Local Boundary Conditions Research Articles

Nonlinear ultrasonic waves in a magneto-flexo-thermally actuated single walled armchair carbon nanotube embedded on polymer matrix

PurposeThe purpose of this paper is concerned with the study of nonlinear ultrasonic waves in a magneto-flexo-thermo (MFT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix.Design/methodology/approachA mathematical model is developed for the analytical study of nonlinear ultrasonic waves in a MFT elastic armchair single walled carbon nanotube rested on polymer matrix using Euler beam theory. The analytical formulation is developed based on Eringen’s nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analysed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations.FindingsFrom the literature survey, it is evident that the analytical formulation of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix is not discussed by any researchers. So, in this paper the analytical solutions of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix are studied. Parametric studies is carried out to scrutinize the influence of the nonlocal scaling, magneto-electro-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter and tube geometrical parameters have significant effects on dimensionless frequency of nanotubes.Originality/valueThis paper contributes the analytical model to find the solution of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix. It is observed that the increase in the foundation constants raises the stiffness of the medium and the structure is able to attain higher frequency once the edge condition is C-C followed by S-S. Further, it is noticed that the natural frequency is arrived below 1% in both local and nonlocal boundary conditions in the presence of temperature coefficients. Also, it is found that the density and Poisson ratio variation affects the natural frequency with below 2%. The results presented in this study can provide mechanism for the study and design of the nano devices such as component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro--magneto-mechanical systems that make use of the wave propagation properties of ASWCNTs embedded on polymer matrix.

Generalization of Perfect Electromagnetic Conductor Boundary

Certain classes of electromagnetic boundaries satisfying linear and local boundary conditions can be defined in terms of the dispersion equation of waves matched to the boundary. A single plane wave is matched to the boundary when it satisfies the boundary conditions identically. The wave vector of a matched wave is a solution of a dispersion equation characteristic to the boundary. The equation is of the second order, in general. Conditions for the boundary are studied under which the dispersion equation is reduced to one of the first order or to an identity, whence it is satisfied for any wave vector of the plane wave. It is shown that, boundaries associated to a dispersion equation of the first order, form a natural generalization of the class of perfect electromagnetic conductor (PEMC) boundaries. As a consequence, the novel class is labeled as that of generalized perfect electromagnetic conductor (GPEMC) boundaries. As another case, boundaries for which there is no dispersion equation (NDE) for the matched wave (because it is an identity) are labeled as NDE boundaries. They are shown to be special cases of GPEMC boundaries. Reflection of the general plane wave from the GPEMC boundary is considered and an analytic expression for the reflection dyadic is found. Some numerical examples on its application are presented for visualization.

Spectral-element formulation of multi-transmitting formula and its accuracy and stability in 1D and 2D seismic wave modeling

Application of local artificial boundary conditions in high-efficient spectral element method (SEM) is a problem that needs further study, where difficulties focus on how to design an appropriate numerical scheme of artificial boundaries that is in good accordance with the unequally-spaced grid nodes and high-order property of the element. Liao's local artificial boundary, i.e. multi-transmitting formula (MTF), provides a convenient way of implementing arbitrary-order displacement-type boundaries because it is defined directly in discrete form and can be transformed into numerical schemes by using merely some interpolation approaches. A new set of numerical schemes of MTF is developed and its accuracy and stability are thoroughly discussed in the application of spectral-element simulation of 1D and 2D seismic wave propagation. The new MTF scheme cannot be written into a binomial form like the traditional one does. This fact has a significant influence on numerical properties of high-order boundary, but merely slightly affects the performance of lower-order boundaries which are daily used in practical simulations. Numerical examples compared with viscous-spring or perfectly matched layer (PML) boundary exhibits that stable and quite good accuracy can be achieved by using the proposed method.

Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method

We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the local and nonlocal problem domains, and the virtual controls are the nonlocal volume constraint and the local boundary condition. We present the method in the context of Local-to-Nonlocal diffusion coupling. Numerical examples illustrate the theoretical properties of the approach.

Generalized elastodynamic model for nanophotonics

A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with spatial dispersion have been solved by the introduction of the so-called Additional Boundary Conditions. In this paper, we derive an approach where non-local effects are studied in a precise and uniquely defined way, thus allowing the treatment of all solid-solid interfaces (metals, semiconductors or insulators), as well as solid-vacuum interfaces in the same framework. The theory is based on the derivation of a potential energy for an ensemble of electrons in a given potential, where the deformation of the ensemble is treated as in a solid, including both shear and compressional deformations, instead of a fluid described only by a bulk compressibility like in the hydrodynamical approach. The derived classical equation of motion for the ensemble describes the deformation vector and the corresponding polarization vector as an elastodynamic field, including viscous forces, from which a generalized non-local constitutive equation for the dielectric constant is derived. Boundary conditions are identical to that of elastodynamics and they emerge in a natural way, without any physical hypothesis outside the current description, as it is commonly required in other non-local approaches. This description does not require the discontinuity of any component of the electric, magnetic or polarization fields and, consequently, no bounded currents or charges are present at the interface, which is a more suitable description from the microscopic point of view. It is shown that the method converges to the local boundary conditions in the low spatial dispersion limit for insulators and conductors, quantified by means of a parameter defined as the "characteristic length".

Effect of boundary conditions and constitutive relations on the free vibration of nonlocal beams

The free vibrations of nonlocal Euler and Timoshenko beams have been studied extensively, but there still remain some problems concerning boundary conditions and constitutive relations. For cantilever beams, a counterintuitive stiffening phenomenon is widely observed. And to the best of the authors’ knowledge, there is no work concerning about the Timoshenko beam with nonlocal shear force and local bending moment. This work reconsiders and explains these problems based on nonlocal differential theory. After obtaining the governing equation for nonlocal Euler beam, it is observed that the governing equation has the same form as that for the vibration of local beam with axial compressive force. Thus by comparing the nonlocal effects to the effects of end axial force, the stiffening phenomenon of cantilever beams is found to be caused by a meaningless term in boundary bending moment. This explanation is also suitable for nonlocal Timoshenko cantilever beams. Besides, for Timoshenko beams, the nonlocal effects on tensile and shear stress constitutive relations are considered separately. Three kinds of nonlocal Timoshenko beam models are solved. Numerical comparison shows that the effects of nonlocal tensile are bigger than that of nonlocal shear stress. Especially, for Timoshenko beams with nonlocal shear force only, the nonlocal effects lower the natural frequency for all boundary conditions. This finding can verify our explanation for the stiffening phenomenon of cantilever beams. In addition, it is also observed that, for both nonlocal beam theories, if all nonlocal internal forces are included in the governing equations, the eigenvalue equations and natural frequencies corresponding to local and nonlocal boundary conditions are the same.

Dynamic Pore-Scale Network Modeling of Spontaneous Water Imbibition in Shale and Tight Reservoirs

Spontaneous water imbibition plays an imperative role in the development of shale or tight oil reservoirs. Spontaneous water imbibition is helpful in the extraction of crude oil from the matrix, although it decreases the relative permeability of the hydrocarbon phase dramatically. The dynamic pore-scale network modeling of water imbibition in shale and tight reservoirs is presented in this work; pore network generation, local capillary pressure function, conductance calculation and boundary conditions for imbibition are all presented in detail in this paper. The pore network is generated based on the characteristics of Barnett shale formations, and the corresponding laboratory imbibition experiments are matched using this established dynamic pore network model. The effects of the wettability, throat aspect ratio, viscosity, shape factor, micro-fractures, etc. are all investigated in this work. Attempts are made to investigate the water imbibition mechanisms from a micro-scale perspective. According to the simulated results, wettability dominates the imbibition characteristics. Besides this, the viscous effects including viscosity, initial capillary pressure and micro-fractures increase the imbibition rate, while the final recovery factor is more controlled by the capillarity effect including the cross-area shape factor, contact angle and the average pore-throat aspect ratio.

Risk analysis of High-Temperature Aquifer Thermal Energy Storage (HT-ATES)

The storage of heat in aquifers, also referred to as Aquifer Thermal Energy Storage (ATES), bears a high potential to bridge the seasonal gap between periods of highest thermal energy demand and supply. With storage temperatures higher than 50 °C, High-Temperature (HT) ATES is capable to facilitate the integration of (non-)renewable heat sources into complex energy systems. While the complexity of ATES technology is positively correlated to the required storage temperature, HT-ATES faces multidisciplinary challenges and risks impeding a rapid market uptake worldwide. Therefore, the aim of this study is to provide an overview and analysis of these risks of HT-ATES to facilitate global technology adoption. Risk are identified considering experiences of past HT-ATES projects and analyzed by ATES and geothermal energy experts. An online survey among 38 international experts revealed that technical risks are expected to be less critical than legal, social and organizational risks. This is confirmed by the lessons learned from past HT-ATES projects, where high heat recovery values were achieved, and technical feasibility was demonstrated. Although HT-ATES is less flexible than competing technologies such as pits or buffer tanks, the main problems encountered are attributed to a loss of the heat source and fluctuating or decreasing heating demands. Considering that a HT-ATES system has a lifetime of more than 30 years, it is crucial to develop energy concepts which take into account the conditions both for heat sources and heat sinks. Finally, a site-specific risk analysis for HT-ATES in the city of Hamburg revealed that some risks strongly depend on local boundary conditions. A project-specific risk management is therefore indispensable and should be addressed in future research and project developments.

An innovative semi-analytical determination approach to numerical loaded tooth contact analysis (NLTCA) for spiral bevel and hypoid gears

Loaded tooth contact analysis (LTCA) has always been a significant contact mechanical performance optimization technique for spiral bevel and hypoid gears. To distinguish with the conventional simulated loaded tooth contact analysis (SLTCA) based on economical software package, numerical loaded tooth contact analysis (NLTCA) and its innovative semi-analytical determination approach is developed. In full consideration of tooth flank flexural behavior characteristic, double-curved shell finite element modeling is performed and then improved tooth contact analysis (TCA) is applied for data-driven determination of loaded tooth contact points. Then, in additional to the global boundary condition, the accurate local boundary conditions is also investigated. In particular, local Rayleigh-Ritz method is used to get new semi-analytically tooth compliance determination by considering computational accuracy and efficiency. Furthermore, NLTCA model is established in considerations of the accurate contact point matching, compatibility and equilibrium conditions. Finally, the main NLTCA evaluations including load distribution, loaded contact pattern, loaded contact pressure and distribution, and loaded transmission error in consideration of time-varying meshing characteristics, respectively. The provided numerical instance can verify the proposed methodology.

Quantum chaos, thermodynamics and black hole microstates in the mass deformed SYK model

We study various aspects of the mass deformation of the SYK model which makes the black hole microstates escapable. SYK boundary states are given by a simple local boundary condition on the Majorana fermions and then evolved in Euclidean time in the SYK Hamiltonian. We study the ground state of this mass deformed SYK model in detail. We also use SYK boundary states as a variational approximation to the ground state of the mass deformed SYK model. We compare variational approximation with the exact ground state results and they showed a good agreement. We also study the time evolution of the mass deformed ground state under the SYK Hamiltonian. We give a gravity interpretation of the mass deformed ground state and its time evolutions. In gravity side, mass deformation gives a way to prepare black hole microstates that are similar to pure boundary state black holes. Escaping protocol on these ground states simply gives a global AdS2 with an IR end of the world brane. We also study the thermodynamics and quantum chaotic properties of this mass deformed SYK model. Interestingly, we do not observe the Hawking Page like phase transition in this model in spite of similarity of the Hamiltonian with eternal traversable wormhole model where we have the phase transition.

Applications of the local gradient elasticity to the description of the size effect of shear modulus

The classical theory of elasticity does not describe the experimentally observed phenomenon of change in the mechanical characteristics of the material in micro/nano-scale structures. In the present paper, it is shown that a local gradient theory of elasticity describes the size effect of the shear modulus in thin strips. The mentioned theory is based on taking account of non-convective and non-diffusive mass flux associated with the changes in the material microstructure. In the paper, the governing differential equations of the local gradient mechanics and related boundary conditions are obtained by implementing a variational principle. Based on these equations, the stationary stress–strain state of an infinite isotropic strip whose surfaces are subjected to shear displacements is studied. It is shown that in thin strips, the displacement profile deviates significantly from the linear law predicted by the classical theory. Using the solution to this boundary value problem, a formula that describes the size effect of shear modulus is proposed. Such a study is important for modeling micro- and nano-mechanical structures that are widely used in modern technologies.

Modelling strain rate and temperature dependent mechanical response of PMMAs at large deformation from below to above Tg

The potential and the interest of the development of mechanical approach based on concepts issued from the physics of polymers, as well as of the use of the time temperature equivalence principle, are illustrated. To achieve that point, a revisited constitutive model [1], [2] was used to model the mechanical behaviour of amorphous PMMA with different molecular weights. The model accounts for the elastic contribution of an equivalent network which experiences inelastic mechanisms coming from the evolution of internal state variables when the polymer is deformed. The experimental database included non-monotonic tensile tests at targeted “equivalent strain rate at reference temperature” coupled with DIC for obtaining local boundary conditions. Model exhibited good capabilities to capture the mechanical response of the material at different temperatures and strain rates corresponding to material state ranging from the end of the glassy state to near-liquid state going through viscoelastic and rubbery regime. Analysis of the parameters allowed introducing empirical equations to consider the time/temperature dependence into the model. It was possible to pretty well reproduce the behaviour of PMMAs from rubbery like domains to their glassy state with one unique formalism and one unique and of reduced number set of parameters. Effect of molar mass and crosslinking are discussed.

A Re-Examination of Wave Dispersion and on Equivalent Spatial Gradient of the Integral in Bond-Based Peridynamics

In this paper, wave dispersion properties in bond-based peridynamics (BBPD) are re-examined. By BBPD formulation, wave dispersion (frequency (ω) - wavenumber (k)) relation is known to be transcendental in nature. In fact, for uniform micromodulus function (C), there exists a frequency bandwidth with multiple k. Further, there is a ω within this bandwidth at which propagating k are infinite in number. Question that needs an answer is can all k propagate in the BBPD? In literature, an agreement between certain continuum gradient models (CM) and BBPD has been reported. This agreement is established in the sense that, for a judicious choice of C, wave dispersion properties are the same between BBPD and CM. This equivalence between a finite-ordered (CM) and an infinite-ordered (BBPD) displacement gradient model motivates to an associated converse question: given a C, does BBPD integral represent an effective displacement gradient of a finite order? In this paper, an attempt has been made to fix an order to the BBPD integral with the help of a Fourier frequency-based spectral study, under a one-dimensional rod setting. Both kinetically local and nonlocal formulations of BBPD are considered. It is argued that only one wave mode may propagate in a BBPD rod. This implies, Neumann force condition at a boundary should read as a spatial gradient of order one. This further implies, the BBPD spatial integral effectively represents a second-order displacement gradient in space. The wave motion study of this paper corroborates with the literature that applies local boundary conditions to nonlocal boundary value problems.

The glacial landsystem of Fjallsjökull, Iceland: Spatial and temporal evolution of process-form regimes at an active temperate glacier

This study assesses the spatial and temporal evolution of the glacial landsystem signature at Fjallsjökull, southeast Iceland, using (a) mapping of the glacial geomorphology and surficial geology and (b) repeat uncrewed aerial vehicle (UAV) surveys. A small-scale (1: 15,000 scale) landsystem map has been compiled using LiDAR data (2011−2012) and historical aerial photographs (1945–1998), along with a large-scale (1: 2000 scale) map based on UAV imagery from May 2019. From our mapping and UAV surveys, we identify sediment-landform assemblages that are typical of active temperate glacial landsystems, including recessional push/squeeze moraines and intervening flutings, overridden moraine arcs, proglacial outwash (sandur) fans and linear/ribbon sandar. We recognize three landform zones that are defined by changes in moraine morphology and the nature of proglacial outwash deposition: (1) the outer foreland is characterized by proglacial outwash fans, overridden moraine arcs and broadly linear recessional moraines; (2) the middle foreland contains sawtooth moraines and linear sandar; and (3) the innermost zone comprises extremely sawtooth and hairpin moraines as well as associated crevasse-squeeze ridge limbs. This landform zonation reflects spatio-temporal changes in moraine-forming processes and outwash deposition as determined by changes in snout morphology and proglacial drainage characteristics. Within this general tripartite zonation, we also identify localized (azonal/intrazonal) sediment-landform assemblages that are not typically found at active temperate glaciers, including ice-cored/hummocky terrain and localized kame and kettle topography. Repeat UAV surveying in 2016–2019 has allowed us to capture and quantify recent intrazonal landsystem change at the southern glacier margin. We identify a switch from moraine formation to the development of ice-cored terrain and an ice-cored esker complex in association with the uncovering of a depositional overdeepening. Our study demonstrates the important role that variations in local boundary conditions (e.g. topography) can play in the process-form response of individual active temperate outlet glaciers, contributing to the expanding database on modern glacial landsystems.

Existence and multiplicity of positive radial solutions to the Dirichlet problem for nonlinear elliptic equations on annular domains

In this paper, we study the existence and nonexistence of mono- tone positive radial solutions of elliptic boundary value problems on bounded annular domains subject to local boundary condition. By using Krasnoselskii's xed point theorem of cone expansion-compression type we show that there exists > 0 such that the elliptic equation has at least two, one and no radial positive solutions for 0 respectively. We include an example to illustrate our results.

Adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media (ADM-LTS)

We present ADM-LTS, an adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media. At each time step, firstly, the flow (pressure) solution is obtained. Then, the transport equation is solved using the ADM-LTS method, which consists of two stages. In the first stage, an initial solution is obtained by imposing the coarsest space-time grid. This initial solution is then improved, in the second stage, by imposing a space-time adaptive grid on the cells where the solution does not satisfy the desired quality. The quality control is based on error estimators with user-defined threshold values. The time-integration procedure, in which the coarsest-scale solution provides local flux boundary conditions for sub-domains with local time refinement, is strictly mass conservative. In addition, the method employs space-time fine grid cells only at the moving saturation fronts. In order to ensure local mass conservation at all levels, finite-volume restriction operators and unity prolongation operators are developed. Several numerical experiments have been performed to analyze the efficiency and accuracy of the proposed ADM-LTS method for both homogeneous and heterogeneous permeability fields on two and three dimensional domains. The results show that the method provides accurate solutions, at the same time it maintains the computational efficiency. The ADM-LTS implementation is publicly available at https://gitlab.com/darsim2simulator.

On Nonlocal Problems with Inhomogeneous Local Boundary Conditions

This work aims to provide a comprehensive treatment on how to enforce inhomogeneous local boundary conditions (BC) in nonlocal problems in 1D. In prior work, we have presented novel governing operators with homogeneous BC. Here, we extend the construction to inhomogeneous BC. The construction of the operators is inspired by peridynamics. The operators agree with the original peridynamic operator in the bulk of the domain and simultaneously enforce local Dirichlet or Neumann BC. We explain methodically how to construct forcing functions to enforce local BC and their relationship to initial values. We present exact solutions with both homogeneous and inhomogeneous BC and utilize the resulting error to verify numerical experiments. We explain the critical role of the Hilbert-Schmidt property in enforcing local BC rigorously. For the Neumann BC, we prescribe an interpolation strategy to find the appropriate value of the forcing function from its derivative. We also present numerical experiments with unknown solution and report the computed displacement and strain fields.

Numerical solution of coupled nonlinear Schrödinger equations on unbounded domains

In this paper, we investigate the numerical solution of general N-coupled nonlinear Schrödinger equations on unbounded domains, that describe the multiple solitary waves in physics. Due to the unboundedness of the physical domain and strong nonlinearity, how to design appropriate numerical approach to obtain the numerical solution and simulate the real physical phenomena is a major challenge. Based on the ideas of artificial boundary method and operator splitting approach, we develop local artificial boundary conditions for the N-coupled nonlinear Schrödinger equations on the introduced artificial boundaries. Then the original initial value problem was reduced into an initial boundary value problem on the truncated computational domain, which can be solved by the finite difference method efficiently. We rigorously prove the stability of the reduced problem by introducing a series of auxiliary variables, which are vital to overcome the difficulty of the mixed partial derivatives in the local artificial boundary conditions. Numerical simulations are also presented to validate accuracy and the stability of our proposed method.

Evaluation of automotive shredder residues (ASR) landfill behavior through lysimetric and traditional leaching tests.

With regards to European wastecatalog, automotive shredder residues (ASR) can be classified both as a hazardous or non-hazardous waste according to its hazardous properties (H1-H14). It is thus important to carry out an adequate chemical-physical characterization to identify the presence and concentration of those substances able to give, to this extremely heterogeneous material, the hazardousness character of. The issue of waste characterization, to identify the proper site for appropriate waste disposal, is based, according to the relevant laws, to the use of leaching tests. The analysis of the potential effects of landfilled waste in laboratory, however, run into several difficulties in reproducing phenomena depending both on the characteristics of small, heterogeneous quantity of waste and on the local boundary conditions. These difficulties are much more significant as the waste is heterogeneous at the small scale of the laboratory. This is one of the main problems often leading to scattered results even when starting from the same waste parcel. Present research aimed to overcome the above-mentioned difficulties deriving from waste heterogeneity and was based on a lysimetric simulation. Experimentation with lysimeter has shown it effectiveness in the comparison between leachate from the lysimeter and an ASR landfill leachate, from which similar distribution of metal mass ratios, close values for both BOD5 and COD, as well as the absence in both the fluids of organochlorinated compounds, emerge.

Full-field identification of mixed-mode adhesion properties in a flexible, multi-layer microelectronic material system

The identification of relevant adhesion properties is important for the development of microelectronic systems, e.g., microprocessors, light-emitting diodes, etc. This is best done on an actual device, rather than on dedicated specimens, because such properties are highly specimen specific. This paper discusses how the full-field identification method of integrated digital image correlation (IDIC) can be used to identify three mixed-mode cohesive zone parameters of a flexible, organic light-emitting diode (OLED) from a single mechanical test. A tri-axial, micro-mechanical testing setup is employed for the in situ, on-device delamination experiment, employing optical microscopy.The microscopic magnification, required for capturing the relevant kinematics, prevents the experimentally imposed loading conditions to be captured within the field of view. Virtual experiments are firstly conducted to optimize the local boundary conditions therefore required by the finite element simulation within the IDIC-framework, and which constitutes the cohesive zone model. The virtual experiments also allow for selecting an adequate load-case for the actual experiment, in order to maximize the kinematic sensitivity of IDIC with respect to the three mixed-mode cohesive zone parameters, and identify them accurately. The image residual, minimized in IDIC, together with the convergence behavior towards the associated global minimum, provide adequate measures for assessing the trustworthiness of the solution.The optimized load-case is subsequently used to trigger delamination of a 50 [μm] thick barrier stack from its substrate in a real in situ experiment on a flexible OLED. The optimized boundary conditions from the virtual experiments are used in a corresponding simulation for identifying the three mixed-mode cohesive zone parameters by IDIC. The optimization scheme within IDIC was found to be robust against deviating initial guesses, and consistently converged to a unique solution for the cohesive zone parameters.