1,720,974 research outputs found
Design and optimization under uncertainty of Energy Systems
No full textIn many engineering design and optimisation problems, the presence of uncertainty in data
and parameters is a central and critical issue. The analysis and design of advanced complex
energy systems is generally performed starting from a single operating condition and
assuming a series of design and operating parameters as fixed values. However, many of
the variables on which the design is based are subject to uncertainty because they are not
determinable with an adequate precision and they can affect both performance and cost.
Uncertainties stem naturally from our limitations in measurements, predictions and
manufacturing, and we can say that any system used in engineering is subject to some
degree of uncertainty. Different fields of engineering use different ways to describe this
uncertainty and adopt a variety of techniques to approach the problem. The past decade has
seen a significant growth of research and development in uncertainty quantification
methods to analyse the propagation of uncertain inputs through the systems. One of the
main challenges in this field are identifying sources of uncertainty that potentially affect the outcomes and the efficiency in propagating these uncertainties from the sources to the
quantities of interest, especially when there are many sources of uncertainties. Hence, the
level of rigor in uncertainty analysis depends on the quality of uncertainty quantification
method. The main obstacle of this analysis is often the computational effort, because the
representative model is typically highly non-linear and complex. Therefore, it is necessary
to have a robust tool that can perform the uncertainty propagation through a non-intrusive
approach with as few evaluations as possible.
The primary goal of this work is to show a robust method for uncertainty quantification applied to energy systems. The first step in this direction was made doing a work on the analysis of uncertainties on a recuperator for micro gas turbines, making use of the Monte Carlo and Response Sensitivity Analysis methodologies to perform this study.
However, when considering more complex energy systems, one of the main weaknesses of uncertainty quantification methods arises: the extremely high computational effort needed. For this reason, the application of a so-called metamodel was found necessary and useful. This approach was applied to perform a complete analysis under uncertainty of a solid oxide fuel cell hybrid system, starting from the evaluation of the impact of several uncertainties on the system up to a robust design including a multi-objective optimization. The response surfaces have allowed the authors to consider the uncertainties in the system when performing an acceptable number of simulations. These response were then used to perform a Monte Carlo simulation to evaluate the impact of the uncertainties on the monitored outputs, giving an insight on the spread of the resulting probability density functions and so on the outputs which should be considered more carefully during the design phase.
Finally, the analysis of a complex combined cycle with a flue gas condesing heat pump subject to market uncertainties was performed. To consider the uncertainties in the electrical price, which would impact directly the revenues of the system, a statistical study on the behaviour of such price along the years was performed. From the data obtained it was possible to create a probability density function for each hour of the day which would represent its behaviour, and then those distributions were used to analyze the variability of the system in terms of revenues and emissions
Matter and gravitons in the gravitational collapse
Full text linkAbstractWe consider the effects of gravitons in the collapse of baryonic matter that forms a black hole. We first note that the effective number of (soft off-shell) gravitons that account for the (negative) Newtonian potential energy generated by the baryons is conserved and always in agreement with Bekenstein's area law of black holes. Moreover, their (positive) interaction energy reproduces the expected post-Newtonian correction and becomes of the order of the total ADM mass of the system when the size of the collapsing object approaches its gravitational radius. This result supports a scenario in which the gravitational collapse of regular baryonic matter produces a corpuscular black hole without central singularity, in which both gravitons and baryons are marginally bound and form a Bose–Einstein condensate at the critical point. The Hawking emission of baryons and gravitons is then described by the quantum depletion of the condensate and we show the two energy fluxes are comparable, albeit negligibly small on astrophysical scales
Horizon quantum mechanics: A hitchhiker's guide to quantum black holes
No full textIt is congruous with the quantum nature of the world to view the spacetime geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the spacetime manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantization of Einstein–Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the “superspace” of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble “min- isuperspace” approach and choose the gravitational observables not simply by imposing some symmetry, but motivated by their proven relevance in the (classical) description of a given system. In particular, this review focuses on compact, spherically symmetric, quantum mechanical sources, in order to determine the probability that they are black holes (BHs) rather than regular particles. The gravitational radius is therefore lifted to the status of a quantum mechanical operator acting on the “horizon wave function (HWF),” the latter being determined by the quantum state of the source. This formal- ism is then applied to several sources with a mass around the fundamental scale, which are viewed as natural candidates of quantum BHs
Global and local horizon quantum mechanics
No full textHorizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. A global gravitational radius operator can be introduced for a static and spherically symmetric quantum mechanical matter state by lifting the classical “Hamiltonian” constraint that relates the gravita- tional radius to the ADM mass, thus giving rise to a “horizon wave-function”. This minisuperspace-like formalism is shown here to be able to consistently describe also the local gravitational radius related to the Misner–Sharp mass function of the quantum source, provided its energy spectrum is determined by spatially localised modes
Analysis of uncertainties in compact plate-fin recuperators for microturbines
No full textThe current study aims to perform a stochastic analysis on microturbine compact recuperators to evaluate the impact of uncertainties in design parameters on their cost and volume, by using two different probabilistic approaches: Monte Carlo (MC) and Response Sensitivity Analysis (RSA). These two methods have been developed in Matlab® and then coupled with CHEOPE (Compact Heat Exchanger Optimisation and Performance Evaluation) software, which allows to analyze two different types of recuperators, used in microturbine applications: the furnace-brazed plate-fin type and the welded primary surface type. This paper focuses on an analysis of plate-fin type recuperators, for which the cost function adopted was tuned and verified in a previous study. Three main parameters of the recuperator have been considered as uncertain: effectiveness, hot side and cold side pressure drops. The uncertainties associated with these three parameters are based on industrial knowledge. The aforementioned stochastic methods have been used to propagate such uncertainties on the relevant outputs, such as cost and volume, allowing us to evaluate the least expensive and the most compact recuperator among those analysed
Quantum formation of primordial black holes
No full textWe provide a (simplified) quantum description of primordial black holes at the time of their formation. Specifically, we employ the horizon quantum mechanics to compute the probability of black hole formation starting from a simple quantum mechanical characterization of primordial density fluctuations given by a Planckian spectrum. We then estimate the initial number of primordial black holes in the early universe as a function of their typical mass, spatial width and temperature of the fluctuation
Horizon quantum fuzziness for non-singular black holes
Full text linkAbstract We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein’s field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons
Corpuscular slow-roll inflation
No full textWe show that a corpuscular description of gravity can lead to an inflationary scenario similar to Starobinsky’s model without requiring the introduction of the inflaton field. All relevant properties are determined by the number of gravitons in the cosmological condensate or, equivalently, by their Compton length. In particular, the relation between the Hubble parameter H and its time derivative dot H required by cosmic microwave background observations at the end of inflation, as well as the (minimum) initial value of the slow-roll parameter, are naturally obtained from the Compton size of the condensate
Horizon quantum mechanics of rotating black holes
Full text linkAbstract The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries
Thermal BEC Black Holes
Full text linkWe review some features of Bose–Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately) one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons), resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole) and a continuous spectrum with energy ω > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature). Assuming the main effect of the internal scatterings is the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = Nm and Entropy 2015, 17 6894 a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ω > m is also shown to reduce the Hawking flux. The above corrections suggest that for black holes in this quantum state, the evaporation properly stops for a vanishing mass
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