytic centre, and three constants of motion otherwise. We present several examples, including soliton solutions that asymptote to warped AdS.Comment: 42 pages, 9 figures. v2: Changed potentially confusing labelling of one sector, added references. v3: Minor changes, matches published versio

Hidden Yangian symmetry in sigma model on squashed sphere

We discuss a hidden symmetry of a two-dimensional sigma model on a squashed S^3. The SU(2) current can be improved so that it can be regarded as a flat connection. Then we can obtain an infinite number of conserved non-local charges and show the Yangian algebra by directly checking the Serre relation. This symmetry is also deduced from the coset structure of the squashed sphere. The same argument is applicable to the warped AdS_3 spaces via double Wick rotations.Comment: 11 pages, 1 figure, typos corrected, references adde

Analysis of pore-fluid pressure gradient and effective vertical-stress gradient distribution in layered hydrodynamic systems

A theoretical analysis is carried out to investigate the pore-fluid pressure gradient and effective vertical-stress gradient distribution in fluid saturated porous rock masses in layered hydrodynamic systems. Three important concepts, namely the critical porosity of a porous medium, the intrinsic Fore-fluid pressure and the intrinsic effective vertical stress of the solid matrix, are presented and discussed. Using some basic scientific principles, we derive analytical solutions and explore the conditions under which either the intrinsic pore-fluid pressure gradient or the intrinsic effective vertical-stress gradient can be maintained at the value of the lithostatic pressure gradient. Even though the intrinsic pore-fluid pressure gradient can be maintained at the value of the lithostatic pressure gradient in a single layer, it is impossible to maintain it at this value in all layers in a layered hydrodynamic system, unless all layers have the same permeability and porosity simultaneously. However, the intrinsic effective vertical-stress gradient of the solid matrix can be maintained at a value close to the lithostatic pressure gradient in all layers in any layered hydrodynamic system within the scope of this study

Magnetic Field Induced Quantum Criticality via new Asymptotically AdS_5 Solutions

Using analytical methods, we derive and extend previously obtained numerical results on the low temperature properties of holographic duals to four-dimensional gauge theories at finite density in a nonzero magnetic field. We find a new asymptotically AdS_5 solution representing the system at zero temperature. This solution has vanishing entropy density, and the charge density in the bulk is carried entirely by fluxes. The dimensionless magnetic field to charge density ratio for these solutions is bounded from below, with a quantum critical point appearing at the lower bound. Using matched asymptotic expansions, we extract the low temperature thermodynamics of the system. Above the critical magnetic field, the low temperature entropy density takes a simple form, linear in the temperature, and with a specific heat coefficient diverging at the critical point. At the critical magnetic field, we derive the scaling law s ~ T^{1/3} inferred previously from numerical analysis. We also compute the full scaling function describing the region near the critical point, and identify the dynamical critical exponent: z=3. These solutions are expected to holographically represent boundary theories in which strongly interacting fermions are filling up a Fermi sea. They are fully top-down constructions in which both the bulk and boundary theories have well known embeddings in string theory.Comment: 50 page