Full Decoupling Research Articles

Efficient interior penalty discontinuous Galerkin projection method with unconditional energy stability and second-order temporal accuracy for the incompressible magneto-hydrodynamic system

In this paper, we propose a novel interior penalty discontinuous Galerkin projection method for the incompressible magneto-hydrodynamic equations. The scheme is employed by an implicit-explicit treatment of the nonlinear coupling terms and a second-order rotational pressure-correction scheme for dealing with the Navier-Stokes equations. One noteworthy aspect of this scheme is the introduction of an additional stabilization term to Maxwell's equations, which allows for the explicit treatment of the coupled nonlinear terms and the decoupling of computations for the magnetic and velocity fields, ultimately leading to the achievement of desired linearity, full decoupling, second-order accuracy in time, and unconditional energy stability. The obtained scheme is easy to implement because one only needs to solve a few decoupled linear equations at each time step. We rigorously prove the unique solvability and unconditional energy stability of the developed scheme and present a series of numerical examples to demonstrate the accuracy, stability, and efficiency of the proposed scheme.

Quantifying the partial and general equilibrium effects of sanctions on Russia

AbstractThis paper evaluates the effects of sanctions on Russia between 2014 and 2019 and the resulting countersanctions. We estimate their impact on trade in a gravity framework, allowing for treatment heterogeneity among pairs and sectors, and use the estimated elasticities in a general equilibrium analysis. We find that the sanctions decreased trade with Russia in key sectors, translating to a loss in real income in Russia by 0.3%. Full decoupling of the EU and its allies from Russia would increase this effect to over 4%. Our results emphasize the role of deep sanctions as a foreign policy instrument and international cooperation.

Quantum Beam Scattering—Beam’s Coherence Length, Which-Path Information and Weak Values

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e., with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e., the concept of a neutron’s (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle’s dynamics from the quantum dynamics of the scatterer—a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum-theoretical approaches (e.g., quantum entanglement, “which-path information” versus interference, von Neumann measurement, Weak Values (WV), etc.), new observable effects of non-relativistic quantum beam scattering may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. A new WV-theoretical treatment is provided, which explains both these “deficit effects” from first principles and on equal footing.

Fully discrete, decoupled and energy-stable Fourier-Spectral numerical scheme for the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy flow regime of two-phase incompressible flows

In this paper, we introduce fully discrete Fourier-Spectral numerical scheme to solve the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy equations, which represent a phase-field model for two-phase incompressible flow in either the free flow regime or a Hele-Shaw cell. The proposed scheme achieves full decoupling while maintaining linearity and energy stability through a combination of the Scalar Auxiliary Variable (SAV) method, which discretizes the nonlinear potential, and the “Zero-Energy-Contribution” (ZEC) method, which handles the coupled nonlinear advective/surface tension terms. The efficiency of this scheme is attributed to its linear decoupling structure and the fact that it requires only a few elliptic equations with constant coefficients to be solved at each time step. We rigorously establish the scheme’s unconditional energy stability. Further, some numerical simulations are provided in both 2D and 3D to show its effectiveness, including its accuracy, stability, and efficiency.

Economic growth, trade, and greenhouse gas emissions in the european union - investigating pollution leakage

Methods. This research employs econometric modeling and panel data analysis to investigate the intricate relationship between economic growth, environmental policies, and greenhouse gas (GHG) emissions within the European Union (EU). Panel data from 27 EU countries during the period from 2008 to 2021 is used to assess the impact of various factors on GHG emissions, including per capita GDP, primary energy consumption, renewable energy share, technological development, and extra-EU trade. Results. The study reveals that there is a positive correlation between GDP per capita and emissions, suggesting that the EU has not yet reached full decoupling of GDP growth and growth in GHG emissions. Increased primary energy consumption is associated with higher emissions, while a greater proportion of renewable energy sources is linked to reduced emissions. Technological advancements are found to mitigate GHG emissions. Importantly, the research uncovers a positive relationship between extra-EU trade and emissions, indicating the pollution leakage through trade. Novelty. This study contributes to the literature by offering a comprehensive examination of the dynamics between economic growth, changes in energy consumption, technological advancement, trade patterns, and GHG emissions within the EU. A more specific international trade variable is introduced into the model – the trade balance of EU countries with the outside EU countries. It explores the concept of pollution leakage, shedding light on how changes in foreign trade may impact emissions levels. Practical Value. The findings have significant policy implications, highlighting the need for a holistic approach to environmental policymaking within the EU. The study emphasizes that while progress has been made in adopting cleaner technologies and supporting renewable energy, challenges remain, including the potential for pollution leakage through international trade. This insight underscores the importance of globally impactful environmental policies and international cooperation to address GHG emissions effectively.

A two-field approach to multibody dynamics of rotating flexible bodies

A two-field version of the floating frame-of-reference approach is developed to describe the dynamics of a flexible body in the case of motion in a uniformly rotating frame. Full decoupling of the kinetic energy results from splitting of the motion into rigid-body modes of the floating center of mass and a velocity field orthogonal to them. The motion equations are developed from a canonical variational expression in which displacement and velocity fields play independent roles. They turn out to keep the same global structure as in the case of motion in an inertial frame. The discretization of all inertia terms is discussed in depth. It is also shown that, in the case of discretization of the continuum with 3D solid elements, all gyroscopic terms can be derived from a mass kernel and associated Si\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{S} _{i}$\\end{document} matrices. Model reduction is proposed using the Herting–Martinez method in order to automatically satisfy orthogonality of the velocity field to rigid-body modes. Two application examples of high-speed rotating systems are developed at length to assess the efficiency of the proposed methodology.

Fully decoupled linear BDF2 scheme for the penalty incompressible Ericksen–Leslie equations

This work focuses on the numerical approximation of the penalized Ericksen–Leslie equations. A second-order numerical scheme which has the advantages of full decoupling, linearization and unconditional stability in energy is constructed. Firstly, an equivalent new system is established by introducing two scalar auxiliary variables. One is added to the convective term in the Navier–Stokes equation and the other is added to the rest nonlinear terms. Secondly, a second-order BDF(backward differentiation formula) scheme for the new system is constructed while the pressure-correction method is used and the unconditional stability in energy is subsequently proved. Thirdly, the detailed implementation process is given to clarify that the scheme is fully decoupled and linear. Finally, several numerical simulations are shown to illustrate the accuracy and effectiveness of the scheme. Moreover, the annihilation phenomena of singularities are also performed.

Symmetrization of contact stresses in coating under frictional sliding indentation

Frictional contact problem of a layer-substrate structure is an important topic in coating optimization design. The present work carries out a comprehensive analysis on the coupling effect of coefficient of friction, Poisson’s ratio, and layer thickness on contact stresses distribution. A physical property namely full decoupling under interaction between material and geometric couplings is explicitly observed. Eccentricity in contact could be virtually diminished, and symmetrization on contact pressure of non-Hertzian type is presented at a specific Poisson’s ratio. Additionally, position of tensile peak within in-plane surface stress could not be affected by friction under the full decoupling effect. HIGHLIGHTS Coupling effects of Poisson’s ratio, friction coefficient, and layer thickness on eccentric contact involving soft bonded coating are studied systematically. A physical property namely full normal-tangential decoupling at a specific Poisson’s ratio in thin coating is explicitly observed and analyzed comprehensively. The tensile peak of in-plane stress as a crack initiator at the coating surface is studied under the full decoupling effect mentioned above.

Linear Full Decoupling, Velocity Correction Method for Unsteady Thermally Coupled Incompressible Magneto-Hydrodynamic Equations.

We propose and analyze an effective decoupling algorithm for unsteady thermally coupled magneto-hydrodynamic equations in this paper. The proposed method is a first-order velocity correction projection algorithms in time marching, including standard velocity correction and rotation velocity correction, which can completely decouple all variables in the model. Meanwhile, the schemes are not only linear and only need to solve a series of linear partial differential equations with constant coefficients at each time step, but also the standard velocity correction algorithm can produce the Neumann boundary condition for the pressure field, but the rotational velocity correction algorithm can produce the consistent boundary which improve the accuracy of the pressure field. Thus, improving our computational efficiency. Then, we give the energy stability of the algorithms and give a detailed proofs. The key idea to establish the stability results of the rotation velocity correction algorithm is to transform the rotation term into a telescopic symmetric form by means of the Gauge–Uzawa formula. Finally, numerical experiments show that the rotation velocity correction projection algorithm is efficient to solve the thermally coupled magneto-hydrodynamic equations.

Efficient linear, fully-decoupled and energy stable numerical scheme for a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field elastic bending energy model of lipid vesicles

We first establish a variable density and viscosity, volume-conserved, hydrodynamically coupled phase-field variable elastic bending energy model for lipid vesicles, and then construct an efficient time-discrete scheme for solving it. The numerical scheme combines the penalty method for solving the Navier–Stokes equation, the explicit-IEQ (invariant energy quadratization) method for the nonlinear potentials, and the operator-splitting method. Hence it is not only fully decoupled but also owns some desired properties of linearity and unconditional energy stability. The feature of full decoupling is achieved by introducing some auxiliary variables and designing additional ordinary differential equations which are used for discretizing the coupled and nonlinear terms. The solvability and the unconditional energy stability of the numerical scheme have been further rigorously and numerically proven. Several numerical examples are carried out on the sedimentation process of the vesicle cell to show the effectiveness of the model and scheme.

Comparative Analysis of Canonical Forms in Fault Diagnosis and Estimation Problems

The paper considers the methods of different canonical forms application to the problems of fault diagnosis and estimation in technical systems described by linear dynamic models under disturbances. Identification and Jordan canonical forms are investigated. The main relations describing fault diagnosis and estimation problems for different canonical forms are given, and comparative analysis of possibility of their application is performed. An analysis shows that the identification canonical form produces relations enable developing algorithms for the diagnostic observer and estimator design while Jordan canonical form assumes using some heuristic methods. It was shown that Jordan canonical form is more preferable to guarantee full disturbance decoupling, that is invariance with respect to the disturbance. On the other hand, when full decoupling is impossible, the identification canonical form enables developing algorithm of partial decoupling while Jordan canonical form assumes using some heuristic methods. The advantage of Jordan canonical form is that it ensures stability of the designed system based on properties of the matrix describing this form while the identification canonical form assumes using feedback based on the residual which must be generated. This allows for Jordan canonical form to reduce the dimension of the designed diagnostic observer and estimator. The new method to guarantee sensitivity of the diagnostic observer to the faults is developed. The method is based on analysis of the observability matrix and new rules to calculate matrices describing the diagnostic observer. Theoretical results are illustrated by practical example of well known three tank system.

Maximum reduction of energy losses in multicore MgB2 wires by metastructured soft-ferromagnetic coatings

When compared with rare-earth coated conductors, magnesium diboride superconducting cables are known to show significant advantages by cost and easy production. However, the inherent difficulty for achieving a significant reduction of their magnetization losses in multifilamentary wires, without degrading the high critical current density that is so characteristic of the monowire, is considered as one of the major drawbacks for their practical use in high power density applications. Being this one of the major markets for superconducting cables, from fundamental principles and computational optimization techniques, in this paper we demonstrate how the embedding of the superconducting filaments into soft-ferromagnetic metastructures can render to their full magnetic decoupling, and therefore, to the maximum reduction of the energy losses that can be achieved without deteriorate the critical current density of the cable. The designed multifilamentary metastructure is made of NbTi coated MgB2 superconducting filaments in a Cu-matrix, serving as a reference for validating our model with actual experimental measurements in monowires and multifilamentary wires. The novelty in our computationally aided multifilamentary wires, is that each one of the filaments is embedded within a thin metastructure made of a soft-ferromagnetic layer and a resistive layer. We have found that for soft-ferromagnetic layers with magnetic permeabilities in the range of mu _{r}= 20–100, nearly a full magnetic decoupling between the superconducting filaments can be achieved, leading to efficiencies higher than 92%, and an overall reduction of the AC-losses (including eddy currents at the Cu-matrix) higher than 50%.

Circular Economy: Illusion or First Step towards a Sustainable Economy: A Physico-Economic Perspective

“A circular economy is one that is regenerative by design and aims to keep products, components, and materials at their highest utility and value at all times, distinguishing between technical and biological cycles. This new economic model seeks to ultimately decouple global economic development from finite resource consumption”, states the widely used definition of the Ellen MacArthur Foundation. This definition conveys two messages. First, it acknowledges that economic activities need natural inputs (energy and material) and generate outputs in the form of waste as well as emissions. Second, it embodies the promise that, through technological innovations, human ingenuity and the market, a full decoupling of the economy from nature can be reached. Obviously both messages are not consistent with each other. Analyzing these issues through the lens of a transdisciplinary approach, which combines insight from thermodynamics with conventional economic theory, is the purpose of this paper. By using such physico-economic perspective, it is argued that not any kind of a circular economy is sustainable. Therefore, indicators are required through which it can be assured that a particular fashion of a circular economy reduces both environmental and social harm.

Research and Design on the Coordinate Control System of Once-through Boiler Power Unit

Taking the 1000 MW ultra supercritical unit as an object of study, The nonlinear model is builded through mechanism analysis, which is linearized based on small error, the multi-variable decoupling controller is designed to achieve full decoupling of the input and output variables, and finally the three-input-three-output coordinated control system (CCS) is established. The control system is verified by coal quality and the specific enthalpy of feed water disturbance when load changing, the simulation result shows that the improved CCS has good control performance.

Efficient Fully decoupled and second-order time-accurate scheme for the Navier–Stokes coupled Cahn–Hilliard Ohta–Kawaski Phase-Field model of Diblock copolymer melt

In this work, we aim to develop a highly efficient numerical scheme for the flow-coupled phase-field model of diblock copolymer melt. Formally, the model is a very complicated nonlinear system that consists of the Navier–Stokes equations and the Cahn–Hilliard type equations with the Ohta–Kawaski potential. Through a combination of a novel decoupling technique and the projection method, we develop the first full decoupling, energy stable, and second-order time-accurate numerical scheme for this model. The decoupling technique is based on the design of an auxiliary ODE, which plays a vital role in obtaining the full decoupling structure while maintaining energy stability. The high efficiency of the scheme is not only reflected by its linear and decoupled structure but also because it only needs to solve a few elliptic equations at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Numerical experiments further verify the convergence rate, energy stability, and effectiveness of the developed algorithm.

Fully-discrete spectral-Galerkin scheme with decoupled structure and second-order time accuracy for the anisotropic phase-field dendritic crystal growth model

In this work, we consider numerical approximations of the anisotropic phase-field dendritic crystal growth model, which is a highly complex coupled nonlinear system consisting of the anisotropic Allen-Cahn equation and the heat equation. Through the combination of a novel explicit auxiliary variable IEQ approach for temporal discretization and the spectral-Galerkin approach for spatial discretization, we develop the first fully-discrete numerical scheme with linearity, decoupled structure, unconditional energy stability, and second-order time accuracy for the particular phase-field dendritic model. In the process of obtaining a full decoupling structure and maintaining energy stability, the introduction of two auxiliary variables and the design of two auxiliary ODEs play a vital role. The designed scheme is highly efficient because only a few elliptic equations with constant coefficients are needed to be solved at each time step. The unconditional energy stability of the scheme has been strictly proved, and the detailed implementation process is given. Through several numerical simulations of 2D and 3D dendritic crystal growth examples, we further verify the convergence rate, energy stability, and effectiveness of the developed algorithm.

On a novel full decoupling, linear, second‐order accurate, and unconditionally energy stable numerical scheme for the anisotropic phase‐field dendritic crystal growth model

AbstractThe anisotropic phase‐field dendritic crystal growth model is a highly nonlinear system that couples the anisotropic Allen–Cahn equation and the thermal equation together. Due to the high anisotropy and nonlinear couplings in the system, how to develop an accurate and efficient, especially a fully decoupled scheme, has always been a challenging problem. To solve the challenge, in this article, we construct a novel fully decoupled numerical scheme which is also linear, energy stable, and second‐order time accurate. The key idea to realize the full decoupling structure is to introduce an ordinary differential equation to deal with the nonlinear coupling terms satisfying the so‐called “zero‐energy‐contribution” property. This scheme is very effective and easy to implement since only a few fully decoupled elliptic equations with constant coefficients need to be solved at each time step. We rigorously prove the solvability of each step and the unconditional energy stability, and perform a large number of numerical simulations in 2D and 3D to demonstrate its stability and accuracy numerically.

Analyzing the Impact of Subsidies on Beef Production Efficiency in Selected European Union Countries. A Stochastic Metafrontier Approach

The European Union Common Agricultural Policy reforms since the early 2000s allowed for the implementation of different types of agricultural subsidies, such as direct support in the form of decoupled and coupled payments, or agri‐environmental payments. As a result, there are significant differences in agricultural subsidies granted in each member state of the European Union. However, there is limited cross‐country comparative empirical evidence regarding the effects of the implementation of different levels and types of subsidies on farm efficiency. Using farm level data for beef farms in Ireland, France, Great Britain, and Germany between 2005 and 2012, we implement the stochastic metafrontier proposed by Huang et al. (2014) and attempt to correct for endogeneity applying the method in Shee and Stefanou (2015). Using these approaches, we contribute to the literature by consistently comparing cross‐country farm performance, as well as exploring the disaggregated effects of different types of subsidies on farm level technical efficiency and on the technology gaps. Our estimates show that although beef farms included operate on average close to the global frontier, there is scope to improve farm level managerial performance. However, they do operate close to the global frontier, although not on it. We also find evidence that implementing full decoupling benefited efficiency, whereas implementing partial decoupling might have hindered technical efficiency improvements for beef farms, as well as technology catch up.

On a novel fully-decoupled, linear and second-order accurate numerical scheme for the Cahn–Hilliard–Darcy system of two-phase Hele–Shaw flow

We construct a novel fully-decoupled and second-order accurate time marching numerical scheme with unconditional energy stability for the Cahn–Hilliard–Darcy phase-field model of the two-phase Hele–Shaw flow, in which, the key idea to realize the full decoupling structure is to use the so-called “zero-energy-contribution” function and design a special ordinary differential equation to deal with the nonlinear coupling terms between the flow field and the phase-field variable. Compared with the existing decoupling type schemes, the scheme developed here is more effective, efficient and easy to implement. At each time step, one only needs to solve a few fully-decoupled linear equations only with constant coefficients. We also strictly prove the solvability and unconditional energy stability of the scheme, and implement various numerical simulations in 2D and 3D to show the efficiency and stability of the proposed scheme numerically.

A novel decoupled second-order time marching scheme for the two-phase incompressible Navier–Stokes/Darcy coupled nonlocal Allen–Cahn model

We construct a novel second-order time marching scheme with the full decoupling structure to solve a highly coupled nonlinear two-phase fluid flow system consisting of the nonlocal mass-conserved Allen–Cahn equation where two types of flow regimes are considered (Navier–Stokes and Darcy). We achieve the full decoupled structure by introducing a nonlocal variable and designing an additional ordinary differential equation for it which plays the key role to maintain the unconditional energy stability. The whole scheme is built upon the pressure correction/ quadratization approach for the fluid equation and nonlinear double-well potential, respectively. At each time step, one only needs to solve several independent elliptic equations with constant coefficients illustrating the high practical efficiency. We strictly prove that the scheme satisfies the unconditional energy stability, and carry out various numerical simulations to prove its stability and accuracy numerically, such as spinodal decomposition and fingering instability due to the continuous injection flow, etc.