Nonlinear Surface Research Articles

Lattice Boltzmann finite-difference-based model for fully nonlinear electrohydrodynamic deformation of a liquid droplet.

Electric field-induced flows involving multiple fluid components with a range of different electrical properties are described by the coupled Taylor-Melcher leaky-dielectric model. We present a lattice Boltzmann (LB)-finite difference (FD) method-based hybrid framework to solve the complete Taylor-Melcher leaky-dielectric model considering the nonlinear surface charge convection effects. Unlike the existing LB-based models, we treat the interfacial discontinuities using direction-specific continuous gradients, which prevents the miscalculation arising due to volumetric gradients without directional derivatives, simultaneously maintaining the electroneutrality of the bulk. While fluid transport is recovered through the LB method using a multiple relaxation time (MRT) scheme, the FD method with a central difference scheme is applied to discretize the charge transport equationat the interface, in addition to the electric field governing equationsin the bulk and at the interface. We apply the developed numerical model to study the different regimes of droplet deformation due to an external electric field. Similar to the existing analytical and other numerical models, excluding the surface charge convection (SCC) term from the charge transport equation, the present methodology has shown excellent agreement with the existing literature. In addition, the effect of SCC in each of the regimes is analyzed. With the present numerical model, we observe a strong presence of SCC in the oblate deformation regime, contrary to the weak effect on prolate deformations. We further discuss the reason behind such differences in the magnitude of nonlinearity induced by the SCC in all the regimes of deformation.

Pressure analysis in nonlinear waves by revisiting the breaking wave onset

Breaking waves are numerically simulated by solving the two dimensional nonlinear free surface boundary conditions in potential theory. Onset of breaking wave is determined for two configurations: A focused wave in intermediate depth and a dambreaking flow leading to a soliton. Two criteria are identified: first, a kinematic criterion follows from the ratio of the horizontal velocity at the crest to the phase velocity; second, a dynamic criterion is formulated in terms of the vertical pressure gradient. Thresholds of these criteria are proposed in the literature. For the two configurations studied here, it is shown that these thresholds are not universal but they are reasonable estimates of the onset of breaking wave. To facilitate this study, the Hessian matrix of the pressure is analyzed. It is shown that there exists a continuous curve that links the crest of the wave to the sea bottom. This line follows from the colinearity of the pressure gradient and one of the two eigenvectors of the Hessian matrix. The analysis of the pressure, its gradient and its second derivatives along this line gives more insights into the definition of the thresholds associated to the onset of breaking wave.

Geometrically nonlinear rapid surface heating in FGM hermetic capsule

Geometrically nonlinear rapid surface heating in FGM hermetic capsule

Peridynamic modeling of nonlinear surface acoustic waves propagating in orthotropic materials

Due to the elastic nonlinearity of the material, high-amplitude surface acoustic waves undergo nonlinear evolution during propagation and may lead to material failure. To enable the acoustical quantification of material nonlinearity and strength, a comprehensive understanding of this nonlinear evolution is necessary. This paper presents a novel ordinary state-based nonlinear peridynamic model for the analysis of the nonlinear propagation of surface acoustic waves and brittle fracture in anisotropic elastic media. The relationship between seven peridynamic constants and second- and third-order elastic constants is established. The capability of the developed peridynamic model has been demonstrated by predicting surface strain profiles of surface acoustic waves after propagating in the silicon (111) plane and the 〈112¯〉 direction. On this basis, the nonlinear wave-induced spatially localized dynamic fracture is also studied. The numerical results reproduce the main features of nonlinear surface acoustic waves and fracture observed in experiments.

A unified steady and unsteady formulation for hydrodynamic potential flow simulations with fully nonlinear free surface boundary conditions

This work discusses the correct modeling of the fully nonlinear free surface boundary conditions to be prescribed in water waves flow simulations based on potential flow theory. The main goal of such a discussion is that of identifying a mathematical formulation and a numerical treatment that can be used both to carry out transient simulations, and to compute steady solutions — for any flow admitting them. In the literature on numerical towing tank in fact, steady and unsteady fully nonlinear potential flow solvers are characterized by different mathematical formulations. The kinematic and dynamic fully nonlinear free surface boundary conditions are discussed, and in particular it is proven that the kinematic free surface boundary condition, written in semi-Lagrangian form, can be manipulated to derive an alternative non penetration boundary condition by all means identical to the one used on the surface of floating bodies or on the basin bottom. The simplified mathematical problem obtained is discretized over space and time via Boundary Element Method (BEM) and Implicit Backward Difference Formula (BDF) scheme, respectively. The results confirm that the solver implemented is able to solve steady potential flow problems just by eliminating null time derivatives in the unsteady formulation. Numerical results obtained confirm that the solver implemented is able to accurately reproduce results of classical steady flow solvers available in the literature.

USV Parameter Estimation: Adaptive Unscented Kalman Filter-Based Approach

In this article, a new kind of adaptive unscented Kalman filter (AUKF) is proposed to deal with the parameter estimation problem for a class of nonlinear unmanned surface vessel (USV) models with unknown statistical characteristics of process noises. Specifically, the considered parameter estimation problem is first transformed into the state estimation problem by extending eighteen parameters and three unknown inputs into augmented states for the USVs. With the help of such a transformation, the unknown inputs including disturbances and modeling errors are estimated effectively, and employed to construct the estimators such that the effect of these unknown inputs on parameter estimation can be significantly suppressed. Under the condition that the structure of the covariance matrix of the process noise is available, an adaptive law is further designed to estimate such a high-dimensional covariance matrix where the covariance estimation errors can be reduced. Finally, the proposed estimation approach is verified via performing the practical experiment as well as numerical simulations.

Robust optimal control of a nonlinear surface vessel model with parametric uncertainties

This paper presents a fast alternative optimization method for developing a reliable optimal controller that can handle system model parameter uncertainties. The source of uncertainty in this study is identified as hydrodynamic coefficients, which are prone to errors due to the challenges involved in obtaining accurate values. The proposed optimization method utilizes a complex nonlinear ship model provided by Maneuver Modelling Group (MMG) as the reference for the ship motion model. The optimization process is divided into two stages: a blind search followed by bisection optimization, to obtain a robust optimal controller. To demonstrate the effectiveness of the proposed approach, system response analysis and practical tests were performed on Step, M-Turn, and Doublet maneuvers. The results show that the controller parameters obtained from the proposed optimization method are capable of achieving high success rates in controlling a system with uncertain parameters.

Three-dimensional aerodynamic shape inverse design based on ISOMAP

Due to the numerous challenges associated with CFD calculations and high-dimensional data processing, it is challenging for the current approaches to satisfy the demands of inverse design of three-dimensional aerodynamic configuration. This work provides an effective inverse design method for three-dimensional aerodynamic configuration based on Isometric Feature Mapping (ISOMAP) in manifold learning. In this approach, the aerodynamic shape and parameterized control volume are regarded as the spatial nonlinear coupling surface, which is then projected into the low-dimensional manifold space via the ISOMAP approach to producing the manifold structure. The deformation control points' pressure distribution, which is paired with the samples to create a snapshot matrix, is interpolated from the resultant manifold structure. The Gappy POD (Proper Orthogonal Decomposition) approach is then employed to complete the missing design variables within the target pressure distribution of the deformation control points. The original aerodynamic shape is then parameterized using the FFD (Free Form Deform) method to create an aerodynamic shape that matches the target pressure distribution. The M6 wing and the RAE2822 wing are used as the initial models to verify the design method. The aerodynamic response error of the inverse design wing and the target wing is within 2%. The results demonstrate that the proposed three-dimensional aerodynamic shape inverse design approach has a high design accuracy, dramatically improves design efficiency, and significantly reduces the dimensionality required for three-dimensional aerodynamic shape inverse design.

An improved M-SPEM for modeling complex hydroelastic fluid-structure interaction problems

Hydroelastic fluid-structure interaction (FSI) problems usually involve nonlinear free surface flows, large structure deformations and changing interfaces, which present great challenges for numerical modeling. To deal with violent FSIs, the authors proposed a multi-resolution smoothed particle element method (M-SPEM), which adaptively simulates local fluid regions with an improved smoothed particle hydrodynamics (SPH) method and models other solid/fluid regions with a smoothed finite element method (S-FEM). Both computational accuracy in local fluid domain and entire efficiency can be improved by M-SPEM compared with the conventional partitioned FSI solvers based on SPH-FEM coupling schemes. In this work, an improved M-SPEM is developed and extended to simulate the complex hydroelastic FSI problems with structural deformations considered in the numerical model. To solve the accuracy reduction problem in the multi-resolution simulations, we developed a velocity and position correction technique for the generated fluid and virtual particles. The computational results demonstrated that the new correction technique can effectively improve the computational accuracy of M-SPEM while the corrected schemes produce results very close to the reference ones. The positions of the generated particles should also be appropriately optimized during the element-particle conversion process. With both accuracy and efficiency improved, the improved M-SPEM is proven to be suitable to deal with some challenging hydroelastic FSI problems.

Optimization of roller teeth based on the analysis of the crushing mechanism of sintered ore

ABSTRACT In this paper, relevant mechanical tests were conducted on sintered ore specimens, and found that the ultimate strength of sintered ore under different strain rates had significant differences. The JH-2 constitutive model of sintered ore was obtained based on relevant tests and theoretical derivation, and used finite element method to reveal the crushing mechanism of sintered ore, and found that the maximum stress was mainly concentrated near the tooth root and tooth tip. By analyzing the variation rate of the fitted nonlinear surfaces about the stress of the tooth root and tooth tip versus the width of the tooth root and tooth tip and considering the engineering reality, it was found that the best choice of the roll tooth parameters was found when the tooth tip and root widths were both 160 mm.

The consequence of heat radiation on MHD flow of Carreau nanofluid on a nonlinear stretchable surface with chemical process

In this paper, we examine the Carreau nanofluid flow past a nonlinearly stretchable surface accompanied by chemical reactions, thermal slip parameter and thermal radiation. A two-phase nanofluid criterion is considered to examine the behavior of flowing fluid and temperature profile. We used the similarity transition to change the basic equations into the set of ordinary differential equations in order to obtain the results. Shooting criteria are applied to calculate the solution of momentum, energy, and concentration fields using MATLAB. The effects of physical entities on the velocity, concentration, and temperature fields are analyzed by numeric tabular data. Furthermore, it is analyzed that the temperature field and concentration profile are diminished while velocity and thermal slip parameters are increased. The increasing nature of Brownian movement [Formula: see text] corresponds to a lower nanoparticle profile concentration is observed. The temperature profile is a growing function of magnetic parameter. As the Eckert number rises, so does the thermal pattern.

High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model

AbstractWe propose and analyze a second order accurate in time, energy stable numerical scheme for the strongly anisotropic Cahn–Hilliard system, in which a biharmonic regularization has to be introduced to make the equation well‐posed. A convexity analysis on the anisotropic interfacial energy is necessary to overcome an essential difficulty associated with its highly nonlinear and singular nature. The second order backward differentiation formula temporal approximation is applied, combined with Fourier pseudo‐spectral spatial discretization. The nonlinear surface energy part is updated by an explicit extrapolation formula. Meanwhile, the energy stability analysis is enforced by the fact that all the second order functional derivatives of the energy stay uniformly bounded by a global constant. A Douglas‐Dupont type regularization is added to stabilize the numerical scheme, and a careful estimate ensures a modified energy stability with a uniform constraint for the regularization parameter . In turn, the combination with an appropriate treatment for the nonlinear double well potential terms leads to a weakly nonlinear scheme. More importantly, such an energy stability is in terms of the interfacial energy with respect to the original phase variable, which enables us to derive an optimal rate convergence analysis.

Strong field enhancement and hot spot manipulation based on anapole state in Si disk-ring metasurface

In this work, a metasurface consisting of disk-ring Si nanostructures on a SiO2 substrate is proposed and numerically simulated. The Si disk-ring structure can excite and manipulate anapole state, and periodic array supports lattice resonance simultaneously, which can improve the near-field enhancement in the gap region. The maximum E-field enhancement can be up to 346 times, and a transmission dip with an ultra-narrow bandwidth of 0.34 nm and a Q-factor of 4460 is shown. When the central disk has an offset, the near-field enhancement can be affected. In the case of y-direction offset, the maximum E-field enhancement can be up to 468 times. The near field energy is concentrated in the gap region, easy to interact with probing molecule in surrounding environment. Meanwhile, the designed metasurface shows a sensing performance of 387 nm/RIU. The strong energy confinement and high Q-factor of the proposed structure give an opportunity to enhance the interaction between light and matter, which may have potential applications in nonlinear optics, optical sensors and surface enhanced Raman scattering.

Thermal Discharge Temperature Retrieval and Monitoring of NPPs Based on SDGSAT-1 Images

High-accuracy sea surface temperature (SST) retrieval near nuclear power plants (NPPs) is one of the most significant indicators for evaluating marine ecological environment quality, monitoring the real-time situation of thermal discharge, and supporting planning decisions. However, complex computations, the inaccessible real-time vertical profile of the atmosphere, and the uncertainty of atmospheric profile data increase the error of SST retrieval. Additionally, influenced by their low spatial resolution, the widely used AVHRR/MODIS remote sensing images (RSIs) are unable to retrieve the detailed distribution of SST in small scale regions such as coastal NPPs. In this paper, we propose a simplified split-window-based temperature retrieval method (the SW method) suitable for SDGSAT-1 30 m thermal infrared spectrometer (TIS) RSIs. Specially, this method only needs atmospheric transmittance and surface emissivity by counteracting the average atmospheric temperature to monitor the thermal discharge of offshore NPPs. First, the geometric and radiometric calibrated thermal infrared and multi-spectral cloudless data of the target regions are selected to obtain the corresponding apparent radiance of the RSIs. Second, in accordance with the red and near-infrared (NIR) bands of multi-spectral RSIs, the surface emissivity is calculated to distinguish water from land. Next, we determine the atmospheric profile parameters from the weather conditions of the target region at the imaging time. Finally, according to the theory of surface-atmosphere radiative transfer, the SST of target regions is retrieved with the proposed SW method, and the results are compared with those of the conventional radiative transfer equation (RTE), mono-window (MW), and the nonlinear sea surface temperature (NLSST) algorithms. The experimental results indicate that the SST retrieved from the split-window algorithms (i.e., SW and NLSST) are generally higher than those of the single-channel algorithms (i.e., RTE and MW). The SST difference between the SW algorithm and the NLSST algorithm is within 0.5 °C. In addition, SDGSAT-1 can monitor the seasonal detailed variation of the thermal discharge near coastal NPPs. This article is the first to attempt to quantitative small-scale SST retrieval based on thermal infrared and multi-spectral images obtained from the SDGSAT-1 TIS and a multispectral imager (MII), and therefore, provide an effective reference for marine environment monitoring.

Parametric Optimization on HPC Clusters with Geneva

Many challenges of today’s science are parametric optimization problems that are extremely complex and computationally intensive to calculate. At the same time, the hardware for high-performance computing is becoming increasingly powerful. Geneva is a framework for parallel optimization of large-scale problems with highly nonlinear quality surfaces in grid and cloud environments. To harness the immense computing power of high-performance computing clusters, we have developed a new networking component for Geneva—the so-called MPI Consumer—which makes Geneva suitable for HPC. Geneva is most prominent for its evolutionary algorithm, which requires repeatedly evaluating a user-defined cost function. The MPI Consumer parallelizes the computation of the candidate solutions’ cost functions by sending them to remote cluster nodes. By using an advanced multithreading mechanism on the master node and by using asynchronous requests on the worker nodes, the MPI Consumer is highly scalable. Additionally, it provides fault tolerance, which is usually not the case for MPI programs but becomes increasingly important for HPC. Moreover, the MPI Consumer provides a framework for the intuitive implementation of fine-grained parallelization of the cost function. Since the MPI Consumer conforms to the standard paradigm of HPC programs, it vastly improves Geneva’s user-friendliness on HPC clusters. This article gives insight into Geneva’s general system architecture and the system design of the MPI Consumer as well as the underlying concepts. Geneva—including the novel MPI Consumer—is publicly available as an open source project on GitHub (https://github.com/gemfony/geneva) and is currently used for fundamental physics research at GSI in Darmstadt, Germany.

Volumetric thermo-convective casson fluid flow over a nonlinear inclined extended surface

The thermophysical features of Casson fluid flow caused by a nonlinear permeable stretchable surface are assessed in the present study. The computational model of Casson fluid is used to define viscoelasticity, which is quantified rheologically in the momentum equation. Exothermic chemical reactions, heat absorption/generation, magnetic field and nonlinear volumetric thermal/mass expansion over the stretched surface are also considered. The proposed model equations are lessened by the similarity transformation to the dimensionless system of ODEs. The obtained set of differential equations are numerically computed through parametric continuation approach. The results are displayed and discussed via figures and tables. The outcomes of the proposed problem are compared to the existing literature and bvp4c package for the validity and accuracy purposes. It has been perceived that the energy and mass transition rate of Casson fluid increased with the flourishing trend of heat source parameter and chemical reaction respectively. Casson fluid velocity can be elevated by the rising effect of thermal, mass Grashof number and nonlinear thermal convection.

On coupled envelope evolution equations in the Hamiltonian theory of nonlinear surface gravity waves

This paper presents a novel theoretical framework in the Hamiltonian theory of nonlinear surface gravity waves. The envelope of surface elevation and the velocity potential on the free water surface are introduced in the framework, which are shown to be a new pair of canonical variables. Using the two envelopes as the main unknowns, coupled envelope evolution equations (CEEEs) are derived based on a perturbation expansion. Similar to the high-order spectral method, the CEEEs can be derived up to arbitrary order in wave steepness. In contrast, they have a temporal scale as slow as the rate of change of a wave spectrum and allow for the wave fields prescribed on a computational (spatial) domain with a much larger size and with spacing longer than the characteristic wavelength at no expense of accuracy and numerical efficiency. The energy balance equation is derived based on the CEEEs. The nonlinear terms in the CEEEs are in a form of the separation of wave harmonics, due to which an individual term is shown to have clear physical meanings in terms of whether or not it is able to force free waves that obey the dispersion relation. Both the nonlinear terms that can only lead to the forcing of bound waves and those that are capable of forcing free waves are demonstrated, in the case of the latter through the analysis of the quartet and quintet resonant interactions of linear waves. The relations between the CEEEs and two other existing theoretical frameworks are established, including the theory for a train of Stokes waves up to second order in wave steepness (Fenton, ASCE J. Waterway Port Coastal Ocean Engng, vol. 111, issue 2, 1985, pp. 216–234) and a semi-analytical framework for three-dimensional weakly nonlinear surface waves with arbitrary bandwidth and large directional spreading by Li & Li (Phys. Fluids, vol. 33, issue 7, 2021, 076609).

Adaptive Exploration and Optimization of Materials Crystal Structures

A central problem of materials science is to determine whether a hypothetical material is stable without being synthesized, which is mathematically equivalent to a global optimization problem on a highly nonlinear and multimodal potential energy surface (PES). This optimization problem poses multiple outstanding challenges, including the exceedingly high dimensionality of the PES, and that PES must be constructed from a reliable, sophisticated, parameters-free, and thus very expensive computational method, for which density functional theory (DFT) is an example. DFT is a quantum mechanics-based method that can predict, among other things, the total potential energy of a given configuration of atoms. DFT, although accurate, is computationally expensive. In this work, we propose a novel expansion-exploration-exploitation framework to find the global minimum of the PES. Starting from a few atomic configurations, this “known” space is expanded to construct a big candidate set. The expansion begins in a nonadaptive manner, where new configurations are added without their potential energy being considered. A novel feature of this step is that it tends to generate a space-filling design without the knowledge of the boundaries of the domain space. If needed, the nonadaptive expansion of the space of configurations is followed by adaptive expansion, where “promising regions” of the domain space (those with low-energy configurations) are further expanded. Once a candidate set of configurations is obtained, it is simultaneously explored and exploited using Bayesian optimization to find the global minimum. The methodology is demonstrated using a problem of finding the most stable crystal structure of aluminum. History: Kwok Tsui served as the senior editor for this article. Funding: The authors acknowledge a U.S. National Science Foundation Grant DMREF-1921873 and XSEDE through Grant DMR170031. Data Ethics & Reproducibility Note: The code capsule is available on Code Ocean at https://doi.org/10.24433/CO.3366149.v1 and in the e-Companion to this article (available at https://doi.org/10.1287/ijds.2023.0028 ).

Parametric excitation of plane waves and traveling nonlinear surface charge structures by an oscillating electric field at the plasma boundary

With the help of a single equation, to which it was possible to reduce the original system of equations, it turned out to be possible to describe the excitation of parametric instability on plane surface waves in an alternating electric field, its saturation due to the nonlinearity of the surface charge and the generation of nonlinear structures of this charge propagating along the boundary and depending on the parameters of external influence. The amplitude of saturation of the increasing plane waves was found as a result of stabilization of parametric instability by the nonlinear effect of the surface charge. An example of a nonlinear wave structure propagating along the surface of the boundary as a result of the interaction of an external electric field with a nonlinear surface charge is presented.

Reliability Index of Simply Supported Beam Based on HL Method

In this paper, reliability of simply supported I-beam is studied under point load at the mid-point of span. Reliability index has been obtained by using Hasofer-Lind method. In the analysis, yield strength of material, depth of the section and load are considered as basic random variables and those are assumed to follow normal distribution. Non-linear limit state surface function has been considered. Derived design point in each case and found the reliability.