Earth's Inner Core dynamics induced by the Lorentz force

Seismic studies indicate that the Earth's inner core has a complex structure and exhibits a strong elastic anisotropy with a cylindrical symmetry. Among the various models which have been proposed to explain this anisotropy, one class of models considers the effect of the Lorentz force associated with the magnetic field diffused within the inner core. In this paper we extend previous studies and use analytical calculations and numerical simulations to predict the geometry and strength of the flow induced by the poloidal component of the Lorentz force in a neutrally or stably stratified growing inner core, exploring also the effect of different types of boundary conditions at the inner core boundary (ICB). Unlike previous studies, we show that the boundary condition that is most likely to produce a significant deformation and seismic anisotropy is impermeable, with negligible radial flow through the boundary. Exact analytical solutions are found in the case of a negligible effect of buoyancy forces in the inner core (neutral stratification), while numerical simulations are used to investigate the case of stable stratification. In this situation, the flow induced by the Lorentz force is found to be localized in a shear layer below the ICB, which thickness depends on the strength of the stratification, but not on the magnetic field strength. We obtain scaling laws for the thickness of this layer, as well as for the flow velocity and strain rate in this shear layer as a function of the control parameters, which include the magnitude of the magnetic field, the strength of the density stratification, the viscosity of the inner core, and the growth rate of the inner core. We find that the resulting strain rate is probably too small to produce significant texturing unless the inner core viscosity is smaller than about $10^{12}$ Pa.s.Comment: submitted to Geophysical Journal Internationa

Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

Analyzing real options and flexibility in engineering systems design using decision rules and deep reinforcement learning

Engineering systems provide essential services to society e.g., power generation, transportation. Their performance, however, is directly affected by their ability to cope with uncertainty, especially given the realities of climate change and pandemics. Standard design methods often fail to recognize uncertainty in early conceptual activities, leading to rigid systems that are vulnerable to change. Real Options and Flexibility in Design are important paradigms to improve a system’s ability to adapt and respond to unforeseen conditions. Existing approaches to analyze flexibility, however, do not leverage sufficiently recent developments in machine learning enabling deeper exploration of the computational design space. There is untapped potential for new solutions that are not readily accessible using existing methods. Here, a novel approach to analyze flexibility is proposed based on Deep Reinforcement Learning (DRL). It explores available datasets systematically and considers a wider range of adaptability strategies. The methodology is evaluated on an example waste-toenergy system. Low and high flexibility DRL models are compared against stochastically optimal inflexible and flexible solutions using decision rules. The results show highly dynamic solutions, with action space parametrized via artificial neural network. They show improved expected economic value up to 69% compared to previous solutions. Combining information from action space probability distributions along expert insights and risk tolerance helps make better decisions in real-world design and system operations. Out of sample testing shows that the policies are generalizable, but subject to tradeoffs between flexibility and inherent limitations of the learning process

Economic evaluation of flexible IGCC plants with integrated membrane reactor modules

Integrated Gasification Combined Cycle with embedded membrane reactor modules (IGCC-MR) represents a new technology option for the co-production of electricity and pure hydrogen endowed with enhanced environmental performance capacity. It is an alternative to conventional coaland gas-fired power generation technologies. As a new technology, the IGCC-MR power plant needs to be evaluated in the presence of irreducible regulatory and fuel market uncertainties for the potential deployment of an initial fleet of demonstration plants at the commercial scale. This paper presents the development of a systematic and comprehensive three-step methodological framework to assess the economic value of flexible alternatives in the design and operations of an IGCC-MR plant under the aforementioned sources of uncertainty. The main objective is to demonstrate the potential value enhancements stemming to the long-term economic performance of flexible IGCC-MR project investments, by managing the uncertainty associated with future environmental regulations and fuel costs. The paper provides an overview of promising design flexibility concepts for IGCC-MR power plants and focuses on operational and constructional flexibility. The operational flexibility is realized through the option of a temporary shutdown of the plant with considerations of regulatory and market uncertainties. This option reduces the probability of loss and the downside risk compared to the base case. The constructional flexibility considers installation of a Carbon Capture and Storage (CCS) unit in the plant under three different alternatives: 1) installing CCS in the initial construction phase, 2) retrofitting CCS at a later stage and 3) retrofitting CCS with pre-investment at a later stage. Monte Carlo simulations and financial analysis are used to demonstrate that the most economically advantageous flexibility option is to install CCS in the initial IGCC-MR construction phase

Conformational modulation of sequence recognition in synthetic macromolecules

The different triplet sequences in high molecular weight aromatic copolyimides comprising pyromellitimide units ("I") flanked by either ether-ketone ("K") or ether-sulfone residues ("S") show different binding strengths for pyrene-based tweezer-molecules. Such molecules bind primarily to the diimide unit through complementary π-π-stacking and hydrogen bonding. However, as shown by the magnitudes of 1H NMR complexation shifts and tweezer-polymer binding constants, the triplet "SIS" binds tweezer-molecules more strongly than "KIS" which in turn bind such molecules more strongly than "KIK". Computational models for tweezer-polymer binding, together with single-crystal X-ray analyses of tweezer-complexes with macrocyclic ether-imides, reveal that the variations in binding strength between the different triplet sequences arise from the different conformational preferences of aromatic rings at diarylketone and diarylsulfone linkages. These preferences determine whether or not chain-folding and secondary π−π-stacking occurs between the arms of the tweezermolecule and the 4,4'-biphenylene units which flank the central diimide residue

TEMPORAL EVOLUTION OF THERMAL STRUCTURES AND WINTER HEAT CONTENT CHANGE FROM VOS-XBT DATA IN THE CENTRAL MEDITERRANEAN SEA

Seasonal and year-to-year time evolution of the thermal structure, including the heat content change in the upper water column and its relationship with the surface net heat fluxes, have been studied at five locations in the central Mediterranean Sea. The study is based on temperature profiles collected during XBT surveys (eXpendable Bathy- Thermograph) carried out on ships of opportunity, in the framework of the MFSPP (Mediterranean Forecasting System Pilot Project), between September 1999 and May 2001. The five investigated zones are located in the southern Adriatic, NW Ionian, southern and northern Tyrrhenian, and Ligurian Sea. Gradual erosion of the thermocline in autumn, formation of a mixed layer in winter, and the onset of the stratification in spring, are common properties of the temporal evolution of thermal structures at all five locations. Moreover, in the southern Adriatic, a deep convection took place down to about 600m in winter 1999/2000. On the other hand, mild climatic conditions and small surface heat loss in autumn and winter 2000/2001 drastically reduced a mixing/ convection depth which hardly reached 200 m. Simultaneously, the NW Ionian remained slightly stratified throughout the winter period. The heat storage rate in the upper portion of the water column (down to 450 m) is compared with the air-sea net heat flux at a monthly scale. A heat content decrease is determined by the surface heat loss, and the processes such as lateral advection, or upwelling of the colder waters through the base of the water column (for example, in the southern Adriatic and Ionian Seas). Elsewhere (for example, in the northern Tyrrhenian and Ligurian Seas), the upwelling does not contribute significantly to the heat balance within the water column, since the vertical temperature gradients in deeper layers are negligible

Flexibility and real options analysis in power system generation expansion planning under uncertainty

Over many years, there has been a drive in the electricity industry towards better integration of environmentally friendly and renewable generation resources for power systems. Such resources show highly variable availability, impacting the design and performance of power systems. In this paper, we propose using a stochastic programming approach to optimize generation expansion planning (GEP), with explicit consideration of generator output capacity uncertainty. Flexibility implementation - via real options exercised in response to uncertainty realizations - is considered as an important design approach to the GEP problem. It more effectively captures upside opportunities, while reducing exposure to downside risks. A decision-rule based approach to real options modeling is used, combining conditional-go and finite adaptability principles. The solutions provide decision makers with easy-to-use guidelines with threshold values from which to exercise the options in operations. To demonstrate application of the proposed methodologies and decision rules, a case study situated in the Midwest United States is used. The case study demonstrates how to quantify the value of flexibility, and showcases the usefulness of the proposed approach