Spherical Slices Research Articles

Spherical path planning for multi axis support free additive manufacturing of truss structures

Multi-axis additive manufacturing systems are gaining increasing attention due to their potential for unsupported manufacturing and reduced stair-stepping effects. In response to the challenges of unsupported printing for truss structures, a five-axis path planning method based on spherical slicing has been proposed. Leveraging the implicit expression equation based on cylinders, this study has effectively achieved the generation of efficient surface slicing and five-axis spherical path. The employed path planning method demonstrates significant advantages in both generation efficiency and stability. In the testing experiments, various unsupported path planning schemes are generated for different truss cells and truss structures, including configurations such as the “bridge” and cross-cylinder truss cells. To validate and extend the applicability of this method, two types of five-axis additive manufacturing devices are utilized: one based on a five-axis CNC system and the other employing a UR10 robot. The manufacturing experiments have effectively verified the feasibility of the spherical slicing algorithm in manufacturing various truss unit types, which provides a new technical way for the unsupported manufacturing of truss structures in the future.

Beta functions of ( 3+1 )-dimensional projectable Hořava gravity

We derive the full set of beta functions for the marginal essential couplings of projectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava gravity in ($3+1$)-dimensional spacetime. To this end we compute the divergent part of the one-loop effective action in static background with an arbitrary spatial metric. The computation is done in several steps: reduction of the problem to three dimensions, extraction of an operator square root from the spatial part of the fluctuation operator, and evaluation of its trace using the method of universal functional traces. This provides us with the renormalization of couplings in the potential part of the action which we combine with the results for the kinetic part obtained previously. The calculation uses symbolic computer algebra and is performed in four different gauges yielding identical results for the essential beta functions. We additionally check the calculation by evaluating the effective action on a special background with spherical spatial slices using an alternative method of spectral summation. We conclude with a preliminary discussion of the properties of the beta functions and the resulting renormalization group flow, identifying several candidate asymptotically free fixed points.

Simple delineations cannot substitute full 3d tumor delineations for MR-based radiomics prediction of locoregional control in oropharyngeal cancer

Background and purposeManual delineation of head and neck tumor contours for radiomics analyses is tedious and time consuming. This study investigates if fast or readily available tumor contours can substitute full tumor contours by an experienced observer for an MR-based radiomics model to predict locoregional control (LRC) in oropharyngeal squamous cell carcinoma (OPSCC) tumors. Materials and methodsRadiomic features were extracted from postcontrast T1-weighted MRIs of 177 OPSCC primary tumors using six different manual delineation strategies. LRC prediction models based on recursive feature elimination combined with logistic regression were built. Models were trained and tested on data from each separate delineation. Additionally, the model derived from segmentations from the experienced reader was tested by each of the alternative delineations. Complementary, this was repeated with removal of size and shape features. Model performance was evaluated using area under the curve (AUC). ResultsPrediction performance of the experienced radiologist tumor delineation (AUC: 0.74) was superior compared to all other delineations when trained and tested (AUCs: 0.41–0.56) or trained on experienced delineations and tested (AUC: 0.56–0.67) on alternative segmentations. Removal of size and shape features considerably decreases prediction performance (AUC: 0.54). Applying the model based on expert delineations to spherical or single slice delineations makes prediction worthless since these models predict one class. ConclusionFast or readily available contours cannot substitute full expert tumor delineations in radiomics models predictive of LRC in OPSCC.

On the spherical slice transform

We study the spherical slice transform [Formula: see text] which assigns to a function f on the unit sphere Sn in [Formula: see text] the integrals of f over cross-sections of Sn by k-dimensional affine planes passing through the north pole (0,…, 0, 1). These transforms are known when k = n. We consider all 2 ≤ k ≤ n and obtain an explicit formula connecting [Formula: see text] with the classical (k − 1)-plane Radon–John transform [Formula: see text] on [Formula: see text]. Using this connection, known facts for Rk−1, like inversion formulas, support theorems, representation on zonal functions, and some others, are reformulated for [Formula: see text].

Analysis on CHF deviation caused by geometry of the heater blocks in a validation test of IVR-ERVC technology

The innovative technology of In-Vessel Retention – External Reactor Vessel Cooling (IVR-ERVC) is a mitigation countermeasure for severe accidents, which has been applied in the design of advanced pressurized water reactors. The validity of IVR-ERVC is restricted to boiling crisis and critical heat flux (CHF) of the reactor vessel lower head. A cylindrical slice heater block was usually employed to simulate the reactor vessel lower head in the majority of existing experiments, which may cause some uncertainties in CHF under natural circulation conditions. In the present paper, an experiment was constructed to study the characteristics of natural circulation and critical heat flux. Apart from the conventional cylindrical slice, a spherical slice was also employed as the heater block. The experimental data indicated that the natural circulation flow rate increases with increasing inlet water temperature, and shows large oscillations with the lift of circulation height. Besides, CHF decreases with the increase of inlet temperature. It was found that the CHF in the spherical slice is lower than that in the cylindrical slice from 10.3% to 28.4%, depending on the inlet water temperature. For the first time, the CHF uncertainty caused by the geometrical difference of the heater block was clarified.

THE FEATURES OF SCANNING LIQUID PHASE EPITAXY TECHNIQUE AS APPLIED TO THICK EPITAXIAL LAYERS GROWTH

Background. Growing of both thin and thick epitaxial layers is an essential part of semiconductor device technology. Liquid phase epitaxy is among well-known technological methods. There are pulse methods of liquid phase epitaxy specially developed for obtaining thin epitaxial layers. Their adaptation or modification for obtaining thick epitaxial layers is an actual issue.Objective. This work deals with the possibility of obtaining of thick epitaxial layers by extending the capabilities of scanning liquid phase epitaxy technique which also relates to pulse liquid phase growing methods.Methods. In this work we considered the influence of extra heating of the substrate on the growth of epitaxial layers when using scanning liquid phase epitaxy technique. For this purpose we carried out modelling of heat- and mass transport processes in the apparatus of scanning liquid phase epitaxy in conditions of extra heating of the substrate. To experimentally approve the validity of the model proposed we carried out the growing of Ge epitaxial layer on GaAs substrate in the above mentioned conditions.Results. The modelling showed that if the substrate was in contact with the solution-melt more than 1 second in conditions of substrate extra heating in scanning liquid phase epitaxy method, a segment of epitaxial layer dissolution appeared in plots of the grown epitaxial layer thickness against the growth time. The crystallization front temperature was lower than the initial solution-melt temperature in this case. We showed that it was connected with the magnitude of initial cooling/heating of the substrate heater. The modelling also showed that the epitaxial layer growth occurred in kind of a temperature gradient due to the extra substrate heating. Thus in a few seconds there took place the growth in the time-constant temperature gradient. Using the extra substrate heating we obtained epitaxial Ge layer on GaAs substrate from Ga-Ge solution-melt. The growth time was 60 sec. The layer thickness determined by spherical slice technique was 12.6 um.Conclusions. In this work we showed that using extra heating of the substrate’s back side there appeared the conditions for growing of thick epitaxial layers by scanning liquid phase epitaxy technique in case when the substrate temperature was lower than the solution-melt temperature. Here the growth of thick epitaxial layers took place in the condition of temperature gradient at crystallization front.

Brane cosmology and the self-tuning of the cosmological constant in the presence of bulk black holes

Motivated by the holographic self-tuning proposal of the cosmological constant, we generalize and study the cosmology of brane-worlds embedded in a higher-dimensional bulk black hole geometry. We describe the equations and matching conditions in the case of flat, spherical and hyperbolic slicing of the bulk geometry and find the conditions for the existence of a static solution. We solve the equations that govern dynamical geometries in the probe brane limit and we describe in detail the resulting brane-world cosmologies. Of particular interest are the properties of solutions when the brane-world approaches the black hole horizon. In this case the geometry induced on the brane is that of de Sitter, whose entropy and temperature is related to those of the higher dimensional bulk black hole.

Spherical slicing method and its application on robotic additive manufacturing

This article presents a spherical slicing method for additive manufacturing (AM) which is used to lay additive layers on a spherical surface, thus removing the stair stepping effect, increasing structural integrity and tensile strength. A toolpath is required to guide the extruder in the three-dimensional space and deposit the material in the desired locations. These tool paths are computed using slicing algorithms. The well-established method in AM industry is the planar slicing. In this method, the Computer Aided Design model is sliced using planes and as a result, two-dimensional tool paths are formed. With the introduction of multi-axis AM machines, development of new non-planar slicing algorithms has started. In this article, a novel non-planar, spherical slicing, is introduced. In the proposed spherical slicing method, the model is sliced by spherical shells such as that of an onion. These spherical slices are then used to generate the appropriate tool paths for guiding the robotic manipulator in three-dimensional space together with the corresponding orientation to lay the spherical layers on top of the previously manufactured planar base. Results are verified by manufacturing a model using a six-axis robotic serial manipulator by fused deposition modeling.

Вирощування гетероепітаксійних шарів на неізоперіодних підкладках мeтодом скануючої рідиннофазової епітаксії

Heterostructures with lattice mismatched and compositionally different layers are widely used in modern electronic and optoelectronic device engineering. Generally such structures are manufactured by the methods of metal-organic vapor phase epitaxy, metal-organic chemical vapor deposition and molecular-beam epitaxy. However, the methods of deposition from a liquid phase are the most inexpensive and simple yet. Thus obtaining the above mentioned heterostructures from a liquid phase is still promising. In this work we demonstrated the possibility of using the method of scanning liquid phase epitaxy to grow continuous heteroepitaxial layers over the substrate surface highly mismatched by lattice constant and having different crystal-chemical properties. By controlling basic parameters of the method we created the conditions close to the solution-melt saturation limit. In other words, we created the conditions of ultra-fast solution-melt cooling and, respectively, high growth rate. We obtained the heterostructures of Ge layers grown on GaP substrates where the lattice mismatch made 3.7%. Gallium was used as the solvent for Germanium. The heterostructure was grown by the method of scanning liquid phase epitaxy in the conditions of ultra-fast initial cooling of the solution-melt. Overcooling at the crystallization front was controlled by an extra heater of the substrate back side. The growing time was 1 and 20 seconds for the two test samples. The layers thickness was determined by the spherical slice technique to be 1.2 and 1.5 μm for these two growing time values, accordingly. We showed that it was possible to obtain more perfect Ge layers on GaP substrate by lowering the growth rate in the final growth stage. This method can be used to grow heterostructures used in creating such modern electronic and optoelectronic devices as structures based on А3В5 compounds and their solid solutions, which cannot be obtained by other classical methods of liquid phase epitaxy due to significant differences in lattice constants and / or crystal-chemical properties.

The Vertical Slice Transform on the Unit Sphere

Abstract The vertical slice transform in spherical integral geometry takes a function on the unit sphere Sn to integrals of that function over spherical slices parallel to the last coordinate axis. This transform was investigated for n = 2 in connection with inverse problems of spherical tomography. The present article gives a survey of some methods which were originally developed for the Radon transform, hypersingular integrals, and the spherical mean Radon-like transforms, and can be adapted to obtain new inversion formulas and singular value decompositions for the vertical slice transform in the general case n ≥ 2 for a large class of functions.

Limiting Means for Spherical Slices

We show that for a suitable class of functions of finitely-many variables, the limit of integrals along slices of a high dimensional sphere is a Gaussian integral on a corresponding finite-codimension affine subspace in infinite dimensions.

Real-time halo correction in phase contrast imaging.

As a label-free, nondestructive method, phase contrast is by far the most popular microscopy technique for routine inspection of cell cultures. However, features of interest such as extensions near cell bodies are often obscured by a glow, which came to be known as the halo. Advances in modeling image formation have shown that this artifact is due to the limited spatial coherence of the illumination. Nevertheless, the same incoherent illumination is responsible for superior sensitivity to fine details in the phase contrast geometry. Thus, there exists a trade-off between high-detail (incoherent) and low-detail (coherent) imaging systems. In this work, we propose a method to break this dichotomy, by carefully mixing corrected low-frequency and high-frequency data in a way that eliminates the edge effect. Specifically, our technique is able to remove halo artifacts at video rates, requiring no manual interaction or a priori point spread function measurements. To validate our approach, we imaged standard spherical beads, sperm cells, tissue slices, and red blood cells. We demonstrate real-time operation with a time evolution study of adherent neuron cultures whose neurites are revealed by our halo correction. We show that with our novel technique, we can quantify cell growth in large populations, without the need for thresholds and system variant calibration.

Radon transforms and Gegenbauer–Chebyshev integrals, II; examples

We transfer the results of Part I related to the modified support theorem and the kernel description of the hyperplane Radon transform to totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the spherical mean transform for spheres through the origin. The assumptions for functions are formulated in integral terms and close to minimal.

Renormalized entanglement entropy

We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in $AdS_4$ spacetimes agrees precisely with the holographically renormalized action for $AdS_4$ with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension $3/2 < \Delta < 5/2$ for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our renormalization method for the entanglement entropy is inherited directly from that of the partition function. We show explicitly how the entanglement entropy counterterms can be derived from the standard holographic renormalization counterterms for asymptotically locally anti-de Sitter spacetimes.

Null spaces of Radon transforms

We obtain new descriptions of the null spaces of several projectively equivalent transforms in integral geometry. The paper deals with the hyperplane Radon transform, the totally geodesic transforms on the sphere and the hyperbolic space, the spherical slice transform, and the Cormack–Quinto spherical mean transform for spheres through the origin. The consideration extends to the corresponding dual transforms and the relevant exterior/interior modifications. The method relies on new results for the Gegenbauer–Chebyshev fractional integrals.

3D Magnetic Analysis of Permanent Magnets in Spherical Configuration

The present study aims to increase the amount of surface flux by changing the magnetic directions of a spherical magnet (NdFeB) consisting of four poles. For this purpose, the magnetic directions of quartile spherical slices constituting the spherical magnet are manipulated and their three-dimensional analyses are carried out by using finite-element method via Maxwell environment. The analysis of the magnetic quartile spheres with four different magnetic directions are compared to the each other, and then the quartile sphere with the best surface flux distribution is suggested for rotor structure. It is clear emphasized that the induced torque of the spherical motor, in which such a rotor is used, will be improved as well.

TWO OPTIMISATION PROBLEMS FOR CONVEX BODIES

In this paper, we will show that the spherical symmetric slices are the convex bodies that maximise the volume, the surface area and the integral of mean curvature when the minimum width and the circumradius are prescribed and the symmetric $2$-cap-bodies are the ones which minimise the volume, the surface area and the integral of mean curvature given the diameter and the inradius.

Effects of sulphiting and osmotic pre-treatments on the effective moisture diffusion coefficients D&lt;sub&gt;EFF&lt;/sub&gt; of air drying of pineapple slices

Air dehydration of fruits has been reported to be limiting in some factors especially on the drying kinetics and quality of the dried fruits. Removal of moisture during drying is attributed to these. This study was designed to evaluate the effects of sulphiting and osmotic pretreatments on effective diffusion coefficient (Deff) of air drying pineapple slices at 50o and 70 oC temperatures. Smooth cayenne pineapple obtained from Ajanla farms, Ibadan, Nigeria was used for the study. The fruits were hand peeled and sliced to spherical slices of 5 cm radius and 0.5 cm thickness. Pineapplefruit slices were pretreated at three levels of sulphiting and sucrose/osmosis and two conditions of drying (50 oC at 16 h and 70 oC at 10 h), resulting in 18 treatments in a factorial experimental design. Changes in moisture were monitored hourly and Fick’s second law was used to describe the rate of moisture transfer to determine the Deff as the slices were dried using a cabinet dryer. Results showed that the Deff was strongly affected by sulphiting at 2500 ppm equalling 9.10+ 0.13 x 10-6 and 6.78 + 0.53 x 10-6cm/s for 70 oC and 50 oC drying temperatures, respectively. The osmotic pretreatment at 40% sucrose recorded 4.91 + 0.15 x 10-6cm/s and 6.93 + 0.03 x 10-6cm/s for 70 oC and 50 oC drying temperature respectively. The control samples had 3.14 + 0.23 x 10-6 and 4.19 + 0.21 x 10-6 at 70 oC and 50 oC drying temperature, respectively. The high values obtained from the pretreated samples may be due to the restructuring of the cell walls. The combination of sulphiting and osmotic pretreatments also exhibited significant impact on the Deff value, ranging between 5.13 to 8.42 x 10-6, though not as pronounced as with the single pretreatment method. Furthermore, drying at 70 oC influenced the Deff value more than drying at 50 oC with both pretreatment methods. The study, therefore, showed that pretreatment methods improved the Deff of the pineapple slices, with the sulphiting pretreatment at 2500 ppm having the highest value.Key words: Sulphiting, osmotic, pretreatment, drying, kinetics

CMB tomography: Reconstruction of adiabatic primordial scalar potential using temperature and polarization maps

Assuming linearity of the perturbations at the time of decoupling, we reconstruct the primordial scalar potential from the temperature and polarization anisotropies in the cosmic microwave background radiation. In doing so we derive an optimal linear filter which, when operated on the spherical harmonic coefficients of the anisotropy maps, returns an estimate of the primordial scalar potential fluctuations in a spherical slice. The reconstruction is best in a thick shell around the decoupling epoch; the quality of the reconstruction depends on the redshift of the slice within this shell. With high-quality maps of the temperature and polarization anisotropies it will be possible to obtain a reconstruction of potential fluctuation on scales between $\ensuremath{\ell}=2$ and $\ensuremath{\ell}\ensuremath{\sim}300$ at the redshift of decoupling, with some information about the three-dimensional shapes of the perturbations in a shell of width 250 Mpc.

A fast content-based indexing and retrieval technique by the shape information in large image database

In this paper, we present an efficient content-based image retrieval (CBIR) system which employs the shape information of images to facilitate the retrieval process. For efficient feature extraction, we extract the shape feature of images automatically using edge detection and wavelet transform which is widely used in digital signal processing and image compression. To facilitate speedy retrieval, we also propose the Spherical Pyramid-Technique (SPY-TEC), a new indexing method for similarity search in high-dimensional data space. The SPY-TEC is based on a special space partitioning strategy, which is to divide the d-dimensional data space first into 2 d spherical pyramids, and then cut the single spherical pyramid into several spherical slices. This partition provides a transformation of d-dimensional space into 1-dimensional space. Thus, we are able to use a B +-tree to manage the transformed 1-dimensional data. We show that our image indexing method supports faster retrieval than other multi-dimensional indexing methods such as the R *-tree through various experiments. Finally, we show the retrieval effectiveness of our CBIR system using the measure proposed by the QBIC (C. Faloutsos et al., 1994) system.