Surfaces Of Arbitrary Shape Research Articles

Semi-analytical method for calculating ground vibrations from a tunnel in a homogeneous half-space with an irregular surface

This paper proposes a novel two-dimensional (2D) semi-analytical method for calculating ground vibrations from a tunnel situated in a homogeneous half-space with an irregular surface. The circular tunnel is conceptualized as an elastic solid, while the soil is modelled as an elastic, isotropic, and homogeneous half-space with an irregular surface. A virtual horizontal interface is introduced to divide the soil domain into an irregular region with an arbitrary-shaped surface and a half-space with a circular hollow. The wavefield scattered by the irregular surface is simulated by the boundary integral equation. Through the application of the discrete wavenumber approach and expansion of wavefield on the irregular surface, the boundary integral equation is transformed into a set of simultaneous matrix equations containing unknown expansion coefficients. By utilizing the transformation between cylindrical and plane waves, the boundary conditions on soil-tunnel interface are satisfied, yielding a solution for a harmonic point load acting on the tunnel in a half-space with an irregular surface. The proposed method can simulate topographies with arbitrary shapes and only requires the discretization of the irregular part of the ground surface, which provides a highly efficient tool to investigate the propagation characteristics of train-induced vibrations in complex topographies. The proposed method is verified through comparisons with the existing analytical methods and the finite element method. The dynamic responses of a tunnel embedded in a half-space with a Gaussian-shaped surface are meticulously investigated. A case study involving a site for the Shenzhen metro line 5 is performed. The numerical results demonstrate that the presence of irregular topography alters the distribution of ground vibrations, leading to significant differences in responses within the irregular region and certain disparities in the regular region. The effect of the location, size, and undulating direction of the irregular topography on ground vibrations is frequency-dependent.

Transport of a passive scalar in wide channels with surface topography: An asymptotic theory

We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection–diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our asymptotic theory relies on a domain perturbation approach for small roughness amplitudes of the channel and holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e. the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion diffusion tensor.

Analysis of scientific research conducted to improve the efficiency of solar concentrator systems

The article presents a scientific analysis based on scientific research conducted in the field of solar concentrators in leading institutions of the world. Parabolocylindrical concentrators with a free surface have been shown to be more efficient. concentrator model with free surface shape is proposed and based on its ability to solve problems in the design and analysis of optical systems, including boundary surfaces of arbitrary shape.

Adhesion of graded elastic materials: A full self-consistent model and its application

A full self-consistent model (FSCM) of the axisymmetric adhesive contact between a rigid punch with an arbitrary surface shape and a power-law graded elastic half-space is developed. The self-consistent equation between the surface gap and the surface interaction (e.g., the Lennard–Jones force law) involves a nonlinear singular integral, posing a great challenge to numerical calculations. By applying the properties of Gauss’s hypergeometric function, the integral singularity is eliminated in the numerical calculation through Riemann–Stieltjes integral. Case studies for power-law punch profiles are performed and the self-consistent equation can be expressed in a dimensionless form with three dimensionless parameters, namely a shape index, a gradient exponent, and a new generalized Tabor number. The FSCM results are obtained by solving the self-consistent equation through the surface central gap control method and Newton–Raphson iterative method. For large generalized Tabor numbers, the force–displacement curves are ‘S-shaped’ and condense to the extended JKR limit in the high-load branch. As the generalized Tabor number decreases, a continuous transition from the extended JKR model to the Bradley model for the adhesion of power-law graded materials is obtained. It is found that the pull-off force of a graded material usually depends on the three dimensionless parameters, but for some cases of the shape index, it is not sensitive to the gradient exponent when the generalized Tabor number is fixed. Asymptotic solutions are derived to predict the unstable jump points, which coincide well with the FSCM predictions. The FSCM is applied to validate the extended Maugis–Dugdale (M–D) model of graded materials and it is found that the accuracy of the original M–D-n-k model using the maximum strength condition to determine the cohesive stress is limited. By introducing the rigid-limit-consistency condition of the pull-off force to determine the cohesive stress, the M–D-n-k model is improved and its predictions show good consistency with the FSCM results.

3D Vision Based Robot Assisted Electrical Impedance Scanning for Soft Tissue Conductivity Sensing

Advanced Sensing Technologies (ASTs) have a great potential to improve surgical quality and to further develop Surgical Robotic Systems (SRSs), enhancing their technical and autonomy capabilities. Among these sensing techniques, Electrical Bioimpedance (EBI) provides a non-invasive, low-cost, and safe AST for the intraoperative localization of abnormal regions. The current EBI integration into SRS has only been demonstrated in an over-simplified condition (i.e. nearly flat surfaces), which are almost never encountered in real anatomies. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">To overcome this limitation, we develop a robotic assisted EBI scanning system able to work with tissues’ surfaces of arbitrary shapes, leveraging 3D vision based tissue reconstruction in the scanning process. In addition, we propose a novel model based conductivity estimation method that exploits Finite Element (FE) simulation to compensate for errors introduced by non-planar surfaces and uncertainty in the electrodes’ position. The system is evaluated through experiments in simulation and using ex vivo animal tissues. The experimental results show that the model based method achieves an accuracy of 99% independently of the curvature of the tissue surface, while the previous method achieves an accuracy ranging from 70% to 88% depending on the surface curvature. The obtained results are very promising and show a great potential to be integrated into existing SRSs for identifying different tissues during a robotic surgery without involving any additional tool.

Multifocal Stereoscopic Projection Mapping.

Stereoscopic projection mapping (PM) allows a user to see a three-dimensional (3D) computer-generated (CG) object floating over physical surfaces of arbitrary shapes around us using projected imagery. However, the current stereoscopic PM technology only satisfies binocular cues and is not capable of providing correct focus cues, which causes a vergence-accommodation conflict (VAC). Therefore, we propose a multifocal approach to mitigate VAC in stereoscopic PM. Our primary technical contribution is to attach electrically focus-tunable lenses (ETLs) to active shutter glasses to control both vergence and accommodation. Specifically, we apply fast and periodical focal sweeps to the ETLs, which causes the "virtual image" (as an optical term) of a scene observed through the ETLs to move back and forth during each sweep period. A 3D CG object is projected from a synchronized high-speed projector only when the virtual image of the projected imagery is located at a desired distance. This provides an observer with the correct focus cues required. In this study, we solve three technical issues that are unique to stereoscopic PM: (1) The 3D CG object is displayed on non-planar and even moving surfaces; (2) the physical surfaces need to be shown without the focus modulation; (3) the shutter glasses additionally need to be synchronized with the ETLs and the projector. We also develop a novel compensation technique to deal with the "lens breathing" artifact that varies the retinal size of the virtual image through focal length modulation. Further, using a proof-of-concept prototype, we demonstrate that our technique can present the virtual image of a target 3D CG object at the correct depth. Finally, we validate the advantage provided by our technique by comparing it with conventional stereoscopic PM using a user study on a depth-matching task.

Generalized chromatic aberrations in non-rotationally symmetric optical systems–Part I: mathematical approach

In non-rotationally symmetric optical systems, chromatic aberrations must be defined in a generalized way with reference to the optical axis ray and optimal tilted parabasal image plane of the central wavelength. In this paper, the definition of generalized chromatic aberrations is clarified. The mathematical calculation in optical systems with arbitrary symmetry and surface shape is realized by ray- and wavefront-based methods, respectively, that are originally identical. The additivity of wavefront after each surface ensures the surface decomposition of chromatic aberrations. In the end, the influence of pupil aberration, which is of a higher order, is discussed. The consistency of our methods with Seidel aberrations in the lowest aberration order of the rotationally symmetric system and the application of our methods in diverse non-rotationally symmetric refractive systems will be addressed in detail in Part II.

Highly Versatile Upconverting Oxyfluoride-Based Nanophosphor Films.

Fluoride-based compounds doped with rare-earth cations are the preferred choice of materials to achieve efficient upconversion, of interest for a plethora of applications ranging from bioimaging to energy harvesting. Herein, we demonstrate a simple route to fabricate bright upconverting films that are transparent, self-standing, flexible, and emit different colors. Starting from the solvothermal synthesis of uniform and colloidally stable yttrium fluoride nanoparticles doped with Yb3+ and Er3+, Ho3+, or Tm3+, we find the experimental conditions to process the nanophosphors as optical quality films of controlled thickness between few hundreds of nanometers and several micrometers. A thorough analysis of both structural and photophysical properties of films annealed at different temperatures reveals a tradeoff between the oxidation of the matrix, which transitions through an oxyfluoride crystal phase, and the efficiency of the upconversion photoluminescence process. It represents a significant step forward in the understanding of the fundamental properties of upconverting materials and can be leveraged for the optimization of upconversion systems in general. We prove bright multicolor upconversion photoluminescence in oxyfluoride-based phosphor transparent films upon excitation with a 980 nm laser for both rigid and flexible versions of the layers, being possible to use the latter to coat surfaces of arbitrary shape. Our results pave the way toward the development of upconverting coatings that can be conveniently integrated in applications that demand a large degree of versatility.

Automated Geometric Registration for Multi-Projector Displays on Arbitrary 3D Shapes Using Uncalibrated Devices.

In this article we present a completely automated and scalable multi-projector registration system that allows multiple uncalibrated projectors and cameras on arbitrary shape surfaces. Our method estimates the parameters of multiple uncalibrated tiled or superimposed projectors, the extrinsic parameters of the observing cameras (with known intrinsic parameters), the shape of the illuminated 3D geometry and geometrically registers the projectors on it. This is achieved without using any fiducials, even if part of the surface is visible to only one camera. The method uses a completely automatic approach for cross-correlation and cross-validation of the device parameters and the surface geometry resulting in an accurate registration on the arbitrary unknown geometry that does not need an accurate prior calibration of each of the uncalibrated devices using physical patterns or fiducials. Estimating projector parameters allows for quick recalibration of the system in the face of projector movements, by re-estimating only the parameters of the moved projector and not the entire system. Thus, our work can enable easy deployment of spatially augmented reality environments of different sizes (from small table top objects to large immersive environments), different shapes (inside-looking-out or outside-looking in), and different configurations (tiled or superimposed) using the same proposed method.

Microswimmers near corrugated, periodic surfaces.

We explore hydrodynamic interactions between microswimmers and corrugated, or rough, surfaces, as found often in biological systems and microfluidic devices. Using the Lorentz reciprocal theorem for viscous flows we derive exact expressions for the roughness-induced velocities up to first order in the surface-height fluctuations and provide solutions for the translational and angular velocities valid for arbitrary surface shapes. We apply our theoretical predictions to elucidate the impact of a periodic, wavy surface on the velocities of microswimmers modeled in terms of a superposition of Stokes singularities. Our findings, valid in the framework of a far-field analysis, show that the roughness-induced velocities vary non-monotonically with the wavelength of the surface. For wavelengths comparable to the swimmer-surface distance a pusher can experience a repulsive contribution due to the reflection of flow fields at the edge of a surface cavity, which decreases the overall attraction to the wall.

Приближенные асимптотические выражения для электромагнитного поля и взаимной проводимости щелей в проводящей выпуклой поверхности вращения в виде рядов по азимутальным гармоникам

In this paper, we obtain approximate asymptotic expressions for the electromagnetic field and the self and mutual admittances of "single-mode" slots in a smooth convex surface of rotation of large sizes in the form of a series of azimuthal harmonics. The coefficients of the series are expressed as integrals over the wave spectrum and can be calculated numerically or as a sum series of deductions (for mutual admittances). The expressions for the coefficients are uniformly valid in the boundary surface layer, except for the vicinity of the poles of the surface of rotation, and do not have discontinuities on the caustics of the surface rays. The resulting expressions can be directly used to calculate the fields and the self and mutual admittances of annular slots. In contrast to the eigenfunction method, asymptotic expressions allow us to cover the case of an arbitrary-shaped surface and avoid summing slowly converging double series. A comparison of the results of calculating the admittances of annular slots in a conducting spherical surface obtained by the proposed method and the method of eigenfunctions was executed, and their good agreement shown even for a small radius of the sphere equal to 3λ.

Strain rate on curved surfaces: A differential-geometric approach

Utilizing the geometrical characteristics of a simple smooth curve embedded in an orientable surface of arbitrary shape, expressions are derived in boundary-fitted curvilinear coordinates, for the normal and tangential strain rate of a fluid which contacts the surface. The derived expressions can be applied to stream-surfaces, solid walls with hydrodynamic slippage and two-fluid interfaces. The use of the expressions is discussed with specific examples and critical examination of the literature.

Numerical modeling of turbulent flows near axially symmetric surfaces

The relevance of performing numerical modeling of turbulent flows around axially symmetric surfaces is presented. A review of similar scientific works is carried out. A mathematical model of a turbulent axially symmetric flow around particles of an arbitrary shape surface is constructed. A numerical method for performing calculations is described. Numerical methods for constructing a curvilinear orthogonal grid have been developed. Examples of flow around particles are presented for the turbulent boundary layer.

Embedding Soft Material Channels for Tactile Sensing of Complex Surfaces—Mathematical Modeling

Currently most of tactile array technologies is difficult to cope with three dimensional complex surfaces and there is an urgent need to develop tactile sensors that can provide a high-density integrated array on a surface of arbitrary shape. Our laboratory has been working on the development of a novel tactile sensing technique to solve this challenge, by “Embedding Soft material into Structure ENabling Tactile sensing” of complex surfaces (ESSENT). This method creates sub-millimeter multiple channels filled with low compressibility elastic material. Tactile information is obtained by measuring the micro deformation of the soft material via projecting light to the material channel and measuring light reflection. However, the relationship between light reflection and soft material deformation is a complex function related to the geometry of reflective surface, elasticity of the soft channel and lighting conditions. To gain fundamental understanding of this new tactile sensing principle, we developed a mathematical model which is able to predict the precise deformation of the reflective surface of a soft material and provide the theoretical prediction of sensing sensitivity with respect to the lighting condition and the magnitude of the applied force. We demonstrated that the shape of soft material channel, the shape of reflective surface, as well as the location of light resource have significant influence on the sensor behavior.

System reliability analysis of soil slopes through constrained optimization

As a slope may have numerous potential slip surfaces, its failure probability as a system is usually different from that of a single slip surface. Nevertheless, the system failure probability of a slope is often governed by several representative slip surfaces. How to identify the representative slip surfaces is important for system reliability analysis of soil slopes. Previous studies on representative slip surface identification mainly focus on circular slip surfaces within the framework of limit equilibrium methods; there are also relevant researches, albeit limited, within the framework of finite element/finite difference analyses based on the shear strength reduction method. By viewing the task of representative slip surface identification as a multidesign point identification problem, a barrier-based optimization method is suggested in this paper to identify representative slip surfaces of arbitrary shape based on the shear strength reduction method. A multiple starting point strategy is suggested to enhance its efficiency. For the three slopes examined in this paper, the method suggested is capable of identifying representative slip surfaces efficiently without prior assumption on their shapes.

Magnetic field modeling with surface currents. Part II. Implementation and usage of bfieldtools

We present a novel open-source Python software package, bfieldtools, for magneto-quasistatic calculations using current densities on surfaces of arbitrary shape. The core functionality of the software relies on a stream-function representation of surface-current density and its discretization on a triangle mesh. Although this stream-function technique is well known in certain fields, to date, the related software implementations have not been published or have been limited to specific applications. With bfieldtools, we aimed to produce a general, easy-to-use, and well-documented open-source software. The software package is written purely in Python; instead of explicitly using lower-level languages, we address computational bottlenecks through extensive vectorization and use of the NumPy library. The package enables easy deployment, rapid code development, and facilitates application of the software to practical problems. In this paper, we describe the software package and give an extensive demonstration of its use with an emphasis on one of its main applications—coil design.

Level set splitting in DEM for modeling breakage mechanics

Brittle breakage of particles in granular materials has often been modeled using the discrete element method (DEM). DEM is often limited however in its ability to capture particle shape, particularly when used for breakage. This paper presents the first brittle breakage technique where level set functions will allow for the description of arbitrary shape for both particles and fracture surfaces. The breakage model to be described here uses fracture surfaces defined by level sets to take advantage of simple intersection and difference set operations to split particles in both two and three dimensions. We show how this method is implemented and how we can use it to define and apply arbitrary fracture surface shapes. We then give qualitative examples of using the method in both simple and exotic ways. Finally, we model oedometric tests and rock crushing, both very common uses for previous DEM breakage techniques, to present a validation that the method captures the physics of the problem.

A Fast Boundary Integral Method for High-Order Multiscale Mesh Generation

In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original...

Output Signal Prediction of an Eddy-Current Probe When Scanning Arbitrary-Shape Surface Cracks in Metals

This article proposes an efficient modeling technique to predict the output signal of an eddy-current (EC) probe when scanning arbitrary-shape surface cracks in metals. The probe is excited by an arbitrary-shape wire carrying an ac current of arbitrary frequency with no restriction on the crack depth profile or magnetic permeability of the metal. In the proposed technique, the equivalence principle is adopted to replace the crack with the equivalent electric and magnetic current densities, and the governing volume integral equations (VIEs) are derived using appropriate Green’s functions. The VIEs are solved by the method of moments (MoM) for the unknown electric and magnetic fields inside the crack. This is done by expanding the electric and magnetic fields in terms of basis functions compatible with the problem. To support the validity of the proposed modeling technique, we compare the predicted output signals of various EC probes with their experimental counterparts and those available in the literature.

Finite-temperature entanglement negativity of free fermions

The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper (Shapourian et al 2017 Phys. Rev. B 95 165101). In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.