Solution Of Problem Research Articles

Adjoint-based enforcement of state constraints in PDE optimization problems

This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a projection of the gradient of the objective functional onto a subspace tangent to the manifold defined by the constraint. This projection is realized by solving an adjoint problem defined in terms of the same adjoint operator as used in the system employed to determine the gradient, but with a different forcing. We focus on the “optimize-then-discretize” paradigm in the infinite-dimensional setting where the required regularity of both the gradient and of the projection is ensured. The proposed approach is illustrated with two examples: a simple test problem describing optimization of heat transfer in one direction and a more involved problem where an optimal closure is found for a turbulent flow described by the Navier-Stokes system in two dimensions, both considered subject to different state constraints. The accuracy of the gradients and projections computed by solving suitable adjoint systems is carefully verified and the presented computational results show that the solutions of the optimization problems obtained with the proposed approach satisfy the state constraints with a good accuracy, although not exactly.

Adaptive Bregman–Kaczmarz: an approach to solve linear inverse problems with independent noise exactly

We consider the block Bregman–Kaczmarz method for finite dimensional linear inverse problems. The block Bregman–Kaczmarz method uses blocks of the linear system and performs iterative steps with these blocks only. We assume a noise model that we call independent noise, i.e. each time the method performs a step for some block, one obtains a noisy sample of the respective part of the right-hand side which is contaminated with new noise that is independent of all previous steps of the method. One can view these noise models as making a fresh noisy measurement of the respective block each time it is used. In this framework, we are able to show that a well-chosen adaptive stepsize of the block Bregman–Kaczmarz method is able to converge to the exact solution of the linear inverse problem. The plain form of this adaptive stepsize relies on unknown quantities (like the Bregman distance to the solution), but we show a way how these quantities can be estimated purely from given data. We illustrate the finding in numerical experiments and confirm that these heuristic estimates lead to effective stepsizes.

CIBORG: CIrcuit-Based and ORiented Graph theory permutation routing protocol for single-hop IoT networks

The Internet of Things (IoT) has emerged as a promising paradigm which facilitates the seamless integration of physical devices and digital systems, thereby transforming multiple sectors such as healthcare, transportation, and urban planning. This paradigm is also known as ad-hoc networks. IoT is characterized by several pieces of equipment called objects. These objects have different and limited capacities such as battery, memory, and computing power. These limited capabilities make it difficult to design routing protocols for IoT networks because of the high number of objects in a network. In IoT, objects often have data which does not belong to them and which should be sent to other objects, then leading to a problem known as permutation routing problems. The solution to that problem is found when each object receives its items. In this paper, we propose a new approach to addressing the permutation routing problem in single-hop IoT networks. To this end, we start by representing an IoT network as an oriented graph, and then, based on a reservation channel protocol, we first define a permutation routing protocol for an IoT in a single channel. Secondly, we generalize the previous protocol to make it work in multiple channels. Routing is done using graph theory approaches. The obtained results show that the wake-up times and activities of IoT objects are greatly reduced, thus optimizing network lifetime. This is an effective solution for the permutation routing problem in IoT networks. The proposed approach considerably reduces energy consumption and computation time. It saves 5.2 to 32.04% residual energy depending on the number of items and channels used. Low energy and low computational cost demonstrate that the performance of circuit-based and oriented graph theory is better than the state-of-the-art protocol and therefore is a better candidate for the resolution of the permutation routing problem in single-hop environment.

Using GIS-based multicriteria decision analysis to prioritize invasive plant treatment: A creative solution for a pernicious problem

Invasive plant infestations are projected to rapidly increase with continued habitat fragmentation and climate change. The rate of spread often outpaces land managers’ ability to effectively detect and control infestations. Land stewards need tools that can match the rapid pace and scale of invasive infestations and help prioritize control efforts in the most ecologically important areas and optimize resource allocation. It is imperative that proposed control be informed by the best available ecological information. We present a spatially explicit modeling framework for prioritizing invasive plant treatment. In our case study from Michigan, we employ a multicriteria decision analysis model that synthesizes four critical factors for prioritizing invasive plant stewardship: integrity, biodiversity, resilience, and ecosystem services. Data for quantifying these factors were compiled from several state, federal, university, and non-governmental data sources. The model uses a geographic information system (GIS) to identify places that are impacted by invasive plant infestations that threaten to degrade ecosystem composition, structure, and function; are characterized by high ecosystem integrity; support high biodiversity; are resilient to disturbance; and provide ecosystem services. While specific to Michigan, our modeling framework is broadly applicable. This type of integrated analysis can help inform decisions about allocation of limited resources for numerous biodiversity stewardship and landscape-level conservation planning needs, regardless of geographic location.

Impact of the numerical conversion to optical depth on the transfer of polarized radiation

Making the conversion from the geometrical spatial scale to the optical depth spatial scale is useful in obtaining numerical solutions for the radiative transfer equation. This is because it allows for the use of exponential integrators, while enforcing numerical stability. Such a conversion involves the integration of the total opacity of the medium along the considered ray path. This is usually approximated by applying a piecewise quadrature in each spatial cell of the discretized medium. However, a rigorous analysis of this numerical step is lacking. This work is aimed at clearly assessing the performance of different optical depth conversion schemes with respect to the solution of the radiative transfer problem for polarized radiation, out of the local thermodynamic equilibrium. We analyzed different optical depth conversion schemes and their combinations with common formal solvers, both in terms of the rate of convergence as a function of the number of spatial points and the accuracy of the emergent Stokes profiles. The analysis was performed in a 1D semi-empirical model of the solar atmosphere, both in the absence and in the presence of a magnetic field. We solved the transfer problem of polarized radiation in different settings: the continuum, the photospheric Sr i AA modeled under the assumption of complete frequency redistribution, and the chromospheric Ca i AA taking the partial frequency redistribution effects into account during the modeling. High-order conversion schemes generally outperform low-order methods when a sufficiently high number of spatial grid points is considered. In the synthesis of the emergent Stokes profiles, the convergence rate, as a function of the number of spatial points, is impacted by both the conversion scheme and formal solver. The use of low-order conversion schemes significantly reduces the accuracy of high-order formal solvers. In practical applications, the use of low-order optical depth conversion schemes introduces large numerical errors in the formal solution. To fully exploit high-order formal solvers and obtain accurate synthetic emergent Stokes profiles, it is necessary to use high-order optical depth conversion schemes.

Bending the Iron Law: The distribution of power within political parties

AbstractHow do political parties share power internally? We study the internal organization of political parties as the solution of a moral hazard problem between a party conference and its factions. Factions' mobilization efforts benefit the party electorally, but can only be imperfectly monitored. In contrast with the logic of Michel's Iron Law, we provide a functionalist rationale for intraparty power sharing: We show that internal power sharing can enhance a party's electoral performance. This effect is stronger in settings that award more resources to election winners: Low interparty power sharing produces high intraparty power sharing. We also show that intraparty power sharing should be more frequent within smaller parties, when monitoring of factional effort is more precise (e.g., preferential voting systems), and when factions' ideological disagreements span multiple dimensions.

Radiomic feature robustness in CT scans affected by fiducial marker induced streak artifacts for patients with hepatocellular carcinoma.

Stereotactic body radiation therapy for hepatocellular carcinoma necessitates the implantation of gold fiducial markers in the liver, resulting in artifacts on computed tomography (CT) scans, which affect radiomic feature values. This report aims to assess the effect of these artifacts on radiomic features and how removing CT slices affects radiomic features extracted from 3D regions of interest (ROI). First, the range variation in 38 tumor contours unaffected by artifacts was assessed after sequentially and randomly removing 25%, 50%, 75% of slices. Subsequently, the agreement of feature values before and after removing ROI slices containing artifacts from 186 patients' CT scans was assessed with Lin's concordance correlation coefficient (CCC) and a Wilcoxon signed-rank test. In artifact-free tumor volumes, at least 71% of features remain robust with up to 50% of slices removed, while 56% remains robust with up to 75% of slices removed. When comparing contours before and after removing slices containing artifacts, around a third of features in the tumor contour and surrounding area remain robust (CCC>0.9), compared to 44% in the healthy liver. Concerning the tumor, 13% (Gray Level Size Zone Matrix) to 61% (first order) of the features remain robust (CCC>0.9). Over 90% of features differ significantly as assessed by Wilcoxon signed-rank test, however. This study demonstrates that removing slices containing artifacts is a feasible solution for the CT fiducial problem in this patient population and provides insight into which features are affected.

Symmetrization results for general nonlocal linear elliptic and parabolic problems

We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions.In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in [20].Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems.

Regularized kernel function methods for the backward heat conduction problem

In this letter, we are interested in the regularized numerical techniques for backward heat conduction problems, which aim at the detection of the previous status of physical field from its present information. It is well known that backward heat conduction problems are ill-posed. The small perturbation in the final status may result in large change in the previous status of physical field. It is difficult to get the stable numerical solutions of backward heat conduction problems. Based on the reproducing kernel theory, the letter aims at finding a new regularized kernel function methods for backward heat conduction problems.

Data-driven stabilized finite element solution of advection-dominated flow problems

In this article, we address the solution of advection-dominated flow problems by stabilized methods, by means of data-driven least-squares computed stabilized coefficients. As main methodological tool, we introduce a data-driven off-line/on-line strategy to compute them with low computational cost.We compare the errors provided by the data-driven stabilized coefficients to those provided by several previously established stabilized coefficients within the solution of advection–diffusion and Navier–Stokes flows, on structured and un-structured grids, with Lagrange Finite Elements up to third degree of interpolation. We obtain substantial error improvements for high-order finite element interpolation.We conclude that the data-driven procedure is a rewarding procedure, worth to be applied to general stabilized solutions of general flow problems.

Modeling and solution of eigenvalue problems of laminated cylindrical shells consisting of nanocomposite plies in thermal environments

This work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.

Evaluation of the possibility of searching for groundwater using electrical resistivity tomography based on the data of numerical modelling in complicated permafrost conditions (the case of the territory in the eastern part of the Republic of Buryatia)

Relevance. Groundwater is the main source of industrial and technical water supply for mining facilities. The geological structure of the studied areas can be complicated by various factors that make it difficult to search for and localize groundwater. In this regard, electrical geophysical prospecting methods are often included in the complex of prospecting and exploration works, before which it is necessary to justify the application of the chosen method for solving the problems by performing numerical modelling. Aim. To substantiate the use of electrical resistivity tomography for the search for groundwater, taking into account complicating factors, including perennially frozen rocks, taliks, and fault zone, by numerical modelling. Objects. Geological environment represented by Quaternary system rocks and permafrost rocks of Cretaceous sediments of the Zazinskaya intermontane area, fault zone, talik zones. Methods. Solution of the direct problem, solution of the inverse problem, ground geophysical surveys using electrical resistivity tomography. Results. Based on the performed numerical modelling, it is shown that the use of electrical resistivity tomography is expedient when searching for groundwater in the area characterized by various factors: permafrost, talik, and a fault zone. Based on the results of solving direct and inverse problems of electrical survey, using field works performed in 2020 in the Eravninsky district of the Republic of Buryatia as an example, it is shown that pole-dipole arrays in electric resistivity survey with electrode distance of 5 m, successfully confirmed by drilling operations, allow us reliably delineate potential zones of water inflow. These zones, characterized by low values of electrical resistivity, in this area, are related to talik zones, which are powered by heat flow from the bowels of the earth.

Exploring existence, uniqueness, and stability in nonlinear fractional boundary value problems with three-point boundary conditions

This study investigates the analysis of the existence, uniqueness, and stability of solutions for a Ψ-Caputo three-point nonlinear fractional boundary value problem using the Banach contraction principle and Sadovskii’s fixed point theorem. We demonstrate the practical implications of our analytical advancements for each situation, illustrating how the components of the fractional boundary value problem emerge in real-life occurrences. Our work significantly enhances the field of applied mathematics by offering analytical solutions and valuable insights.

A decision support scheme for solving the mobile coverage gap in rural areas in developing countries – Demonstrated with a case in Indonesia

As a primary means of communication, the role of mobile telecommunications networks is important for a developing country's economic and social development. However, especially rural areas in low-income countries still lack mobile coverage. In the academic literature, only segmented solution strategies for this mobile coverage problem in rural areas are proposed. These are either technological, regulatory, or organizational solutions, whereas solving the mobile coverage gap requires an integrated approach to develop arrangements for mobile network rollout in rural areas. This paper presents a comprehensive overview of the causes of the lack of mobile coverage, the available solutions, and how they can be combined. Based on this overview, the paper proposes a decision support scheme for selecting a suitable arrangement for solving the mobile coverage gap. In this decision support scheme, the technical, organizational, and regulatory solutions are combined to develop a set of arrangements that match the local key causes of the lack of mobile coverage and that fit with the local context. In the last phase of the decision support scheme, the relevant stakeholders are involved in selecting the most suitable arrangement. We demonstrate the decision support scheme by applying it to the case of an unserved rural village in Indonesia, Unipa on the island of Papua, to show how it can guide a developing country to initiate the process of developing a solution for mobile coverage problems in rural areas.

Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative

In this study, a precise and analytical method, namely Shehu transform decomposition method (STDM), is applied to examine multi-dimensional fractional diffusion equations, which will describe density dynamics in a material undergoing diffusion. The fractional derivative is taken into account by the Caputo–Fabrizio (CF) derivative. The proposed approach combines the Shehu transformation (ST) with the Adomian decomposition method (ADM), employing Adomain polynomials to handle nonlinear terms. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. To validate the accuracy of proposed method, we present the analytical solutions of three applications of multi-dimensional fractional diffusion equations. Furthermore, we compute the graphical and numerical results using MATLAB to demonstrate the close-form analytical solution in the comparison of the exact solution. The obtained findings are promising and suitable for the solution of multi-dimensional diffusion problems with time-fractional derivatives. The main advantage is that our developed scheme does not require assumptions or restrictions on variables that ruin the actual problem. This scheme plays a significant role in finding the solution and overcoming the restriction of variables that may cause difficulty in modeling the problem.

Non-negative solutions of a sublinear elliptic problem

Non-negative solutions of a sublinear elliptic problem

Development of an optimal adaptive finite element stabiliser for the simulation of complex flows

An optimal adaptive multiscale finite element method(AMsFEM) for numerical solutions of flow problems modelled by the Oldroyd B model is developed. Complex flows experience instabilities due to a phenomena known as the high Weissenberg number problem. The stabilisers are terms in-cooperated into the variational formulation when applying the finite element method. For the selected few stabilisers, numerical experiments are performed to study the convergence of the solutions. These demonstrate that adaptive strategies reduce the computational load of flow simulation. A best performing combination of choice of stabiliser and adaptive strategy is suggested.

A new method for solving fractional optimal control problems

In this article, we present a novel approach that utilizes the operational matrix method to solve fractional optimal control problems. We address the challenge of missing initial conditions for the co-state function by incorporating the linear shooting method. Our objective is to provide a method that not only enhances computational efficiency and reduces cost but also improves accuracy and usability. With our new approach, we can calculate the coefficients of the expansion solution without the need to solve an algebraic system. These coefficients can be generated explicitly or through an iterative process. We provide a proof of the uniform convergence of the approximate series of functions to the unique solution of the optimal control problem. To demonstrate the effectiveness of our proposed method, we solve several numerical examples and compare the results with those obtained by other researchers. Additionally, we extend the application of this new method to solve problems with multiple states, thereby expanding its scope to a wider range of problem domains. This allows us to address diverse scenarios using the same efficient and accurate approach. Through our research, we contribute to the development of a powerful and versatile method for solving fractional optimal control problems, offering significant advantages over existing techniques.

Thermal analysis of batteries and prediction with artificial neural networks

PurposeIn this study, it is aimed to develop cooling models for the efficient use of batteries and to show how important the busbar material is. Batteries, which are indispensable energy sources of electric aircraft, automobiles and portable devices, may eventually run out. Battery life decreases over time; the most critical factor is temperature. The temperature of batteries should not exceed the safe operating temperature of 313 K and it is recommended to have a balanced temperature distribution through the battery.Design/methodology/approachIn this study, the effect on the battery temperature caused by using different busbar materials to connect batteries together was investigated. Gold, copper and titanium were chosen as the different busbar material. The Air velocities used were 1 m/s and 2 m/s, the air inlet temperatures were 295 and 300 K and the discharge rates 1.0–1.5–2.0–2.5C were chosen for cooling the batteries.FindingsThe best busbar material was identified as copper. Because these studies are long-term studies, it is also suggested to estimate the data obtained with ANN (Artificial Neural Networks). The purpose of ANN is to enable the solution of many different complex problems by creating systems that do not require human intelligence. Four different program (BR-LM-CGP-SCG) were used to estimate the data obtained with ANN. It was found that the most reliable algorithm was BR18. The R2 size of the BR18 algorithm in the test phase was 0.999552, the CoV size was 0.007697 and the RMSE size was 0.005076.Originality/valueWhen the literature is considered, the cooling part of the battery modules has been taken into consideration during the temperature observation of the battery modules, but busbar materials connecting the batteries have always been ignored. In this study, various busbar materials were used and it was noticed how the temperature of the battery model changed under the same working conditions. These studies are very time-consuming and costly studies. Therefore, an estimation of the data obtained with artificial neural networks (ANN) was also evaluated.

Solution of fuzzy transportation problem based upon pentagonal and hexagonal fuzzy numbers

Solution of fuzzy transportation problem based upon pentagonal and hexagonal fuzzy numbers