Planar Front Research Articles

Guided wave skew velocity correction in anisotropic laminates

Guided ultrasonic wave propagation in anisotropic structures results in directional dependency of velocity and wave skewing effects that can impact the accuracy of damage detection. Phase and group velocities of the A0 guided wave mode, propagating in a unidirectional carbon fiber reinforced laminate, were investigated experimentally and through finite element analysis. A correction for the significant offset in phase and group velocities due to wave skewing effects is illustrated for both point and short line sources, achieving good agreement with theoretical calculations assuming planar wave fronts. The influence of the line excitation length on velocity measurements is discussed.

Towards the theory of how a constitutional supercooling layer appears ahead of the planar crystallization front

This study, the effect of constitutional supercooling appearing ahead of the crystallization front and leading to the mushy layer origination is considered. An approximate analytical theory determining the time of mushy layer initiation is constructed. Theoretical predictions are in good agreement with numerical simulations carried out in previous studies.

Gas–Water Characteristics of Tight Sandstone in Xihu Sag, East China Sea Basin under Different Charging Models

The Xihu sag has two main oil−gas fields: Huagang Gas Field and Pinghu Oil Field. The Huagang formation is the reservoir of the Huagang Gas Field in the Central Tectonic Zone, while the Pinghu formation is the reservoir of the Pinghu Oil Field in the Western Slope Zone. In this paper, which mainly focusses on the Huagang formation, we conducted gas-driven water displacement–magnetic resonance imaging (GWD-MRI) experiments to simulate the charging characteristics of the sandstone migration layer, centrifugal magnetic resonance (Cen-NMR) experiments to simulate the short-term rapid trap charging process, and semi-permeable baffle (SPB) charging experiments to simulate the slow trap accumulation process. The results indicate that a start-up pressure exists for migration layer charging, where the start-up pressure for a core with a permeability of 0.3 mD is about 0.6 MPa. Our experimental simulations confirm that a planar front of changing water saturation exists, which has a width of about 1–1.5 cm. Migration layer charging is mainly influenced by two actions: the drive effect and the carrying effect. The drive effect can reduce the water saturation to 70–80%, while the carrying effect can further reduce the water saturation by 5–10%. The water saturation in the rapid charging scenario is mainly affected by the petrophysical characteristics of the rock: if the porosity is high, the water saturation is low. The water saturation decreases significantly with the increase in centrifugal force when the centrifugal force is small; however, when the centrifugal force is greater than 0.8 MPa, the water saturation decreases slowly. In the slowly charging trap experiment, the water saturation was basically stable at 40–50%, which matched the measured water saturation of the airtight cores well (ranging from 40–55%), and the petrophysical characteristics of the rock did not have a significant effect on the final water saturation.

Morphological stability analysis of a planar crystallization front with convection

Morphological stability analysis of a planar crystallization front with convection

Two-beam interferometry with a definitive phase-shift sign

Subject of study. The shift direction of interference fringes depending on the sign of the local phase shift introduced to one of the interfering waves was investigated in terms of two-beam interferometry. Aim of study. This study aimed to validate the fact that two-beam interferometry based on a single interferogram enables definitive determination of the phase-shift sign using the shift direction of the interference fringe. Method. Positions of the interference fringes and their shifts were calculated considering the phase distribution of interfering waves in the observation plane. The Mach–Zehnder interferometer was used to experimentally confirm the obtained theoretical results. Two closely adjacent substrates were used as objects. A subwavelength layer of a standard material was deposited on a part of the surface of one substrate, and a layer of metamaterial was deposited on the part of the second substrate. Main results. Expressions determining the direction and amplitude of the shift of interference fringes depending on the sign and amplitude of the local phase shift in one of the two interfering waves with a plane or spherical front were obtained. Strict rules of interference fringe shift depending on the sign of the phase shift were formulated based on the calculations. Results of the experiment using the Mach–Zehnder interferometer with different combinations of beams with spherical and plane wavefronts confirmed the theoretical calculations. Practical significance. Classic interferometric methods require significant time and the application of complex experimental procedures to determine the sign of the phase shift. The application of the results obtained in this study enables the determination of the sign of the introduced local phase shift based on a single interferogram without additional time expenditures. Thus, the method investigating the metamaterial layers of a subwavelength thickness is significantly simplified.

Multi-fidelity Bayesian optimization to solve the inverse Stefan problem

In this work, we propose an efficient solution of the inverse Stefan problem by multi-fidelity Bayesian optimization. We construct a multi-fidelity Gaussian process surrogate model by combining many low-fidelity estimates of a solidification problem with only a few high-fidelity measurements. To solve the inverse problem, we employ the Gaussian process model in a Bayesian optimization approach based on a multi-fidelity knowledge gradient acquisition function. To account for the specific structure of the target function, we reformulate it as a composite function and thus significantly improve the stability of the optimization procedure. Target values can be switched easily, and previously obtained samples and surrogate models can be reused. The proposed method iteratively improves the recommended solution of the inverse problem. Explicitly adding recommended points of previous iterations to the solution procedure enhances the convergence properties of the algorithm.We demonstrate the applicability of the algorithm by solving the inverse problem for a planar solidification front in a single-fidelity setting. Process parameters are identified for targeted crystal-growth velocities during directional dendritic solidification. The relation between these velocities and process parameters, such as undercooling, thermal diffusivity, capillarity, and capillary anisotropy, defines the thermo-mechanical properties of the solidified part in metal-based additive manufacturing. Material design is based on the corresponding inverse problem. Cost-efficiency of solving the inverse problem is improved by introducing a fidelity hierarchy based on coarse-grid approximations of high-fidelity numerical simulations. The open-source simulation framework ALPACA for multiphase flows allows to generate data at all fidelities. We demonstrate the superior convergence properties of the presented multi-fidelity approach by comparison with an approach solely based on high-fidelity measurements of the tip velocity.

The Hidden Dimension of Façades: Fractal Analysis Reveals Composition Rules in Classical and Renaissance Architecture

This study uses fractal analysis to measure the detailed intensity of well-known Classical and Renaissance façades. The study develops a method to understand their interrelated design principles more comprehensively. With this evaluation tool, one can observe intrinsic connections that support the historical continuity and point out balancing composition protocols, such as the ‘compensation rule’, that regulated design for centuries. The calculations offer mathematical constants to identify Classical and Renaissance details by plasticity rates. Finally, we base this method on spatial evaluation. Our calculations involve depth, which connects planar front views with the haptic reality of the façades’ tectonic layers. The article also discusses the cultural and urban implications of our results.

Nonplanar traveling fronts of the diffusion system with Belousov-Zhabotinskii reaction in [formula omitted

This paper studies nonplanar traveling fronts for a diffusion system with Belousov-Zhabotinskii (BZ for short) reaction in R3. First, we show the existence and stability results of pyramidal traveling fronts, and investigate their qualitative properties. By taking the limit of a pyramidal traveling front sequence, we obtain the conical traveling front and study its qualitative properties. Although both the pyramidal fronts and the conical fronts have larger traveling speeds than the planar front, their global mean speed equals that of the planar front in R3.

Persistence of the steady planar normal shock structure in 3‐D unsteady potential flows

AbstractThis paper concerns the dynamic stability of the steady three‐dimensional (3‐D) wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free boundary problem of a quasi‐linear hyperbolic equation of second order in a dihedral‐space domain between the shock front and the solid wall. The key difficulty is brought by the edge singularity of the space domain, the intersection curve between the shock front and the solid wall. Different from the two‐dimensional (2‐D) case, for which the singular part of the boundary is only a point, it is a curve for the 3‐D case in this paper. This difference brings new difficulties to the mathematical analysis of the stability problem. A modified partial hodograph transformation is introduced such that the extension technique developed for the 2‐D case can be employed to establish the well‐posed theory for the initial‐boundary value problem of the linearized hyperbolic equation of second order in a dihedral‐space domain. Moreover, the extension technique is improved in this paper such that loss of regularity in the a priori estimates on the shock front does not occur. Thus, the classical nonlinear iteration scheme can be constructed to prove the existence of the solution to the stability problem, which shows the dynamic stability of the steady planar normal shock without applying the Nash–Moser iteration method.

Maximizing Current Density in Monolithic Perovskite Silicon Tandem Solar Cells

Perovskite silicon tandem solar cells can overcome the efficiency limit of silicon single‐junction solar cells. In two‐terminal perovskite silicon tandem solar cells, current matching of subcells is an important requirement. Herein, a current‐matched tandem solar cell using a planar front/ rear side‐textured silicon heterojunction bottom solar cell with a p–i–n perovskite top solar cell that yields a high certified short‐circuit current density of 19.6 mA cm−2 is reported. Measures taken to improve the device are guided by optical simulation and a derived optical roadmap toward maximized tandem current density. To realize current matching of the two subcells, variation of the perovskite bandgap from ≈1.68 to 1.64 eV and thickness is investigated. Spectrometric characterization, in which current–voltage curves of tandem devices are recorded at systematically varied spectral irradiance conditions, is applied to determine the current matching point. In addition, remaining device limitations such as nonradiative recombination at the perovskite's interfaces are analyzed. Replacing the hole transport layer PTAA by 2PACz results in an overall certified power conversion efficiency of up to 26.8%. Precise simulation based on the device structure is essential as it provides efficient paths toward improving the device efficiency.

Aero Graphene in Modern Aircraft & UAV

The paper focuses on aero graphene and carbon nanotube (CNT) aerogel which will use in aircraft such as battery, engine, pitot probe, wings, fuselage, plane front glass which will also protect the aircraft from rain and wind because of the buoyant force. There are several ways to make aero graphene, but the most common approach includes reducing a precursor graphene oxide solution to make a graphene hydrogel. Through freeze-drying, any solvent is removed from the pores and replaced with air. A new method for producing aero graphene has emerged: 3-D printing. This is a significant scientific achievement. It creates a resin by diffusing graphene in a gel. The graphene resin can be cured into a solid and then dried in a furnace using UV LED light. Aero-graphene coating into the fuselage, wings and front glasses of the cockpit will give a great impact on the next-generation aircraft. Making an aircraft with aero-graphene will give the aircraft a strong and light skeleton.

Reaction-diffusion fronts in funnel-shaped domains

We consider bistable reaction-diffusion equations in funnel-shaped domains of RN made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front in the straight part of such a domain and moving into the conical part. We show a dichotomy between blocking and spreading, by proving especially some new Liouville type results on stable solutions of semilinear elliptic equations in the whole space RN. We also show that any spreading solution is a transition front having a global mean speed, which is the unique speed of planar fronts, and that it converges at large time in the conical part of the domain to a well-formed front whose position is approximated by expanding spheres. Moreover, we provide sufficient conditions on the size R of the straight part of the domain and on the opening angle α of the conical part, under which the solution emanating from a planar front is blocked or spreads completely in the conical part. We finally show the openness of the set of parameters (R,α) for which the propagation is complete.

Pattern formation and front stability for a moving-boundary model of biological invasion and recession

We investigate pattern formation in a two-dimensional (2D) Fisher–Stefan model, which involves solving the Fisher–KPP equation on a compactly-supported region with a moving boundary. The boundary evolves analogously to the classical one-phase Stefan problem, such that boundary speed is proportional to the local population density gradient. By combining the Fisher–KPP and classical Stefan theory, the Fisher–Stefan model alleviates two limitations of the Fisher–KPP equation for biological populations. Unlike the Fisher–KPP equation, solutions to the Fisher–Stefan model have compact support, explicitly defining the region occupied by the population. Furthermore, the Fisher–Stefan model admits travelling wave solutions with non-negative density for all wave speeds c∈(−∞,∞), and can thus model both population invasion and population recession. In this work, we investigate whether the 2D Fisher–Stefan model predicts pattern formation, by analysing the linear stability of planar travelling wave solutions to sinusoidal transverse perturbations. Planar fronts of the Fisher–KPP equation are linearly stable. Similarly, we demonstrate that invading planar fronts (c>0) of the Fisher–Stefan model are linearly stable to perturbations of all wave numbers. However, our analysis demonstrates that receding planar fronts (c<0) of the Fisher–Stefan model are linearly unstable for all wave numbers. This is analogous to unstable solutions for planar solidification in the classical Stefan problem. Introducing a surface tension regularisation stabilises receding fronts for short-wavelength perturbations, giving rise to a range of unstable modes and a most unstable wave number. We supplement linear stability analysis with level-set numerical solutions that corroborate theoretical results. Overall, front instability in the Fisher–Stefan model suggests a new mechanism for pattern formation in receding biological populations.

Stability of the Steady States in Multidimensional Reaction Diffusion Systems Arising in Combustion Theory

We prove that the steady states of a class of multidimensional reaction–diffusion systems are asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, paying particular attention to a special case, namely, systems of equations that arise in combustion theory. The steady-state solutions considered here are the end states of the planar fronts associated with these systems. The present work can be seen as a complement to the previous results on the stability of multidimensional planar fronts.

On planar reaction front in condensed materials: Reduced model, propagation speed, reaction zone balance, and insights into battery thermal runaway

In this work, the propagation and structure of planar reaction front in condensed materials is theoretically investigated and compared to the gas-phase cases. For condensed materials, the Lewis number (ratio of heat to mass diffusivities) approaches infinity due to negligible effect of mass diffusion, as such unique features are associated with a propagating reaction front, including distinct reduced models, discontinuity in wave propagation dynamics, and different controlling balance within the inner reaction zone. Large Ze number asymptotic analysis is performed to acquire the reaction front propagation speed and reveal the key controlling parameters, achieving very good agreement with numerical solutions. The results are further compared to those based on the large β asymptotic theory with different nondimensionalization strategies and controlling physical parameters. It is found that results in these two limits are in general different. Consistency can only be achieved when further assuming large thermal expansion ratio in the large β limit. In addition, by comparing to the finite Le number reaction front propagation in the large Ze number limit, it is shown that the reaction front in condensed phase propagates at least 2-3 times faster with the same thermochemistry. The dominant balance in the reaction zone is found to be fundamentally different when Le is taken infinity, further confirming the distinct nature of combustion. It is hence incorrect to tackle a combustion problem with infinite Le by extrapolating the results based on finite Le assumption. This study can provide useful guidance toward battery thermal runaway propagation and reaction front propagation in general condensed phase.

Different Modes of Combustion Wave on a Lattice Burner

The stabilization of a planar premixed flame front on a lattice (porous) burner is considered. The developed model captures all the important features of the phenomenon, while also admitting qualitative analytical investigation. It has been rigorously mathematically proven that there exist two different stabilization regimes: one with flame front located nearby the surface of the burner, and another with the flame front located inside the lattice. These two regimes result in qualitatively different gas temperature profiles along the flow that is monotonic and non-monotonic, respectively. The boundary between the two regimes is described in terms of dependence of the lattice solid material temperature on flow Peclet number. With similar temperature profiles, such dependencies may be both monotonic and non-monotonic. The transition between the two types of dependencies is controlled by the Arrhenius number. Conclusions of the study are supported by numerical analysis. They also compare favorably with the available experimental data. The novelty of the present approach is a fundamentally rigorous analytical analysis of the problem. The proposed analytical model, based on δ-function approximation of the chemical source term, agrees well (within 7% relative error) with the model based on the distributed description of the chemical reaction zone. The obtained results are important from both a theoretical and practical point of view. They demonstrate the existence of the two qualitatively different operating regimes for lattice burners, thus impacting design solutions for such devices. The results will be of great interest to the broader academic community, particularly in research areas where similar wave structures may emerge.

Propagation Phenomena for Nonlocal Dispersal Equations in Exterior Domains

This paper is concerned with the spatial propagation of bistable nonlocal dispersal equations in exterior domains. We first obtain the existence and uniqueness of an entire solution which behaves like a planar traveling wave front for large negative time. Then, when the entire solution comes to the interior domain, the profile of the front will be disturbed. However, the disturbance is local in space for finite time, which means the disturbance disappears as its location is far away from the interior domain. Furthermore, we prove that the solution can gradually recover its planar wave profile uniformly in space and continue to propagate in the same direction for large positive time provided that the interior domain is compact and convex. Our work generalizes the local (Laplace) diffusion results obtained by Berestycki et al. (2009) to the nonlocal dispersal setting by using new known Liouville results and Lipschitz continuity of entire solutions due to Li et al. (2010).

A novel algorithm for implementing perturbations in computational simulations of chemical dissolution‐front instability problems within fluid‐saturated porous media

AbstractThis paper deals with how to implement perturbations in the computational simulations of chemical dissolution‐front instability (CDFI) problems in fluid‐saturated porous media. On the basis of theoretical analysis, it is found that the application of a perturbation to the chemical dissolution front is equivalent to the application of an alternative perturbation to the dimensionless pore‐fluid normal velocity (relative to the planar chemical dissolution front) in the chemical dissolution zone, where the chemical dissolution front is located. This avoids the difficulty to find the spatial coordinates of the chemical dissolution front locations in the computational simulations of CDFI problems. Based on this new finding, a novel algorithm for implementing perturbations in the computational simulations of CDFI problems is proposed. The key point of the proposed algorithm is that the perturbed pore‐fluid normal velocity (relative to the planar chemical dissolution front) is used to directly replace the original pore‐fluid normal velocity (relative to the planar chemical dissolution front) in the related mathematical governing equations (MGEs), so that the proposed algorithm works for the porosity‐velocity‐concentration scheme when it is used to solve CDFI problems in fluid‐saturated porous media. In addition, the related theoretical analysis in this study has answered the previous unanswered question why the application of a perturbation to porosity works in the porosity‐pressure‐concentration scheme but does not work in the porosity‐velocity‐concentration scheme for solving the same CDFI problems in fluid‐saturated porous media. Through solving two illustrative examples with two different distributions of initial porosity, in which one is homogeneous and another is heterogeneous in the chemical dissolution system, the validity and usefulness of the proposed algorithm for implementing perturbations in the computational simulations of CDFI problems have been demonstrated.

Attenuation and inflection of initially planar shock wave generated by femtosecond laser pulse

Evolution of wavefront geometry during propagation and attenuation of initially planar shock waves generated by femtosecond laser pulses in aluminum is studied. We demonstrate that three stages of shock front inflection take place in consistent hydrodynamics and molecular dynamics simulations.During the first stage, the distance traveled by a near-planar wave DSW≲RL is smaller than the radius of heated laser spot RL. Wave attenuation is associated with one-dimensional plane (1D) rarefaction wave coming from the free surface. Such rarefaction wave shapes the shock wave to a 1D triangular pressure profile along direction normal to target surface with a shock front followed by an unloading tail. The second transitional stage starts after propagation of DSW∼RL, at which the unloading lateral waves begin to arrive to a symmetry axis of flow and initiate inflection of the initially planar shock front. Next at the third stage, the wavefront geometry is finally rounded and rapid attenuation of shock pressure begins at DSW≳RL.It is shown that such divergent shock wave cannot generate plastic deformations in aluminum shortly after propagation of DSW∼RL. Thus, we may estimate the maximal peening depth as a radius of focal spot, which sets an upper limit for the laser shock peening.The cessation of plastic deformation is caused by the fall of the shockwave amplitude below the elastic limit. In this case, the elastic-plastic wave transitions to a purely elastic mode of propagation. For large-sized light spots, this transition ends in the 1D mode of propagation.

Stability of entire solutions emanating from bistable planar traveling waves in exterior domains

This paper is devoted to the Lyapunov stability of entire solutions emanating from a planar front for bistable (bistable-type or multistable-type) reaction–diffusion equations in exterior domains Ω=RN∖K. Applying the super- and sub-solution method, we prove that the entire solution is Lyapunov stable under the small initial perturbations. In addition, the Lyapunov stability is independent of the geometrical conditions of the obstacle K.