Hyperscaling violation for scalar black branes in arbitrary dimensions

We extend to black branes (BB) in arbitrary dimensions the results of Ref. [1] about hyperscaling violation and phase transition for scalar black 2-branes. We derive the analytic form of the (d+1)-dimensional scalar soliton interpolating between a conformal invariant AdS vacuum in the infrared and a scale covariant metric in the ultraviolet. We show that the thermodynamical system undergoes a phase transition between Schwarzschild-AdS and a scalar-dressed BB. We calculate the critical exponent and the hyperscaling violation parameter in the two phases. We show that our scalar BB solutions generically emerge as compactifications of p-brane solutions of supergravity theories. We also derive the short distance form of the correlators for the scalar operators corresponding to an UV exponential potential supporting our black brane solution. We show that also for negative values of the hyperscaling violation parameter these correlators have a short distance power-law behavior.Comment: Final version accepted for publication in JHE

Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity

We investigate static, planar, solutions of Einstein-scalar gravity admitting an anti-de Sitter (AdS) vacuum. When the squared mass of the scalar field is positive and the scalar potential can be derived from a superpotential, minimum energy theorems indicate the existence of a scalar soliton. On the other hand, for these models, no-hair theorems forbid the existence of hairy black brane solutions with AdS asymptotics. By considering a specific example (an exact integrable model which has the form of a Toda molecule) and by deriving explicit exact solution, we show that these models allow for hairy black brane solutions with non-AdS domain wall asymptotics, whose extremal limit is a scalar soliton. The soliton smoothly interpolates between a non-AdS domain wall solution at $r=\infty$ and an AdS solution near $r=0$.Comment: 5 pages, no figure

Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field

We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together with the metric functions, the corresponding form of the scalar self-interaction potential. Using this method we prove a new no-hair theorem about the existence of hairy black-hole and black-brane solutions and derive broad classes of static solutions with radial symmetry of the theory, which may play an important role in applications of the AdS/CFT correspondence to condensed matter and strongly coupled QFTs. These solutions include: 1) four- or generic $(d+2)$-dimensional solutions with planar, spherical or hyperbolic horizon topology; 2) solutions with AdS, domain wall and Lifshitz asymptotics; 3) solutions interpolating between an AdS spacetime in the asymptotic region and a domain wall or conformal Lifshitz spacetime in the near-horizon region.Comment: Some references adde

Analysis of Multigrid Preconditioning for Implicit PDE Solvers for Degenerate Parabolic Equations

Abstract. In this paper an implicit numerical method designed for nonlinear degenerate parabolic equations is proposed. A convergence analysis and the study of the related computa-tional cost are provided. In fact, due to the nonlinear nature of the underlying mathematical model, the use of a fixed point scheme is required. The chosen scheme is the Newton method and its con-vergence is proven under mild assumptions. Every step of the Newton method implies the solution of large, locally structured, linear systems. A special effort is devoted to the spectral analysis of the relevant matrices and to the design of appropriate multigrid preconditioned Krylov methods. Numerical experiments for the validation of our analysis complement this contribution

Black brane solutions of Einstein-scalar-Maxwell gravity and their holographic applications

Black hole solutions of Einstein (and Einstein-Maxwell) gravity coupled to scalar fields have acquired a growing interest and importance in recent years. This interest is motivated both by more \classical" issues, as the problem of the uniqueness of classical black holes solutions (and related \no-hair" theorems), and mainly by recent applications of the AdS/CFT correspondence, an holographic duality which allows to describe, starting from a gravitational theory, strongly coupled quantum field theories. In this thesis, we treat this topic both from a pure gravitational point of view and from the holographic perspective. In particular, we propose a general method for exactly solving, in some cases, the field equations of Einstein-scalar-Maxwell gravity, and present some new analytical and numerical solutions (we mainly focus on black brane solutions, i.e. solutions with a planar event horizon). Moreover, we discuss hyperscaling violation, a particular scaling behavior of free energy and entropy (as functions of the temperature), typical of some phase transitions of real condensed matter systems. Hyperscaling violation can be described, via AdS/CFT, starting from a gravitational solution with a particular symmetry. Finally, we perform some interesting results about the mass spectrum and stability of black brane solutions in a wide class of gravitational models. In particular, the thermodynamics of some solutions of these models provides important information about the possible existence of physicallyrelevant phase transitions in the dual field theories

Black brane solutions of Einstein-scalar-Maxwell gravity and their holographic applications

Black hole solutions of Einstein (and Einstein-Maxwell) gravity coupled to scalar fields have acquired a growing interest and importance in recent years. This interest is motivated both by more \classical" issues, as the problem of the uniqueness of classical black holes solutions (and related \no-hair" theorems), and mainly by recent applications of the AdS/CFT correspondence, an holographic duality which allows to describe, starting from a gravitational theory, strongly coupled quantum field theories. In this thesis, we treat this topic both from a pure gravitational point of view and from the holographic perspective. In particular, we propose a general method for exactly solving, in some cases, the field equations of Einstein-scalar-Maxwell gravity, and present some new analytical and numerical solutions (we mainly focus on black brane solutions, i.e. solutions with a planar event horizon). Moreover, we discuss hyperscaling violation, a particular scaling behavior of free energy and entropy (as functions of the temperature), typical of some phase transitions of real condensed matter systems. Hyperscaling violation can be described, via AdS/CFT, starting from a gravitational solution with a particular symmetry. Finally, we perform some interesting results about the mass spectrum and stability of black brane solutions in a wide class of gravitational models. In particular, the thermodynamics of some solutions of these models provides important information about the possible existence of physicallyrelevant phase transitions in the dual field theories

The fluorine in surface waters: origin, weight on human health, and defluoridation techniques

In order to understand the distribution of fluorine in surface environments, also linked to fluoride deposits, this paper discusses the role of rift systems in fluorine enrichment of surface waters, with two examples: the Sardinia Island and the East African Rift. The main goal of this study is aimed to highlighting the areas that could potentially host fluorine in the surface waters in order to make it easier the lecture also for people to search and read not experts in the field, such as the biomedical field. Furthermore, potentialities and limitations of the currently available defluoridation techniques were examined, in order to identify the best intervention technology. From a careful review of the literature, to the addition of the extensive field observations in Sardinia and Ethiopia carried by the authors in the previous decades, we highlight the origin, processes and evolution of F-migration in Rift systems. The given examples of Sardinia and Ethiopia show that the origin and consequent behaviour of fluorine is strictly controlled by the rift systems. In this framework, the availability of fluorine for surface waters depends on two possible types of sources: a direct supply and an indirect supply. Directly from spring waters and ground waters fed by hydrothermal systems related to rifting, and indirectly from the leaching of products of rift-related activities, such as fluorite-bearing deposits, sedimentary or meta-sedimentary rift-related sequences, and volcanic or metavolcanic complexes emplaced along rift structures. The whole geological history of a given area must be taken into account in interpreting its present fluorine geochemistry. In conclusion, we underline the aspects of a possible control of these areas where fluoride exposure might lead to a long-term harm to local communities and we point out the nowadays best remediation-technologies, discussing their pro and cons in their applicability to different scales and social-contexts

Energy Evaluation of a {PV}-Based Test Facility for Assessing Future Self-Sufficient Buildings

In recent years, investigations on advanced technological solutions aiming to achieve high-energy performance in buildings have been carried out by research centers and universities, in accordance with the reduction in buildings’ energy consumption required by European Union. However, even if the research and design of new technological solutions makes it possible to achieve the regulatory objectives, a building’s performance during operation deviates from simulations. To deepen this topic, interesting studies have focused on testing these solutions on full-scale facilities used for real-life activities. In this context, a test facility will be built in the university campus of Politecnico di Torino (Italy). The facility has been designed to be an all-electric nearly Zero Energy Building (nZEB), where heating and cooling demand will be fulfilled by an air-source heat pump and photovoltaic generators will meet the energy demand. In this paper, the facility energy performance is evaluated through a dynamic simulation model. To improve energy self-sufficiency, the integration of lithium-ion batteries in a HVAC system is investigated and their storage size is optimized. Moreover, the facility has been divided into three units equipped with independent electric systems with the aim of estimating the benefits of local energy sharing. The simulation results clarify that the facility meets the expected energy performance, and that it is consistent with a typical European nZEB. The results also demonstrate that the local use of photovoltaic energy can be enhanced thanks to batteries and local energy sharing, achieving a greater independence from the external electrical grid. Furthermore, the analysis of the impact of the local energy sharing makes the case study of particular interest, as it represents a simplified approach to the energy community concept. Thus, the results clarify the academic potential for this facility, in terms of both research and didactic purposes