Flat Boundary Research Articles

Bounds on buoyancy driven flows with Navier-slip conditions on rough boundaries

We consider two-dimensional Rayleigh–Bénard convection with Navier-slip and fixed temperature boundary conditions at the two horizontal rough walls described by the height function h. We prove rigorous upper bounds on the Nusselt number Nu which capture the dependence on the curvature of the boundary κ and the (non-constant) friction coefficient α explicitly. If h∈W2,∞ and κ satisfies a smallness condition with respect to α, we find Nu≲Ra12+∥κ∥∞, where Ra is the Rayleigh number, which agrees with the predicted Spiegel–Kraichnan scaling when κ = 0. This bound is obtained via local regularity estimates in a small strip at the boundary. When h∈W3,∞ , the functions κ and α are sufficiently small in L∞ and the Prandtl number Pr is sufficiently large, we prove upper bounds using the background field method, which interpolate between Ra12 and Ra512 with non-trivial dependence on α and κ. These bounds agree with the result in Drivas et al (2022 Phil. Trans. R. Soc. A 380 20210025) for flat boundaries and constant friction coefficient. Furthermore, in the regime Pr⩾Ra57 , we improve the Ra12 -upper bound, showing Nu≲α,κRa37, where ≲α,κ hides an additional dependency of the implicit constant on α and κ.

Optimizing thermosolutal and hydrothermal performance of radiative hybrid ferrofluid and entropy generation in a wavy porous enclosure

This research conducts a comprehensive investigation to enhance the thermosolutal and hydrothermal efficiency of a radiative Fe3O4–Cu–H2O hybrid ferrofluid within a wavy porous enclosure with the enlightenment for heat transfer and material science. The primary focus is on optimizing the thermosolutal performance in this irregular enclosure in which the lower boundary undergoes non-uniform heating and concentration, and the curved lateral boundaries keep cooling, lower concentration. Simultaneously, the upper flat boundary remains adiabatic. Using an efficient Higher Order Compact (HOC) scheme, we solve the governing streamfunction (ψ)-vorticity (ζ) form with the incorporation of energy and species transport equations of the coupled Navier–Stokes equations. Our results are robust and validated against established experimental and numerical data sources. The investigation delves into the impacts of well-defined parameters such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), Buoyancy ratio (N), Lewis number (Le), Radiation parameter (Rd), shape factor of nanoparticles (m) and solid volume fraction (ϕhnp) of the hybrid ferrofluid. Key findings underscore the consistent enhancement of both average Nusselt number (Nu¯) and average Sherwood number (Sh¯) with higher Buoyancy Ratio Numbers (N). Blades-shaped nanoparticles (m=8.6) demonstrate superior performance in both unitary and hybrid ferrofluid systems. Optimal conditions, identified at ϕhnp=0.04 and Ra=104 by the Bejan number (Be), underscore the positive impact of higher Buoyancy Ratio Numbers (N), resulting in a 25.41% increase in Nu¯ and an impressive 43.81% boost in Sh¯ observed from the shifting of N=0 to N=10.

Reconstruction of the time-dependent source in thermal grooving by surface diffusion

In hot polycrystalline materials, when a vertical flat grain boundary meets a horizontal surface the grain boundary forms a groove in the surface. Mathematically modelling features of such thermal grooving mechanism is therefore very important in characterizing polycrystalline materials composed of tiny grains intersecting an external free surface. With this aim in mind, we formulate and investigate a novel inverse problem of reconstructing the unknown time-dependent source term entering the fourth-order parabolic equation of thermal grooving by surface diffusion from a given integral observation. We formulate and prove in Theorems 2.3–2.7 that this linear inverse problem is well-posed. However, in practice, the ideal regularity of data under which the inverse source problem is stable is never satisfied due to the inherent non-smoothness of the measurement. Consequently, this leads to the inverse problem with raw data becoming ill-posed. In order to obtain accurate and stable solutions, we develop and compare two numerical methods, namely, a time-discrete method and an optimization method. We obtain error estimates and convergence rates for the time-discrete method. For the optimization method, an objective functional, which is proved to be Fréchet differentiable, is introduced and the conjugate gradient method (CGM), regularized by the discrepancy principle, is developed to compute the minimizer yielding the source term. The results of two numerical tests illustrate the performance of the two methods for both exact and noisy measured data.

Designer artificial chiral kagome lattice with tunable flat bands and topological boundary states

The kagome lattice is a well-known model system for the investigation of strong correlation and topological electronic phenomena due to the intrinsic flat band, magnetic frustration, etc. Introducing chirality into the kagome lattice would bring about new physics due to the unique symmetry, which is still yet to be fully explored. Here we report the investigation on a two-dimensional chiral kagome lattice utilizing tight binding band calculation and topological index analysis. It is found that the periodic chiral kagome lattice would bring about a robust zero-energy flat band. Furthermore, in the Su–Schrieffer–Heeger type dimer-/trimerized breathing chiral kagome lattice with particular edge terminations, topological corner states or metallic edge states would appear, implying new candidates for the second-order topological insulator. We also proposed the construction strategy for such lattices employing the scanning tunneling microscope atom manipulation technique.

The lie group analysis method for heat transfer in steady boundary layer flow field of nanofluid

In order to reveal the mechanism of the abnormal movement (Brownian motion enhances thermal scattering) of nanoparticles on the fluid enhanced heat transfer, the two-phase model was used to study the abnormal convection and diffusion of viscous nanofluids in the flat boundary layer of porous medium. Firstly, for the two-dimensional steady boundary layer stagnation point flow of incompressible Newtonian-nanofluids, the nonlinear governing equations of the flow field and temperature field of nanofluids are established from the Oberbeck-Boussinesq approximate equations. Secondly, the modern Lie group analysis method is introduced, we give the Lie symmetry determining equation of the flow field partial differential equations and the characteristics of the solutions. Further, using the relationship between the Lie symmetries and the conserved quantities, the conservation vector form of the flow field and the group invariant solution are derived in detail, and the reduced order model of the nanofluid flat boundary layer is obtained. Finally, the correctness of the analytical results obtained by the Lie group method was verified for different values of the flow parameter Prandtl. Research has shown that the Lie group method can be used to analytically solve the velocity and temperature distribution functions of abnormal motion of nanoparticles. The fluid temperature increases with the increase of the volume fraction parameter of nanoparticles, but decreases with the increase of the Prandtl value of the base fluid, and decreases with the increase of the plate stretching speed. The Lie group analysis method in this paper provides reference value for numerical simulation solutions of various heat and mass transfer in nanofluids.

Vacuum Effects Induced by a Plate in de Sitter Spacetime in the Presence of a Cosmic String

In this paper, we investigate the vacuum expectation values of the field squared and the energy–momentum tensor associated to a charged massive scalar quantum field in a (1+D)-dimensional de Sitter spacetime induced by a plate (flat boundary) and a carrying-magnetic-flux cosmic string. In our analysis, we admit that the flat boundary is perpendicular to the string, and the scalar field obeys the Robin boundary condition on the plate. In order to develop this analysis, we obtain the complete set of normalized positive-energy solutions of the Klein–Gordon equation compatible with the model setup. Having obtained these bosonic modes, we construct the corresponding Wightman function. The latter is given by the sum of two terms: one associated with the boundary-free spacetime, and the other induced by the flat boundary. Although we have imposed the Robin boundary condition on the field, we apply our formalism considering specifically the Dirichlet and Neumann boundary conditions. The corresponding parts have opposite signs. Because the analysis of bosonic vacuum polarization in boundary-free de Sitter space and in the presence of a cosmic string, in some sense, has been developed in the literature, here we are mainly interested in the calculations of the effects induced by the boundary. In this way, closed expressions for the corresponding expectation values are provided, as well as their asymptotic behavior in different limiting regions. We show that the conical topology due to the cosmic string enhances the boundary-induced vacuum polarization effects for both field squared and the energy–momentum tensor, compared to the case of a boundary in pure de Sitter spacetime. Moreover, the presence of a cosmic string and boundary induces non-zero stress along the direction normal to the boundary. The corresponding vacuum force acting on the boundary is also investigated.

Recursive analytical quadrature for the close evaluation of Laplace and Helmholtz layer potentials over flat boundary elements in [formula omitted

A method for the analytical evaluation of singular and nearly singular layer potentials arising in the collocation boundary element method for the Laplace and Helmholtz equation is developed for flat boundary elements with polynomial shape functions. The method is based on dimension-reduction via the divergence theorem and a Recursive scheme for evaluating the resulting line Integrals for Polynomial Elements (RIPE). It is used to evaluate single layer, double layer, adjoint double layer, and hypersingular potentials, for both the Laplace and the Helmholtz kernels. It naturally supports nearly singular, singular, and hypersingular integrals under a single framework. The developed recursive algorithm allows accurate evaluation of layer potentials associated with O(p2) density functions used in a pth order boundary element in O(p3) time for the Laplace case.

Magnetic field-enhanced orifice traversal of droplets: Minimizing surface adhesion for improved efficiency

In this article, we propose the feasibility of replacing traditional materials with ferrofluid droplets to actively regulate their behavior as they traverse an orifice in the presence of an external magnetic field. The traversal behavior of the droplet is investigated using both rectangular and curved orifice boundaries. We employed a simplified multiphase lattice Boltzmann method (SMLBM) to simulate the flow field and interface, which considerably improves computational efficiency. For magnetic field generation, a self-correction procedure is coupled with SMLBM. For curved boundaries, we used our recently developed immersed boundary approach, which can specify wetting boundary conditions for both stationary and moving boundaries, in the same way as flat boundaries are handled. To check the validity of our methods, we first simulated three benchmark phenomena and compared our results with experimental and numerical findings. This research includes orifice geometries, including straight and curved boundaries, and investigates the dynamic behavior of droplets traversing through narrow opening, increased orifice thicknesses, and large diameter droplets passing through confined and multiple orifices. All simulations are initially carried out without the use of magnetic fields, then the experiments are repeated and compared with the addition of a uniform magnetic field. It is found that, in the absence of a magnetic field, the droplets can successfully pass only through wide orifices. However, for narrow or thick orifices, a significant portion of droplet volume adheres to the orifice walls, causing an apparent decrease in falling velocity. In contrast, the addition of a magnetic field enables the droplet to efficiently traverse through even narrower and thicker orifices, attaining faster speeds and reduced mass loss. Furthermore, the influence of Reynold number and magnetic field strengths on the droplet velocity, its wetting dynamics, and relative shedding area are also discussed in detail.

Generalized Integration over Nonrectifiable Flat Curves and Boundary Value Problems

Generalized Integration over Nonrectifiable Flat Curves and Boundary Value Problems

Method of solution composition in contact problems with friction of deformable bodies

A new iterative method for solving static contact problems of two deformable bodies is proposed. The method is based on alternately solving the unilateral contact problem for the first body and the linear elasticity problem with natural boundary conditions for the second body. Fulfillment of Coulomb's friction law involves correction of tangential nodal forces in the sliding area and setting kinematic boundary conditions in the sticking area for the contact boundary of the first body. The goal of solving the linear elasticity problem for the second body is to gradually equalize contact loads on the interacting surfaces. The advantages of the method are demonstrated by solving a number of model examples, including unilateral contact of a linear-elastic plate with a solid foundation, bilateral contact of pressing a deformable block into the foundation, the Hertz problem of contact of two deformable cylinders etc. The method can solve problems on flat and curvilinear contact boundaries.

Pricing first-touch digitals with a multi-step double boundary and American barrier options

A first-touch digital option delivers a payoff when an underlying variable first touches a given boundary, and most studies discuss its pricing by assuming a single flat boundary and a fixed payout amount. This paper derives explicit pricing formulas for first-touch digital options with a multi-step double boundary and customizable payoffs. To this end, we establish the probabilities of the first-hitting times of a Brownian motion for the multi-step double boundary. Furthermore, we explain how the first-touch digital option pricing formulas approximate an American knock-out multi-step barrier option.

Reconstruction of Co-Seismic and Post-Seismic Processes for the February 6, 2023 Earthquake in Turkey from Data of Satellite SAR Interferometry

Abstract—Using different methods for processing SAR images from the Sentinel-1A satellite, the displacement fields were determined in the region of the East Anatolian Fault Zone (EAFZ) and the Sürgü-Çardak faults, as well as a small fault on the continuation of the East Hatay fault zone, which rupture initiated a series of catastrophic earthquakes in Turkey on February 06, 2023. DInSAR and offset methods were applied. The most detailed data on the displacements were obtained by the offset method using images from the descending orbit. When constructing the model from the available SAR data, the data with the maximum signal-to-noise ratio were selected. For the northern part of the region, above 37.4° N, the range displacements obtained by the offset method from a descending orbit were used. South of parallel 37.0° N, we used azimuth displacements from the same descending orbit. The model of the seismic rupture was constructed on the basis of solution of (Pollitz, 1996) of the problem of deformations at the surface of a layered spherical Earth caused by along dip and strike displacements on a rectangular cut located inside the planet. Pollitz (1996) demonstrated that ignoring the spherical layering of the planet leads to errors up to 20%, with the largest errors occurring in the presence of a large strike-slip component. Ignoring sphericity also introduces an error when using the solution in the framework of the idealization of an elastic homogeneous half-space with a flat free boundary (Okada, 1985) which was used when constructing USGS and (Barbot et al., 2023) models. In our model the surfaces of seismic rupture are approximated by 19 rectangular elements along the strike, divided into three levels along the dip. Another element approximated a rupture along the extension of the East Hatay Fault Zone. As in the models of other authors (USGS; Barbot et al., 2023), in our model in the southern part of the EAFZ, the displacements increase from south to north, and are mainly concentrated in the upper part of the Earth’s crust to a depth of 10 km. At the southern end of this rupture, displacements in our model with an amplitude of up to 2 m are obtained at the lower levels of the model, and at its upper level, the displacements were only 0.11 m, and in this area on February 20, 2023 an earthquake of magnitude 6.3 occurred with a hypocentre depth of 11.5 km. The main displacements on the EAFZ are determined on its central segment. Here, the displacements go to a greater depth, their value reaches 10.2 m. On the Sürgü-Çardak fault, significant displacements occurred down to a depth of 20 km; displacements exceeded 9.8 m. In our model, at the northeast end of the seismic rupture along the EAFZ, a displacement area of 6.8 m overlaps with the southwest end of the seismic rupture model of the Doğanyol-Sivrice earthquake of January 24, 2020 with Mw 6.7, published on the USGS website. Therefore, our model does not confirm the hypothesis of the presence of a seismic gap here, which, according to (Barbot et al., 2023), is a zone of a possible nearest earthquake.

In-Situ Observation and Analysis of the Evolution of Copper Aluminum Composite Interface

To study the micromorphology and dynamic evolution law of copper aluminum composite interface evolution, ultra-high temperature laser Confocal microscopy (CLSM) was used to observe and analyze the evolution of copper aluminum interface in situ, and then SEM, EDS and other advanced material analysis methods were used to observe the micromorphology of the composite layer, and study the composition of the interface layer and the formation process of the copper aluminum composite interface. The results indicate that the formation of the copper aluminum composite interface layer is mainly related to the mutual diffusion of copper aluminum atoms and the interface reaction between copper and aluminum. The bonding of the copper aluminum composite interface is mainly related to the melting of the metal surface of the interface layer and the mutual diffusion of copper aluminum atoms, which is the main mechanism of the copper aluminum composite interface bonding. The intermetallic compound is mainly Al2Cu. In situ, observation of copper aluminum composite interface shows that there is a clear and relatively flat boundary between copper and the interface layer, while the boundary between aluminum and the interface layer is not straight, which is caused by the difference in thermal expansion coefficient, Lattice constant and hardness between intermetallic compounds and matrix and between intermetallic compounds. At the same time, it was found that there is a certain relationship between the visual changes of the copper aluminum composite interface image and reaction-diffusion migration during in-situ observation using a confocal laser scanning high-temperature microscope. Moreover, under no pressure, the oxide layer and interface inclusions can seriously affect the interface bonding.

Towards a solid-fluid territory: Sand dredging, volumetric practices, and earthly elements

Since 2020, although Taiwan has expelled dredgers and sand-transporting vessels from areas under its control, it has failed to stop sand loss. Marine researchers have noted that such issues problematise the ontology that underlies work on territory and ocean governance, wherein the ocean is regarded as a flat space that can be zoned and territorialised. Attention has thus shifted from considering the ocean as a flat terrestrial legal boundary to regarding it as a dynamic, volumetric entity, constantly shaped by the distinct qualities of the ocean and human endeavours. While such thought-provoking work offers crucial insight into our understanding of territory, its emphasis on the distinct qualities of water unconsciously reinforces the distinction between the land and the sea. Informed by recent materials-related social studies, this paper proposes the notion of the marine environment as a solid-fluid territory that foregrounds the importance of planetary dynamic geological processes. I argue that in this sense, territory is always involved in the governance of solid-fluid transitions in different voluminous contexts. The solid-fluid territory, I suggest, is characterised by three elements: solid-fluid transitions, resources, and volumetric practices. With reference to the controversy over sand mining in the Taiwan Strait, this paper reveals that while various geotechnologies are deployed to manage solid-fluid materials, state security practices often complicate our understanding of these shifting, dynamic geological processes and challenge human boundary-making. Therefore, geopolitics must acknowledge the nuances resulting from such solid-fluid movements and transitions, as well as their impacts on territorial issues.

Finite-difference method for modeling the surface wave propagation with surface topography in anisotropic-viscoelastic media

The growth of urbanization makes it increasingly important to accurately investigate underground spaces. Surface-wave-based inversion methods are becoming popular due to their cost-effectiveness and efficiency in reconstructing underground space. However, these methods may produce inaccurate results in the presence of media anisotropy or/and viscoelasticity. To investigate the influence of media anisotropy or viscoelasticity on surface waves, it is crucial to develop an efficient and accurate forward modeling method in anisotropic-viscoelastic (AV) media. The finite-difference (FD) method is a widely used forward modeling method in surface-wave-based inversion methods. However, implementing the free-surface boundary condition and representing non-flat topography can be challenging. Considering the challenges described above, this study proposes a simple and efficient FD method for modeling surface-wave propagation. The proposed method employs a parameter-modified strategy to implement the stress-free condition by modifying the model parameters near the (non-) flat free-surface boundary. A staircase discretization strategy is then used to represent the non-flat free surface. To suppress the staircase diffractions caused by the staircase discretization strategy, an independent wavefield superposition is adopted with modeling results of different parameter configurations. Compared with conventional FD methods, the proposed method can reduce computational costs while accurately simulating surface waves. Numerical experiments have demonstrated the accuracy and feasibility of the proposed method. The proposed method provides a theoretical basis for surface-wave-based inversion methods and contributes to the development of accurate underground space investigation.

A Multi-Scale Investigation to Predict the Dynamic Instabilities Induced by Frictional Contact

We propose a new variational formulation to model and predict friction-induced vibrations. The multi-scale computational framework exploits the results of (i) the roughness measurements and (ii) the micro-scale contact simulations, using the boundary element method, to enrich the contact zone of the macroscopic finite element model of rubbing systems with nominally flat contact boundaries. The resulting finite elements at the contact interface of the macroscopic model include (i) a modified normal gap and (ii) a micro-scale description of the contact law (i.e., pressure gap) derived by solving the frictionless contact problem on a rough surface indenting a rigid half-plane. The method is applied to a disc brake system to show its robustness in comparison with classical deterministic formulations. With respect to the traditional complex eigenvalues analysis, the proposed multi-scale approach shows that the inclusion of roughness significantly improves the results at low frequencies. In this panorama, any improvement of dynamic instabilities predictions should be based on an uncertainty analysis incorporating roughness combined with other parameters such as friction coefficient and shear moduli of the pads, rather than on roughness itself.

Constructing aerotolerant bioanode with flat and compact biofilm for high power generation of microbial fuel cells

Reducing electrode spacing is consideredthemost effective way to maximize the power density of microbial fuel cell (MFC) due totheeffective reduction of internal resistance. However, reducing electrode spacing presents the challenge of diffusing oxygen from the cathode to the anode, therebyreducinganode performance.Constructing aerotolerant anode may be one of the effective ways to minimize the effect of oxygen on anode performance.Here, wereportthat usingsmall external resistance ormaintaining high nitrogen sparging rate during bioanode enrichment could significantly enhance the aerotolerant characteristic ofthebioanode. The voltage loss affected by oxygenwassignificantly reduced and, as a result, the power density of the compact electrode assembly MFCincreasedby 85% reaching4300 mW/m2.Theaerotolerant bioanodehada flat and compact biofilm structure andalarger laminar boundary layer (over 300 μm)to reduceoxygen diffusion,whiletheaerointolerant bioanodehada rough and porous biofilm structure andasmaller laminar boundary layer (less than 80 μm). The microbial community of all the bioanodeswasdominated by Geobacter (over 55%). Therefore, this study providesasample way to constructanaerotolerant bioanode for high power generationinMFCs.

Repetitive Acoustic Streaming Patterns in Sinusoidal Shaped Microchannels

Geometry of the fluid container plays a key role in the shape of acoustic streaming patterns. Inadvertent vortices can be troublesome in some cases, but if treated properly, the problem turns into a very useful parameter in acoustic tweezing or micromixing applications. In this paper, the effects of sinusoidal boundaries of a microchannel on acoustic streaming patterns are studied. The results show that while top and bottom sinusoidal walls are vertically actuated at the resonance frequency of basic hypothetical rectangular microchannel, some repetitive acoustic streaming patterns are recognised in classifiable cases. Such patterns can never be produced in the rectangular geometry with flat boundaries. Relations between geometrical parameters and emerging acoustic streaming patterns lead us to propose formulas in order to predict more cases. Such results and formulations were not trivial at a glance.

Modulation of the reflected signal due to a nonlinear surface charge excited on a plasma boundary by an electromagnetic beam

The description of the nonlinear surface charge was supplemented by an equation linking the distortion of the surface shape of the plasma boundary with the characteristics of the motion of electrons in this region for the selected type of external influence. As a result, it became possible to study the interrelated appearance and development of these two effects in conditions of commonality of processes that cause their occurrence. On a simple example when a flat boundary of a cold plasma interacts with intense electromagnetic radiation, it was shown that there is development of non linear surface charge, which results in change of the surface curvature and causes fluctuations in the amplitude of the reflected wave. The “shallow water theory” has been used for the derivation of the equation which to link the spatial and temporal structures and evolution of surface charge and curvature, which affect the reflected wave. Both qualitative and numerical analyses have been performed.

Study on the separation in the shock wave/boundary layer interaction induced by a curved fin

The effect of an isentropic compression wave fan on shock wave/turbulent boundary layer interaction induced by a curved fin is studied by the nanoparticle-based planar laser scattering method, oil flow method, and numerical method. The curved fin consists of two parts: A curved surface generating an isentropic compression fan and a planar surface ensuring the compression fan focuses into a swept shock wave. The flowfield is compared with the three-dimensional separation flowfield induced by a planar fin with the same deflection angle. The results show that the compression fan can compress the turbulent boundary layer without separation, while the focused swept shock wave drives the whole turbulent boundary layer to separate. The flat plate turbulent boundary layer beside the fin is mainly rolled into the separation vortex. The focused swept shock wave adjusts the separation zone to be quasi-conical, suggesting that the quasi-conical separation is the nature of the flowfield in which a turbulent boundary layer interacts with a swept shock wave. The isentropic compression part of the curved fin can prevent the secondary separation of the planar swept shock wave/turbulent boundary layer interaction by changing the attachment process. Based on the focus point of the compression wave fan, the equivalent apex of the curved fin is proposed. The area and intensity of the separation vortex induced by the curved fin are nearly linear as those in the planar fin interaction flowfield. However, the area of the separation vortex induced by the curved fin is larger. The intensity growth of the vortex caused by the curved fin is slower than that of the planar fin.