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We study the metric corresponding to a three-dimensional coset space SO(4)/SO(3) in the lattice setting. With the use of three integers n 1 , n 2 , and n 3 , and a length scale, l μ , the continuous metric is transformed into a discrete space. The numerical outcomes are compared with the continuous ones. The singularity of the black hole is explored and different domains are studied. [ABSTRACT FROM AUTHOR]

We study numerically the curvature tensor in a three-dimensional discrete space. Starting from the continuous metric of a three-sphere, we transformed it into a discrete space using three integers n 1 , n 2 , and n 3 . The numerical results are compared with the expected values in the continuous limit. We show that as the number of cells in the lattice increases, the continuous limit is recovered. [ABSTRACT FROM AUTHOR]

In this paper, using Lebanon's capital, Beirut, as a case study, a methodology is proposed to assess the potential for solar photovoltaics (PV) in urban areas incorporating both economic and non-economic factors. Utilizing a rich spatial dataset of solar irradiation augmented with electricity bills at the building level, the cost and benefit of installing rooftop PV systems for each building is estimated. Additionally, incentives and barriers for adopting those systems are investigated using a probabilistic choice model. The results show that Beirut city has a potential for distributed rooftop solar PV to be between 195 and 295 MWp. However, adoption rates are low at 0.49% and 1.23% for residential and commercial buildings, respectively, reflecting the limitation of financial incentives alone to promote the deployment of distributed renewable energy systems in transition economies. The impact of different incentive policy instruments and the role of solar PV in today's economic crisis in Lebanon is analyzed. The biggest impact was achieved through removing (or lowering) electricity tariff subsidy, although this option remains highly constrained by political calculus. We argue that the Lebanese government should fast-track and implement the required legal framework to facilitate and incentivize distributed power generation from renewable sources to promote both green energy and its financial resilience. The proposed modeling framework together with the results obtained in this study will have important implications for energy policy makers in Lebanon and other transition economies. • The potential for distributed rooftop solar energy in Beirut is estimated at the building level. • The effects of economic and non-economic factors on solar PV adoption are analyzed using a probabilistic choice model. • The impacts of various incentive policies and societal factors on promoting PV are investigated with policy implications. • Electricity subsidy removal increases solar PV adoption rates, partly compensating for weak non-financial incentives. • The government should fast-track implementing the legal framework for distributed power generation including PV systems. [ABSTRACT FROM AUTHOR]

We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers, while in the second we consider the case where one of the coordinates is ignorable. The numerical results of both cases are then compared with the expected values in the continuous limit as the number of cells of the lattice becomes very large. [ABSTRACT FROM AUTHOR]

Experiments with groups of fish inside a circular tank have provided valuable insights into the nature of leadership in social groups. Sophisticated mathematical models were constructed with a view to recovering observed schooling and leadership behavior in such experiments. Here, and with the help of variations on a promising class of such models, we explore a dual set of social concerns, namely the likelihood of permanent evasion from a cohesive group by a controlled individual in confinement. Our minimal model reduces to a leader-follower configuration, with cone-of-vision driven interactions inside a circular domain. We show that the resulting dynamical system sustains a rich supply of non-aligned, straying "follower" states, the dynamics on which displays (chaotic) intermittency between boundary following behavior and infrequent long flights. We map these states in configuration space and explore transitions between them. We demonstrate robustness of observed behavior by considering model variations, as well as alternate leader control trajectory. While it is too early to draw the implications of leader-follower dynamics to collective behavior, we do confirm that a model stray fish relates to a self-organized school bouncing back and forth along the diameter very much like a follower responds to a point leader in our model. We further draw the implications of our results to the study of dynamical systems with discontinuities, robotics, and the study of human behavior in the face of normative control and confinement. [ABSTRACT FROM AUTHOR]

In this paper we focus on a critical component of the city: its building stock, which holds much of its socio-economic activities. In our case, the lack of a comprehensive database about their features and its limitation to a surveyed subset lead us to adopt data-driven techniques to extend our knowledge to the near-city-scale. Neural networks and random forests are applied to identify the buildings' number of floors and construction periods' dependencies on a set of shape features: area, perimeter, and height along with the annual electricity consumption, relying a surveyed data in the city of Beirut. The predicted results are then compared with established scaling laws of urban forms, which constitutes a further consistency check and validation of our workflow. [ABSTRACT FROM AUTHOR]

Urban expansion, driven by population and economic growth, has been a major contributor to increased levels of energy consumption across the globe. Beirut, Lebanon's capital, is no exception in facing a surge in its demand for electricity as it expands. However, with frequent power outages, underpinning a largely problematic power sector, Beirut's demand for electricity is becoming a real hurdle that impedes the city's economic growth and development. This paper introduces a near-city-scale building energy model, BEirut Energy Model BEEM, which estimates the building stock's electricity consumption in two different districts in Beirut. The methodology uses rule-based expert data for an archetypal classification of the buildings based on their functions and periods of construction with their corresponding attributes including the number of floors, number of apartments, and bimonthly electricity consumption to generate a 3D model for 3630 buildings coupled to the hourly weather conditions and topographic map, which is then simulated in EnergyPlus. The predicted consumption of 2311 buildings is then calibrated with actual available metered data, to adapt the model to Beirut's occupancy and users' behaviors. Calibrated results are mapped to reveal the spatiotemporal distribution of energy peak demands which provide insights for future interventions. An analysis of the spatial distribution of electricity use demonstrates a spatial clustering that underlies urban energy demand which can be used for smart grid zoning. [ABSTRACT FROM AUTHOR]