Arbitrary Surface Research Articles

Scalable and view-independent calibration of multi-projector display for arbitrary uneven surfaces

Most existing systems for calibrating multi-projector display suffered from several important limitations such as dependence on point of view, restriction on the display surface and moreover the number of projectors and using obtrusive markers. In this paper, a new method for view-independent calibration for multi-projector displays is presented. Given that the calibration problem of a multi-projector display is an optimization problem, we compute the calibration parameters by writing the appropriate energy functions for the geometric calibration phase. In this method, the camera and projector are introduced as a pair. In the first step, calibration of the pair of camera and projector was carried out. After that, the calibration problem of the system decreases to estimation of the number of camera positions relative to each other. In this method, there is no particular shape for the screen. In addition, due to the 3D shape of the screen, this method is view independent and eventually the image can be wallpapered on the screen. According to the tests carried out to evaluate the system, the accuracy of the proposed system is sub-pixel, and as a result, no misalignment is observed by the human eye in the overlapping area of projectors.

New approach to moisture accumulation assessment

We suggest an innovative approach to simulate moisture buildup on structures with arbitrary geometries and different surface adhesion characteristics. Using 3D particle physics, rain, snow and freezing rain buildup on flat and cylindrical surfaces was assessed. The numerically simulated moisture accumulations were subsequently successfully verified experimentally through a series of outdoor and indoor moisture accumulation experiments. We also conducted molecular dynamics simulations to assess how hydrogen bonds influence snow and rain adhesion on high and low energy substrates. The simulations supported the experimental observations, namely that freezing rain results in increased moisture adhesion and accumulation due to the spreading of the water droplets, resulting in more hydrogen bonds between water droplets and substrates than snow.

Perturbation theory of optical resonances of deformed dielectric spheres

We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of non-Hermitian operators characterized by complex eigenvalues and not normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism which enables us to extend the popular Rayleigh-Schr\"{o}dinger perturbation theory to the case of electromagnetic Debye's potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first- and second-order corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones finding full agreement.

Analytical and Numerical Methods and Test Calculations of One-dimensional Force-free Magnetodynamics on Arbitrary Magnetic Surfaces across Horizons of Spinning Black Holes

Numerical simulations of the force-free magnetodynamics (FFMD) of the electromagnetic field around a spinning black hole are useful to investigate the dynamic electromagnetic processes around a spinning black hole, such as the emergence of the Blandford--Znajek mechanism. To reveal the basic physics of magnetic fields around a black hole through the dynamic process, we use one-dimensional (1D) FFMD along the axisymmetric magnetic surface, which provides a relatively simple, sufficiently precise, and powerful tool to analyze the dynamic process around a spinning black hole. We review the analytic and numerical aspects of 1D FFMD for an arbitrary magnetic surface around a black hole. In addition, we also show some numerical simulation test results for three types of magnetic surfaces at the equatorial plane of the black hole.

A highly adhesive flexible strain sensor based on ultra-violet adhesive filled by graphene and carbon black for wearable monitoring

Ensuring the accuracy of signal detection under repeated deformation is a challenge for flexible sensor reported in recent years, and achieving reliable adhension between the sensor and substrate is a key factor. Here, this article reported a highly adhesive flexible strain sensor based on ultra-violet adhesive filled by modified graphene and carbon black for wearable monitoring. This strain sensor with a typical resistive behavior shows gauge factor calculated at 0∼10% strain is 2.1. It exhibits short curing time (∼1 h), fast response (∼40 ms), excellent adhesive strength (4500 kPa), and adhesiveness to various bending surfaces. Furthermore, this strain sensor can be directly prepared on elastic columns and rubber gloves, and exhibits excellent performance in three-dimensional force detection and writing gesture recognition. The ability of adhesive conformability to arbitrary and complex surfaces shows that the strain sensor has broad application prospects in wearable devices.

Position-based impedance force controller with sensorless force estimation

Purpose This paper aims to purpose an improved sensorless position-based force controller in gravitational direction for applications including polishing, milling and deburring. Design/methodology/approach The first issue is the external force/torque estimation at end-effector. By using motor’s current information and Moore-Penrose generalized inverse matrix, it can be derived from the external torques of every joints for nonsingular cases. The second issue is the force control strategy which is based on position-based impedance control model. Two novel improvements were made to achieve a better performance. One is combination of impedance control and explicit force control. The other one is the real-time prediction of the surface’s shape allowing the controller adaptive to arbitrary surfaces. Findings The result of validation experiments indicates that the estimation of external force and prediction of surface’s shape are credible, and the position-based constant contact force controller in gravitational direction is functional. The accuracy of force tracking is adequate for targeted applications such as polishing, deburring and milling. Originality/value The value of this paper lies in three aspects which are sensorless external force estimation, the combination of impedance control and explicit force control and the independence of surface shape information achieved by real-time surface prediction.

Design and development of a new portable test setup to study friction and wear

In this paper, a novel portable sliding friction and wear test rig is introduced. Unlike other laboratory-based test setups, this setup can be used for both indoor and outdoor experiments. There is also no limitation on the size and type of the substrate surface that can be used for the friction and wear test in contrast to typical test rigs, which have some limitations for the size and type of substrate surface. A small six-wheel ground robot is developed to drag the sample on an arbitrary surface for a desired distance and velocity. A ground robot is an unmanned ground vehicle, capable of driving on the ground without humans on board. The speed of this robot can be measured and controlled precisely. The nominal normal load is adjusted using dead weights placed on the sample holder and the friction force is measured using a load cell. An adjustable sample holder was also designed and built to hold different-size specimens. The results of styrene–butadiene rubber block sliding on an asphalt track are presented to validate the test setup and illustrate the potential of the system for friction and wear testing. In addition, the effect of sliding velocity on the friction and wear is studied, and the correlation between the wear rate and the friction coefficient is investigated. These experimental results can be used to estimate the friction and life span of a tire tread compound on the real asphalt road. Finally, the formation of abrasion pattern observed on the rubber surface sliding on an asphalt track is discussed, which provides an insight into the understanding of dominant wear mechanism of tire tread compound on typical asphalt surfaces.

The Forward Kinematics of Rolling Contact of Timelike Surfaces With Spacelike Trajectory Curves

In this paper, we investigate the forward kinematics of spin-rolling motion without sliding of one timelike surface on another timelike surface along the spacelike contact trajectory curves of the surfaces in Lorentzian 3-space. A Darboux frame method is adopted to develop instantaneous kinematics of spin-rolling motion, which occurs in a nonholonomic system. Then, new kinematic formulations of spin-rolling motion of timelike moving surface with regards to contravariant vectors, rolling velocity, and geometric invariants are obtained. Namely, the translational velocity formulation of an arbitrary point and the equation of the angular velocity formulation on the timelike moving surface are derived. The equation, which is represented with geometric invariants, can be easily applied to arbitrary spacelike parametric surface and spacelike contact trajectory curve and can be differentiated to any order. The influence of the relative curvatures and torsion on spin-rolling kinematics is clearly presented.

Classification of solar sail attitude dynamics with and without angular momentum

This paper describes attitude dynamics properties of spinning, momentum-biased and zero-momentum solar sail spacecraft. The model called “Generalized Sail Dynamics Model” (GSDM) is introduced, which can deal with general and practical sail configurations, such as arbitrary optical property distribution, shape and surface wrinkles. Attitude stability criteria and other key dynamical characteristics are derived and compared by compact analytical equations induced from the GSDM. The newly derived zero-momentum sail dynamics is compared with that of spinning and momentum-biased sails. It is shown that the spinning and momentum sails have an advantage in terms of dynamical stability whereas zero-momentum sails are only statically stable. With this special property, angular momentum-stabilized sails can realize a sun-pointing stable attitude with almost zero-fuel, which are discussed with actual space flight experience of the JAXA’s two interplanetary missions, IKAROS and Hayabusa2.

Compact picometer-scale interferometer using twisted light.

We propose a simple compact interferometer using twisted light to detect picometer displacement on a solid or liquid surface. The heart of the interferometer lies in producing a daisy petal pattern formed by interference between two oppositely charged twisted beams. The sample being probed is an active component of the interferometer. By analyzing the rotation of the petal pattern, caused by the relative displacement between the cylindrical lens (CL) and solid/liquid surface, we exhibit picometer resolution in displacement measurements. Remarkably, we explore the significance of a radial quantum number in the measurement of surface displacement and surface tilt angle. We also investigate the arbitrary surface deformation profile with similar precision by modifying the set-up. We perform simulations in realistic experimental settings and show that they are in excellent agreement with the predictions of analytic expressions. The proposed set-up can be further miniaturized by a small focal length CL and will open routes for tremendous applications in picometer-scale displacement measurement of a solid or liquid interface by various excitations.

In-situ electrospun aligned and maize-like AgNPs/PVA@Ag nanofibers for surface-enhanced Raman scattering on arbitrary surface

Abstract An efficient electrospun aligned surface enhanced Raman scattering (SERS) and maize-like substrate of polyvinyl alcohol (PVA) composite and Ag colloid nanofibers decorated with thermal evaporated Ag nanoparticles (AgNPs) has been developed by taking advantage of electrostatic interactions. The synergistic effects of the evaporated AgNPs (niblets) and the Ag colloid in PVA (corncob) could arouse strong electromagnetic field between the lateral and vertical nanogaps which has been demonstrated by experiment and finite-different time-domain (FDTD) simulation. In this experiment, the aligned nanofibers possesses an excellent sensitivity by detection of crystal violet (CV) and malachite green (MG) molecule at low concentration. Moreover, the proposed flexible SERS sensor was measured with outstanding uniformity and reproducibility. We also carried out in-situ electrospinning on a curved surface to detect the mixture of Sudan I, CV and MG molecule, which demonstrates that flexible SERS sensor, has enormous potential in accurate and in-situ detection on the complex geometric structure.

Machine Learning for Haptics: Inferring Multi-Contact Stimulation From Sparse Sensor Configuration.

Robust haptic sensation systems are essential for obtaining dexterous robots. Currently, we have solutions for small surface areas, such as fingers, but affordable and robust techniques for covering large areas of an arbitrary 3D surface are still missing. Here, we introduce a general machine learning framework to infer multi-contact haptic forces on a 3D robot's limb surface from internal deformation measured by only a few physical sensors. The general idea of this framework is to predict first the whole surface deformation pattern from the sparsely placed sensors and then to infer number, locations, and force magnitudes of unknown contact points. We show how this can be done even if training data can only be obtained for single-contact points using transfer learning at the example of a modified limb of the Poppy robot. With only 10 strain-gauge sensors we obtain a high accuracy also for multiple-contact points. The method can be applied to arbitrarily shaped surfaces and physical sensor types, as long as training data can be obtained.

Visualization Method for Arbitrary Cutting of Finite Element Data Based on Radial-Basis Functions

Finite element data form an important basis for engineers to undertake analysis and research. In most cases, it is difficult to generate the internal sections of finite element data and professional operations are required. To display the internal data of entities, a method for generating the arbitrary sections of finite element data based on radial basis function (RBF) interpolation is proposed in this paper. The RBF interpolation function is used to realize arbitrary surface cutting of the entity, and the section can be generated by the triangulation of discrete tangent points. Experimental studies have proved that the method is very convenient for allowing users to obtain visualization results for an arbitrary section through simple and intuitive interactions.

Relationship between the Discrete and Resonance Spectrum for the Laplace Operator on a Noncompact Hyperbolic Riemann Surface

We consider arbitrary noncompact hyperbolic Riemann surfaces of finite area. For such surfaces, we obtain identities relating the discrete spectrum of the Laplace operator to the resonance spectrum (formed by the poles of the scattering matrix). These identities depend on the choice of a test function. We indicate a class of admissible test functions and consider two examples corresponding to specific choices of the test function.

A Functional Integral Approaches to the Makeenko–Migdal Equations

Makeenko and Migdal (Phys Lett B 88(1):135–137, 1979) gave heuristic identities involving the expectation of the product of two Wilson loop functionals associated to splitting a single loop at a self-intersection point. Kazakov and Kostov (Nucl Phys B 176(1):199–215, 1980) reformulated the Makeenko–Migdal equations in the plane case into a form which made rigorous sense. Nevertheless, the first rigorous proof of these equations (and their generalizations) was not given until the fundamental paper of Levy (2017). Subsequently Driver, Kemp, and Hall Commun. Math. Phys. 351(2), 741–774 (2017) gave a simplified proof of Levy’s result and then with Driver, Gabriel, Kemp, and Hall Commun. Math. Phys. 352(3), 967–978 (2017) we showed that these simplified proofs extend to the Yang–Mills measure over arbitrary compact surfaces. All of the proofs to date are elementary but tricky exercises in finite dimensional integration by parts. The goal of this article is to give a rigorous functional integral proof of the Makeenko–Migdal equations guided by the original heuristic machinery invented by Makeenko and Migdal. Although this stochastic proof is technically more difficult, it is conceptually clearer and explains “why” the Makeenko–Migdal equations are true. It is hoped that this paper will also serve as an introduction to some of the problems involved in making sense of quantizing Yang–Mill’s fields.

Shape-Adaptive, Self-Healable Triboelectric Nanogenerator with Enhanced Performances by Soft Solid-Solid Contact Electrification.

The viable application of soft electronics/robotics relies on the development of power devices which are desired to be flexible, deformable, or even self-healable. We report here a shape-adaptive, self-healable triboelectric nanogenerator (SS-TENG) for harvesting biomechanical energies. The use of a viscoelastic polymer, normally known as Silly Putty, as the electrification material and as the matrix of a carbon-nanotube-filled composite (CNT-putty) electrode endows the SS-TENG the capability of adapting to arbitrary irregular surfaces and instantaneous healing from mechanical damage (almost completely recovered in 3 min without extra stimuli). Furthermore, the output performances of the SS-TENG have also been significantly improved because (i) the ideal soft contact is achieved at the solid-solid interfaces for more effective contact electrification and (ii) the introduced cation dopants make the putty even more tribo-negative than polytetrafluoroethylene. The SS-TENG can be adhered to any curvy surface, tailored, and reshaped into arbitrary configurations and utilized as a power supply for small electronics, suggesting promising applications in soft electronics/robotics in the future.

3-D Rotation Representation of Multiple Reflections and Parametric Model for Bistatic Scattering From Arbitrary Multiplate Structure

Based on geometrical optics (GO), this paper develops a representation theory of multiple specular reflections from perfect electric conducting target with an arbitrary patchwise smooth surface. In the course of rays' multiple reflections, the polarization of each ray is found to change in a manner consistent with the variations of its propagating direction, which can be described with an equivalent 3-D rotation transformation. This transformation provides a new representation of the polarization rotation effect induced by multiple reflections. More importantly, the parameters of this transformation characterize the target's GO field response, and their values can classify six classes of geometrical structures. Furthermore, we derive explicit formulas relating these parameters to target's geometrical attributes for double and triple reflections, by using a quaternion algebra method. In order to validate this representation theory, we construct a parametric model of bistatic scattering from an arbitrary multiplate structure, by combining the GO-physical optics (PO) method with this representation. Through two special cases, the representation theory is validated by comparing the RCSs calculated by the parametric model with those by a shooting and bouncing ray (SBR) algorithm. The representation and derived concise parametric model are useful for extracting geometrically relevant features from bistatic radar measurement.

The Gravity First (on Reincarnation of Third Kepler’s Law)

About four centuries ago, considering flat sections of cone x2 + y2 = z2 (along the axis of revolution on the plane Oxy), Robert Hooke wrote one fundamental differential equation \((x,y,z)^{\prime\prime} = - {{4{\pi ^2}k} \over {{{(\sqrt {{x^2} + {y^2} + {z^2}})}^3}}}\; \cdot \;(x,y,z)\), which thereafter set the foundation of the law of universal gravitation and explanation of movement of charged particle in the classical stationary Coulomb field. In this paper, differential-algebraic models arising as the result of replacement of a cone by an arbitrary quadric surface F(x, y, z) = 0 with respect to (as we call it) the Kepler parametrization of quadratic curves {F(x, y, α · x + β · y + δ)=0 | α, β, δ ∈ K}, K = ℝ, ℂ, are proposed and studied.

Conservation laws and the equivalence group

The paper generalizes differential conservation laws for the two-dimensional hydrodynamic Euler equations and their equivalent conservation laws for families of streamlines previously derived by the author. Three-dimensional analogues of these results, i.e., differential conservation laws for the three-dimensional hydrodynamic Euler equations, are presented. All conservation laws are divergent identities of the form div F = 0 and are found in two equivalent forms: in “mathematical-physical” form, where the vector field F is expressed in terms of quantities included in the Euler equations and their partial derivatives, and in geometric form. The second form represents conservation laws for families of streamlines where the vector field F under the divergence sign is expressed in terms of the classical geometric characteristics of curves — their Frenet unit vectors τ, ν, and β (the unit tangent, principal normal, and binormal vectors), the first curvature k, and the second curvature ϰ. Special attention is paid to the geometric interpretation of the obtained conservation laws and their constituent expressions. Issues related to the equivalence group of the eikonal equation and other equations are discussed.All results were obtained using the general vector and geometric formulas (differential conservation laws and other formulas), obtained by the author for families of arbitrary smooth curves, families of arbitrary smooth surfaces, and arbitrary smooth vector fields.

Interface balance laws, phase growth and nucleation conditions for multiphase solids with inhomogeneous surface stress

In this paper, the thermodynamic configurational force associated with a moving interface is used to derive the conditions for phase growth and nucleation in bodies with multiple diffusing species and arbitrary surface stress at the phase interface. First, the mass, momentum and energy balances are derived on the evolving phase interface. The thermodynamic conditions that result from free energy inequality at the interface are derived leading to the analytical form of the configurational force for bodies subject to mechanical loads, heat and multiple diffusing species. The derived second law condition naturally extends the Eshelby energy–momentum tensor to include species diffusion terms. The above second law restriction is then used to derive the condition for the growth of new phases in a body undergoing finite deformation subject to inhomogeneous as well as anisotropic interface stress, and multiple diffusing species. The growth conditions are derived in both current and reference configurations. The statistical temperature-dependent growth velocity is next derived using the Boltzmann distribution. The derived finite deformation form of growth requirement is simplified to obtain the small deformation diffusive void growth condition. Next, a general, finite deformation, arbitrary surface stress form of phase nucleation condition is derived by considering uncertainty in growth of a small nucleus. The probability of nucleation is shown to naturally depend on a theoretical estimate of critical volumetric energy density, which is directly related to the surface stress. The classical nucleation theory is shown to result from a simplified special case of the general criterion. As an application of the developed theory, the classical Blech electromigration experiment is simulated to estimate the critical energy density corresponding to the onset of electromigration voids at Al–TiN interface.