Multilayer Problem Research Articles

Multilayer one-dimensional Convection-Diffusion-Reaction (CDR) problem: Analytical solution and imaginary eigenvalue analysis

• Presents analytical solution for 1D multilayer Convection-Diffusion-Reaction problem. • Derives orthogonality relationship for this problem. • Shows that eigenvalues may become imaginary can certain conditions. • Presents detailed mathematical analysis of conditions leading to imaginary eigenvalues. This paper presents a theoretical analysis of a one-dimensional multilayer heat transfer problem with diffusion, advection and linear temperature-dependent heat generation occurring in each layer. A general solution of the problem is derived. Orthogonality of eigenfunctions is proved, and an explicit expression for the eigenequation is derived. The special case of a two-layer body is discussed. It is shown that, under specific conditions, this problem admits two types of imaginary eigenvalues, one of which is related to divergence of temperature at large times, corresponding to the thermal runaway phenomenon in batteries. The impact of various problem parameters related to diffusion, advection and heat generation on the appearance of imaginary eigenvalues is discussed. Specifically, due to the directional nature of fluid flow, advection in each layer of a two-layer body has opposing impact on the occurrence of imaginary eigenvalues. It is also shown that a balance between heat generation, diffusion and advection determines whether an imaginary eigenvalue is encountered, and consequently, whether thermal runaway occurs. Results presented here expand the theoretical understanding of multilayer heat transfer, and may also contribute towards improved thermal design of multilayer engineering systems such as flow batteries.

Energy Consumption in a Distributional Warehouse: A Practical Case Study for Different Warehouse Technologies

Energy consumption by distribution warehouses has become an essential component of green warehousing and research on reducing the carbon footprint of supply chains. Energy consumption in warehousing is a complex and multilayered problem, which is generally considered in the literature in relation to its detailed components, not as part of comparative studies. In this article, the authors consider six cross-sectional variants of warehouse technology, from manual to fully automatic, and analyze the energy consumption of a warehouse in various configurations. A methodology for estimating storage space and determining energy consumption is proposed. The energy balance of the warehouse variants includes energy for material handling equipment operation, energy consumption for building maintenance (heating, cooling, lighting, etc.), and energy generated by the photovoltaic system on the roof. Then, the operational costs of the variants are estimated and, on their basis, an automation index is determined. The index allows for a comparative analysis of energy consumption and the mechanization and automation of a warehouse. It is shown that a significant part of the energy is spent on maintaining a warehouse building, especially in the case of facilities with a low degree of automation.

NewH(div)-conforming multiscale hybrid-mixed methods for the elasticity problem on polygonal meshes

This work proposes a family of multiscale hybrid-mixed methods for the two-dimensional linear elasticity problem on general polygonal meshes. The new methods approximate displacement, stress, and rotation using two-scale discretizations. The first scale level setting consists of approximating the traction variable (Lagrange multiplier) in discontinuous polynomial spaces, and of computing elementwise rigid body modes. In the second level, the methods are made effective by solving completely independent local boundary Neumann elasticity problems written in a mixed form with weak symmetry enforcedviathe rotation multiplier. Since the finite-dimensional space for the traction variable constraints the local stress approximations, the discrete stress field lies in theH(div) space globally and stays in local equilibrium with external forces. We propose different choices to approximate local problems based on pairs of finite element spaces defined on affine second-level meshes. Those choices generate the family of multiscale finite element methods for which stability and convergence are proved in a unified framework. Notably, we prove that the methods are optimal and high-order convergent in the natural norms. Also, it emerges that the approximate displacement and stress divergence are super-convergent in theL2-norm. Numerical verifications assess theoretical results and highlight the high precision of the new methods on coarse meshes for multilayered heterogeneous material problems.

Nonlinear vibration analysis of elastically supported multi-layer composite plates using efficient quadrature techniques

Different numerical schemes are introduced to formulate and solve nonlinear vibration analysis of elastically supported multilayer composite plate problems. The type of elastic foundation is Winkler - Pasternak foundation model. The governing equations are formulated according to a first order transverse shear theory. Examined schemes are based on polynomial, sinc, discrete singular convolution differential quadrature (DSCDQ) methods. These schemes are appointed to reduce the problem to nonlinear Eigen-value problem. The reduced system is solved iteratively. Numerical analysis is performed to explore influence of different computational characteristics on convergence and efficiency of the obtained results. Comprehensive numerical results validate the solutions by comparison with those obtained by the exact and numerical ones. Moreover, a parametric study is introduced to investigate the influence of supporting conditions, foundation parameters, elastic and geometric characteristics of the vibrated plate, on natural frequencies and mode shapes. The obtained results exhibit that the (DSCDQM) is an accurate efficient method in the dynamic analysis of discontinuity plates resting on nonlinear elastic foundation.

Policy implementation in the health sector of the federal state of Belgium: An ethnographic approach

ABSTRACT When analysing public policies, an implementation gap is often attributed to unclear or irrelevant goals, implementers’ disobedience and/or the numerous layers of government involved. This paper focuses on the multi-layer problem, wondering whether aspects other than the number of layers have an influence on the implementation gap in federal contexts, for example, the layers’ degree of autonomy or the competencies ‘allocation. It addresses the following research question: from an organizational point of view, to what extent does federalism, as a specific institutional configuration, influence the constitution of an implementation gap as part of a public policy implementation process? This research focuses on the implementation of public policy in the Belgian health sector intended to integrate care for chronic patients. It highlights the blockages that may occur in a multi-layer federal country like Belgium, showing that federalism can become dysfunctional if the allocation of competencies was made in an incoherent manner.

Prioritization of K-12 School Maintenance Construction Projects Using Genetic Algorithm and Dynamic Programming Models

High quality education standards and safe learning environments are the fundamental goals of most educational systems. One step towards achieving these goals is to keep existing school facilities in good working conditions through continues repair and maintenance programs. Due to limited resources, efficient use of allocated funds is necessary. This paper presents an optimization tool using Genetic Algorithm (GA) and Dynamic Programming (DP) that manages the expenses of K-12 school rehabilitation projects. These models help to find the optimum solutions among the given data through mutations and crossover in deriving a possible solution to a multi-layered problem. The proposed optimization tools maximize the benefits of K-12 school repair projects, and focus primarily on serving at-risk students, including those who come from low-income families. To demonstrate the use and capabilities of the proposed tool, a case study is presented. The results revealed by the case study show high potential for better management of school rehabilitation projects and better provision of service to disadvantaged students.

Pudendal nerve block as a countermeasure to postoperative chronic pain after removal of Bartholin's cyst

The chronic pain syndrome is a serious post-operative complication. In our practice we have discovered a certain percent of neuralgia of the pudendal nerve in vaginal surgery – more precisely in Bartholin’s cyst removal. As a highly efficient countermeasure we propose a nerve block of the pudendal nerve. We have performed a retrospective study of patients who underwent a Bartholin’s cyst removal in the span of 1 year from January 1st 2019 to December 31st 2019. All of the patients included are diagnosed with chronic pain in the area innervated from the pudendal nerve. In all of the patients a pudendal nerve block with local anesthetic was performed under the guidance of ultrasound. A total of 11 patients were included in the study. There was a time interval between the Bartholin’s cyst removal surgery and the performance of the nerve block. All patients expressed moderate pain before the procedure. In only 1 case a repeat of the nerve block was imposed. There were no short- or long-term complications of any kind. The patients have been followed-up in the duration of 1 year and 100% has been reported. Accurate and precise pain assessment is vital of the diagnosing and subsequent treatment of the chronic pain syndrome. There are many ways of treating the syndrome both conventional (non-steroidal anti-inflammatory drugs, opioids, topical analgesics and adjuvant analgesics) and unconventional. Chronic pain syndrome is an important multilayered problem that requires personal approach. The nerve block of the pudendal nerve is a highly efficient method of coping with that disease.

Real-time robot manipulator tracking control as multilayered time-varying problem

• Robot manipulator tracking control is directly formulated as multilayered time-varying problem. • All joint angle limits are considered including time-varying upper and lower bounds. • A solution is proposed to solve the multilayered time-varying problem. When kinematic control of robot manipulator is modeled as time-varying problems, control algorithms generated by solving time-varying problems perform well in the aspect of real-time control and control precision. However, conventional algorithms are based on relatively simple time-varying problems modeling and solving, and thus, it is difficult for them to solve more other problems while completing tracking task. In this work, the kinematic control of robot manipulator is first modeled as more complicated multilayered time-varying problem, which simultaneously formulates the tracking task and joint angle limits. Then, zeroing neural dynamics method is future investigated to find the equivalence of multilayers. Finally, three explicit solutions based on three discretization formulas are presented to solve the multilayered time-varying problem. The presented solutions not only complete the tracking task in real time with different precision, but also solve the problem of joint angle limits during the control process.

Optimization of multilayer thermal protection system by using phase change material under aerodynamic heating

• MTPSs using PCM for insulation are numerically studied. • The addition of PCM helps MTPS fulfill the thermal requirements. • PCM proportion plays a major role in the mass optimization result. • The contents of the two insulation layers affect the system differently. • The optimized designs in terms of mass and size is related to the type of PCM. A multilayer thermal protection system (MTPS) capable to work constantly during multiple launches is important for the new generation of reusable re-entry vehicles to significantly reduce launch costs and protect instruments from overheating. In this paper, phase change material (PCM) is introduced into the MTPS for the optimization purpose in terms of heat performance and structure design. The transient heat transfer characteristics of the system under aerodynamic heating is numerically analyzed, and 2D models using different insulation materials are compared to optimize the system, with respect to temperature distribution, areal density and overall thickness. The finite volume method with the enthalpy-porosity technique is used to resolve the involved multilayer heat transfer problem and the phase transition process. The thermal radiation between the system and the environment, the heat conduction through multi layers, and the convective phenomenon occurring in the PCM section are all considered. The calculation result confirms that the addition of PCM can successfully decrease the temperature of each part in the system below their maximum temperature limits (the C/SiC, Saffil and aluminum alloy layers lower than 1923.15 K, 1873.5 K and 450 K, simultaneously), accordingly help to find the optimal designs with a lighter mass and a smaller size.

Imaginary Eigenvalues in Multilayer One-Dimensional Thermal Conduction Problem with Linear Temperature-Dependent Heat Generation

• Solves a thermal conduction problem for 1D multilayer body. • Considers temperature-dependent source term. • Demonstrates existence of two types of imaginary eigenvalues for this problem. • Presents physical interpretation of imaginary eigenvalues. • Proves that despite imaginary eigenvalues, temperature remains real. Diffusion in a multi-layer body is a common problem in heat and mass transfer, with applications in multiple engineering systems, such as Li-ion battery packs and first-order chemical reactions occurring in a multilayer body. Development of analytical models to describe diffusion in such systems is helpful for both heat and mass transfer. This paper addresses a multi-layer one-dimensional diffusion problem, in which, generation/consumption in each layer is proportional to the local temperature/concentration. This could occur, for example, due to temperature-dependent heat generation or species generation/consumption associated with a first-order chemical reaction. It is shown that eigenvalues of this problem may become imaginary under two distinct conditions. A physical interpretation of these conditions is discussed, and a mathematical requirement for existence of imaginary eigenvalues is derived. The relationships between imaginary eigenvalues and various non-dimensional problem parameters are discussed. It is also shown that the computed temperature in the multilayer body remains real even if some eigenvalues may become imaginary. Therefore, all eigenvalues, whether real or imaginary must be accounted for in temperature computation. While presented in the context of heat transfer, these results are also valid for multi-layer mass transfer problems involving species generation/consumption due to chemical reaction. This work improves the theoretical understanding of diffusion in a multilayer body under conditions relevant for several engineering processes and systems.

Russian Migration Policy: New Starting Points

The author traces the evolution of the conceptual foundations of Russia’s migration policy and the features of its implementation at various stages of social, economic and political development of the country. The analysis focuses on the geopolitical specifics of Russia’s migration policy: after the collapse of the USSR, tens of millions of the country’s citizens ended up abroad. Return to the sources of the conceptualization of the Russian migration policy, capture of the underrated factors has a significant practical importance to mainstream and optimize it nowadays. Contradictory tendencies in the development of migration processes, unrealized opportunities, mistakes and miscalculations made in the first post-Soviet years are revealed; all the positive things that have been brought into the migration sphere over three decades are noted. The author identifies several stages that have their peculiarities that characterize the dynamics of changes and the evolution of the conceptual approaches of the state to this very complex and multi-layered problem. And at each stage there is a difficult search for answers to unresolved old and new questions that life poses to Russia with its contradictions, illogisms, and paradoxes. The author concludes that the coronavirus pandemic, which caused global social and economic upheavals in the world, will become a force majeure test for Russia’s migration policy.

Research on channel routing model of integrated circuit

Based on the research and analysis of integrated circuit routing problem, this paper puts forward a judgment method of no solution for one layer metal channel routing, establishes an optimal routing model for one layer metal routing problem based on 0-1 integer linear programming, an optimal routing algorithm for multi-layer metal routing problem with via, and an improved model for multi-layer metal routing problem with via spacing.

An integrated multi-objective mathematical programming and simulation model for a multi-layer facility location problem

Multi-layer facility location problems deal with providing service to customers in different layers. In the context of system performance and complexity, all the needed services of a customer that ...

An integrated multi-objective mathematical programming and simulation model for a multi-layer facility location problem

An integrated multi-objective mathematical programming and simulation model for a multi-layer facility location problem

Efficient Intrusion detection of malicious node using Bayesian Hybrid Detection in MANET

In the past several years there have been considerable interest developed towards study on distributed networks. The key underlying application under such technology is mobile ad hoc networks (MANETs), which have been exploiting the range of research opportunity. In MANET due to infrastructure less network and dynamic topology changes, security becomes one of the important issues. The defense strategies such as intrusion detection system (IDS) impose a method to build efficient detection of malicious nodes. Game theory is mainly used to study security problems identification in MANET. The Bayesian Hybrid Detection (BHD) is applied to detect the malicious nodes. A BHD allows the defender to adjust based on opponent observation. The simulation is carried out using the MATLAB for malicious nodes detection. The security degree is measured by the payoff index and system stability index (SSI). Also the processing vs. accuracy index level is measured to identify reliability of detection. The proposed system enables for enhancing security in MANET’s by modeling the interactions among a malicious node with number of legitimate nodes. This is suitable for future works on multilayer security problem in MANET.

Forward-Backward Alternating Parallel Shooting Method for Multi-layer Boundary Value Problems

Multi-layer boundary value problems have received a great deal of attention in the past few years. This is due to the fact that they model many engineering applications. Examples of applications include fluid flow though multi-layer porous media such as ground water and oil reservoirs. In this work, we present a new method for solving multi-layer boundary value problems. The method is based on an efficient adaption of the classical shooting method, where a boundary value problem is solved by means of solving a sequence of initial value problems. We propose, an alternating forward-backward shooting strategy that reduces computational cost. Illustration of the method is presented on application to fluid flow through multi-layer porous media. The examples presented suggested that the method is reliable and accurate.

Continuous-Time Laser Frames Associating and Mapping via Multilayer Optimization.

To achieve the ability of associating continuous-time laser frames is of vital importance but challenging for hand-held or backpack simultaneous localization and mapping (SLAM). In this study, the complex associating and mapping problem is investigated and modeled as a multilayer optimization problem to realize low drift localization and point cloud map reconstruction without the assistance of the GNSS/INS navigation systems. 3D point clouds are aligned among consecutive frames, submaps, and closed-loop frames using the normal distributions transform (NDT) algorithm and the iterative closest point (ICP) algorithm. The ground points are extracted automatically, while the non-ground points are automatically segmented to different point clusters with some noise point clusters omitted before 3D point clouds are aligned. Through the three levels of interframe association, submap matching and closed-loop optimization, the continuous-time laser frames can be accurately associated to guarantee the consistency of 3D point cloud map. Finally, the proposed method was evaluated in different scenarios, the experimental results showed that the proposed method could not only achieve accurate mapping even in the complex scenes, but also successfully handle sparse laser frames well, which is critical for the scanners such as the new Velodyne VLP-16 scanner’s performance.

Analytical Solution for Temperature Distribution in a Multilayer Body With Spatially Varying Convective Heat Transfer Boundary Conditions on Both Ends

Abstract Analytical modeling of thermal conduction in a multilayer body is of practical importance in several engineering applications such as microelectronics cooling, building insulation, and micro-electromechanical systems. A number of analytical methods have been used in past work to determine multilayer temperature distribution for various boundary conditions. However, there is a lack of work on solving the multilayer thermal conduction problem in the presence of spatially varying convective heat transfer boundary condition. This paper derives the steady-state temperature distribution in a multilayer body with spatially varying convective heat transfer coefficients on both ends of the body. Internal heat generation within each layer and thermal contact resistance between layers are both accounted for. The solution is presented in the form of an eigenfunction series, the coefficients of which are shown to be governed by a set of linear, algebraic equations that can be easily solved. Results are shown to be in good agreement with numerical simulation and with a standard solution for a special case. The model is used to analyze heat transfer for two specific problems of interest involving spatially varying convective heat transfer representative of jet impingement and laminar flow past a flat plate. In addition to enhancing the theoretical understanding of multilayer heat transfer, this work also contributes toward design and optimization of practical engineering systems comprising multilayer bodies.

Multi-Layer Transient Heat Conduction Involving Perfectly-Conducting Solids

Boundary conditions of high kinds (fourth and sixth kind) as defined by Carslaw and Jaeger are used in this work to model the thermal behavior of perfect conductors when involved in multi-layer transient heat conduction problems. In detail, two- and three-layer configurations are analyzed. In the former, a thin layer modeled as a lumped body is subject to a surface heat flux on the front side while it is in perfect (fourth kind) or in imperfect (sixth kind) thermal contact with a semi-infinite or finite body on the back side. When dealing with a semi-infinite body in imperfect contact, the temperature solution is derived by means of the Laplace transform method. Green’s function approach is also used but for solving the companion case of a finite body in perfect contact with the thin film. In the latter, a thin layer with internal heat generation is located between two semi-infinite or finite bodies in perfect/imperfect contact. For the sake of thermal symmetry, such a three-layer structure reduces to a two-layer configuration. Results are given in both tabular and graphical forms and show the effect of heat capacity and thermal resistance on the temperature distribution of conductive layers.

The mass-preserving solution-flux scheme for multi-layer interface parabolic equations

• It is challenging to develop mass-preserving schemes for parabolic equations with interfaces. • We develop a new mass-preserving solution-flux schemes for multi-layer interface equations. • The novel corrected fluxes are proposed at the irregular mesh points by using the interface conditions. • The developed scheme satisfies mass conservation for the 1D and 2D parabolic interface equations. • Numerical experiments show mass conservation and convergence orders of our scheme. Interface partial differential equations (PDEs) are very important in science and engineering. A new mass preserving solution-flux scheme is proposed in this paper for solving parabolic multi-layer interface problems. In the scheme, the domain is divided into staggered meshes for layers. At grid points in each subdomain, the solution-flux scheme is proposed to approximate the equation. However, due to the interface jump conditions, it is difficult to define the approximate fluxes at the irregular points next to interfaces for satisfying mass conservation for the scheme across the interfaces. The important feature of our work is that at the irregular grid points, the novel corrected approximate fluxes from two sides of the interface are proposed by combining with the interface jump conditions at interfaces, which ensure the developed solution-flux scheme mass conservative while keeping the same accuracy. We prove theoretically that our scheme satisfies mass conservation in the discrete form over the whole domain for the parabolic interface equations with multi-layers. Numerical experiments show mass conservation and convergence orders of our scheme and numerical results in multi-layer media show its excellent performance.