Strong Boundary Conditions Research Articles

Finite element analysis of repairing tympanic membrane perforation using autologous graft material and biodegradable bionic cobweb scaffold

Background and objectiveAs for repairing the perforated tympanic membranes (TM), temporalis fascia and tragal cartilage are popular in clinics as autologous graft materials. However, there is a significant hearing loss after repairing the TM with autologous graft materials, which needs to be addressed in biomechanical engineering. MethodsThe finite element model of normal middle ear is improved from two aspects: the repair method of tympanic fibrous layer and the bionic spider web tympanic scaffold. By creating the solid-shell coupling condition and strong coupling boundary condition to simulate the repair, TM umbo and stapes footplate displacement-frequency response are explored in 200–8000 Hz. ResultsThe tympanic membrane perforation (TMP) causes a significant conductive hearing loss in high frequency region, which is positively correlated with perforation area. Both temporalis fascia and tragal cartilage still perform a certain degree of high-frequency hearing loss after repairing TMP. The TM attachment the magnesium alloy scaffold (MAS) prevents appropriately the high frequency hearing loss after autologous graft repair and makes the sound transmission closer to the normal condition. Significantly, the density of graft material has a negative effect on high-frequency sound transmission without the MAS. The modal-motion of TM repaired with temporalis fascia and tragal cartilage is improved significantly after attaching the MAS. In addition, the MAS restores effectively the configuration and vibration frequency of the repaired TM, which is similar to that of the native TM. ConclusionThe area size of TMP is studied through the finite element method, which includes autologous graft materials, the MAS, parameter sensitivity analysis, modal analysis of graft material and the MAS in biological form on the effect of middle ear sound transmission. Relevant conclusions provide some references for clinical trial protocol and the follow-up repair ideas of TM of tympanoplasty.

Weak Versus Strong Wall Boundary Conditions for the Incompressible Navier-Stokes Equations

The pressure-velocity formulation of the incompressible Navier-Stokes equations is solved using high-order finite difference operators satisfying a summation-by-parts property. Two methods for imposing Dirichlet boundary conditions (one strong and one weak) are presented and proven stable using the energy method. Additionally, novel diagonal-norm second-derivative finite difference operators are derived with highly improved boundary accuracy. Accuracy and convergence measurements are presented and verified against theoretical expectations. Numerical experiments also show that subtle effects close to solid walls are more efficiently captured with strong boundary condition imposition methods rather than weak (less degrees of freedom required).

Time Stability of Strong Boundary Conditions in Finite-Difference Schemes for Hyperbolic Systems

Time Stability of Strong Boundary Conditions in Finite-Difference Schemes for Hyperbolic Systems

A mathematical framework for ejecta cloud dynamics with application to source models and piezoelectric mass measurements

We present a mathematical framework for describing the dynamical evolution of an ejecta cloud generated by a generic ejecta source model. We consider a piezoelectric sensor fielded in the path of an ejecta cloud, for experimental configurations in which the ejecta are created at a singly shocked planar surface and fly ballistically through vacuum to the stationary sensor. To do so, we introduce the concept of a time- and velocity-dependent ejecta “areal mass function.” We derive expressions for the analytic (“true”) accumulated ejecta areal mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltages. In this way, we derive an exact expression and upper bound for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation, which is commonly required for momentum diagnostic analyses. This error term is zero for truly instantaneous source models; otherwise, the standard piezoelectric analysis is guaranteed to overestimate the true mass. When combined with a piezoelectric dataset, this framework provides a unique solution for the ejecta particle velocity distribution, subject to the assumptions inherent in the data analysis. The framework also leads to strong boundary conditions that any ejecta source model must satisfy in order to be consistent with apparently global properties of piezoelectric measurements from a wide range of experiments. We demonstrate this methodology by applying it to the Richtmyer–Meshkov instability+self-similar velocity distribution ejecta source model currently under development at Los Alamos National Laboratory.

On the ordinal sum of fuzzy implications: New results and the distributivity over a class of overlap and grouping functions

Similar to the construction of ordinal sums of overlap functions, Baczyński et al. introduced two new kinds of ordinal sums of fuzzy implications without additional restrictions on summands in 2017. In this paper, based on the ordinal sum of fuzzy implications with the first method, we discuss its basic properties, such as iterative Boolean law, right ordering property and strong boundary condition. Meanwhile, we give characterizations of such ordinal sum of fuzzy implications that is a QL-implication constructed from tuples (O,G,N⊤) or a D-implication derived from grouping function G, and show some conclusions about its relations with (G,N)- and RO-implications. Moreover, we study the distributivity of such ordinal sum of fuzzy implications over a class of overlap and grouping functions. More specifically, we give necessary and sufficient conditions under which this ordinal sum of fuzzy implications is distributive over overlap and grouping functions satisfying some conditions.

Effective operators for Robin eigenvalues in domains with corners

We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings, while only rough estimates were available for the next eigenvalues. Under some geometric assumptions, we go beyond the critical eigenvalue number and give a precise asymptotics of any individual eigenvalue by establishing a link with an effective Schr\"odinger-type operator on the boundary of the domain with boundary conditions at the corners.

Locally Conservative Immersed Finite Element Method for Elliptic Interface Problems

In this paper, we introduce a locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the interface. However, all the currently available method under IFEM framework may not be designed to consider the conservative flux conservation. We provide an efficient and effective remedy for this issue by introducing a local piecewise constant enrichment, which provides the locally conservative flux. We have also constructed and analyzed an auxiliary space preconditioner for the resulting system based on the application of algebraic multigrid method. The new observation in this work is that by imposing strong Dirichlet boundary condition for the standard IFEM part of EIFEM, we are able to remove the zero eigen-mode of the EIFEM system while still imposing the Dirichlet boundary condition weakly assigned to the piecewise constant enrichment part of EIFEM. A couple of issues relevant to the piecewise constant enrichment given for the mesh unfit to the interface has been discussed and clarified as well. Numerical tests are provided to confirm the theoretical development.

Strong Solutions for PDE-Based Tomography by Unsupervised Learning

We introduce a novel neural network-based PDEs solver for forward and inverse problems. The solver is grid free, mesh free, and shape free, and the solution is approximated by a neural network. We employ an unsupervised approach such that the input to the network is a point set in an arbitrary domain, and the output is the set of the corresponding function values. The network is trained to minimize deviations of the learned function from the PDE solution and satisfy the boundary conditions. The resulting solution in turn is an explicit, smooth, differentiable function with a known analytical form. We solve the forward problem (observations given the underlying model's parameters), semi-inverse problem (model's parameters given the observations in the whole domain), and full tomography inverse problem (model's parameters given the observations on the boundary) by solving the forward and semi-inverse problems at the same time. The optimized loss function consists of few elements: fidelity term of $L_2$ norm that enforces the PDE in the weak sense, an $L_\infty$ norm term that enforces pointwise fidelity and thus promotes a strong solution, and boundary and initial conditions constraints. It further accommodates regularizers for the solution and/or the model's parameters of the differential operator. This setting is flexible in the sense that regularizers can be tailored to specific problems. We demonstrate our method on several free shape two dimensional (2D) second order systems with application to electrical impedance tomography (EIT) and diffusion equation. Unlike other numerical methods such as finite differences and finite elements, the derivatives of the desired function can be analytically calculated to any order. This framework enables, in principle, the solution of high order and high dimensional nonlinear PDEs.

An Improved DC Fault Protection Scheme Independent of Boundary Components for MMC Based HVDC Grids

For modular multilevel converter (MMC) based DC grids, current-limiting reactors (CLRs) are mainly employed to suppress the fault current and provide boundary effects to detect internal faults. Thus, most existing protection schemes are highly dependent on the larger CLRs to guarantee high selectivity. However, in existing MMC based HVDC projects, the size of CLRs is restrained by the cost, weight, and system stability under normal state. Thus, boundary protections may fail to detect high-resistance faults and pole-to-ground faults under weak boundary conditions. To overcome these shortcomings, this paper proposes a fast and selective DC fault detection scheme independent of boundary components. The propagation characteristics of line-mode backward traveling-waves (TW) are analyzed to identify external and internal faults. The polarities of zero-mode backward TWs are employed to select faulted poles. The directional overcurrent based pilot protection is adopted as a complementary criterion to detect remote faults. The proposed method can be applied in MMC-HVDC systems with small CLRs that cannot provide strong boundary conditions. Besides, the detection speed is fast (less than 1.5ms). Moreover, it is robust to fault resistance and immune to noise. Various simulation results in PSCAD/EMTDC verifies the effectiveness of the proposed scheme.

Structure and grating efficiency of thin cells filled by a twist-bend nematic liquid crystal.

A twist-bend nematic (N_{TB}) liquid crystalline phase spontaneously forms modulated structures on a microscale level when confined in thin planar cells. Preliminary studies showed that these cells can be used as polarization gratings. Here we present a theoretical description of the formation of a two-dimensionally modulated structure. By considering the N_{TB} phase as a pseudolayer medium, a threshold condition for the onset of a modulated structure is calculated for weak and strong boundary conditions in the case of initially bookshelf or pretilt alignment of pseudolayers. Based on the modeled structure we determine spatial variation of the optic axis and calculate properties of the transmitted diffracted light. Results of the beam propagation method (BPM) and transfer matrix method are compared and it is shown that a more complex BPM gives better agreement with experimental results, meaning that even in thin cells the diffraction of light inside the grating should not be neglected.

Effect of boundary conditions on progressive collapse resistance of RC beam-slab assemblies under edge column removal scenario

Perimeter columns of building structures are the most susceptible to accidental loading (say, terrorist attacks or vehicle impact) due to their accessibility to the public, and thus progressive collapse is more likely caused by damage of perimeter columns. Previous studies show contrary or inconsistent conclusions of structural resistance form of RC beam-slab assemblies under an edge column removal scenario (CRS), probably because of inconsistent boundary restraints. Therefore, in this paper two specimens, each of which consisted of two square slab panels and seven beams, were experimentally investigated under a perimeter middle (PM) column removal scenario (CRS) and a penultimate exterior (PE) CRS, respectively, in which the former and the latter represent strong and weak boundary conditions in terms of lateral and rotational restraints to the assemblies in longitudinal direction. During the tests a static-determinate test-up was designed so that all the vertical reaction forces could be recorded. Through systematic instrumentation, progressive collapse resistance and load-transfer mechanisms of the assemblies are demonstrated, and the effects of boundary conditions are illustrated at the global behavior level and micro strain level. Thereafter, high-fidelity numerical models are built to evaluate the validity of the simplified boundary conditions in the tests and to investigate the effects of supporting column stiffness and restraint due to building continuity on progressive collapse resistance of PES. Finally, based on failure modes, analytical models to calculate the progressive resistance are derived using yield-line theory. The results indicate that structural resistance form of PES depends on the stiffness of supporting corner column, and adding slab flanges to the free boundary beam of PES is able to avoid torsional failure of boundary beams, as well as significantly increases structural resistance at large deformation stage.

COMPARATIVE ANALYSIS OF PLATE GIRDER DESIGNS ON NON-COMPOSITE BRIDGES BETWEEN AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2017 CODE WITH SNI 1729:2015 CODE

This study aims to the structural design of non-composite plate girders using AASHTO LRFD Bridge Design Specifications 2017 code compared to SNI 1729:2015 code. The span of the bridge used as the object of study is 40 meters with a width of 10 meters. In this study, plate girders are designed based on AASHTO code and SNI code, then also given the loading according to SNI 1725:2016 code, and in the analysis of the structure using CSi Bridge software to get the value of internal forces i.e. Moment Force (Mu) of 3595.38 kNm and Shear Force (Vu) of 449.9968 kNm. The results obtained from this study are the non-composite bridge plate girder designed with AASHTO LRFD Bridge Design Specifications 2017 and SNI 1729:2015 obtained the stability requirements of strong boundary conditions flexure design. Then obtained Nominal Moment value (ØMn) of 8016.843 kNm for AASHTO LRFD Bridge Design Specifications 2017 and Nominal Moment value (ØMn) of 6081.97 kNm for SNI 1729:2015. From the values obtained it can be concluded that the two regulations produce a safe and strong plan as per the applicable provisions namely Moment (Mu <ØMn).

Nematic reorientation effects on resonant modes, wavelength mismatch, and slow-light phenomena in one-dimensional magnetophotonic crystals with a dual anisotropic defect.

The present study is devoted to the investigation of spectral properties of an alternated sequence of magnetic and dielectric layers containing a dual defect based on magnetic and nematic layers. Combining the Hydrodynamic Continuum Theory for nematic liquid crystals and Berreman's formalism, we determine how the nematic ordering affects the light localization, polarization rotation, and slow-light phenomena observed in the magnetophotonic system. In particular, we analyze the effects associated with a field-induced reorientation of the director in a nematic defect with strong planar boundary conditions. Our results reveal that field-induced reorientation of the nematic ordering can be used as an efficient mechanism to tune and control the spectral properties of magnetophotonic structure, anomalies in group velocity, and the wavelength mismatch between resonant mode and maximum polarization. The effects of nematic layer thickness are also analyzed.

An immersed boundary method based on domain decomposition

A novel immersed boundary method based on a domain decomposition approach is proposed in the context of a finite element discretisation method. It is applicable to incompressible flows past rigid, deforming, or moving bodies. In this method, unlike most immersed boundary methods, strong boundary conditions are imposed in the regions of the computational domain that are occupied by the structure. In order to achieve this, the proposed formulation decomposes the computational domain by splitting the finite element test functions into solid and fluid parts. In the continuous Galerkin formulation, this produces a smeared representation of the fluid-structure interface. The absence of an immersed boundary forcing term implies that the method itself has no influence on the CFL stability criterion. Furthermore, the stiffness matrix in the momentum equation is sparser than compared with other forcing immersed boundary methods, and symmetry and positive-definiteness of the Laplacian operator in the pressure equation is preserved. As shown in this paper, stability and accurate imposition of boundary conditions make the method promising for high Reynolds number flows. The method is applied to the simulations of two-dimensional laminar flow over stationary and moving cylinders, as well as a moderately high Reynolds number flow past an aerofoil. Good results are obtained when compared with those from previous experimental and numerical studies.

Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

We study parabolic Hamilton-Jacobi-Bellman (HJB) equations in bounded domains with strong Dirichlet boundary conditions. We work under the assumption of the existence of a sufficiently regular barrier function for the problem to obtain well-posedness and regularity of a related switching system and the convergence of its components to the HJB equation. In particular, we show existence of a viscosity solution to the switching system by a novel construction of sub- and supersolutions and application of Perron's method. Error bounds for monotone schemes for the HJB equation are then derived from estimates near the boundary, where the standard regularisation procedure for viscosity solutions is not applicable, and are found to be of the same order as known results for the whole space. We deduce error bounds for some common finite difference and truncated semi-Lagrangian schemes.

Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations

In this paper we investigate the parabolic-hyperbolic formulation of the vacuum constraint equations introduced by Rácz with a view to constructing multiple black hole initial data sets without spin. In order to respect the natural properties of this configuration, we foliate the spatial domain with two-spheres. It is then a consequence of these equations that they must be solved as an initial value problem evolving outwards towards spacelike infinity. Choosing the free data and the ‘strong field boundary conditions’ for these equations in a way which mimics asymptotically flat and asymptotically spherical binary black hole initial data sets, our focus in this paper is on the analysis of the asymptotics of the solutions. In agreement with our earlier results, our combination of analytical and numerical tools reveals that these solutions are in general not asymptotically flat, but have a cone geometry instead. In order to remedy this and approximate asymptotically Euclidean data sets, we then propose and test an iterative numerical scheme.

Comparative Analysis of Plate Girder Designs In The Composite Bridge Between AASHTO LRFD Bridge Design Specifications 2017 Regulation with SNI 1729: 2015

In the world of construction there are various methods and types of materials used to support the passage of a construction work. One of them is composite girder plate. Composite girder plate is one of the many construction methods that combine two construction materials that are physically different in nature, namely concrete with steel. This type of composite girder plate construction is commonly used for bridge construction work with a fairly large span and width. In its use, of course, it must be preceded by stages of careful planning on a standard and valid basis as well. In the following research will discuss and look for similarities and differences regarding the two types of rules in the planning of composite girder plates, namely the rules of planning composite girder plates using AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2017 with SNI 1729: 2015. After doing the initial stages of modeling using CSI Bridge software using the profile cross section constraints of the AASHTO provisions, the internal force obtained is Moment Force (Mu) of 3469.13 kNm and Shear Force (Vu) of 225.98 kNm. Then proceed with the analysis of calculations with the help of Microsoft Excel software namely calculating using the AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 2017 regulations for stability requirements of strong boundary conditions on the bending requirements. Then a Nominal Moment (ØMn) value of 6420.19 kNm is obtained. Then proceed to calculate the same planning constraints, but this time using SNI 1729: 2015 regulations. Obtained Nominal Moment Value (ØMn) of 6579.88 kNm. Then it can be concluded that the two regulations produce a safe and strong planning, of course in accordance with applicable regulations namely: Moment (Mu <ØMn).

An exact deflection solution to a type of cantilever with partially built-in end using strong boundary conditions

The problem of cantilever deflection is a classic worked example in most elasticity textbooks. Due to the inability for the displacement field to completely satisfy the boundary condition of zero displacement at the entire built-in end from the top surface to the bottom surface, the best solution so far is attained from weak boundary conditions. This paper proposes a modified problem in which the boundary is partially built-in, i.e. the cantilever is clamped on the top and bottom but free on the other two sides. Therefore, the cantilever’s displacement is prohibited only at the top and bottom surfaces at the partially built-in end. By implementing zero displacement therein, the displacement solution can be obtained based on strong boundary conditions. Furthermore, the condition of zero horizontal displacement at the mid-point of the partially built-in end is also achieved through the prescribed boundary conditions. Results also reveal that the displacement at the partially built-in end can be reduced by selecting materials with negative Poisson’s ratio. As an alternative to being a worked example, the proposed problem can be used as an assessment question.

More on vacua of exotic massive 3D gravity

In a recent paper [arXiv:1806.06254], we explored the space of solutions of the exotic massive 3D gravity theory proposed in [arXiv:1806.04179]. We showed that the theory admits a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying different types of boundary conditions. The examples include black holes dressed with low decaying gravitons. Based on what happens in other theories of massive gravity, we conjectured that such geometries appear on a curve of the parameter space (chiral curve) where the exotic massive gravity on AdS with sufficiently strong boundary conditions results dual to a 2D chiral conformal field theory. Here, we show that this expectation is consistent with the conserved charges and thermodynamical properties of the black holes of the theory, which have recently been computed [arXiv:1812.09525]. When the boundary conditions are relaxed relative to the standard Brown-Henneaux boundary conditions, the theory exhibits solutions consistent with the definition of the so-called Log-gravity. The asymptotic behavior of these solutions presents a logarithmic term in the Fefferman-Graham expansion that, nonetheless, is compatible with the AdS asymptotic symmetries. This long range interaction is due to a mode of the massive gravity that becomes massless precisely on the chiral curve. We construct exact solutions exhibiting this behavior, which admit to be interpreted as fully backreacting gravitational waves propagating on an extremal black hole, and carrying non-vanishing gravitational energy. We also discuss other vacua of the theory, such as Warped-AdS$_3$ black holes, gravitational waves on such backgrounds, AdS$_2\times S^1$ spaces, and black holes in dS$_3$ space.

Vacua of exotic massive 3D gravity

We consider the recently proposed exotic 3D massive gravity. We show that this theory has a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying either the standard Brown-Henneaux boundary conditions or the weakened asymptotic behavior of the so-called Log-gravity. Both sectors contain non-Einstein spaces with SO(2) × mathbb{R} isometry group, showing that the Birkhoff theorem does not hold all over the parameter space, even if strong AdS boundary conditions are imposed. Some of these geometries correspond to 3D black holes dressed with a Log-gravity graviton. We conjecture that such geometries appear in a curve of the parameter space where the exotic 3D massive gravity on AdS3 is dual to a chiral conformal field theory. The theory also contains other interesting vacua, including different families of non-AdS black holes.