Singular Zone Research Articles

Tunable thermal conductivity of surface phonon polaritons in SiC thin film

As an additional heat carrier besides phonons and electrons, the surface phonon polariton (SPhPs) possesses a large potential to increase the thermal conductivity. In this work, the influences of SPhP frequency, film thickness and film permittivity on the SPhP-contributed thermal conductivity of SiC thin films were probed. Results show that: there are two frequency zones which could lead to a much high thermal conductivity, i. e. the frequency which approaching zero and the frequency in singularity zone. The thermal conductivity decreases with the increase of the film thickness, following a power-function relationship, and a thin film with a thickness of 10-nm could have a thermal conductivity higher than 1×104 W·m−1·K−1. However, the experimental observation of this high thermal conductivity is still difficult because of the size effect of the film length. The thermal conductivity will increase with the decrease of the imaginary part of the film permittivity and/or increase of the real part of the film permittivity, and there is approximately a reciprocal dependence of thermal conductivity on the imaginary part of the film permittivity. The thermal conductivity could be tuned by several times with tailoring its permittivity through adding fillers in it or adding dopant in it. This work provides some potential methods to tune the SPhP thermal conductivity in SiC thin film, which could help its application in microscale heat dissipation.

Acoustic full-waveform inversion on land surveys: A case study on the Qademah fault, Saudi Arabia

Geophysical methods have been used to map a Qademah fault near a residential area in western Saudi Arabia. However, the location and spatial extension of the fault zone are still uncertain due to the limited resolution and length of geophysical surveys. We apply seismic full-waveform inversion (FWI) to a land survey 2 km in length, the result of which reveals more details of the fault as well as the subsurface. Before inversion, we remove the surface waves, converted waves, and other elastic phenomena in the f- k domain and normalize the trace amplitude to compensate for attenuation, such that wavefield modeling for FWI can be approximated by acoustic propagators with constant density. Due to the large wavefield amplitudes near the source-receiver positions, the FWI velocity gradient presents a singular zone in the near surface, which is muted to stabilize the inversion. We also invert the short-offset traces before the larger-offset traces to avoid cycle skipping at the far offsets and obtain a reasonable data fit despite some mismatches in the near offsets. The final FWI velocity model shows the Qademah fault at approximately 1000 m distance as well as three low-velocity anomalies at 100 m depth, confirmed by first-arrival traveltime tomography. We also observe a potential low-velocity layer at 250–300 m depth, which was not reported in former studies. This model can also be used for geologic interpretation, hazard assessment, and paleoseismology studies of the local area.

Singular Zone in Quadrotor Yaw–Position Feedback Linearization

Feedback linearization-based controllers are widely exploited in stabilizing a tilt rotor (eight or twelve inputs); each degree of freedom (six degrees of freedom in total) is manipulated individually to track the desired trajectory, since no singular decoupling matrix is introduced while applying this method. The conventional quadrotor (four inputs), on the other hand, is an under-actuated MIMO system that can directly track four independent degrees of freedom at most. Common selections of these outputs can be yaw–position and attitude–altitude. It is reported that no singularity is found in the decoupling matrix while applying feedback linearization in the yaw–position-tracking problem. However, in this research, we argue the existence of the ignored singular zone within the range of interest, which can cause the failure in the controller design. This paper visualizes this noninvertible area and details the process of deduction for the first time. An attempt (switch controller) to avert the singular problem is later discussed with the verification by simulation in Simulink and MATLAB. All the results are sketched in the roll–pitch diagram.

Mapping whole brain seizure network recruitment with optogenetic kindling

Epilepsy is often labeled as a network disorder, though a common view of seizures holds that they initiate in a singular onset zone before expanding contiguously outward. A recent report by Choy et al. (Choy M, Dadgar-Kiani E, Cron GO, Duffy BA, Schmid F, Edelman BJ, Asaad M, Chan RW, Vahdat S, Lee JH. Neuron 2021 Oct 23: S0896-6273(21)00778-9.) leverages new tools to study whole brain dynamics during epileptic seizures originating in the hippocampus. Cell-type-specific kindling and functional imaging revealed how various brain regions were recruited to seizures and uncovered a novel form of migrating seizure core.

Williams Elements With Generalized Degrees of Freedom for Crack Tip SIFs Analysis Under Crack Surface Distributed Loading

Service with cracks is the normal state of engineering structures. Due to the fluid invading into the crack, the crack surface is loaded directly, which makes the crack further expand, and even affects the safety of the structure. In the analysis of fracture problems, according to the Williams element with generalized degrees of freedom (W element), the Williams series was used to establish the displacement field of the singular zone around the crack tip, and the stress intensity factors (SIFs) can be directly obtained by solving the generalized stiffness equation with high precision and high efficiency. However, the W element needs to satisfy the free boundary condition of the crack surface in the singular zone, so it is limited in the analysis of crack surface loading. Based on the SIFs reciprocity, the loading on the crack surface is equivalent to the concentrated force on the crack surface at the periphery of the equivalent singular zone, so the loading on the crack surface in the singular zone can be avoided, and the W element can be easily used for calculation. The numerical examples show that, the size of the equivalent singular zone is 1/20 of the crack length, the suggested equivalent load coefficient <i>P</i> is 2.0, and the calculation accuracy of the W element meets the error limit of 1%. The equivalent treatment method for the analysis of crack surface loading in the singular zone is reasonable and universal, and overcomes the limitation on the W element in analysis of the loading problem on crack surface.

Numerical Modelling of Compression Cure High-Filled Polimer Material

The article presents phenomenological constitutive relations for modeling the compression curing of a highly filled polymer medium, obtained in the framework of the mechanics of an almost incompressible viscoelastic solid using the modified Herrmann variational principle. The relations are based on the representation of the medium as a composition of a fluid and solidified material, taking into account the history of continuous nucleation and deformation of a new phase in the temperature range of phase transformations. During the manufacturing process, different mechanisms lead to process-induced deformations and stresses. These mechanisms depend on thermal expansion, shrinkage, nonlinear viscoelastic properties of the material, and variation in local temperatures. In critical cases, these residual stresses can lead to initial degradation and up to failure of the material. A stable numerical algorithm for the problem’s solution has been developed on the base of finite element method. Numerical investigation of the stress and deformation in system during the polymerization process has been carried out. The evolution of curing stresses in a singular zone of domain has been investigated

The Detachment of an Inclined Micro-Pillar Adhered to a Dissimilar Substrate

Abstract We investigate the mechanics of the detachment of an inclined micro-pillar adhered to a dissimilar substrate when subjected to a combination of an axial load and end moment. When the micro-pillar has adhered to the substrate, singular stress fields exist at the bi-material corners. The order of singularity is estimated using asymptotic analysis. The first two terms in the asymptotic expansion lead to singular stress fields. The magnitude of the singularity is evaluated in terms of the elastic mismatch between the pillar and substrate and the micro-pillar inclination. The asymptotic stress due to the moment loading is more sensitive to the micro-pillar inclination when compared to that due to the axial loading. They are insensitive to the micro-pillar inclination when the micro-pillar is rigid when compared to the substrate. A short interfacial crack is further assumed to exist at the bi-material corner. This crack is embedded in the corner singularity region and is loaded by the singular fields due to axial and bending loads. A boundary layer analysis is performed on the singular zone to estimate the stress intensity factor when a short crack embedded in it is subjected to the singular fields. The stress intensity factors are also calculated for a long interfacial crack at the bi-material corner, which extends beyond the singular zone. By using the aforementioned results, we investigate the detachment of the inclined micro-pillar under the combination of an axial load and end moment.

Construction of a Singularity Zone for a Type of Mechanisms with Parallel Structure

This paper presents a mechanism with parallel structure that is classified to the class of l‑coordinate mechanisms. The section of the singularity zone (of the zone of singular positions) is determined for this mechanism. The section is constructed at a constant orientation of the output linkage.

Patchwise Mapping Method for Solving Elliptic Boundary Value Problems Containing Multiple Singularities

In the paper [1], the geometrical mapping techniques based on Non-Uniform Rational B-Spline (NURBS) were introduced to solve an elliptic boundary value problem containing a singularity. In the mapping techniques, the inverse function of the NURBS geometrical mapping generates singular functions as well as smooth functions by an unconventional choice of control points. It means that the push-forward of the NURBS geometrical mapping that generates singular functions, becomes a piecewise smooth function. However, the mapping method proposed is not able to catch singularities emerging at multiple locations in a domain. Thus, we design the geometrical mapping that generates singular functions for each singular zone in the physical domain. In the design of the geometrical mapping, we should consider the design of control points on the interface between/among patches so that global basis functions are in C0 space. Also, we modify the B-spline functions whose supports include the interface between/among them. We put the idea in practice by solving elliptic boundary value problems containing multiple singularities.

A Two-on-One Linear Pursuit–Evasion Game with Bounded Controls

A linearized engagement with two pursuers versus a single evader is considered, in which the adversaries’ controls are bounded and have first-order dynamics and the pursuers’ intercept times are equal. Wishing to formulate the engagement as a zero-sum differential game, a suitable cost function is proposed and validated, and the resulting optimization problem and its solution are presented. Construction and analysis of the game space is shown, and the players’ closed-form optimal controls are derived for the case of two “strong” pursuers. The results are compared to those of a 1-on-1 engagement with a “strong” pursuer, and it is shown that the addition of a second pursuer enlarges the capture zone and introduces a new singular zone to the game space, in which the pursuers can guarantee equal misses, regardless of the evader’s actions. Additionally, it is concluded that in the regular zones the closed-form optimal pursuit strategies are unchanged compared to two 1-on-1 engagements, whereas the optimal evasion strategy is more complex. Several simulations are performed, illustrating the adversaries’ behavior in different regions of the game space.

Detachment of an adhered micropillar from a dissimilar substrate

The mechanics of detachment is analysed for 2D flat-bottomed planar pillars and 3D cylindrical pillars from a dissimilar elastic substrate. Application of an axial stress to the free end of the pillar results in a singularity in stress at the corner with the substrate. An eigenvalue analysis reveals that the stress field near the corner is dominated by two singular eigenfields having eigenvalues (λ1,λ2) with corresponding intensities (H1,H2). The asymptotic stress field σij is of the form σij=H1rλ1−1fij(λ1,θ)+H2rλ2−1fij(λ2,θ), where fij describe the angular dependence θ of σij, and r is the radial distance from the corner. The stress intensities (H1,H2) are calculated numerically, using a domain integral approach, as a function of the elastic mismatch between the pillar and substrate. The singular zone extends across approximately 10% of the pillar diameter (in 3D) or pillar width (in 2D).Interfacial failure is predicted for an assumed crack emanating from the corner of pillar and substrate. For the case of an interfacial crack that resides within the domain of corner singularity, a boundary layer analysis is performed to calculate the dependence of the interfacial stress intensity factor K upon (H1,H2). When the crack extends beyond the domain of corner singularity, it is necessary to consider the full geometry in order to obtain K. A case study explores the sensitivity of the pull-off stress to the flaw size and to the degree of material mismatch. The study has implications for the optimum design of adhesive surface micropatterns, for bonding to either stiffer or more compliant substrates.

Trigonal representation of quantum orbitals, from hydrogen to calcium

Inspired from the work of Van Meersshe and Feneau-Dupont (1984), the ternary representation of the basic models in crystallography offers interesting perspectives to illustrate quantum orbitals, the classical S, P, D and F orbitals, by using a 3D representation of a trigonal system in place of the orthogonal system . On the other hand, the studies of the molecular orbitals of orthohydrogen (spins in the same sense) induces the hypothesis of a singularity zone between the atoms of hydrogen which could be a neutral zone favourable to the emergence of neutral particles and potentially can reorganize the repartition of electronic orbitals. Therefore, the nuclear spins can be related to the quantum orbitals distribution. Finally, by associating the ternary system in crystallisation with the orientation of nuclear spins and chemical bonds between the elements, we could work out a "trigonal" representation for the first elements of the periodic table, from hydrogen to calcium. The trigonal approach can facilitate the 3D representation of complex orbital systems. It offers a theoretical potential for crystallographic studies and it can support a large program of experimentation about the formation of the isotopes, the ionic character of covalent bonds and the gas state at low temperature for the electronegative elements of the periodic table.

Use of Artificial Neural Networks for the Development of an Inverse Kinematic Solution and Visual Identification of Singularity Zone(s)

This paper presents a non-conventional technique for solving the inverse kinematics problem using artificial neural networks. A feed forward multi-layer perceptron with backpropagation neural network is selected for this research. An inverse kinematic solution for a PUMA 560 robot is developed by training the neural network with the robot's end-effector Cartesian co-ordinates and its corresponding joint configurations. Once the network is well trained (90th percentile) and confident predictions can be achieved, a test input set (singularity conditions) is introduced to the trained network to simulate results. This technique proves promising since it requires little computation time over other traditional methods.

Dynamic Fracture Properties of Modified S-FPZ Model for Concrete

The fracture energy evaluated from the previous experimental results can be simulated by using the modified singular fracture process zone (S-FPZ) model. The fracture model has two fracture properties of strain energy release rate for crack extension and crack close stress versus crack width relationship for fracture process zone (FPZ) development. The relationship is not sensitive to specimen geometry and crack velocity. The fracture energy rate in the FPZ increases linearly with crack extension until the FPZ is fully developed. The fracture criterion of the strain energy release rate depends on specimen geometry and crack velocity as a function of crack extension. The behaviors of micro-cracking, micro-crack localization and full development of the FPZ in concrete can be explained theoretically with the variation of strain energy release rate with crack extension.

Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium

The self-similar elastoplastic field induced by dynamic expansion of a pressurized spherical cavity is investigated for pressure sensitive solids. Material behavior is described by the hypoelastic model of the Drucker–Prager material with a non-associated flow rule, with arbitrary strain-hardening. We examine in detail the external elastic field, which is expected to develop at a distance from the cavity prior to plastic yielding. A new observation that emerges from that elastic solution is the possible existence of a compressive elastic zone where yielding is prevented since the effective stress remains negative. Simple analytical solutions are given for the fully incompressible elastic/perfectly plastic material with a non-associated flow rule. In particular, we study the influence of plastic pressure sensitivity on the dynamic cavitation pressure. A few useful relations are derived for the cavitation pressure which reveal the coupled effect of plastic pressure sensitivity and material inertia. A separate numerical analysis is given for the fully incompressible strain-hardening solid with a non-associated flow rule. Several numerical illustrations are presented for the solid with an associated flow rule along with a plastic boundary layer analysis for the thin singular zone near the cavity wall.

On the analysis of singular stress fields Part 1: Finite element formulation and application to notches

The state of stress at the apex of a notch is characterized by a unique singular spatial distribution. The use of a special finite element to enable this stress state to be represented in a genreal model is discussed and details of the implementation are provided. Separately, an analytical description of the stress state is found from Williams' asymptotics and the generalized stress intensity factor for the configuration is found. This enables the region of domination of the singular term to be found and hence the domain within which any notch root singular process zone is controlled by the singular field to be quantified.

439 ナノ薄膜界面端における応力特異領域寸法(OS01-5 電子デバイス実装・電子材料と計算力学(5))(OS01 電子デバイス実装・電子材料と計算力学)

439 ナノ薄膜界面端における応力特異領域寸法(OS01-5 電子デバイス実装・電子材料と計算力学(5))(OS01 電子デバイス実装・電子材料と計算力学)

Complex fracture parameters for an interface crack between twohardening materials: a photoelastic study

In this paper, complex stress intensity factors (SIFs) at an interface crack are determined for a range of applied loads, crack lengths and remote mode mixes using automated photoelasticity. The specimen geometries comprise epoxy resin and aluminium alloy halves bonded together, and are loaded in either compact tension in mixed-mode conditions or in three-point bend under mode I conditions. In the experiments, full-field isochromatic data were obtained from the epoxy half using an established phase-stepping technique. A reworked approach to the determination of the SIFs was developed by combining a least-squares over-deterministic method for fitting crack-tip stress equations to the data and a weighting factor that ensures that only data in the singularity zone are used. For comparison, some of the specimens were tested using a linear-elastic finite element (FE) analysis and/or by experiment using homogeneous test specimens. Excellent agreement between the experimental and numerical SIF moduli was achieved for remote mode I loadings. However, for good agreement to be made between the phase angle results requires an additional phase term to be added to the FE solution at each load to account for the development of a crack-tip plastic zone. Further, results for the SIFs from remote mixed-mode loadings of the compact tension specimen only have a meaningful interpretation in light of small-scale yielding conditions. It is shown, qualitatively, that the experiments verify some of the predictions made in the literature of asymptotic behaviour at interface crack tips from results of elasto-plastic FE analyses.

An investigation of the stress singularity near the free edge of scarf joints

The singular stress field which develops at the interface corner of a scarf joint between two bonded elastic solids is investigated. Depending upon the scarf angle and the material elastic properties, the singular stresses at a radial distance r from an interface corner may be expressed in the form Hr λ−1 , where λ−1 is the order of the stress singularity and H is the intensity of the singularity. The intensity H of the singularity at the interface corner of scarf joints subjected to a remote uniform tension is evaluated for various material combinations and a range of scarf angles using a combination of the finite element method and a path independent contour integral. Two types of scarf joints are considered: (i) a scarf joint between two long bi-material strips and (ii) a scarf joint consisting of a thin elastic layer sandwiched between two substrates. The role of the intensity H, which determines the amplitude of the stress field within the singularity zone, is examined and the implications of the results for the initiation of joint failure are discussed.

Interfacial cracking from the freeedge of a long bi-material strip

A singular stress field develops at the corner where an interface between two bonded materials intersects a traction-free edge. Depending upon the geometry of the interface-corner, the free-edge stress singularity may be of the form Hrλ-1, where r is the radial distance from the corner, λ-1 is the order of the stress singularity and H is the intensity of the singularity. The intensity H of the singularity developed at the free-edge of a long bi-material strip subjected to uniform tension is evaluated for various combinations of materials, using the finite element method. The role of the intensity H in controlling the initial growth of an interfacial edge crack embedded within the singularity zone is examined. The implications of the results for the initiation of free-edge cracks are discussed.