Solution Of Problem Research Articles

Multiobjective optimal control problems. Stationary Navier–Stokes equations

This paper deals with the solution of some multi-objective optimal control problems for stationary Navier–Stokes equations. More precisely, we look for Pareto and Nash equilibria associated to standard cost functionals. First, we prove the existence of equilibria and we deduce appropriate optimality systems. Then, we analyse the existence and characterization of Pareto and Nash equilibria for the Navier–Stokes equations. Here, we use the formalism of Dubovitskii and Milyoutin., see [Girsanov FV. Lectures on mathematical theory of extremum problems. Berlin: Springer-Verlag; 1972. (Notes in economics and mathematical systems; vol. 67)]. Finally, we also present a finite element approximation of the bi-objective problem, we illustrate the techniques with several numerical experiments and we compare the Pareto and Nash equilibria.

SLAPE solar panels: a possible solution for the future energy problems of our society

Today, the silicon photovoltaic cell (SPVC) solar panels are being deployed across the globe by all most all the governments to generate renewable carbon neutral electricity to use in place of the one generated at thermal power plants by burning fossil fuels. These SPVC solar panels generate electricity with less than 20% efficiency, and heat energy with more than 30% efficiency. This 10% excess heat energy released into the atmosphere can cause a very severe damage to the environment and ecology as it is million times higher than the one caused by the equivalent CO2 gas in the atmosphere with a concentration of about 421 ppm. To avoid the harmful and danger effects of heat energy released by these SPVC solar panels into the atmosphere, either they have to be stopped using or the heat generated by them has to be trapped to use for the beneficial purposes of the society or any other alternate safe solar panels have to be developed. In this study, for the first time, the SLAPE (Semiconductor and Liquid Assisted Photothermal Effect) solar panels are introduced to generate electricity from sunlight. In these new solar panels, a semiconducting material along with a stable organic solvent is employed to capture the sunlight reaching the earth surface and to convert it into the heat energy. This in situ generated heat energy is then converted into a rotational mechanical energy with the help of an heat engine, and then into electricity with the help of suitable electric generator. To establish the Proof of Concept (poc), in this study, SPV cells as semiconducting material and γ-butyrolactone were employed to fabricate a one square meter area SLAPE solar panel and generated about 17 V AC electricity with the help of a custom manufactured reciprocally moved steam engine (RMSE) and an electric generator. Thus obtained results are presented and discussed along this article.

Landau levels for charged particles with anisotropic mass

The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem.

Tracking Control for $(x,u)$-Flat Systems by Quasi-Static Feedback of Classical States

It is well known that for flat systems the tracking control problem can be solved by utilizing a linearizing quasi-static feedback of generalized states. If measurements (or estimates) of a so-called generalized Brunovský state are available, a linear, decoupled and asymptotically stable tracking error dynamics can be achieved. However, from a practical point of view, it is often desirable to achieve the same tracking error dynamics by feedback of a classical state instead of a generalized one. This is due to the fact that the components of a classical state typically correspond to measurable physical quantities, whereas a generalized Brunovský state often contains higher order time derivatives of the (fictitious) flat output which are not directly accessible by measurements. In this paper, a systematic solution for the tracking control problem based on quasi-static feedback and measurements of classical states only is derived for the subclass of $(x,u)$-flat systems.

The eigenfunctions method in relation to diffuse reflection problems of the radiative energy transfer theory

Using the new method proposed earlier by the author, a solution of diffuse reflection problem is given in this report. A case of diffuse reflection of radiation from a semi-infinite absorbing and isotropically reflecting medium is presented, when in the elementary act of scattering there is a general law of redistribution of radiation by frequencies. In the approach presented here, conventionally called the method of ”decomposition of the resulting field” - DRF, in contrast to the previously widely used traditional method of ”decomposition of a single act” of scattering - DSA, the problem of diffuse reflection is solved without the use of any decomposition or special representation of the characteristic of the elementary act of scattering, i.e., the redistribution function of radiation by frequencies. The resulting radiation field, formed in the medium by means of multiple scatterings, is sought and constructed directly in the form of a bilinear series through a specially derived system of its own eigenfunctions. The physical basis of this approach lies in the fact that after each successive act of scattering, the field formed in the medium becomes more and more smoothed, so its direct representation in a decomposed form is more expedient than the traditionally used decomposition of a pre-known ”unsmoothed” characteristic of the elementary act of scattering.

PRECIPITATION DATA FROM GOOGLE EARTH ENGINE (GEE) IN REVETMENT DRAINAGE EVALUATION IN KALIANDA

Floods can occur frequently if there are no organized and constant changes in land use. Flood issues in Waymuli, South Lampung, has been occurring due to changes in land use in the area. Prior studies regarding drainage of coastal revetments may have been done before. However, the analysis was done using precipitation data from GEE and therefore, new findings as the solution for the flood problems in the region were necessary. The main objective of this research is to assess the extent of success of drainage system management using rainfall information obtained via GEE. The method used was by evaluating the capability of the drainage system using data from GEE, which involve identifying and measuring the drainage capacity with the HEC-RAS application. This study conclude that the use of GEE can be accurately used to evaluate revetment drainage. Rainfall in the last two years were 54.0340 mm, 81.8905 mm in the last five years, and 104.0784 mm in the last ten years. However, GEE results show that the highest rainfall recorded in September 2022 was 46.857 mm. Based on the HEC-RAS evaluation, it was also found that the drainage system does not have the capacity to drain rain within a 2-year period. It can be concluded that the function of the drainage system in this area is to support the coastal revetment system, not as the main drainage system.

Forward and Inverse Modeling of Ice Sheet Flow Using Physics‐Informed Neural Networks: Application to Helheim Glacier, Greenland

AbstractPredicting the future contribution of the ice sheets to sea level rise over the next decades presents several challenges due to a poor understanding of critical boundary conditions, such as basal sliding. Traditional numerical models often rely on data assimilation methods to infer spatially variable friction coefficients by solving an inverse problem, given an empirical friction law. However, these approaches are not versatile, as they sometimes demand extensive code development efforts when integrating new physics into the model. Furthermore, this approach makes it difficult to handle sparse data effectively. To tackle these challenges, we use the Physics‐Informed Neural Networks (PINNs) to seamlessly integrate observational data and governing equations of ice flow into a unified loss function, facilitating the solution of both forward and inverse problems within the same framework. We illustrate the versatility of this approach by applying the framework to two‐dimensional problems on the Helheim Glacier in southeast Greenland. By systematically concealing one variable (e.g., ice speed, ice thickness, etc.), we demonstrate the ability of PINNs to accurately reconstruct hidden information. Furthermore, we extend this application to address a challenging mixed inversion problem. We show how PINNs are capable of inferring the basal friction coefficient while simultaneously filling gaps in the sparsely observed ice thickness. This unified framework offers a promising avenue to enhance the predictive capabilities of ice sheet models, reducing uncertainties, and advancing our understanding of poorly constrained physical processes.

Comprehensive evaluation and systematic comparison of Gaussian process (GP) modelling applications in peptide quantitative structure-activity relationship

Peptide quantitative structure-activity relationship (pQSAR) is a specific extension of traditional QSARs from small-molecule drugs to bioactive peptides. Since peptides are linear biopolymers that are essentially different to small-molecule compounds in terms of their structural features such as ordering sequence, large size and intrinsic flexibility, the pQSAR methodology (including structural characterization and regression modelling) should be further exploited relative to traditional QSARs. Gaussian process (GP) serves as a pioneering Bayesian-based machine learning (ML) solution for tackling linear/nonlinear-hybrid regression issues in intricate domains. However, the applications of GP regression in QSAR and, particularly, the pQSAR still remain largely unexplored to date. In this work, we launched a comprehensive pQSAR study with GP regression modelling, aiming to the deep evaluation of GP performance based on different characterizations and also the systematic comparison of GP with other routine MLs. Here, we culled two distinct classes of peptide datasets, which separately comprise 12 panels of sophisticated benchmarks and 46 panels of extended samples, totally containing 8804 peptide samples and systematically resulting in 522 regression models. Our study indicated that the GP can generally provide an effective solution for many pQSAR problems with the potential to promote ML regression modelling in this area, which is comparable with or even better than those widely used methods on both the sophisticated benchmarks and extended samples. In addition, GP also has many advantages as compared to traditional MLs, such as hyperparameter self-consistency, overfitting resistance, interpretable output and estimable uncertainty.

Sample-efficient and surrogate-based design optimization of underwater vehicle hulls

Physics simulations like computational fluid dynamics (CFD) are a computational bottleneck in computer-aided design (CAD) optimization processes. To overcome this bottleneck, one requires either an optimization framework that is highly sample-efficient, or a fast data-driven proxy (surrogate model) for long-running simulations. Both approaches have benefits and limitations. Bayesian optimization is often used for sample efficiency, but it solves one specific problem and struggles with transferability; alternatively, surrogate models can offer fast and often more generalizable solutions for CFD problems, but gathering data for and training such models can be computationally demanding. In this work, we leverage recent advances in optimization and artificial intelligence (AI) to explore both of these potential approaches, in the context of designing an optimal unmanned underwater vehicle (UUV) hull. For first approach, we investigate and compare the sample efficiency and convergence behavior of different optimization techniques with a standard CFD solver in the optimization loop. For the second approach, we develop a deep neural network (DNN) based surrogate model to approximate drag forces that would otherwise be computed via the CFD solver. The surrogate model is in turn used in the optimization loop of the hull design. Our study finds that the Bayesian Optimization—Lower Condition Bound (BO-LCB) algorithm is the most sample-efficient optimization framework and has the best convergence behavior of those considered. Subsequently, we show that our DNN-based surrogate model predicts drag force on test data in tight agreement with CFD simulations, with a mean absolute percentage error (MAPE) of 1.85%. Combining these results, we demonstrate a two-orders-of-magnitude speedup (with comparable accuracy) for the design optimization process when the surrogate model is used. To our knowledge, this is the first study applying Bayesian optimization and DNN-based surrogate modeling to the problem of UUV design optimization, and we share our developments as open-source software.

APPLICATION OF A NEURONETWORK FOR DETERMINING THE TYPE OF ELEMENTS OF A SYMMETRICAL COMPENSATION DEVICE OF AN UNSYMMETRICAL SYSTEM WITH A ZERO WIRE

In article the possibility of using neural networks in the field of increasing the energy performance of a four-wire power supply system with an uneven load in the phases is being investigated. An uneven load in the phases causes asymmetry of currents in the network and contributes to the increase in the current in the neutral wire, which has an extremely negative effect on both the supply itself and its consumers. To eliminate asymmetry and reduce the current in the neutral wire, you can connect a symmetrical compensating device. Such a device is a set of reactive elements, the parameters of which are determined by search optimization. To determine the type of the required element, the defined parameters are recalculated. That is, the solution of such a problem consists of two component sub-problems – structural and parametric synthesis. This approach provides a high accuracy of calculations, but has a significant drawback: the calculations are cumbersome. In order to simplify the solution of the synthesis problem, it makes sense to determine the type of elements using neural networks, which will significantly reduce the time and resources spent on calculating the values of the parameters of the symmetrical compensating device. The subject of the article is the study of the possibility of using neural networks to predict the types of reactive elements of the symmetrical compensating device. During of the study, the parameters and type of neural network were determined, which provide the most accurate prediction of the topology of the structure of the symmetric-compensating device. The input parameters of the neural network were formed from sets consisting of eight parameters – resistances and inductances of the transmission lines and the neutral wire. The target matrix was formed from a set of data sets consisting of six elements containing information on the types of elements connected (0 – capacitor, 1 – inductance) between phases and between phases and the neutral wire. During research, the results of a quasi-solution were obtained, the values of which turned out to be commensurate with the accurate calculations for determining the structure of the symmetrical compensating device of the power supply system with a zero wire. This indicates the high quality of the developed neural network. Applying the minimax strategy to the received results provides an opportunity to reduce the received values to 0 and 1 to ensure clarity of the results obtained by the neural network.

Qualitative properties for a Moore–Gibson–Thompson thermoelastic problem with heat radiation

AbstractIn this work, we study some qualitative properties arising in the solution of a thermoelastic problem with heat radiation. The so-called Moore–Gibson–Thompson equation is used to model the heat conduction. By using the logarithmic convexity argument, the uniqueness and instability of solutions are proved without imposing any condition on the elasticity tensor. Then, the existence of solutions is obtained assuming that the elastic tensor is positive definite applying the theory of linear semigroups, and the exponential energy decay is shown in the one-dimensional case. Finally, we consider the one-dimensional quasi-static version and we assume that the elastic coefficient is negative. The existence and decay of solutions are proved, and a justification of the quasi-static approach is also provided.

The Hampered [formula omitted]-Median Problem with Neighbourhoods

This paper deals with facility location problems in a continuous space with neighbours and barriers. Each one of these two elements, neighbours and barriers, makes the problems harder than their standard counterparts. Combining all together results in a new challenging problem that, as far as we know, has not been addressed before, but has applications for inspection and surveillance activities and the delivery industry assuming uniformly distributed demand in some regions. Specifically, we analyse the k-Median problem with neighbours and polygonal barriers in two different situations. None of these problems can be seen as a simple incremental contribution since in both cases the tools required to analyse and solve them go beyond any standard overlapping of techniques used in the separated problems. As a first building block, we deal with the problem assuming that the neighbourhoods are not visible from one another and therefore there are no rectilinear paths that join two of them without crossing barriers. Under this hypothesis, we derive a valid mixed-integer linear formulation. Removing that hypothesis leads to a more general and realistic problem, but at the price of making it more challenging. Adapting the elements of the first formulation, we also develop another valid mixed-integer bilinear formulation. Both formulations rely on tools borrowed from computational geometry that allow to handle polygonal barriers and neighbours that are second-order cone (SOC) representable, which we preprocess and strengthen with valid inequalities. These mathematical programming formulations are also instrumental to derive an adapted matheuristic algorithm that provides good quality solutions for both problems in short computing time. The paper also reports extensive computational experience, counting 2400 experiments, showing that our exact and heuristic approaches are useful: the exact approach can solve optimally instances with up to 50 neighbourhoods and different number of barriers within one hour of CPU time, whereas the matheuristic approach always returns good feasible solutions in less than 300 s.

Distributionally Robust Newsvendor Under Stochastic Dominance with a Feature-Based Application

Problem definition: In this paper, we study the newsvendor problem under some distributional ambiguity sets and explore their relations. Additionally, we explore the benefits of implementing this robust solution in the feature-based newsvendor problem. Methodology and results: We propose a new type of discrepancy-based ambiguity set, the JW ambiguity set, and analyze it within the framework of first-order stochastic dominance. We show that the distributionally robust optimization (DRO) problem with this ambiguity set admits a closed-form solution for the newsvendor loss. This result also implies that the newsvendor problem under the well-known infinity-Wasserstein ambiguity set and Lévy ball ambiguity set admit closed-form inventory levels as a by-product. In the application of feature-based newsvendor, we adopt general kernel methods to estimate the conditional demand distribution and apply our proposed DRO solutions to account for the estimation error. Managerial implications: The closed-form solutions enable an efficient computation of optimal inventory levels. In addition, we explore the property of optimal robust inventory levels with respect to the nonrobust version via concepts of perceived critical ratio and mean repulsion. The results of numerical experiments and the case study indicate that the proposed model outperforms other state-of-the-art approaches, particularly in environments where demand is influenced by covariates and difficult to estimate. Funding: X. Li is supported by the Singapore Ministry of Education [Tier 1 Grant 23-0619-P0001, 24-0500-A0001] and National Natural Science Foundation of China [Grant 72331004]. L. Zhang is partially supported by the National Natural Science Foundation of China [Grants 72171156 and 72231002] and the Hong Kong Research Grants Council [Grant 16212419]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0159 .

Sublinear Elliptic Equations with Unbounded Coefficients in Lipschitz Domains

This paper is concerned with the homogeneous Dirichlet problem for a sublinear elliptic equation with unbounded coefficients in a Lipschitz domain. Bilateral a priori estimates for positive solutions and a priori upper estimates for their gradients are presented as a byproduct of the boundary Harnack principle. These estimates allow us to show the uniqueness of a positive solution of the homogeneous Dirichlet problem under no information about normal derivatives unlike in smooth domains.

Experience of psychological problems in crisis events: how does social support affect teenagers’ psychological security through emotion during the COVID-19 pandemic?

ABSTRACT The outbreak of coronavirus disease 2019 (COVID-19) has brought a series of psychological shocks to adolescents, it may cause psychological security problems. The purpose of this study was to explore the influence of social support on psychological security of adolescents and the role of emotional regulation and the experience of COVID-19 infection. 615 ( 14.64 ± 1.29) randomly selected Chinese adolescents were tested with the Perceived Social Support Scale (PSSS), Emotion Regulation Questionnaire (ERQ), and Psychological Security Questionnaire (PSQ). Structural equation modelling results show that: (1) Social support positively predicted psychological security; (2) Social support positively predicted cognitive reappraisal, and cognitive reappraisal positively predicted psychological security. At the same time, cognitive reappraisal played a mediating role in the relationship between social support and psychological security; (3) Social support negatively predicted expressive suppression, and expressive suppression negatively predicted psychological security. Meanwhile, expressive suppression played a mediating role in the relationship between social support and psychological security; (4) COVID-19 infection experience positively moderates the relationship between expression inhibition and psychological safety. This study provides theoretical experience reference for the solution of adolescent psychological problems in crisis situation.

Solar-Powered Desalination as a Sustainable Long-Term Solution for the Water Scarcity Problem: Case Studies in Portugal

Solar-Powered Desalination as a Sustainable Long-Term Solution for the Water Scarcity Problem: Case Studies in Portugal

Electrified fleet and infrastructure aware energy efficient routing

This paper presents an optimization framework to improve the energy efficiency and cost-effectiveness of fleets of commercial trucks operating pickups and deliveries in urban areas. As the electrification of transportation is moving from passenger cars to medium- and heavy-duty vehicles, the proposed analysis considers a fleet of pickup and delivery trucks that includes conventional internal combustion engine vehicles (ICEV), as well as battery electric vehicles (BEV), and plug-in hybrid electric vehicles (PHEV). Given a set of pickups and deliveries, and a fleet including different types of vehicles, the goal is twofold: assign the best vehicle to each task, and solve the vehicle routing problem, i.e., find the optimal route to navigate the vehicle from the origin to the destination(s). To estimate the energy consumption of the different vehicles, vehicle dynamics are considered, together with actual charging infrastructure and road data, including speed limits, road grade, and stop signs. Moreover, the total cost of ownership (TCO) is evaluated to estimate the cost-effectiveness of different fleet compositions and operations. To solve this problem, a hybrid simulated annealing (HSA) heuristic algorithm is proposed. The algorithm is validated against a benchmark exact solver based on mixed integer linear programming (MILP). The proposed methodology achieves optimal results with a 1.2% optimality gap compared to the benchmark, surpassing MILP in computational efficiency. The research findings highlight how fleet composition and operational strategies can vary significantly based on whether the focus is on energy efficiency, total cost of ownership, or a combination of the two, also depending on the number of years of operation. Simulation case studies in the Columbus, OH area demonstrate that integrating fleet and recharging infrastructure information alongside energy savings in vehicle routing problem solutions can achieve 20% to 50% savings in fleet operation costs compared to solely optimizing for minimum energy consumption.

Simulating Chemistry on Bosonic Quantum Devices.

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this Perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.

Teaching Innovation of University Grade in Automotive Engineering

In this work, we present the implementation of a flipped classroom methodology in two engineering courses, both with a heavy weight given to problem solution. In class, the students are first evaluated by a test, in order to encourage them to see the videos. In one course the test is gamified, while not in the other, so that the different level of encouragement can be assessed. Then conceptual problems are proposed to help the students think and discuss about the theoretical background. Finally, the problem sessions are approached seeking an active involvement by the students. The aim of this methodology is to facilitate a deeper learning of the needed theoretical background, an issue in which students struggled due to lack of motivation and the student's ability to access information during their study. The results of the methodology are evaluated by using standard questioners passed to the students. Answers were obtained from 31 students, which corresponds to 40 % of all involved students. The results obtained showcase an improvement of student motivation and learning. Key aspects identified leading to the success are a good organization of the curse, the adaptation of all activities to form a coherent course and the active and approachable attitude showcased by the teachers.

A general solution for electromechanical analysis of electroelastic composite plates with arbitrary holes

Stroh formalism provides an elegant method of solution for two-dimensional anisotropic elasticity problems through the generalized eigen relation associated with the dual coordinate system that gives the material eigen values and eigen vectors, and also the fundamental elasticity matrix and its associated Barnett-Lothe tensors. The extended Stroh-like formalism of Hwu and Hsieh has expanded the scope of basic Stroh formalism by addressing the electro-mechanical coupling effects in electro elastic plates. This paper presents an inclusive solution that addresses the two-dimensional problems in infinite electro-elastic, anisotropic, and isotropic plates with an arbitrary hole under remote arbitrary coupled electro-mechanical loading. This is achieved by adopting the Stroh formalism and its subsequent versions to consider the anisotropic and electro-elastic plates, and further, by incorporating the arbitrary biaxial loading condition into the boundary conditions, and the generalized mapping function into the basic formulation to accommodate all types of in plane loading and a variety of hole shapes respectively. Various equations of the solution are derived explicitly for easy understanding and computer implementation. The stress function is derived explicitly to satisfy the condition of traction free hole with remote electro-mechanical loading under generalized plane stress-open circuit condition. The stresses and electric displacements around the hole boundary are obtained by taking the derivative of the stress function with respect to unit normal along the hole boundary. The solution presented can be degenerated to the anisotropic or isotropic case by choosing the corresponding material properties, or appropriate values of complex parameters respectively. This general solution has exactly reproduced the results of other solutions in the literature for piezoelectric plates given by different methods. New results of stresses and electric displacements are obtained for various arbitrary holes in [PZT5H/45/-45/PZT5H]s graphite/epoxy plate and PZT 4 plates. Results for holes in piezoelectric laminates and PZT 4 piezo layer are also presented by FEM.