Interface Problems Research Articles

A New Class of Lithium Conductive Polymers for Solid State Lithium Metal Batteries at Room Temperature

Lithium-ion batteries (LIBs), among various secondary battery technologies, have received a significant amount of attention in the last decades, becoming the most successful commercial batteries. Extensively used in portable electronics, electric vehicles, and energy storage stations, LIBs meet many challenges, such as safety problems, low energy densities and so on, which drives much research toward developing the next generation of battery technology. Solid-state batteries emerge as one of the most potential alternatives for mainstream LIBs. Polymer-based solid-state electrolytes (SSEs) have been widely studied due to their softness and flexibility, relieving interface problems between electrodes and separators, especially compared with inorganic solid electrolytes. However, their limitations, such as limited Li+ conductivity or narrow electrochemical windows (< 4 V), restrict their potential applications. In this presentation, a new type of polymer (PG23), developed by Piersica Inc. (www.piersica.com) were applied as excellent binder to organic electrolyte based LIBs, and also to all solid state LIBs. Solid state electrolyte (SSEs) based on the polymer PG23 exhibits impressive conductivity (0.1 mS/cm) at room temperature and extremely high oxidized stability (approx. 4.9 V). When the SSEs was applied to both solid cathode (NMC622 as active material) and SSEs, combined with Li metal as anode, the LIBs demonstrated excellent capacity and cycling stability operating at room temperature. This polymer from Piersica Inc. exhibits considerable promise for the development and enhancement of solid-state batteries.

Study on the interface of high specific energy High stability

High nickel terterial oxide, with high specific capacity and low cost advantages, is the preferred positive electrode for high specific energy lithium-ion power batteries at present. However, the high nickel ternary cathode material is easy to have side reactions with the electrolyte in the high delithium state, which can not only lead to the dissolution of transition metal ions and the formation of the surface salt phase, but also cause the lattice oxygen loss and surface interface side reactions, resulting in rapid attenuation of electrode capacity. In this paper, the development history and structural characteristics of high nickel ternary cathode materials are introduced, and the surface interface problems leading to capacity attenuation and structural degradation are comprehensively analyzed. From this perspective, three effective strategies for improving electrochemical performance of high nickel ternary cathode materials are summarized. Finally, by describing the advantages and disadvantages of these layered cathode materials, the challenges faced by these layered cathode materials are discussed, and it is pointed out that in the future, composite modification strategies should be adopted to optimize their structures and improve their properties.

Optimum design of uniform and non-uniform infill-coated structures with discrete variables

This article introduces a novel computer-aided procedure to design optimised coated structures with precise shell thickness control using the Smallest Univalue Segment Assimilating Nucleus operator and a novel augmentation-projection technique. Structures with heterogeneous sections, or coated structures, combine two different materials for the nucleus and the shell, which are generally chosen so that the material in the infill is lighter and the material in the coating is stiffer, which in this work are supposed homogeneous. Solving the interface problem requires material properties interpolation equations that consider three material phases, accurate placement of the coating over the base material, and precise control over the coating's thickness. The formation of the coating is controlled by the Smallest Univalue Segment Assimilating Nucleus, an edge detection operator developed in Digital Image Processing. The coating's thickness is controlled by an innovative methodology consisting of the projection of an augmented contour field, which is shown to create a constant thickness coating around the material domain. The optimisation problem is solved with the Sequential Element Rejection and Admission method. The validity of the procedure has been verified by solving various numerical application examples.

Generalized weak Galerkin finite element method for linear elasticity interface problems

Generalized weak Galerkin finite element method for linear elasticity interface problems

Hybrid Haar wavelet and meshfree methods for hyperbolic double interface problems: Numerical implementations and comparative performance analysis

This paper introduces a variety of approaches for solving 2D and 3D hyperbolic double interface problems. The methods are based on the Haar wavelet method, multiquadric radial basis function method, and integrated multiquadric radial basis function method. Temporal derivatives are handled using the second central difference and the Houbolt method. Various numerical approaches based on these methods are developed, and their implementations are discussed in complete detail. The paper evaluates and compares the performances of these approaches using both linear and nonlinear 2D and 3D double interface hyperbolic problems. Error analysis, conducted using the L-infinity norm, and efficiency assessments measured through CPU times contribute to a comprehensive understanding of the applicability and comparative effectiveness of the proposed methods. This study provides valuable insights for researchers and practitioners dealing with the challenges posed by interface problems in general.

Case Studies – an Indispensable Source of Experience and Knowledge

Owing to the peculiarities of the design environment that structural engineers have to face – an environment where prototypes are designed and erected without intensive and purposeful development and testing – case studies of failures and/or near misses are an indispensable source of experience and knowledge and form the basis for enhancing and updating the set of technical rules and regulations. By discussing actual and historic case studies, the development of the tools and methods of forensic engineering as well as of the findings from these for the design, erection, supervision, inspection and maintenance of civil engineering structures will be addressed. The interface problems, when different parties are involved, are highlighted, and the necessity of establishing a good and reliable co-ordination mechanism is carved out. Because of the increasing fragmentation of the design process, in combination with the use of complex software tools and inevitable pressure of time, often a comprehensive design review process is the last line of defence to avoid incidents due to minor lapses or serious misjudgements.

Solving parametric elliptic interface problems via interfaced operator network

Learning operators mapping between infinite-dimensional Banach spaces via neural networks has attracted a considerable amount of attention in recent years. In this paper, we propose an interfaced operator network (IONet) to solve parametric elliptic interface PDEs, where different coefficients, source terms, and boundary conditions are considered as input features. To capture the discontinuities in both the input functions and the output solutions across the interface, IONet divides the entire domain into several separate subdomains according to the interface and uses multiple branch nets and trunk nets. Each branch net extracts latent representations of input functions at a fixed number of sensors on a specific subdomain, and each trunk net is responsible for output solutions on one subdomain. Additionally, tailored physics-informed loss of IONet is proposed to ensure physical consistency, which greatly reduces the training dataset requirement and makes IONet effective without any paired input-output observations inside the computational domain. Extensive numerical studies demonstrate that IONet outperforms existing state-of-the-art deep operator networks in terms of accuracy and versatility.

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

We present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

Solution of the Elliptic Interface Problem by a Hybrid Mixed Finite Element Method

This paper addresses the elliptic interface problem involving jump conditions across the interface. We propose a hybrid mixed finite element method on the triangulation where the interfaces are aligned with the mesh. The second-order elliptic equation is initially decomposed into two equations by introducing a gradient term. Subsequently, weak formulations are applied to these equations. Scheme continuity is enforced using the Lagrange multiplier technique. Finally, we derive an explicit formula for the entries of the matrix equation representing Lagrange multiplier unknowns resulting from hybridization. The method yields approximations of all variables, including the solution and gradient, with optimal order. Furthermore, the matrix representing the final linear algebra systems is not only symmetric but also positive definite. Numerical examples convincingly demonstrate the effectiveness of the hybrid mixed finite element method in addressing elliptic interface problems.

A Compact Coupling Interface Method with Second-Order Gradient Approximation for Elliptic Interface Problems

A Compact Coupling Interface Method with Second-Order Gradient Approximation for Elliptic Interface Problems

Quantum simulation of Maxwell's equations via Schrödingerisation

We present quantum algorithms for electromagnetic fields governed by Maxwell's equations. The algorithms are based on the Schrödingerisation approach, which transforms any linear PDEs and ODEs with non-unitary dynamics into a system evolving under unitary dynamics, via a warped phase transformation that maps the equation into one higher dimension. In this paper, our quantum algorithms are based on either a direct approximation of Maxwell's equations combined with Yee's algorithm, or a matrix representation in terms of Riemann-Silberstein vectors combined with a spectral approach and an upwind scheme. We implement these algorithms with physical boundary conditions, including perfect conductor and impedance boundaries. We also solve Maxwell's equations for a linear inhomogeneous medium, specifically the interface problem. Several numerical experiments are performed to demonstrate the validity of this approach. In addition, instead of qubits, the quantum algorithms can also be formulated in the continuous variable quantum framework, which allows the quantum simulation of Maxwell's equations in analog quantum simulation.

Decoupling numerical method based on deep neural network for nonlinear degenerate interface problems

Many practical problems, including modeling composite materials, nuclear waste disposal, oil reservoir simulations, and flows in porous medium, commonly involve interface problems. However, the solution to interface problems with discontinuous coefficients of PDEs using fully decoupled numerical methods is challenging. The main objective is to solve the interface problems with fully decoupled numerical methods. This paper proposes an efficient decoupled numerical method for solving degenerate interface problems with double singularities. First, we divide the whole domain into singular and regular subdomains. Then, we use the Deep Neural Network (DNN) to find the solution on the singular subdomain and approximate the solution on the regular subdomain using the finite difference method. The scheme combines the solutions of singular and regular subdomains, which is an exciting idea. The key to the new approach is to split nonlinear degenerate partial differential equations with an interface into two independent boundary value problems based on deep learning. In this way, the expansion of the solution on the singular domain does not contain undetermined parameters, and two independent boundary value problems can be solved with any well-known traditional numerical methods. The main advantage of the proposed scheme is that we not only get the order of convergence of the degenerate interface problems on the whole domain, but we also can calculate VERY BIG jump ratio (such as 1012:1 or 1:1012) for the interface problems including degenerate and non-degenerate cases. Finally, with examples, we demonstrate the efficiency and accuracy of methods for 1 and 2D problems. It is also interesting that the proposed method is valid for the interface problems with degenerate and non-degenerate cases, we show it with some examples.

Concepts for compensation of wave effects when measuring through water surfaces in photogrammetric applications

Abstract. A common problem when imaging and measuring through moving water surfaces is the quasi-random refraction caused by waves. The article presents two strategies to overcome this problem by lowering the complexity down to a planer air/water interface problem. In general, the methods assume that the shape of the water surface changes randomly over time and that the water surface moves around an idle-state (calm planar water surface). Thus, moments at which the surface normal is orientated vertically should occur more frequently than others should. By analysing a sequence of images taken from a stable camera position these moments could be identified – this can be done in the image or object space. It will be shown, that a simple median filtering of grey values in each pixel position can provide a corrected image freed from wave and glint effects. This should have the geometry of an image taken through calm water surface. However, in case of multi camera setups, the problem can be analysed in object space. By tracking homological underwater features, sets of image rays hitting accidently horizontal orientated water surface areas can be identified. Both methods are described in depth and evaluated on real and simulated data.

Well-Posedness of the Two-Dimensional Compressible Plasma-Vacuum Interface Problem

We consider the two-dimensional plasma-vacuum interface problem in ideal compressible magnetohydrodynamics (MHD). This is a hyperbolic-elliptic coupled system with a characteristic free boundary. In the plasma region the 2D planar flow is governed by the hyperbolic equations of ideal compressible MHD, while in the vacuum region the magnetic field obeys the elliptic system of pre-Maxwell dynamics. At the free interface moving with the velocity of plasma particles, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, since it is driven by a given surface current which forces oscillations onto the system. We prove the local-in-time existence and uniqueness of solutions to this nonlinear free boundary problem, provided that at least one of the two magnetic fields, in the plasma or in the vacuum region, is non-zero at each point of the initial interface. The proof follows from the analysis of the linearized MHD equations in the plasma region and the elliptic system for the vacuum magnetic field, suitable tame estimates in Sobolev spaces for the full linearized problem, and a Nash–Moser iteration.

AgF-PEO composite interfacial layer for electrolyte-free LAGP-based lithium metal batteries

NASICON-type LAGP solid state electrolyte has become one of the most promising solid-state electrolytes due to its superior performance such as favorable room-temperature ionic conductivity, high stability in air, wide electrochemically stable window, and low cost. The key constraint to the development of LAGP electrolyte is the LAGP/Li interface problem. In this paper, a composite interfacial layer (AgF@Li-PEO@LAGP) is introduced between LAGP electrolyte and electrode material. The LiF and Ag nanoparticles are generated on the Li surface by utilizing the substitution reaction to uniform lithium flux and prevent the side reaction, while the flexible PEO polymer buffer layer on the LAGP will improve the interface wettability. The Li/LAGP/Li symmetric cell modified with composite interfacial layer can maintain a low polarization voltage of 0.11 V at 0.1 mA cm−2 for stable cycling for more than 1200 h. The full cell also shows excellent cycling stability with the capacity retention of 93.6 % after 100 cycles. The composite interface layer can realize the elimination of liquid electrolyte and greatly reduce interface resistance. This broadens the road for the realization of all-solid-state batteries.

A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems

A High Order Unfitted Finite Element Method for Time-Harmonic Maxwell Interface Problems

A Direct Method for Solving Three-Dimensional Elliptic Interface Problems

A Direct Method for Solving Three-Dimensional Elliptic Interface Problems

A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact

A Finite Difference Method for Two Dimensional Elliptic Interface Problems with Imperfect Contact

Generalization of PINNs for elliptic interface problems

In this letter, we investigate the statistical limits of deep learning for learning solutions of elliptic interface problems from randomly generated data by employing Physics-informed Neural Networks (PINNs). We prove a lower bound and an upper bound for the generalization error of PINNs for solving elliptic interface equations with the Dirichlet boundary condition. In particular, the upper bound on the generalization error of PINNs is obtained by computing the fixed points of the local Rademacher complexity. We show that variations in volume across distinct regions exert influence on the requisite sample complexity. This unveils an underlying principle within the sampling strategy: the sample size of the data is contingent upon the Lebesgue measure of the domain, coupled with the smoothness and dimensionality characteristics of the interface problem. This letter sheds light on the network architecture design for solving interface problems using PINNs.

Synergistic effect of amino and hydroxyl bifunctional modified h-BN on interfacial thermal conductivity in polydimethylsiloxane matrix: Simulations and experiments

As a widely used thermal conductive matrix material, the interface problem between polydimethylsiloxane (PDMS) and thermal conductive fillers needs to be solved urgently. The interfacial heat transfer mechanism between PDMS and hexagonal boron nitride (h-BN) modified by different groups was studied by combining density functional theory (DFT) simulation and molecular dynamics (MD) simulation. The bi-functionalization of h-BN was achieved by the environmentally friendly 6-aminocaproic acid (ACA) additive-assisted water ball milling process. The h-BN/PDMS composite thermal interface materials were prepared using a simple rolling method. The thermal conductivity of the obtained sample reached 1.256 W m−1 K−1 at a filler loading of 15 wt%. The proposed bifunctional synergistic heat transfer mechanism is expected to provide theoretical guidance for the preparation of high thermal conductivity and insulating PDMS used in electronic communications.