Rigorous Solution Research Articles

The role of the second non-vanishing terms in the material failure curve on APL 5L steel

PurposeIt is now well-known in the fracture-mechanics community that a single fracture parameter alone may not be adequate to describe crack-tip condition. To address this problem, there has been a recent surge of interest in crack-growth behaviour under conditions of low crack-tip stress triaxiality. This paper exploited the K-A3 crack approach, which was derived from a rigorous asymptotic solution and has been developed for a two-parameter fracture.Design/methodology/approachThe material failure curve or master curve, has been established as a result of the notched specimen tests. It was shown that the notch fracture toughness is a linear decreasing function of the stress. The use of the material failure curve to predict fracture conditions was demonstrated on gas pipes with the longitudinal surface notch.FindingsNo finding.Originality/valueThis approach requires that the constraint in the test specimen approximate that of the structure to provide an “effective” toughness for use in a structural integrity assessment. The appropriate constraint is achieved by matching thickness and crack depth between the specimen and structure.

Strong signature of right-handed circularly polarized photoionization close to the cyclotron line in the atmosphere of magnetic white dwarfs

Magnetic fields break the symmetry of the interaction of atoms with photons with different polarizations, yielding chirality and anisotropy properties. The dependence of the absorption spectrum on the polarization, a phenomenon known as dichroism, is present in the atmosphere of magnetic white dwarfs. Its evaluation for processes in the continuum spectrum has been elusive so far due to the absence of appropriate ionization equilibrium models and incomplete data on photoionization cross sections. We combined rigorous solutions to the equilibrium of atomic populations with approximate cross sections to calculate the absolute opacity due to photoionization in a magnetized hydrogen gas. We predict a strong right-handed circularly polarized absorption (χ+) formed blueward of the cyclotron resonance for fields from about 14 to several hundred megagauss. In energies lower than the cyclotron fundamental, this absorption shows a deep trough with respect to linear and left-handed circular polarizations that steepens with the field strength. The jump in χ+ is due to the confluence of a large number of photoionization continua produced by right-handed circularly polarized transitions from atomic states with a nonnegative magnetic quantum number toward different Landau levels.

Protein Design by Integrating Machine Learning and Quantum-Encoded Optimization

The protein design problem involves finding polypeptide sequences folding into a given three-dimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces. Structure searches can now be bypassed thanks to recent machine-learning breakthroughs, which have enabled accurate and rapid structure predictions. Similarly, sequence searches might be entirely transformed by the advent of quantum annealing machines and by the required new encodings of the search problem, which could be performative even on classical machines. In this work, we introduce a general protein design scheme where algorithmic and technological advancements in machine learning and quantum-inspired algorithms can be integrated, and an optimal physics-based scoring function is iteratively learned. In this first proof-of-concept application, we apply the iterative method to a lattice protein model amenable to exhaustive benchmarks, finding that it can rapidly learn a physics-based scoring function and achieve promising design performances. Strikingly, our quantum-inspired reformulation outperforms conventional sequence optimization even when adopted on classical machines. The scheme is general and can be extended, e.g., to encompass off-lattice models, and it can integrate progress on various computational platforms, thus representing a new paradigm approach for protein design. Published by the American Physical Society 2024

Validation of the blended learning usability evaluation – questionnaire (BLUE-Q) through an innovative Bayesian questionnaire validation approach: a methodological study

The primary aim of this study is to validate the Blended Learning Usability Evaluation - Questionnaire (BLUE-Q) for use in the field of health professions education through a Bayesian approach. As Bayesian questionnaire validation remains elusive, a secondary aim of this article is to serve as a simplified tutorial for engaging in such validation practices in health professions education. A total of 10 health education-based experts in blended learning were recruited to participate in a 30-minute interviewer-administered survey. On a 5-point Likert scale, experts rated how well they perceived each item of the BLUE-Q to reflect its underlying usability domain (i.e., effectiveness, efficiency, satisfaction, accessibility, organization, and learner experience). Ratings were descriptively analyzed and converted into beta prior distributions. Participants were also given the option to provide qualitative comments for each item. After reviewing the computed expert prior distributions, 31 quantitative items were identified as having a probability of 'low endorsement' and were thus removed from the questionnaire. Additionally, qualitative comments were used to revise the phrasing and order of items to ensure clarity and logical flow. The BLUE-Q's final version comprises 23 Likert-scale items and 6 open-ended items. Questionnaire validation can generally be a complex, time-consuming, and costly process, inhibiting many from engaging in proper validation practices. In this study, we demonstrate that a Bayesian questionnaire validation approach can be a simple, resource-efficient, yet rigorous solution to validating a tool for content and item-domain correlation through the elicitation of domain expert endorsement ratings.

Electrically tunable graded photonic crystal lens based on graphene plasmons.

Controlling the nonlinear relationship between surface plasmon polariton (SPP) mode index and chemical potential of graphene can be used in the field of active transformation optics. Here, we propose an electrically tunable 2D Graded Photonic Crystal (GPC) lens based on graphene SPP platform. Our platform comprises a graphene monolayer integrated into a back-gated structure with nano-patterned gate insulators. When the chemical potential of the graphene surface is designed to operate in the nonlinear region, the designed GPC lens can be continuously transformed between a Maxwell's fish-eye lens and a Luneburg lens by tuning the gate voltage. The range of the lens background chemical potential for allowing this transformation is systematically studied. To compensate for the significant errors inherent in the conventional effective medium theory (EMT) during the homogenization of photonic crystals (PCs), we propose a generalized effective medium theory (GEMT). The validity and accuracy of this approach are verified through comparisons with true values (based on rigorous eigenvalue solutions) and EMT values. Due to its advantages of on-site controls and easy fabrication characteristics, the proposed graphene GPC provides a new way for practical on-chip light manipulation.

Existence and Approximate Controllability of Random Impulsive Neutral Functional Differential Equation with Finite Delay

This study investigates second-order neutral functional differential equations with delays, prevalent in various scientific and engineering fields. These equations, characterized by their neutral nature and delays, present unique challenges within Banach spaces. The research focuses on the existence and approximate controllability of solutions, using advanced mathematical tools like cosine family theory and the Leray-Schauder theorem to establish rigorous solution conditions. These theoretical results are empirically validated through practical examples, enhancing understanding of real-life behavior and bridging theory with practice. The study’s findings advance the understanding of delayed feedback systems, facilitating effective control strategies and practical engineering solutions, thereby contributing significantly to dynamical systems and control theory.

Characterizing strong-field tunneling ionization with a phase-dependent THz polarization spectrum.

The terahertz radiation emitted by asymmetrically ionized wavepackets in two-color strong-field tunneling ionization is essential for detecting the system's associated electron dynamics and structural properties. We propose to characterize and control tunneling ionization using a phase-dependent terahertz polarization (PTP) spectrum, analyzed through a combination of the classical trajectory Monte Carlo method, an analytical model based on the virial theorem, and the rigorous solution of the time-dependent Schrödinger equation as a benchmark. Our results demonstrate that the PTP spectrum offers a high-precision measure of the Coulomb effect through the relative phase of the two-color laser. Comparisons of PTP results calculated using different methods suggest how the electron can be manipulated by controlling the relative phase and laser intensity. In particular, the PTP spectrum can be used to calibrate the relative phase and provides a convenient and robust reconstruction of the time-averaging of tunneling positions with high precision using the analytical model. These insights reveal that the PTP spectrum as a whole can be a new and useful tool for the all-optical characterization of ultrafast atomic and molecular ionization.

Three-phase-lag analysis of transversely isotropic double porous thermoelastic waves with liquid medium

This manuscript presents a mathematical framework for a double porous, thermoelastic solid half-space with transverse isotropy in contact with an inviscid liquid half-space. The analysis takes into account the three-phase-lag model within thermoelasticity theory. To gain deeper insights, we formulate the governing equations in a two-dimensional representation and subsequently employ normal mode analysis for their rigorous solution. The governing equations are influenced by both types of voids, anisotropy, thermal effect, and inviscid liquid. It has been discovered that thermoelastic half-space exhibits five coupled longitudinal waves, and in the liquid half-space, there is one mechanical wave. Secular equations are obtained by using thermal and mechanical conditions, resulting in a compact representation of phase velocity, specific loss, penetrating depth, and attenuation coefficient. Analytical presentations have been made to showcase the effects of anisotropy, voids, and liquid on various wave parameters. These effects are compared by illustrating the results graphically using the MATLAB software, allowing for a visual understanding of the comparative outcomes. This study has practical applications in engineering, materials science, geophysics, and environmental studies, contributing to advancements in various industries and scientific fields.

Accurate Ionic Conductivity Calculations of Battery Electrolytes at High Salt Concentration Using Molecular Dynamics Simulations

The ionic conductivity of an electrolyte formulation is a crucial property influencing battery performance. The dependence of ionic conductivity on multiple parameters, such as salt and solvent type, concentration, and temperature complicates the design of next-generation electrolytes. Efficient design of superior electrolytes requires methods capable of accurately and rapidly predicting ionic conductivity. Such methods would enable high-throughput screening of electrolyte chemistries to establish structure-property relationships.The simple Nernst-Einstein approximation is widely used in the literature to estimate ionic conductivity of electrolytes using the measured self-diffusivity. However, the failure of this approximation for concentrated solutions due to stronger intermolecular interactions requires incorporating a rigorous concentrated solution theory, such as Maxwell-Stefan (MS) diffusivity. Here, we present a molecular dynamics (MD) simulation workflow for calculating the ionic conductivity of liquid electrolytes utilizing the ion-correlated MS diffusion approach. We explore the sensitivity of calculated ionic conductivity to various simulation parameters and various methods in the literature to guide a standardized simulation protocol. Through rigorous benchmarking across a diverse range of electrolyte systems, we validate the model's accuracy by directly comparing the calculated ionic conductivities against experiments and existing literature. This work is a significant step toward a more unified and comprehensive evaluation procedure for ionic conductivity, accelerating the development of advanced electrolytes for improved battery performance.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

In the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Analytical solutions for cavity contraction in strain-softening materials with linear or exponential strength decay

This paper presents an analytical investigation into the contraction of spherical and cylindrical cavities excavated in strain-softening rock masses obeying the Mohr–Coulomb or Tresca yield criterion, with linear or exponential uniaxial compressive strength decay. The derivation of the ground response curves is based on the simplifying assumption that the strains inside the plastic zone are completely plastic. This significantly simplifies the mathematical formulation, enabling the derivation of closed-form solutions. An alternative simplifying approach which partially neglects the elastic strains inside the plastic zone and which is commonly adopted in the literature, is also examined. The accuracy of the simplified solutions is evaluated by comparing their predictions with rigorous solutions obtained by numerical finite-difference analyses. The investigation demonstrates that the proposed closed-form solutions represent a significant improvement on those based on the commonly-made simplifying assumption involving partial neglect of elastic strains.

Topography reconstruction of high aspect ratio silicon trench array via near-infrared coherence scanning interferometry.

Topography measurement of high aspect ratio trench array using coherence scanning interferometry presents significant challenges because the numerical aperture of detection light is constrained by the trenches. Altering the detection light to penetrate the sample like near-infrared light for silicon could overcome this obstacle, but the trench array spreads the detection light. This study introduces a coherence scanning interferometry model based on three-dimensional point spread function and assuming sample is transparent to detection light, which is realized by integrating rigorous numerical electromagnetic field solution to quantify the modulation aberrations of detection light by transparent trench arrays, and theoretical angular spectrum diffraction utilized for far-field interference imaging. This model facilitates a thorough analysis of the aberrations introduced by trench arrays, encompassing comparisons between trench arrays and a single trench, as well as between the symmetric region of the array and the asymmetric region at the edge. Additionally, an investigation into the impact of unified compensation for low-order aberrations on the topography reconstruction is presented, and we find the sample-induced aberration compensation method utilizing a deformable mirror that we previously proposed for a single trench is still effective confronting trench array. Experimental measurements are performed on silicon trench arrays with the aspect ratio of up to 20:1 and the period of approximately 10 µm to validate the effectiveness of our model and measurement methods, thus providing valuable insights for enhancing high aspect ratio manufacturing.

A novel semi-analytical model for laterally loaded piles

A new model for laterally loaded piles is proposed, consisting of a linear part and a non-linear iterative part. The linear part is based on the Green's function method, which strictly satisfies the displacement and stress continuity conditions at the pile-soil interface and leads to a rigorous solution. The non-linear iterative part assumes that the shear modulus of the soil around the pile decreases with the average strain of the soil layer. Only two soil parameters need to be calibrated, including the initial shear modulus of the soil and the reference shear strain at half the initial modulus. Compared to the finite element model, the advantage of this model is that it converges quickly while maintaining accuracy, which greatly improves computational efficiency. The advantage of this model over the p-y curve model is that it does not have the difficulty of selecting p-y spring parameters, especially for monopiles. The accuracy of this model is verified by comparison with three-dimensional finite element models and nine existing studies, including numerical models, field tests and centrifuge tests. These cases cover various piles with diameters of D∼0.273–10 m and aspect ratios of L/D∼3–40, installed in sand or clay by driving, jacking or vibration.

Radiation of a TM mode from an open end of a three-layer dielectric capillary

Abstract Modern trends in beam-driven radiation sources include the interaction of Cherenkov wakefields in open-ended circular waveguides with complicated dielectric linings, with a three-layer dielectric capillary recently proposed to reduce radiation divergence being a representative example [Opt. Lett. 45 5416 (2020)]. We present a rigorous approach that allows for an analytical description of the electromagnetic processes that occur when the structure is excited by a single waveguide TM mode. In other words, the corresponding canonical waveguide diffraction problem is solved in a rigorous formulation. This is a continuation of our previous papers which considered simpler cases with a homogeneous or two-layer dielectric filling. Here we use the same analytical approach based on the Wiener–Hopf–Fock technique and deal with the more complicated case of a three-layer dielectric lining. Using the obtained rigorous solution, we discuss the possibility of manipulating the far-field radiation pattern using a third layer made of a low permittivity material.

Methods for optimizing the characteristics of antenna elements and arrays simulating aggregative behavior and evolution of living be-ings in nature

Rigorous analytical solutions to antenna synthesis problems have been obtained for several of their simplest designs, while numerical solutions to specific versions of these problems in a strict electrodynamic formulation for the required practical structures take so much time in most cases that obtaining an optimal solution in an acceptable time is not always possible. For this reason, approximate methods for solving various technical problems, including antenna problems, based on significantly simpler operators than in electrodynamics have become widespread. This allows for a significant gain in time and optimal solutions to synthesis problems in a reasonable time by direct, targeted enumeration of the space of combinations of parameters characterizing the problem under consideration. If it is necessary to increase the accuracy of the solution obtained in this way, approximate methods allow one to select from a possible number of options a significantly smaller number with the best values of the objective function for subsequent analysis of these options by strict methods. A significant place among approximate optimization methods is occupied by evolutionary algorithms (EA), which have been developed since the second half of the last century. They imitate the behavior and evolution of various biological communities, generally obeying the theory of evolution and Darwin's natural selection. The article provides a brief overview of modifications of both well-known algorithms and the control parameters they contain: the genetic algorithm (GA), the method of swarm of biological entities (PSO), the method of differential evolution (DE), with the help of which a number of problems on the synthesis of antennas with discretely and continuously changing parameters have been solved, and a relatively new algorithm – the method of grey wolves (GWO). An example of implementation using the PSO/FDTD optimization algorithm of a dual-frequency and broadband microstrip antenna with an E-shaped plate has been given. A mathematical model and a block diagram of the modified IGWO algorithm have been presented. The superiority of its characteristics in terms of the accuracy of determining the global extremum and the speed of convergence over such well-known algorithms as GWO, SCA, SSA, PSO, FPA, MFO and BA has been shown based on testing these algorithms on twenty-three reference functions.

Innovative numerical modeling for predicting soil relaxation in the design of twin circular culverts

This study presents a finite difference model for analyzing ground stability and settlement of twin circular culverts in undrained clay. The model is verified through simulations of soil movement and relaxation around a tunnel-boring machine's shield. Stability numbers and ground settlement are evaluated across various culvert geometries and soil ratios and compared to rigorous solutions and previous models. The settlement data obtained is used to determine inflection point parameters for practical culvert design, considering dimensionless ratios. The findings highlight the importance of precise design methodologies that consider soil properties and geometry. The finite difference model proves to be a valuable tool in culvert design, providing accurate analysis of stability and settlement characteristics. The presented design figures and regression equations serve as practical tools for engineers in designing stable twin circular culverts in undrained clay. The study emphasizes the need to carefully consider soil properties and geometry for successful culvert design. In conclusion, the finite difference model offers insights into ground stability and settlement of twin circular culverts. The presented design figures and regression equations support engineers in making informed design decisions, ensuring the stability and long-term performance of culverts in undrained clay conditions.

Rigorous Solution for the Kinematic Response of Single Disconnected Piles Subjected to Vertically Incident P-Waves

A rigorous solution for the kinematic response of the disconnected piles under vertically incident P-waves is presented. A new soil–pile column model is proposed with two fictitious soil columns as the extensions of the shaft along the pile top and tip. The discontinuity of the pile at the two ends is modeled using the Heaviside function to simulate the continuity of the soil–pile column. The total displacement of the soil is divided into the free-field and scattered components. The displacement of the soil–pile system is calculated in terms of the method of separation of variables and the soil–pile interaction. A parametric study indicates that for the disconnected pile, the displacement at the pile top increases significantly with the increase of the cushion thickness, and its effect on the scattered field is weak. The axial force of the disconnected pile decreases gradually with the increase of the cushion thickness. The displacement and axial force of the disconnected pile are significantly influenced by the slenderness ratio of the pile.

High-Precision Calculation Using the Method of Analytical Regularization for the Cut-Off Wave Numbers for Waveguides of Arbitrary Cross Sections with Inner Conductors

A method for the accurate calculation of the cut-off wavenumbers of a waveguide with an arbitrary cross section and a number of inner conductors is demonstrated. Concepts of integral and infinite-matrix (summation) operator-valued functions depending nonlinearly on the frequency spectral parameter provide a secure basis for formulating the spectral problem, and the Method of Analytical Regularization is employed to implement an effective algorithm. The algorithm is based on a mathematically rigorous solution of the homogeneous Dirichlet problem for the Helmholtz equation in the interior of the waveguide, excluding the regions occupied by the inner conductor boundaries. A highly efficient method of calculating the cut-off wavenumbers and the corresponding non-trivial solutions representing the modal distribution is developed. The mathematical correctness of the problem statement, the method, and the ability to calculate the cut-off wavenumbers with any prescribed and proven accuracy provide a secure basis for treating these as “benchmark solutions”. In this paper, we use this new approach to validate previously obtained results against our benchmark solutions. Furthermore, we demonstrate its universality in solving some new problems, which are barely accessible by existing methods.

Technique for enhancing the accuracy of the Rayleigh-Sommerfeld convolutional diffraction through the utilization of independent spatial sampling.

The Rayleigh-Sommerfeld diffraction integral (RSD) is a rigorous solution that precisely satisfies both Maxwell's equations and Helmholtz's equations. It seamlessly integrates Huygens' principle, providing an accurate description of the coherent light propagation within the entire diffraction field. Therefore, the rapid and precise computation of the RSD is crucial for light transport simulation and optical technology applications based on it. However, the current FFT-based Rayleigh-Sommerfeld integral convolution algorithm (CRSD) exhibits poor performance in the near field, thereby limiting its applicability and impeding further development across various fields. The present study proposes, to our knowledge, a novel approach to enhance the accuracy of the Rayleigh-Sommerfeld convolution algorithm by employing independent sampling techniques in both spatial and frequency domains. The crux of this methodology involves segregating the spatial and frequency domains, followed by autonomous sampling within each domain. The proposed method significantly enhances the accuracy of RSD during the short distance while ensuring computational efficiency.

Cavity expansion-based interpretation of piezocone penetration test (CPTu) data in clays

A cavity expansion-based method is proposed in this paper to correlate the relevant findings with the piezocone penetration test (CPTu) data in clays. The rigorous and explicit solution for both spherical and cylindrical undrained cavity expansion is adopted based on a unified critical state constitutive model for clays and sands. The analogous model developed is comprehensively validated against two series of advanced numerical simulations and calibration chamber tests of the CPTu in fine-grained soils, along with bias analyses. The effects of the overconsolidation ratio and initial state parameter are extensively investigated for various clay types. Both theoretical and empirical correlations are then proposed for back-calculations of cone factor, undrained shear strength, overconsolidation ratio and initial state parameter of clays. Two case studies of CPTu tests are conducted in addition to examine correlations and contours of the in situ state parameter, demonstrating the applicability of the proposed theoretical approach for interpretation of the CPTu data.