The BIE study. Part 3: Crack growth BIE analysis
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The Bayes Inference Engine (BIE) is a general software tool intended to be used primarily in the analysis of radiographic data for density. An analysis is set up in the BIE by representing the problem as a collection of modules called glyphs. All glyphs to be used in creating the forward model of the experiment will be tested separately for a range of inputs. The testing of the adjoint code is performed in a separate document.
The Bayes Inference Engine (BIE) is a general software tool intended to be used primarily in the analysis of radiographic data for density. An analysis is set up in the BIE by representing the problem as a collection of modules called glyphs. All glyphs to be used in creating the forward model of the experiment will be tested separately for a range of inputs.
The Bayes Inference Engine (BIE) is a general software tool intended to be used primarily in the analysis of radiographic data for density. An analysis is set up in the BIE by representing the problem as a collection of modules called glyphs. All glyphs to be used in creating the forward model of the experiment will be tested separately for a range of inputs.
The Bayes Inference Engine (BIE) is a general software tool intended to be used primarily in the analysis of radiographic data for density. An analysis is set up in the BIE by representing the problem as a collection of modules called glyphs. All glyphs to be used in creating the forward model of the experiment will be tested separately for a range of inputs. The testing of the adjoint code is performed in a separate document.
Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.
Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.
In a recent paper by Zinoviev and Bies in this Journal, the authors have claimed that the well-known theoretical results of Curle and Ffowcs Williams and Hawkings (FW-H) are incorrect. This claim is categorically refuted below and serious errors are pointed out.
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Interlayer doping of the vacancy-ordered 2D perovskite Cs 3 Bi 2 Br 9 (CBB) enables the formation of bound interlayer excitons (BIEs), a unique charge-transfer excited state within the layered solid. BIEs previously reported with silver (Ag + ) as an interlayer dopant exhibited bright broadband photoluminescence (PL) with prolonged lifetime at room temperature, offering potential applications in efficient white light emission, photocatalysis, and optoelectronics. However, the dynamic behavior of radiation and excited carriers remains poorly understood due to the limitations of ensemble spectroscopic measurements. Here, we investigate the temperature-dependent dynamics of Ag-doped Cs 3 Bi 2 Br 9 (Ag-CBB) using single-particle time-resolved PL spectroscopy and ultrafast transient absorption imaging. Single-particle PL measurements reveal three distinct emission regimes across temperature: (i) BIE-dominant emission at high temperatures, (ii) a mixture of radiation from BIEs and self-trapped excitons (STEs) at intermediate temperatures, and (iii) STE-dominant emission below 100 K. Rapid transient absorption mapping using Parallel Rapid Imaging with Spectroscopic Mapping (PRISM) reveals subpicosecond STE formation in pristine CBB and long-lived photoinduced absorption by BIEs, consistent with electron–hole separation and suppressed STE transfer. The spatial uniformity of these signals confirms homogeneous Ag doping across single crystals. These findings highlight the role of Ag interlayer dopants in governing the BIE dynamics.
The application of the boundary integral equation method (BIE) to the elastoplastic torsion problem is considered. It is found that the BIE is very suitable for the elastoplastic analysis of the torsion of prismatic bars. A comparison of the BIE with the finite difference method shows savings for the BIE concerning the number of unknowns which have to be determined and also a much faster convergence rate. Attention is given to the problem of an edge-notched beam in pure bending, taking into account a biharmonic formulation and a displacement formulation.
Cesium bismuth bromide (CBB) has garnered considerable attention as a vacancy-ordered layered perovskite with notable optoelectronic applications. However, its use as a light source has been limited due to its weak photoluminescence (PL). Here, we demonstrate metal intercalation as a novel approach to engineer the room-temperature PL of CBB using experimental and computational methods. Ag, when introduced into CBB, occupies vacant sites in the spacer region, forming octahedral coordination with surrounding Br anions. First-principles density functional theory calculations reveal that intercalated Ag represents the most energetically stable Ag species compared to other potential forms, such as Ag substituting Bi. The intercalated Ag forms a strong polaronic trap state close to the conduction band minimum and quickly captures photoexcited electrons with holes remaining in CBB layers, leading to the formation of a bound interlayer exciton, or BIE. The radiative recombination of this BIE exhibits bright room-temperature PL at 600 nm and a decay time of 38.6 ns, 35 times greater than that of free excitons, originating from the spatial separation of photocarriers by half a unit cell separation distance. The BIE as a new form of interlayer exciton is expected to inspire new research directions for vacancy-ordered perovskites.
A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.
Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.
Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.
In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.
Range prediction is a standard feature in most modern road vehicles, allowing drivers to make informed decisions about when to refuel. Most vehicles make range predictions through data- or model-driven means, monitoring the average fuel consumption rate or using a tuned vehicle model to predict fuel consumption. The uncertainty of future driving conditions makes the range prediction problem challenging, particularly for less pervasive battery electric vehicles (BEV). Most contemporary machine learning-based methods attempt to forecast the battery SOC discharge profile to predict vehicle range. In this work, we propose a novel approach using two recurrent neural networks (RNNs) to predict the remaining range of BEVs and the minimum charge required to safely complete a trip. Each RNN has two outputs that can be used for statistical analysis to account for uncertainties; the first loss function leads to mean and variance estimation (MVE), while the second results in bounded interval estimation (BIE). These outputs of the proposed RNNs are then used to predict the probability of a vehicle completing a given trip without charging, or if charging is needed, the remaining range and minimum charging required to finish the trip with high probability. Training data was generated using a low-order physics model to estimate vehicle energy consumption from historical drive cycle data collected from medium-duty last-mile delivery vehicles. Here, the proposed method demonstrated high accuracy in the presence of day-to-day route variability, with the root-mean-square error (RMSE) below 6% for both RNN models.