Smooth Geometry Research Articles

Extracting sectional contours from scanned point clouds via adaptive surface projection

This paper presents a new and fully automatic method to extract cross-sectional contour profiles of a physical object from the point cloud data scanned from its surface. Correctly extracting the sectional contours is of particular importance in the quality inspection of airfoil blades as the tolerances specified on a manufactured aero-engine blade are generally imposed at specific blade sections. The collected point cloud via 3D laser scanning is, however, distributed all over the blade surface rather than at the desired specific sections. In fact, no point in the point cloud is located exactly on the sectional planes. The desired sectional data have to be extracted from the nearby data points. If the underlying smooth surface geometry of the point cloud in the vicinity of a nearby data point can be approximated by a mathematical function, the approximated local surface formulation can be used to project the nearby point onto the desired sectional plane along a curvilinear trajectory. This is achieved in this work by fitting a local quadric surface to the neighbouring points of the point of interest. A systematic approach to establish a balanced set of neighbouring points is employed to avoid bias in fitting the local quadric surface as well as to guide the selection of points to be projected onto the sectional plane. The projected points are then used to construct the desired sectional contour profile. Implementation results have demonstrated the superior performance of the proposed fully automatic method in comparison with the existing methods.

Smooth Horizonless Geometries Deep Inside the Black-Hole Regime.

We construct the first family of horizonless supergravity solutions that have the same mass, charges, and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically dual states in the N=(4,4) D1-D5 orbifold conformal field theory (CFT). Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.

Non-Abelian bubbles in microstate geometries

We find the first smooth microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of $\mathcal{N}=1$, $d=5$ Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.

Performance evaluation of dental implants: An experimental and numerical simulation study

Dental implants are widely used in replacing missing teeth. However, some problems may occur such as screw loosening or screw fracture which lead to implant failure. In this regard, it is of utmost importance to analyse some of the factors that affect the primary stability and consequently the osseointegration of dental systems. In the present study, particular attention is given to the bone density and the bone-implant contact in order to evaluate the implant performance.Given the difficulty in working with bone in vivo, in the present study two implant systems were inserted in polymeric samples, of different densities, known as Sawbones, which simulate the structure of trabecular bone. The implant systems chosen were external hexagon and Morse taper. The performance of the implants was evaluated through experimental fatigue tests that simulate the chewing or mastication cycles. The qualitative analysis of the damage in the cellular structure of the samples was performed using scanning electron microscopy (SEM).The finite element (FE) method was used to model the penetration of the implants and enable the determination of the stress at the implant and deformations at the Sawbones-implant vicinity. Prior to penetration simulations, a well-known analytical model of indentation was compared with indentation simulations, in order to validate the numerical model. The major difference between numerical and analytical model results, in the case of the displacements, was found to be around 9%.The failure of the Sawbones occurred with the propagation of the collapsed cells according to SEM observations. The fatigue results showed that the Morse taper implant exhibited lower displacements than the external hexagon. Higher density Sawbones also exhibits lower deformations, while keeping the other parameters constant. It means that Morse taper and high dense materials show a better fatigue performance than the other systems and materials.The FE results for penetration showed that a threaded geometry implant when compared to smooth geometry provided a reduction of the stresses in the implant and reduces the deformations in the Sawbones.The results of the penetration simulations follow the same trend as the indentation simulations and analytical model. Simulation results show that the displacements are reduced with the increase of the density of the polymer foam. This is in agreement with the fatigue results. Comparing bones with foams, it could be concluded that, the increase of the bone density will induce a higher stability of the implants.

Smooth non-extremal D1-D5-P solutions as charged gravitational instantons

We present an alternative and more direct construction of the non-supersymmetric D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. We show that these solutions --- with all three charges and both rotations turned on --- can be viewed as a charged version of the Myers-Perry instanton. We present an inverse scattering construction of the Myers-Perry instanton metric in Euclidean five-dimensional gravity. The angular momentum bounds in this construction turn out to be precisely the ones necessary for the smooth microstate geometries. We add charges on the Myers-Perry instanton using appropriate SO(4,4) hidden symmetry transformations. The full construction can be viewed as an extension and simplification of a previous work by Katsimpouri, Kleinschmidt and Virmani.

Tunneling into microstate geometries: quantum effects stop gravitational collapse

Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest the existence of some structure at the black hole horizon. This structure can only form if classical general relativity stops being the correct description of the collapsing shell before it reaches the horizon size. We present strong evidence that classical general relativity can indeed break down prematurely, by explicitly computing the quantum tunneling amplitude of a collapsing shell of branes into smooth horizonless microstate geometries. We show that the amplitude for tunneling into microstate geometries with a large number of topologically non-trivial cycles is parametrically larger than exp(-S), which indicates that the shell can tunnel into a horizonless configuration long before the horizon has any chance to form. We also use this technology to investigate the tunneling of M2 branes into LLM bubbling geometries.

Normal stress measurement in foams and emulsions in the presence of slip

Steady shear measurements on three yield-stress fluids, a foam and two types of emulsions, were carried out using a smooth torsional parallel-plate geometry, with different gap spacings to assess the effect of wall slip on the normal stress differences. The classical Mooney analysis gave slip-corrected flow curves that agreed with data from a roughened cone-and-plate for all three materials, despite the fact that the compatibility requirement between the flow curve and slip velocity functionalities was not satisfied, indicating that the method is robust for this geometry. All three materials exhibited finite normal stresses following yielding, with power-law exponents of approximately 0.4, as well as shear stresses that can be represented by the Herschel–Bulkley model. The systems showed complete slip for shear stresses below the yield stress, with the stress transmitted to the unyielded material through a thin liquid layer causing an elastic deformation that was measurable for the unyielded foam, which can be represented by the Mooney–Rivlin elastic constitutive equation. The unyielded foam exhibited large sample-to-sample variations in the apparent modulus for identical loading conditions.

Tangible 3D modeling of coherent and themed structures

We present CubeBuilder, a system for interactive, tangible 3D shape modeling. CubeBuilder allows the user to create a digital 3D model by placing physical, non-interlocking cubic blocks. These blocks may be placed in a completely arbitrary fashion and combined with other objects. In effect, this turns the task of 3D modeling into a playful activity that hardly requires any learning on the part of the user. The blocks are registered using a depth camera and entered into the cube graph where each block is a node and adjacent blocks are connected by edges. From the cube graph, we transform the initial cubes into coherent structures by generating smooth connection geometry for some edges of the graph. Based on an analysis of the cube graph, we identify subgraphs that match given graph templates. These subgraph templates map to predefined geometric refinements of the basic shape. This, in turn, allows the user to tangibly build structures of greater details than the blocks provide in and of themselves. We show a number of shapes that have been modeled by users and are indicative of the expressive power of the system. Furthermore, we demonstrate the scalability of the tangible interface which appears to be limited only by the number of blocks available.

Micro-Plasma Transferred Arc Additive Manufacturing for Die and Mold Surface Remanufacturing

Micro-plasma transferred arc (µPTA) additive manufacturing is one of the newest options for remanufacturing of dies and molds surfaces in the near-millimeter range leading to extended usage of the same. We deployed an automatic micro-plasma deposition setup to deposit a wire of 300 µm of AISI P20 tool steel on the substrate of same material for the potential application in remanufacturing of the die and mold surface. Our present research effort is to establish µPTA additive manufacturing as a viable economical and cleaner methodology for potential industrial applications. We undertook the optimization of single weld bead geometry as the first step in our present study. Bead-on-plate trials were conducted to deposit single bead geometry at various processing parameters. The bead geometry (shape and size) and dilution were measured and the parametric dependence was derived. A set of parameters leading to reproducible regular and smooth single bead geometry were identified and used to prepare a thin wall for mechanical testing. The deposits were subjected to material characterization such as microscopic studies, micro-hardness measurements and tensile testing. The process was compared qualitatively with other deposition processes involving high-energy density beams and was found to be advantageous in terms of low initial and running costs with comparable properties. The outcome of the study confirmed the process capability of µPTA deposition leading to deployment of cost-effective and environmentally friendlier technology for die and mold remanufacturing.

Effect of the welding process and filler material on the fatigue behavior of 960 MPa structural steel at a butt joint configuration

Ultrahigh-strength steels are being used more and more frequently in the engineering industry. Normally, the welding of these steels is more demanding. The welding requires a controlled heating and cooling rate. In this study, the S-N curves were determined for the laser, the laser-gas metal arc hybrid (Laser-GMA hybrid welding, LHW) and the gas metal arc welding (GMAW) welded joints according to the recommendations of the International Institute of Welding (IIW) by using a constant amplitude loading and a stress ratio of R = 0.1. The frequency of loading varied between 4 and 10 Hz. The tested material was direct quenched steel with a yield strength of 960MPa and a thickness of 6 mm. The total amount of tested specimens was 51. The fatigue test results have proven to be close to the IIW recommendations and the differences between various welding processes were minor. Instead of welding process or filler material, the main factor influencing the fatigue behavior was the geometry of the weld. Consequently, the proper welding parameters should be applied in every welding process in order to achieve a smooth joint geometry and, thus, a high fatigue resistance.

Integration of CAD, CAE and CAM procedures for ceramic components undergoing sintering

The paper discusses a new method to predict sintering deformation of complex ceramic components combining advanced nonlinear simulations and experimental results. Bending creep and dilatometric tests are used to fully characterize the complex material behavior and to determine the viscosity of vitreous china for sanitaryware as a function of relative density. The material model is then implemented into a USERMAT subroutine for the Ansys finite element program and the deformation of ceramic components of complex shapes during sintering is numerically simulated. Finally a method is developed and implemented in Ansys using the APDL language aiming to apply a subdivision algorithm to the final deformed mesh predicted through the finite element analysis. After the application of the subdivision algorithm, a smooth surface geometry of the ceramic component is obtained in a format suitable for manufacturing.

Synthesis and analysis of multi‐mode profile horn using mode matching technique and evolutionary algorithm

This study presents the design and analysis of linear as well as cubic spline interpolated profiled smooth-wall multimode horn using mode matching (MM) technique along with genetic algorithm (GA) and particle swarm optimisation (PSO). To apply the MM technique, the smooth profile conical geometry is assumed to consist of cascaded sections of large number of small symmetrical radial steps. Scattering matrix for each section has been calculated using MM technique and over all scattering matrix of the cascaded junctions has been calculated using generalised scattering matrix technique. The radiation pattern has been calculated using hybrid boundary contour mode matching technique. Optimisation of the linear/spline profile horn has been carried out using GA as well as PSO. Detailed modal analysis along with the convergence of the present technique for the smooth profile structure has also been carried out. A spline profile multimode horn working at 89 GHz has been designed and developed. The present analysis has been verified with the measured results. There is a very good agreement between theoretical and measured results.

Optimizing thermal performance of building-integrated photovoltaics for upgrading informal urbanization

Optimizing building-integrated photovoltaic envelopes (BIPV) to retrofit multistory residential buildings in an informal urban settlement, heat transfer and energy harnessed are key parameters for an efficient upgrade. Firstly, simplified calculation model is deduced for the heat transfer across the PV wall via average outdoor temperature. Secondly, the thermal effect of gap depth and geometry on the performance of a BIPV is parametrically optimized and evaluated for a range of envelope shapes. The numerical model results were validated by energy simulations of TRNSYS and EnergyPlus; CFD simulation by PHOENICS software to explain the thermal behavior of the air in the gap. At constant conditions for a flat vertical PV wall with an air gap from 3cm to 40cm with 3cm increment, the increase of air gap till 22cm depth reduced the heat gain through the envelope, at wider air gaps heat gain increased due to Laminar convective heat flow. PV cooling by natural convection optimizes at smooth flow air gap geometries improving PV efficiency 40%, for altering depth air gaps, overheating areas of PV modules occur decreasing energy harnessed. Upgrading to optimized BIPV envelope of 80° slanted depth air gap can reduce heat transferred through the envelope by 132kWh/m2 annually and reduce cooling load components by 50% decreasing the CO2 emissions monthly by 250–300kg.

Fluxes in F-theory compactifications on genus-one fibrations

We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5) x Z2. The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5) x U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete Z2 gauge anomalies as required by general consistency considerations.

4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block

A class of 3d $\mathcal{N}=2$ supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class, the massive supersymmetric vacua of the theory contain the classical geometries on a 4d simplicial complex. The corresponding 4d simplicial geometries are locally constant curvature (either dS or AdS), in the sense that they are made by gluing geometrical 4-simplices of the same constant curvature. When the simplicial complex is sufficiently refined, the simplicial geometries can approximate all possible smooth geometries on 4-manifold. At the quantum level, we propose that a class of holomorphic blocks defined in arXiv:1211.1986 from the 3d $\mathcal{N}=2$ gauge theories are wave functions of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic behavior of holomorphic block reproduces the classical action of 4d Einstein-Hilbert gravity in the simplicial context.

Enhanced Broadband Light Trapping in c-Si Solar Cells Using Nanosphere-Embedded Metallic Grating Structure

A hexagonal nanosphere (NS)-embedded back plasmonic grating structure is proposed to improve the light absorption of crystalline silicon (c-Si) solar cells. These structures are simple, can be deposited toward the final stages of device processing, and involve no increase in the surface area of the semiconductor layer. Experimental fabrication of this structure on a 200-μm c-Si wafer has been realized using silver, resulting in broadband absorption enhancement in the near-infrared region. In corresponding to the optical measurement, a maximum potential photocurrent density enhancement of around 2.23 mA/cm2 has been predicted, compared with the reference with a planar metal reflector. Three-dimensional finite-element method numerical simulations were also performed on smooth and irregular surface geometries of the NSs. Our results demonstrate that while both configurations perform better than a planar reflector, the irregular nanofeatures on the gratings can adjust the optical resonance to ensure that the light is more efficiently scattered into the Si, which would significantly improve its optical absorption. These structures have the potential to be used as rear metal contacts, in addition to performing the function of a light-trapping layer without increasing the fraction of the metal component.

A Lane consistent optical model potential for nucleon scattering on actinide nuclei with extended coupling

An extension for odd-A actinides of a previously derived dispersive coupledchannel optical model potential (OMP) for 238 U and 232 Th nuclei is presented. It is used to fit simultaneously all the available experimental databases including neutron strength functions for nucleon scattering on 232 Th, 233,235,238 U and 239 Pu nuclei. Quasi-elastic (p,n) scattering data on 232 Th and 238 U to the isobaric analogue states of the target nucleus are also used to constrain the isovector part of the optical potential. For even-even (odd) actinides almost all low-lying collective levels below 1 MeV (0.5 MeV) of excitation energy are coupled. OMP parameters show a smooth energy dependence and energy independent geometry.

Solving the Helmholtz equation for general smooth geometry using simple grids

The method of difference potentials was originally proposed by Ryaben’kii, and is a generalized discrete version of the method of Calderon’s operators. It handles non-conforming curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity of the solver at the level of a finite-difference scheme on a regular structured grid. Compact finite difference schemes enable high order accuracy on small stencils and so require no additional boundary conditions beyond those needed for the differential equation itself. Previously, we have used difference potentials combined with compact schemes for solving transmission/scattering problems in regions of a simple shape. In this paper, we generalize our previous work to incorporate smooth general shaped boundaries and interfaces, including a formulation that involves multiple scattering.

Determination of head conductivity frequency response in vivo with optimized EIT-EEG

Electroencephalography (EEG) benefits from accurate head models. Dipole source modelling errors can be reduced from over 1cm to a few millimetres by replacing generic head geometry and conductivity with tailored ones. When adequate head geometry is available, electrical impedance tomography (EIT) can be used to infer the conductivities of head tissues. In this study, the boundary element method (BEM) is applied with three-compartment (scalp, skull and brain) subject-specific head models.The optimal injection of small currents to the head with a modular EIT current injector, and voltage measurement by an EEG amplifier is first sought by simulations. The measurement with a 64-electrode EEG layout is studied with respect to three noise sources affecting EIT: background EEG, deviations from the fitting assumption of equal scalp and brain conductivities, and smooth model geometry deviations from the true head geometry. The noise source effects were investigated depending on the positioning of the injection and extraction electrode and the number of their combinations used sequentially.The deviation from equal scalp and brain conductivities produces rather deterministic errors in the three conductivities irrespective of the current injection locations. With a realistic measurement of around 2min and around 8 distant distinct current injection pairs, the error from the other noise sources is reduced to around 10% or less in the skull conductivity. The analysis of subsequent real measurements, however, suggests that there could be subject-specific local thinnings in the skull, which could amplify the conductivity fitting errors. With proper analysis of multiplexed sinusoidal EIT current injections, the measurements on average yielded conductivities of 340mS/m (scalp and brain) and 6.6mS/m (skull) at 2Hz. From 11 to 127Hz, the conductivities increased by 1.6% (scalp and brain) and 6.7% (skull) on the average. The proper analysis was ensured by using recombination of the current injections into virtual ones, avoiding problems in location-specific skull morphology variations.The observed large intersubject variations support the need for in vivo measurement of skull conductivity, resulting in calibrated subject-specific head models.

Assessing the influence of biofilm surface roughness on mass transfer by combining optical coherence tomography and two‐dimensional modeling

Imaging and modeling are two major approaches in biofilm research to understand the physical and biochemical processes involved in biofilm development. However, they are often used separately. In this study we combined these two approaches to investigate substrate mass transfer and mass flux. Cross-sectional biofilm images were acquired by means of optical coherence tomography (OCT) for biofilms grown on carriers. A 2D biofilm model was developed incorporating OCT images as well as a simplified biofilm geometry serving as structural templates. The model incorporated fluid flow, substrate transfer and biochemical conversion of substrates and simulated the hydrodynamics surrounding the biofilm structure as well as the substrate distribution. The method allowed detailed analysis of the hydrodynamics and mass transfer characteristics at the micro-scale. Biofilm activity with respect to substrate fluxes was compared among different combinations of flow, substrate availability and biomass density. The combined approach revealed that higher substrate fluxes at heterogeneous biofilm surface under two conditions: pure diffusion and when high flow velocity along the biofilms surface renders the whole liquid-biofilm interface to be highly active. In-between the two conditions the substrate fluxes across the surface of smooth biofilm geometry were higher than that of the heterogeneous biofilms.