Boundary Conditions In Order Research Articles

Study of gravastar admitting Tolman IV spacetime in Rastall theory

In this paper, we present a novel solution representing the gravastar (or gravitational vacuum star) model within the framework of non-conservative Rastall gravity. As a viable alternative to black holes, the geometry of a gravastar comprises three distinct regions: the inner sector, the intermediate layer, and the exterior domain. Utilizing the temporal component of Tolman IV spacetime, we derive the singularity-free radial metric potentials for both the inner and intermediate regions. Further, by aligning the thin shell with the external Schwarzschild line element, we establish boundary conditions in order to determine unknown constants that appear due to the chosen ansatz and performing some integrations. Subsequently, we investigate various properties for the gravastar’s shell, including the equation of state parameter, proper length, energy, entropy and gravitational redshift for four different values of the Rastall parameter. It is concluded that the gravastar structure exists and provides a feasible substitute of black holes in the framework of Rastall theory.

Responsiveness and Precision of Digital IMUs under Linear and Curvilinear Motion Conditions for Local Navigation and Positioning in Advanced Smart Mobility.

Sensors based on MEMS technology, in particular Inertial Measurement Units (IMUs), when installed on vehicles, provide a real-time full estimation of vehicles' state vector (e.g., position, velocity, yaw angle, angular rate, acceleration), which is required for the planning and control of cars' trajectories, as well as managing the in-car local navigation and positioning tasks. Moreover, data provided by the IMUs, integrated with the data of multiple inputs from other sensing systems (such as Lidar, cameras, and GPS) within the vehicle, and with the surrounding information exchanged in real time (vehicle to vehicle, vehicle to infrastructure, or vehicle to other entities), can be exploited to actualize the full implementation of "smart mobility" on a large scale. On the other hand, "smart mobility" (which is expected to improve road safety, reduce traffic congestion and environmental burden, and enhance the sustainability of mobility as a whole), to be safe and functional on a large scale, should be supported by highly accurate and trustworthy technologies based on precise and reliable sensors and systems. It is known that the accuracy and precision of data supplied by appropriately in-lab-calibrated IMUs (with respect to the primary or secondary standard in order to provide traceability to the International System of Units) allow guaranteeing high quality, reliable information managed by processing systems, since they are reproducible, repeatable, and traceable. In this work, the effective responsiveness and the related precision of digital IMUs, under sinusoidal linear and curvilinear motion conditions at 5 Hz, 10 Hz, and 20 Hz, are investigated on the basis of metrological approaches in laboratory standard conditions only. As a first step, in-lab calibrations allow one to reduce the variables of uncontrolled boundary conditions (e.g., occurring in vehicles in on-site tests) in order to identify the IMUs' sensitivity in a stable and reproducible environment. For this purpose, a new calibration system, based on an oscillating rotating table was developed to reproduce the dynamic conditions of use in the field, and the results are compared with calibration data obtained on linear calibration benches.

Numerical investigation of heat transfer improvement in a latent thermal energy storage system using a composite of phase change material and nanoparticles in a porous medium

In the present study, the flow field and heat transfer in an energy storage tank are simulated. The Phase Change Material (PCM) in the present study is paraffin, which is converted to a liquid phase by the introduction of a high-temperature fluid (80 °C) and then the cold fluid enters the flow-carrying tubes, causing the melt to freeze. In the freezing (discharge) phase, the heat released from it increases the temperature of the fluid. Tubes in tank configurations are also used in latent thermal energy storage, which also performs well in terms of heat transfer. In this research, the use of special geometry with special and practical boundary conditions in order to estimate the charging and discharging behavior of the process of melting and freezing nano-phase change materials in it, as well as the instantaneous examination of the temperature field, melting and freezing by using a computer code using the finite volume method, can distinguish the results of this research from other studies. The results of this research show that, the shape of the tube and storage tank is slightly different from the shell-tube type, in which the Heat Transfer Fluid (HTF) flows through the tubes and these tubes also pass through a PCM tank. The study of the effect of porosity coefficient of porous medium shows that the rate of phase changes in porous medium with porosity coefficient of 0.95 is more than porosity coefficient of 0.97. In addition, by adding nanoparticles to paraffin the melting process takes place in a short time. According to the results, the nanoparticles added to the PCM accelerate heat transfer while maintaining energy storage capacity.

A novel continuum dislocation density field-based crystal plasticity theory

In this work, a novel dislocation density field-based crystal plasticity formulation, that incorporates up-scaled continuum dislocation density fields to represent all possible characters of the dislocation density, is presented. The continuum dislocation field theory, formulated assuming large strain kinematics, is based on an all-dislocation concept, whereby individual dislocation density types are described as vector fields. The evolutionary behaviour of the dislocation density fields is defined in terms of a glide component derived from the classical general conservation law for dislocation density fields proposed originally by Kroner and Acharya, a rotation one given by the curl of the dislocation velocity vector as proposed originally by Ngan and co-workers, and a statistically stored dislocation source/sink component.The proposed formulation has been numerically implemented within the finite element method using a modified up-wind stabilisation approach, which results on eight extra independent nodal degrees of freedom per slip system, associated with the upscaled dislocation densities of pure edge and screw character. Furthermore, the required boundary conditions are simple: initial total dislocation density and dislocation flux or velocity, without the need for higher order boundary conditions. Full details of the numerical implementation of the crystal plasticity theory are given.The theory is then used to investigate classical boundary value problems involving 1D and 2D dislocation pile-ups, and the development of boundary layers in a deforming single crystal strip under constrained conditions. The main general understanding that emerges from the case studies is that, as either the dislocation pile-ups or the boundary layers develop with deformation, geometrically necessary dislocations are generated and lead to an overall behaviour that is size-dependent. Furthermore, it is shown that, in the absence of sources or sinks, which are statistically stored in nature, that total number of dislocations in the pile-up problems is preserved. The numerical predictions of the 1D pile-up and strip simple shear problems are in good agreement with published solutions.

Boundary conditions for micromagnetism with spin currents

In this paper we show how the spin current in insulating ferromagnets can be treated in the micromagnetic framework by generalizing the boundary conditions in order to allow for the transport of magnetic moment and energy at the interface with other spin carrying media. As specific examples we demonstrate the spin Hall torque and spin pumping effects for a ferromagnetic layer in contact with a spin Hall metallic layer. In particular we show how by this method we can reproduce the known literature result in the case of thin films and make predictive examples for thick ferromagnets.

Nudging based computational wind engineering simulation of the Atmospheric Boundary Layer

Modeling homogeneous Atmospheric Boundary Layers (ABLs) in Computational Wind Engineering (CWE) requires that all of the conservation equations are in equilibrium. A standard approach is to apply appropriate boundary conditions in order to maintain the inlet prescribed ABL profiles. Recently, the investigation has turned to the implementation of suitable source terms in the momentum equation. In the present work, the ABL is numerically simulated for neutral, stable and unstable atmosphere using nudging, a type of Data Assimilation. Simulations were performed with an in-house code that solves the Reynolds-averaged Navier-Stokes equations and the standard k-ε turbulence model in steady state. The prescribed inlet flow profiles correspond to the reference data, which is used to define the nudging source terms that are added to the equations. The source terms play a role resembling a body-force and a source-sink mechanism in the momentum and TKE equations, respectively. This novel approach is shown to be reliable in ensuring streamwise homogeneity, under both neutral and non-neutral conditions, for the equilibrium ABL.

Assessment of Soil–Structure Interaction Effects on the Beirut Port Silos Due to the 4 August 2020 Explosion: A Coupled Eulerian–Lagrangian Approach

Blast loadings have become the subject of research in recent decades due to the threats they pose to the surrounding medium. On 4 August 2020, a huge explosion occurred in the Port of Beirut that led to massive damages in the medium surrounding it. Researchers have conducted studies in order to estimate the equivalent explosive mass as well as the damage extent left on structures; however, the studies considered the soil–structure interaction by simple methods. For that, this paper aims to understand the effect of explosion on the grain silo structure present at the port with an emphasis on the soil–structure interaction effects. The structure consists of a group of silos resting on a raft footing that is supported by group of driven piles. A soil–structure model analysis is performed in order to investigate the soil behavior, the damage extent in piles, and the soil–structure interaction due to the Beirut explosion using the CEL (Coupled Eulerian–Lagrangian) approach that suits events involving large deformation. The analysis is performed using the ABAQUS/Explicit FEM software (version 6.14) taking into account the properties of soil medium, the contact algorithm at the soil–structure interface, and the boundary conditions in order to better simulate the real field conditions and ensure accurate results. The work is primarily validated through site data such as the crater size and silo damage.

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Seismic wave propagation through geological media is described by linear hyperbolic systems of equations. They correspond to acoustic, isotropic, and anisotropic linear elastic porous fluid-saturated models. They can be solved numerically by applying grid-characteristic schemes, which take into account propagation of solution discontinuities along characteristics. An important property of schemes used in practice is their high order of accuracy, due to which signal wavefronts can be clearly resolved. Previously, much attention was given to this property at interior points of the computational domain. In this paper, we study the order of a scheme up to the boundary of the domain inclusive. An approach is proposed whereby arbitrary linear boundary and contact conditions can be set up to high accuracy. The presentation is given for the system of one-dimensional acoustic equations with constant coefficients.

Second harmonic generation in centrosymmetric multilayered structures: Theoretical approach for nonlinear boundary conditions

Second harmonic generation (SHG) is used to characterize the interfaces of centrosymmetric materials typically used in microelectronic/optoelectronic devices. For such applications, the materials are actually multi-layer stacks, and in this case, the SHG can be difficult to interpret and model. This paper presents the theory of the second harmonic light generated from multilayer structures. The focus is on describing the nonlinear boundary conditions at the interfaces between two different materials, taking into account the distinct contributions of bulk and interface regions. Using these conditions, it is possible to calculate the second harmonic signal from any stack of materials. In this paper, we address stacks containing silicon (100) because it is a material with numerous applications. The nonlinear polarization expressions of the surface and bulk of Si(100), according to Sipe et al. [Phys. Rev. B 35, 1129 (1987)], were integrated into nonlinear boundary conditions in order to determine transmitted and reflected second harmonic waves. An analytical validation was performed on the simple case of an air–silicon interface. For multilayered stacks, the model was compared with experimental results obtained on samples corresponding to pragmatic substrates widely used in microelectronic and optoelectronic applications.

Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition

Tricomi Problem for Mixed Parabolic–Hyperbolic Equation with Higher Order Boundary Condition

A Vector Fitting Approach for the Automated Estimation of Lumped Boundary Conditions of 1D Circulation Models.

The choice of appropriate boundary conditions is a crucial step in the development of cardiovascular models for blood flow simulations. The three-element Windkessel model is usually employed as a lumped boundary condition, providing a reduced order representation of the peripheral circulation. However, the systematic estimation of the Windkessel parameters remains an open problem. Moreover, the Windkessel model is not always adequate to model blood flow dynamics, which often require more elaborate boundary conditions. In this study, we propose a method for the estimation of the parameters of high order boundary conditions, including the Windkessel model, from pressure and flow rate waveforms at the truncation point. Moreover, we investigate the effect of adopting higher order boundary conditions, corresponding to equivalent circuits with more than one storage element, on the accuracy of the model. The proposed technique is based on Time-Domain Vector Fitting, a modeling algorithm that, given samples of the input and output of a system, such as pressure and flow waveforms, can derive a differential equation approximating their relation. The capabilities of the proposed method are tested on a 1D circulation model consisting of the 55 largest human systemic arteries, to demonstrate its accuracy and its usefulness to estimate boundary conditions with order higher than the traditional Windkessel models. The proposed method is compared to other common estimation techniques, and its robustness in parameter estimation is verified in presence of noisy data and of physiological changes of aortic flow rate induced by mental stress. Results suggest that the proposed method is able to accurately estimate boundary conditions of arbitrary order. Higher order boundary conditions can improve the accuracy of cardiovascular simulations, and Time-Domain Vector Fitting can automatically estimate them.

The method of fundamental solutions for electromagnetic scattering by a perfect conductor in chiral environment

The electromagnetic scattering problem for a time-harmonic plane wave by a perfectly conductive body embedded in a chiral medium is considered. Potentials in terms of the fundamental solution in dyadic form for chiral media are defined. The well-posedness of the scattering problem is studied using defined potentials in terms of the fundamental solution for chiral environment and the boundary integral operators associated with them. An extension of the method of fundamental solutions for electromagnetic scattering in chiral media is applied in order to approximate the solution. The electric scattered field is approximated by a finite linear combination of the dyadic fundamental solutions of the equation governing the problem for singularities placed on an auxiliary surface outside the domain of the problem and for unknown coefficients determined by the boundary conditions. Density properties on the surface of the scatterer are proven for a defined system of functions consisting of the tangential components of the dyadic fundamental solution. These density properties together with the well-posedness of the scattering problem are used to reduce the approximation of the solution to the approximation of the known boundary data. The linear system obtained from the boundary conditions in order to determine the appropriate unknown coefficients of the finite linear combination is presented. Using these results we approximate the far-field patterns and the scattering cross section. Numerical results for the special case of a spherical scatterer and an ellipsoidal scatterer are presented.

A Mode-Matching Tailored-Galerkin Approach for Higher Order Interface Conditions and Geometric Variations

The current study focuses on the modeling and analysis of acoustic scattering from an elastic membrane disc located in a cylindrical waveguide that may involve structural discontinuities. The physical problem is governed by Helmholtz’s equation and involves higher order boundary conditions at the interfaces. The Mode-Matching (MM) method in conjunction with Galerkin formulation is developed to solve the governing boundary value problems. The solution procedure is first applied on two prototype problems to formulate the theoretical frame work, which is then used to analyze the structural response of the elastic membranes attached at the mouth of the cylindrical expansion chamber. The aforementioned solution method yields the linear algebraic systems containing infinite equations. These systems are truncated first and then are numerically solved. From the numerical experiments, it is found that geometrical and material properties of the structure significantly affect the transmission loss as well as the scattering energies.

Bulk-boundary eigenvalues for Bilaplacian problems

<p style='text-indent:20px;'>We initiate the study of a bulk-boundary eigenvalue problem for the Bilaplacian with a particular third order boundary condition that arises from the study of dynamical boundary conditions for the Cahn-Hilliard equation. First we consider continuity properties under parameter variation (in which the parameter also affects the domain of definition of the operator). Then we look at the ball and the annulus geometries (together with the punctured ball), obtaining the eigenvalues as solutions of a precise equation involving special functions. An interesting outcome of our analysis in the annulus case is the presence of a bifurcation from the zero eigenvalue depending on the size of the annulus.</p>

Local absorbing boundary conditions for the elastic wave equation

We compare and analyze absorbing boundary conditions for the elastic wave equations. We concentrate on the first order extensions to Clayton–Engquist and show the relationship of the Lysmer–Kuhlemeyer ABC to these generalizations. We derive conditions for the reflection coefficient to have the same accuracy for near normal waves as in the acoustic wave case. Extensions to the first order system, spherical coordinates, higher order boundary conditions and frequency domain are derived. We extend Stacey’s absorbing boundary condition (ABC) to all six sides of a cubic domain, and show that Stacey’s ABC provide good numerical results.

Null controllability for a structurally damped stochastic plate equation

In this paper, we obtain a null controllability result for a structurally damped refined stochastic plate equation with two kinds of boundary conditions. The key point is to establish an observability inequality for the backward structurally damped stochastic plate equation. For this purpose, we derive a new global Carleman estimate for the damped stochastic plate operator with homogeneous Dirichlet boundary conditions on the solution and the laplacian of the solution and with homogeneous Neumann boundary conditions of first and third order, respectively. Such an estimate is obtained by using the Carleman estimate for stochastic parabolic operators with complex coefficients in an iteration manner.

Evaluation of the lightning performance of grounding electrodes using FDTD-based computational model: Influence of absorbing boundary conditions and representation of the frequency-dependence of soil parameters

• Lightning response of grounding electrodes is assessed using FDTD. • The effect of absorbing boundary conditions is shown. • Liao's 3rd order and CPML lead to results better than those of Liao's 2nd order. • Modeling the soil as a Debye medium leads to results closer to those of HEM model. • 6 poles are enough to represent the frequency-dependence of soil parameters. This work evaluates the influence of the absorbing boundary conditions (ABC) and the representation of frequency-dependent soil parameters on the assessment of the lightning performance of grounding electrodes using FDTD-based computational model. The results in terms of grounding potential rise (GPR), grounding impulse impedance (Z P ), and low-frequency grounding resistance (R LF ) showed a better agreement with those calculated by the HEM model when Liao's 3rd order and Convolutional perfect matched layer (CPML) boundary conditions were assumed. The increase of the simulation space contributed to improve the results related to Liao's 2nd order but demanding a longer computation time. Despite the observed improvement, they are still far from those provided by the other ABC. Modeling the soil as a Debye medium to consider frequency-dependent soil parameters leaded to lightning response of grounding electrodes very close to that provided by the HEM model. In terms of Z P , the largest percentage difference was about 6%. Also, the work indicated that the adoption of 6 poles identified by the MATLAB function invfreqs was enough to represent the frequency-dependence of soil parameters, contributing to decrease the computation time.

A deforming‐mesh finite‐element approach applied to the large‐translation and free‐surface scenario of fused deposition modeling

AbstractA numerical study of the fused deposition modeling (FDM) process using a boundary‐conforming free‐surface finite element approach is performed. Due to the complexity of the FDM process, among all of its parts, we focus on the deposition and spreading of an individual filament. The polymer behavior, that is, the shear rate dependent and temperature‐dependent viscosity, is included by the Cross‐WLF viscosity model. The moving domain is addressed by the virtual region mesh update method, which, in the present article, is extended to free‐surface problems. The particularity of dividing the mesh domain into an activated and a deactivated domain makes it possible to handle large translatory mesh deformation. In this work, we make use of the level of detail offered by a boundary‐conforming approach regarding both topology accuracy and the imposition of boundary conditions in order to study the deposition of a single filament at a small scale. Parameters with a direct impact on the mechanical properties of the final object can be straightforwardly computed by a boundary‐conforming approach, for instance, the cross‐section, the contact area, the temperature distribution, and the heat fluxes over the surfaces. The presented approach is validated by a two‐dimensional benchmark test case before the numerical results of the three‐dimensional simulation of the filament deposition are shown.

Effects of Hysteresis on the Dynamic Deformation of Artificial Polymeric Heart Valve

The deformation behavior of an artificial heart valve was analyzed using the explicit dynamic finite element method. Time variations of the left ventricle and the aortic pressure were considered as the mechanical boundary conditions in order to reproduce the opening and closing movements of the valve under the full cardiac cycle. The valve was assumed to be made from a medical polymer and hence, a hyperelastic Mooney–Rivlin model was assigned as the material model. A simple formula of the damage mechanics was also introduced into the theoretical material model to express the hysteresis response under the unloading state. Effects of the hysteresis on the valve deformation were characterized by the delay of response and the enlargement of displacement. Most importantly, the elastic vibration observed in the pure elastic response under the full close state was dramatically reduced by the conversion of a part of elastic energy to the dissipated energy due to hysteresis.