Constant Propagation Research Articles

The enhanced extended finite element method for the propagation of complex branched cracks

By coupling the phantom node method with the mesh cut technique in the framework of the extended finite element method (XFEM), an enhanced XFEM for the propagation of complex branched cracks is proposed. The proposed method aims to solve the complex branched crack problems. Additionally, instead of the constant crack propagation length, a novel crack propagation scheme is introduced into the XFEM, in which the crack propagation length is a variable which is determined by two trial calculations. The feasibility and the accuracy of the proposed method are validated by numerical tests. The numerical results show that the enhanced XFEM can easily handle the complex branched crack problems, and it has the higher accuracy than the standard XFEM. Meanwhile, a smooth crack path can be obtained using the novel crack propagation scheme.

On the Nature of Pressure Wave Propagation through Ducts for Structural Health Monitoring Application

An effective structural health monitoring system fully exploits the flexibility offered by the 3D printing process by integrating a smart structural health monitoring technology inside the 3D-printed components. The system relies on the propagation of pressure waves with constant propagation speed through circular capillaries embedded in the structure. The nature of these waves seems to be determinant for the accuracy of the crack localization system. To achieve a better physical understanding of the nature of the propagating waves through the capillaries, computational fluid dynamics simulations are performed and compared to experimental results obtained with a self-built test setup. The presence of propagating shock waves is observed in the simulations and experiments, as well as a complex reflection mechanism around the leak location. Shock waves show the characteristic of not propagating at a constant velocity. This property complicates the actual localization system. To solve this, the constant velocity assumption should be replaced with the effective velocity evolution to increase the localization accuracy. The amplitude of the shock wave is attenuated with propagating distance, which proves that the effect of friction plays an important role and can, in turn, influence the localization system.

Bistable reaction equations with doubly nonlinear diffusion

Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves that describe the asymptotic behaviour of a larger class of solutions \begin{document}$ 0\leq u(x, t)\leq 1 $\end{document} of the problem posed in the real line. We investigate here the existence of waves with constant propagation speed, when the linear diffusion is replaced by the slow doubly nonlinear diffusion. In the present setting we consider bistable reaction terms, which present interesting differences w.r.t. the Fisher-KPP framework recently studied in [ 5 ]. We find different families of travelling waves that are employed to describe the wave propagation of more general solutions and to study the stability/instability of the steady states, even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call pseudo-linear, i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the pseudo-linear case, the travelling waves of the slow diffusion setting exhibit free boundaries. Finally, as a complement of [ 5 ], we study the asymptotic behaviour of more general solutions in the presence of a heterozygote superior reaction function and doubly nonlinear diffusion (slow and pseudo-linear).

Synthesis and Study of Nanodispersed Carbon in the Combustion of Acetylene in a Flow Detonation Tube

Nanodispersed carbon was obtained via high-temperature combustion of acetylene–oxygen mixtures in a flow-through tubular chamber in cyclic detonation waves (“pulsed detonation”) at a constant propagation velocity (Ddet ≈ 2150 m s–1). It was found that the position of a plateau in the curve describing how the detonation velocity depends on the content of oxygen in the starting detonation mixture in the range 15–30% coincides with the range of descending branches of the dependences of the specific adsorption surface area and adsorption of dibutyl phthalate by aggregated particles. Various physicochemical methods of analysis (X-ray diffraction analysis, Raman spectroscopy, high-resolution transmission electron microscopy, etc.) were used to comparatively examine the properties of nanodispersed carbon and of the known industrially produced domestic and foreign brands of technical-grade carbon. The conditions were found in which detonation nanocarbon particles are obtained in a certain range of parameters of micro- and macrostructures with improved morphology and basic electrical properties.

Investigation on the growth, optical, mechanical and dielectric properties of an inorganic potassium pentaborate dihydrate (KB5H4O10.2H2O) single crystal

Abstract Single crystals of potassium pentaborate dihydrate KB5H4O10. 2H2O (KBH) of dimension (10 × 5 × 2 mm3) were successfully grown through the solution growth technique under slow evaporation condition. The crystal structure of potassium pentaborate dihydrate was determined by single crystal X-ray diffraction and the material was crystallized in the orthorhombic system with space group Aba2 with lattice parameters a = 11.13 (A), b = 11.23 (A), c = 9.10 (A), α = β = γ = 90°, volume = 1137 (A)3. The presence of BO3, BO4 and water molecules were confirmed using Fourier transform infrared (FT-IR) vibrational spectroscopy. The ultraviolet (UV) - visible spectrum reveal the optical and electronic transition properties of the grown crystal. The optical absorption edge of the grown crystal is 210 nm with energy gap of 4.96 eV. The thermogravimetric (TG) and differential scanning calorimetry (DSC) studies showed that the material was stable up to 106 °C, which indicated that the grown crystal could be effectively used for various device applications below the temperature. Vickers microhardness is performed on the grown crystal in the load range from 10 to 50 g. The variation of hardness number with load represents the normal indentation size effect. Mechanical parameters such as yield strength, elastic stiffness constant, fracture toughness, brittleness index and crack propagation of single crystal are discussed in detail. The dielectric behaviour of the single crystal over an extensive range of frequencies and temperature is described. The second harmonic generation (SHG) signal from the KBH crystal is found to be 1.23 mV.

Prophage-Driven Genomic Structural Changes Promote Bartonella Vertical Evolution.

Bartonella is a genetically diverse group of vector-borne bacteria. Over 40 species have been characterized to date, mainly from mammalian reservoirs and arthropod vectors. Rodent reservoirs harbor one of the largest Bartonella diversity described to date, and novel species and genetic variants are continuously identified from these hosts. Yet, it is still unknown if this significant genetic diversity stems from adaptation to different niches or from intrinsic high mutation rates. Here, we explored the vertical occurrence of spontaneous genomic alterations in 18 lines derived from two rodent-associated Bartonella elizabethae-like strains, evolved in nonselective agar plates under conditions mimicking their vector- and mammalian-associated temperatures, and the transmission cycles between them (i.e., 26 °C, 37 °C, and alterations between the two), using mutation accumulation experiments. After ∼1,000 generations, evolved genomes revealed few point mutations (average of one-point mutation per line), evidencing conserved single-nucleotide mutation rates. Interestingly, three large structural genomic changes (two large deletions and an inversion) were identified over all lines, associated with prophages and surface adhesin genes. Particularly, a prophage, deleted during constant propagation at 37 °C, was associated with an increased autonomous replication at 26 °C (the flea-associated temperature). Complementary molecular analyses of wild strains, isolated from desert rodents and their fleas, further supported the occurrence of structural genomic variations and prophage-associated deletions in nature. Our findings suggest that structural genomic changes represent an effective intrinsic mechanism to generate diversity in slow-growing bacteria and emphasize the role of prophages as promoters of diversity in nature.

3‐D Finite Difference Time Domain Simulation of Lightning Strikes to the 634‐m Tokyo Skytree

AbstractWaveforms of vertical electric field observed at distances of 27, 57, and 101 km from the 634‐m tall Tokyo Skytree (Japan) struck by lightning have been reproduced using the 3‐D finite difference time domain method. Optically observed 3‐D lightning channels and currents directly measured in the tower were used. Distribution of current along the lightning channel was represented using the transmission line model, assuming a constant propagation speed v = 0.5c. Simulations with commonly assumed vertical channel did not allow us to reproduce the observed early (within 5 μs or so) field zero crossing when the 1‐D speed was set to be constant and equal to the 3‐D speed (v = 0.5c) used for the actual‐channel‐geometry case. It was, however, possible to achieve a good match for a vertical channel when the vertical component of 3‐D speed was evaluated for each nonvertical channel segment and used in the corresponding range of heights.

Acceleration of chemical reaction fronts

Chemical fronts and waves travelling in reaction-diffusion systems frequently induce hydrodynamic flow. This adds an additional transport process to the mechanism of spatio-temporal structure formation and can lead to an acceleration of the chemical (reaction) front. We report on the acceleration of travelling chemical fronts elicited by convection, as caused by the Marangoni effect in the monostable iodate-arsenous acid reaction in a thin liquid film. At a stoichiometric excess of iodate over arsenous acid, the reaction produces a large amount of iodine, which is surface-active. At the reaction front, iodine is transferred from the bulk to the surface inducing spatio-temporal gradients of surface tension that lead to capillary flows. These flows, in turn, promote further iodine adsorption at the surface through hydrodynamic mixing effects. As a consequence, an acceleration of the chemical fronts is observed, even if the concentration difference across the front is constant. After the transient acceleration of the reaction front, it settles at a constant propagation velocity, which is assumed to be regulated by a balance in the mass transfer between the bulk and the surface.

Nonlocal gap solitons in parity-time symmetric coupler with transverse real potential

In this work, we study the nonlocal gap solitons in a parity-time symmetric coupler with transverse real periodic potential having defocusing nonlocal nonlinearity. The propagation-invariant solutions show that the system supports both high-frequency and low-frequency modes as long as the gain/loss coefficient is less than the coupling coefficient. The high-frequency and low-frequency modes with single-hump, double-hump, and triple-hump structures are obtained. The high-frequency multi-hump modes are observed in the first band gap. The low-frequency single-hump modes lie in the semi-infinite band gap whereas low-frequency double-hump and triple-hump modes lie in the first band gap. The single-hump modes are trapped in the minimum of the potential. The double-hump modes spread through the two consecutive lattices while triple-hump modes lie across three consecutive lattices. As the range of the nonlocal nonlinearity varies, the propagation constants corresponding to different modes also change. Both the linear and dynamical stability analysis of the high-frequency and low-frequency modes have been done. The single-hump and double-hump modes are stable. The triple-hump modes may be stable or unstable. Studies on propagation dynamics reveal that when the range of the nonlocality increases, the width increases and the amplitude decreases, resulting in constant power propagation.

On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models

In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the $k$–$\unicode[STIX]{x1D714}$ closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models ($k$–$\unicode[STIX]{x1D714}$ and $k$–$\unicode[STIX]{x1D700}$ variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above $k$ is the turbulent kinetic energy density, $\unicode[STIX]{x1D714}$ is the specific dissipation rate, and $\unicode[STIX]{x1D700}$ is the dissipation.)

Exploring the role of reinforcement in controlling fatigue crack propagation behavior of perfluorosulfonic-acid membranes

Reinforced composite membranes in polymer-electrolyte fuel cells (PEFCs) are attracting more and more attention due to their simultaneously superior durability and high performance. Despite its improved durability during accelerated stress testing, the underlying mechanism of reinforcement in improving mechanical durability, particularly the crack propagation resistance, has not well been investigated. In this paper, we report the fatigue crack propagation behaviors of reinforced Nafion XL membrane and unreinforced Nafion 212 membrane. It is found that the fatigue crack growth rate of Nafion 212 membrane depends on stress ratios, and that of Nafion XL membrane depends on initial crack length and membrane orientation. In addition, the microstructure changes of reinforced Nafion XL membrane are examined through microscopy studies where two distinct features are observed: crack propagation in outer ionomer layers and interfacial delamination. These two features well explain the distinct fatigue crack propagation behavior of Nafion XL membrane, such as slow and almost constant fatigue crack propagation rate. The findings reported here are not only beneficial for understanding fatigue crack propagation mechanism of reinforced composite membrane but also helpful for designing and optimizing composite ion-conductive membranes.

Interaction between amino-functionalized inorganic nanoshells and acid-autocatalytic reactions.

Amino-functionalized inorganic silica nanoshells with a diameter of 511 ± 57 nm are efficiently used as hydrogen ion binders with a base dissociation constant of (1.2 ± 0.1) × 10-4. The hydrogen removal has been shown to produce reaction-diffusion fronts of constant propagation velocity in the autocatalytic chlorite-tetrathionate reaction when it is run in thin planar slices of nanoshell-containing agarose gel to exclude all convection related effects. By controlling the exact amount of amino-functionalized hollow nanospheres in the gel matrix it is possible to finely tune the propagation velocity of the chemical front in the 0.1-10 cm h-1 range. Remarkably, this can be achieved with very low amino-functionalized hollow inorganic nanosphere loadings between 0.1-0.01 (m V-1)%. The front width has also been determined experimentally, which increases by a factor of two with one magnitude decrease in the front velocity.

Study on the mechanical properties of potassium sodium hydroxide borate hydrate (KSB) single crystals by using Vickers microhardness tester

The mechanical properties of solution grown potassium sodium hydroxide borate hydrate single crystal (KSB) have been obtained by using Vickers microhardness studies in the load range from 10 to 70 g. The variation of microhardness with load represents the load independent value of hardness (Indentation size effect). The meyer’s index number ‘n’ is calculated as 1.81 and it belongs to soft material category. Various mechanical parameters such as yield strength, elastic stiffness constant, fracture toughness, brittleness index, hardness contour and crack propagation of KSB single crystal are discussed in detail.

Modeling observations of solar coronal mass ejections with heliospheric imagers verified with the Heliophysics System Observatory.

We present an advance toward accurately predicting the arrivals of coronal mass ejections (CMEs) at the terrestrial planets, including Earth. For the first time, we are able to assess a CME prediction model using data over two thirds of a solar cycle of observations with the Heliophysics System Observatory. We validate modeling results of 1337 CMEs observed with the Solar Terrestrial Relations Observatory (STEREO) heliospheric imagers (HI) (science data) from 8 years of observations by five in situ observing spacecraft. We use the self‐similar expansion model for CME fronts assuming 60° longitudinal width, constant speed, and constant propagation direction. With these assumptions we find that 23%–35% of all CMEs that were predicted to hit a certain spacecraft lead to clear in situ signatures, so that for one correct prediction, two to three false alarms would have been issued. In addition, we find that the prediction accuracy does not degrade with the HI longitudinal separation from Earth. Predicted arrival times are on average within 2.6 ± 16.6 h difference of the in situ arrival time, similar to analytical and numerical modeling, and a true skill statistic of 0.21. We also discuss various factors that may improve the accuracy of space weather forecasting using wide‐angle heliospheric imager observations. These results form a first‐order approximated baseline of the prediction accuracy that is possible with HI and other methods used for data by an operational space weather mission at the Sun‐Earth L5 point.

Simple Solutions of the Wave Equation with a Singularity at a Running Point, Based on the Complexified Bateman Solution

Simple explicit solutions of the homogeneous wave equation with constant propagation speed, having a power-like singularity at a moving space point, are constructed. The constructions are based on a complexified Bateman-type solution. An example of such a solution showing exponential decay with distance from the singular point is presented.

The Ultrasound Needle Pulse.

Recent theoretical developments have defined the conditions for forming a broadband beam that is narrow in axial extent but extended in range. The formulation is based on the classical angular spectrum decomposition and the requirement for arranging all spatial and temporal frequencies such that all components have constant phase propagation between planes. Analytic formulations are given for a 1-D source and a 2-D axisymmetric source, and comparisons are made against conventional focused Gaussian beams under similar conditions relevant to medical imaging systems.

Bend translation in multimode fiber imaging.

Light propagation in multimode fibers is typically assumed to be extremely sensitive to changes in geometry. We study here a particular configuration where an S-shaped bend is translated between two sections of fiber. In this sliding bend configuration, we show that nearly constant propagation characteristics can be obtained in certain fibers. Several fibers were tested using a bend with a peak radius of curvature of 25 mm. We found large differences in bending behavior between fibers of varying core diameters and numerical apertures. Fibers with a large numerical aperture are found to be more stable. In several fibers, the bend can be translated over a distance of 25 mm with a limited impact on imaging performance. The experimental results are confirmed using simulations. Our findings shed a new light on bending sensitivity in multimode fibers, and open up more possibilities for their use as imaging devices.

Analysis of Crack Extension Mechanism in the Near-Threshold Regime in an Aluminum Alloy

Short cracks initiated from pre-existing flaws are known to propagate in an intermittent way below threshold as the crack tip field interacts with the microstructure. If the stress amplitude is very low, similar effects as observed for short cracks may happen to long cracks leading to unexpected crack extension. This phenomenon is studied in this paper using flat dogbone specimens of a commercial aluminum alloy in two heat treatment states. Compression pre-cracked specimens were used to determine the threshold by continuous load increase according to a procedure proposed by Pippan et al. [Pippan et al. (1994)]. On this basis, crack growth experiments with an approximately constant ΔK-value propagation rate were performed at a stress ratio of R = 0.1. Results indicate that primary precipitates act as microstructural barriers causing crack deflection and crack branching. If the stress amplitude is low enough, shear-dominated crack extension has been found to be possible even for long cracks in the near-threshold regime. Both mechanisms keep the crack from extending continuously.

Strain-based approach for fatigue crack propagation simulation of the 6061-T651 aluminium alloy

Fatigue crack growth models based on elastic-plastic stress-strain histories, at the crack tip vicinity, and strain-life damage models have been proposed. The UniGrow model is a particular case of fatigue crack propagation models. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual fatigue crack driving force, taking into account mean stress and loading sequential effects. The performance of the UniGrow model is assessed based on available experimental constant amplitude crack propagation data, derived for the 6061-T651 aluminium alloy. Key issues in fatigue crack growth prediction, using the UniGrow model, in particular the residual stresses evolution, are discussed. Using available strain-life data, it was possible to model the fatigue crack propagation behaviour for the AA6061-T651, taking into account the stress R-ratio effects. A satisfactory agreement was found, between the predictions and the experimental crack propagation data.

Prediction of mode II delamination propagation life under a standard spectrum loading in a carbon fiber composite

Mode II constant amplitude fatigue delamination propagation tests were conducted at three different stress ratios, viz. R = 0.0, 0.5, and −1.0 using modified three-point bend test fixture and end notched flexure (ENF) test specimens of unidirectional IMA/M21 carbon fiber composite. Delamination length was measured by compliance technique. The delamination propagation rate (da/dN) plots were constructed for various stress ratios. Using an equivalent energy release rate concept, Geq, all the curves were merged into a single curve in the form of Paris equation, da/dN = C(Geq)k. The Paris constants, C and k, determined from the experimental results were subsequently used in predicting the delamination propagation life under a standard mini FALSTAFF spectrum load sequence. Experiments were also conducted under the same spectrum load sequence with various reference loads to determine the propagation lives. A reasonably good correlation was observed between the predicted and experimental mode II delamination propagation life under spectrum loads.