Spherical Section Research Articles

A $p$-spherical section property for matrix Schatten-$p$ quasi-norm minimization

<p style='text-indent:20px;'>Low-rank matrix recovery has become a popular research topic with various applications in recent years. One of the most popular methods to dual with this problem for overcoming its NP-hardness is to relax it into some tractable optimization problems. In this paper, we consider a nonconvex relaxation, the Schatten-<inline-formula><tex-math id="M1">\begin{document}$p$\end{document}</tex-math></inline-formula> quasi-norm minimization (<inline-formula><tex-math id="M2">\begin{document}$0&lt;p&lt;1$\end{document}</tex-math></inline-formula>), and discuss conditions for the equivalence between the original problem and this nonconvex relaxation. Specifically, based on null space analysis, we propose a <inline-formula><tex-math id="M3">\begin{document}$p$\end{document}</tex-math></inline-formula>-spherical section property for the exact and approximate recovery via the Schatten-<inline-formula><tex-math id="M4">\begin{document}$p$\end{document}</tex-math></inline-formula> quasi-norm minimization (<inline-formula><tex-math id="M5">\begin{document}$0&lt;p&lt;1$\end{document}</tex-math></inline-formula>).

Optical spectroscopy of excitons with spatially separated electrons and holes in nanosystems containing dielectric quantum dots

It is shown that in the potential energy of an exciton of spatially separated electrons and holes [hole moves in the amount of quantum dots (QDs), the electron is localized on a spherical surface section (QD—dielectric matrix)], taking into account centrifugal, energy gives rise band of the quasistationary surface exciton states that with the increase of the radius of QD becomes stationary state. The mechanisms of formation of the spectra of interband and intraband absorption (emission) of light in nanosystems containing aluminum oxide QDs, placed in the matrix of vacuum oil, are presented. It is shown that the electron transitions in the area of the surface exciton states cause significant absorption in the visible and near-infrared wavelengths and cause the experimentally observed significant blurring of the absorption edge.

Exciton Spectroscopy of Spatially Separated Electrons and Holes in the Dielectric Quantum Dots

It is shown that in the potential energy of an exciton of spatially separated electrons and holes (hole moves in the amount of quantum dots (QDs), and the electron is localized on a spherical surface section (QD—dielectric matrix)) taking into account centrifugal energy gives rise band of the quasi-stationary surface exciton states that with the increase of the radius of QD becomes stationary state. The mechanisms of formation of the spectra of interband and intraband absorption (emission) of light in nanosystems containing aluminum oxide QDs, placed in the matrix of vacuum oil, are presented. It is shown that the electron transitions in the area of the surface exciton states cause significant absorption in the visible and near infrared wavelengths, and cause the experimentally observed significant blurring of the absorption edge.

An acoustic source model for the signal produced by ground motion over an underground event in mountainous terrain

A confined, large explosion underground launches an infrasonic signal into the atmosphere generated by the heaving of the ground over the explosion. For example, the last three North Korean nuclear weapon tests produced infrasonic signals detected at great distances form the test site. Under flat terrain, modeling the acoustic source from a confined explosion is a classical problem, similar to that of a baffled loudspeaker. In mountainous regions, the problem is more difficult. A boundary element method has been developed to this end. Given the vertical motion of the ground surface, the model predicts an the acoustic pressure on a spherical section centered over the source. From this, a source function for far field propagation can be extracted. The methods used to produce such a model will be presented.

Computational study on the structural and surface properties of amorphous hydroxylated TiO2 spherical nanoparticles

Monte Carlo simulations were carried out on amorphous titanium dioxide (TiO2) for both bulk and hydroxylated nanoparticles with particle sizes ranging from 1 to 10 nm. The potential developed by the Matsui and Akaogi (MA) was used to model the interatomic interactions of TiO2 in both cases (bulk and nanoparticles). Besides, Angular and Morse potentials proposed by the Tether, Cormack, Du et. al. (TCD) were introduced to model the interactions of hydroxyl groups on the TiO2 surfaces, i.e., the Ti-O-H groups with an experimental and theoretical angles of 125 o . The bulk system was developed using periodic boundary conditions. The TiO2 nanoparticles were extracted by applying a spherical cut section in the bulk TiO2 melt structure to obtain the required size. Free valences on the nanoparticle surfaces were saturated via additional hydroxyl groups and then quenched to 300 K under free boundary conditions. The bulk and surface properties of the nanoparticles were calculated at 300 K and zero pressure and characterized via radial distribution functions, bond angle distributions, bond distances, coordination numbers, OH group concentrations and radial density profiles. In addition, to understand the difference in properties of amorphous hydroxylated TiO2 nanoparticles and bulk amorphous TiO2, a comparative study was done at the same thermodynamic conditions. The study shows that the bulk properties of amorphous hydroxylated TiO2 nanoparticles are strongly size-dependent and different from those of the bulk TiO2. As expected, increasing the particle size leads to an approach of the particle’s bulk properties to the bulk properties of the (quasi) infinite system. The size effects show that decreasing the particle size results in increasing the surface effects and surface OH group concentrations. Accordingly, small-sized TiO2 nanoparticles have higher surface OH group concentrations and larger surface effects than large-sized TiO2 nanoparticles. Larger surface effects result significant changes in their bond angles, bond distances, and coordination numbers. The simulation results of the surface properties reveal that the surface titanium atoms in the TiO2 nanoparticles have the capability of accommodating up to 5 hydroxyl groups. The mean surface hydroxyl group density of the amorphous TiO2 spherical nanoparticles is estimated to be around 8.1/nm 2, which lies in the range of 8–16/nm 2, found by experimental and other simulation studies. Details of the modelling, simulations results and the study are presented in this paper.

INVESTIGATION OF INFLUENCE OF SEPARATOR MAGNETIC SYSTEM CONFIGURATION WITH PERMANENT MAGNETS ON MAGNETIC FIELD DISTRIBUTION IN WORKING AREA

Purpose. To carry out research the influence of magnetic system configuration (shape and size of the permanent magnets) on magnetic field spatial distribution in working area of new structure design magnetic separator with active front surface by numerical methods. Methodology. We have applied the magnetic field numerical simulation for permanent magnets system in absence of electrical current in magnetostatic approximation. We have solved the problem by using finite element method. Research of permanent magnets cross-sectional shape influence made in the two-dimensional formulation using software package Elcut. Research of magnetic field induction spatial (three-dimensional) distribution in new construction magnetic separator working area is conducted using software package COMSOL Multiphysics 3.5a. Results. Magnetic flux density maximum in the immediate vicinity of permanent magnet surface provide magnets with spherical and trapezoidal cross-sectional shape. At a distance from pole surface, where the separation process working, magnetic field density produced by trapezoidal and spherical cross section magnets, substantially lower in comparison with rectangular magnets. Rectangular and rectangular with beveled corners cross-section shape magnets create approximately same magnetic field intensity not significantly different in weight. Analysis of the spatial distribution of magnetic field induction in the working area of a new construction magnetic separator has shown that a strong magnetic field with high magnetic flux density gradient value is formed in the interpolar working volume. Originality. For the first time research of magnetic flux density distribution in working area of new construction magnetic separator is conducted. Developed device feature is complex spatial distribution of magnetic field. Practical value. Results of research can be used for selection of rational parameters of separator magnetic system. Received results also can be used for determination of separator force characteristics.

Fermi-surface topologies and low-temperature phases of the filled skutterudite compoundsCeOs4Sb12andNdOs4Sb12

MHz conductivity, torque magnetometer and magnetization measurements are reported on single crystals of CeOs$_4$Sb$_{12}$ and NdOs$_4$Sb$_{12}$ using temperatures down to 0.5~K and magnetic fields of up to 60~tesla. The field-orientation dependence of the de Haas-van Alphen and Shubnikov-de Haas oscillations is deduced by rotating the samples about the $[010]$ and $[0\bar{1}1]$ directions. The results indicate that NdOs$_4$Sb$_{12}$ has a similar Fermi surface topology to that of the unusual superconductor PrOs$_4$Sb$_{12}$, but with significantly smaller effective masses, supporting the importance of local phonon modes in contributing to the low-temperature heat capacity of NdOs$_4$Sb$_{12}$. By contrast, CeOs$_4$Sb$_{12}$ undergoes a field-induced transition from an unusual semimetal into a high-field, high-temperature state characterized by a single, almost spherical Fermi-surface section. The behavior of the phase boundary and comparisons with models of the bandstructure lead us to propose that the field-induced phase transition in CeOs$_4$Sb$_{12}$ is similar in origin to the well-known $\alpha-\gamma$ transition in Ce and its alloys.

Successive Concave Sparsity Approximation for Compressed Sensing

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell_0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell_1$ and $\ell_0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed which leads to a number of weighted $\ell_1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.

Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes

We study scalar perturbations of four dimensional topological nonlinear charged Lifshitz black holes with spherical and plane transverse sections, and we find numerically the quasinormal modes for scalar fields. Then, we study the stability of these black holes under massive and massless scalar field perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear exponent, the angular momentum and the mass of the scalar field in the modes. It is found that the modes are overdamped depending strongly on the dynamical exponent and the angular momentum of the scalar field for a spherical transverse section. In constrast, for plane transverse sections the modes are always overdamped.

Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography.

Wave models that have been used to extract the biomechanical properties of the cornea from the propagation of an elastic wave are based on an assumption of thin-plate geometry. However, this assumption does not account for the effects of corneal curvature and thickness. This study conducts finite element (FE) simulations on four types of cornea-like structures as well as optical coherence elastography (OCE) experiments on contact lenses and tissue-mimicking phantoms to investigate the effects of curvature and thickness on the group velocity of an elastic wave. The elastic wave velocity as determined by FE simulations and OCE of a spherical shell section decreased from ∼2.8 m/s to ∼2.2 m/s as the radius of curvature increased from 19.1 mm to 47.7 mm and increased from ∼3.0 m/s to ∼4.1 m/s as the thickness of the agar phantom increased from 1.9 mm to 5.6 mm. Both the FE simulation and OCE results confirm that the group velocity of the elastic wave decreases with radius of curvature but increases with thickness. These results demonstrate that the effects of the curvature and thickness must be considered in the further development of accurate wave models for reconstructing biomechanical properties of the cornea.

ANALYSIS OF CYLINDRICAL SHELL STRUCTURE WITH VARYING PARAMETERS

The shell structures are composed of a thin shell made of reinforced concrete without the use of internal columns giving an open interior. Most common shells used in industry are flat plates and domes but different shapes like cylindrical, parabolic or spherical section may also used. Sports or storage facilities buildings are common concrete shell structures. However, they can be difficult to design, as the exact shape required for stability of structure depends on the material used, the size of the shell, exterior or interior loading, and other oblique. So by varying the parameter of the shell, behaviour of the shell is also varying. Main goal of this paper is parametric analysis of the multiple cylindrical shell structures with different lengths. For analysis we took two different lengths of cylindrical shell and then, two parameters have been change first one is radius and second is thickness, on the basis of different radius and thickness for same chord width, length, and material of shell we will compare the behaviour of shell for different models.

Unsteady MHD Flow of an Incompressible Elastico-Viscous Fluid in a Tube of Spherical Cross Section on a Porous Boundary

Unsteady MHD Flow of an Incompressible Elastico-Viscous Fluid in a Tube of Spherical Cross Section on a Porous Boundary

Electrodeposited Copper Wire Mesh Formed on Chromium Template, the Formation Mechanism and Application as a Transparent Conductive Film

Copper wire mesh electrodeposits have been formed along the cracks of an electrodeposited chromium template. By reducing the electrodeposition time, the open area ratio increased and wire width of the copper wire decreased. The electrodeposited copper wire mesh has an 84.0% transmittance, 9.8 μm wire width and 0.187 Ω/□ sheet resistance. These characteristics satisfy some practical use requirements of a transparent conductive film. The copper wire mesh electrodeposits initiate at the crack edges. These initial deposits, which form along the crack edge, combine and then form the copper wire mesh. The copper deposition initiated at sites along the crack edges. As electrodeposition progressed, growth from the initiation sites coalesced to give copper wire formation along the crack edges. It eventually forms a spherical cross section shape along the crack. The initial deposit formation along the crack edge is due to the current incubation removal of the local oxide film preferentially along the chromium template crack edges.

Aerodynamic Design Optimization of a Kind of Reentry Capsule Based on CFD and Multi-objective Genetic Algorithm

This paper presents a new kind of aerodynamic shape for reentry capsule, called spherical cap cubic curve segment(SCCS) shape, which is modeled by replacing the reversing cone segment of the traditional spherical cap segment-reversing cone(SCSC) shape with a more various cubic curve segment, however the spherical cap section is retained. In the assumed allowable axial range of centroid under a designed Mach number, a multi-point/objective design optimization mathematical programming model was established against aerodynamic static longitudinal stability characteristics, hypersonic lift-to-drag ratio characteristics under trim angle of attack and off-set location placement of gravity center for the above reentry capsule. Then the aerodynamic design optimization problem of the proposed reentry capsule was investigated through multi-objective genetic algorithm(MOGA) combined numeric parallel field simulation methods, and finally the optimal Pareto front was given. Comparing with the results of the SCSC shape in the literature[1], it shows that the optimal Pareto front of the current cubic curve shape has a wider distribution range relative to the counterparts of the segment-reversing cone shape, however both are relatively close in the overlapping area.

Recovery of Low-Rank Matrices Under Affine Constraints via a Smoothed Rank Function

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this optimization problem. We propose an algorithm based on a smooth approximation of the rank function, which practically improves recovery limits on the rank of the solution. This approximation leads to a non-convex program; thus, to avoid getting trapped in local solutions, we use the following scheme. Initially, a rough approximation of the rank function subject to the affine constraints is optimized. As the algorithm proceeds, finer approximations of the rank are optimized and the solver is initialized with the solution of the previous approximation until reaching the desired accuracy. On the theoretical side, benefiting from the spherical section property, we will show that the sequence of the solutions of the approximating function converges to the minimum rank solution. On the experimental side, it will be shown that the proposed algorithm, termed SRF standing for Smoothed Rank Function, can recover matrices which are unique solutions of the rank minimization problem and yet not recoverable by nuclear norm minimization. Furthermore, it will be demonstrated that, in completing partially observed matrices, the accuracy of SRF is considerably and consistently better than some famous algorithms when the number of revealed entries is close to the minimum number of parameters that uniquely represent a low-rank matrix.

Scattering of high-intensity focused ultrasound by the ribs: Constrained optimization with a complex surface impedance boundary condition

One of the challenges of trans-rib high-intensity focused ultrasound (HIFU) treatment is the need to transmit sufficient energy through the ribcage to ablate tissue whilst minimizing the formation of side lobes, and sparing healthy tissue. Ribs strongly absorb and reflect ultrasound. This may result in overheating of bone and overlying tissue during treatment, leading to skin burns. Successful treatment of a patient with tumors of the liver or the pancreas therefore requires a thorough understanding of the way acoustic and thermal energy is deposited. A boundary element approach was developed to predict the field of a multi-element HIFU array scattered by human ribs in 3D. This forward model has been reformulated as a constrained least squares optimization problem where the velocity of each individual element on the array is an optimization variable. A locally reacting complex surface impedance condition at the surface of the ribs has been implemented. The methodology has been tested at an excitation frequency of 1 MHz on a spherical section multi-element array and a total of six array-rib configurations have been investigated. The results were compared against other focusing and rib-sparing approaches, demonstrating the efficacy and flexibility of the constrained optimization approach.

Augmented $\ell_1$ and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm

This paper studies the long-existing idea of adding a nice smooth function to "smooth" a non-differentiable objective function in the context of sparse optimization, in particular, the minimization of $||x||_1+1/(2\alpha)||x||_2^2$, where $x$ is a vector, as well as the minimization of $||X||_*+1/(2\alpha)||X||_F^2$, where $X$ is a matrix and $||X||_*$ and $||X||_F$ are the nuclear and Frobenius norms of $X$, respectively. We show that they can efficiently recover sparse vectors and low-rank matrices. In particular, they enjoy exact and stable recovery guarantees similar to those known for minimizing $||x||_1$ and $||X||_*$ under the conditions on the sensing operator such as its null-space property, restricted isometry property, spherical section property, or RIPless property. To recover a (nearly) sparse vector $x^0$, minimizing $||x||_1+1/(2\alpha)||x||_2^2$ returns (nearly) the same solution as minimizing $||x||_1$ almost whenever $\alpha\ge 10||x^0||_\infty$. The same relation also holds between minimizing $||X||_*+1/(2\alpha)||X||_F^2$ and minimizing $||X||_*$ for recovering a (nearly) low-rank matrix $X^0$, if $\alpha\ge 10||X^0||_2$. Furthermore, we show that the linearized Bregman algorithm for minimizing $||x||_1+1/(2\alpha)||x||_2^2$ subject to $Ax=b$ enjoys global linear convergence as long as a nonzero solution exists, and we give an explicit rate of convergence. The convergence property does not require a solution solution or any properties on $A$. To our knowledge, this is the best known global convergence result for first-order sparse optimization algorithms.

Tractable Bound for Spherical Section Property in the Presence of Side-Information

This letter provides a tractable bound for a perfect recovery condition in compressed sensing matrices using the spherical section property in the presence of side information. In particular, when the signal of interest is provided with side-information, we derive an equivalent semidefinite relaxation bound by introducing the related prior knowledge as an additional constraint to the semidefinite programming (SDP) problem. We recast a linear program (LP) cone to this problem and found the dual-SDP to be less complex to handle. Numerical evaluations on the proposed dual-SDP, validates the existence of sparse solutions with high- cardinalities.

Unstable resonator with reduced output coupling

The properties of a laser beam coupled out of a standard unstable laser resonator are heavily dependent on the chosen resonator magnification. A higher magnification results in a higher output coupling and a better beam quality. But in some configurations, an unstable resonator with a low output coupling in combination with a good beam quality is desirable. In order to reduce the output coupling for a particular resonator, magnification fractions of the outcoupled radiation are reflected back into the cavity. In the confocal case, the output mirror consists of a spherical inner section with a high reflectivity and a flat outer section with a partial reflectivity coating. With the application of the unstable resonator with reduced output coupling (URROC), magnification and output coupling can be adjusted independently from each other and it is possible to get a good beam quality and a high power extraction for lasers with a large low gain medium. The feasibility of this resonator design is examined numerically and experimentally with the help of a chemical oxygen iodine laser.

Limit analysis of local failure in shallow spherical concrete caps subjected to uniform radial pressure

Many thin-walled shallow concrete shells (or caps or domes) have experienced structural collapse during or subsequent to their erection. Very few experimental investigations have been reported of shallow concrete spherical caps that allow for the effects of geometric and material non-linearities and imperfections to be identified, despite this information being essential for the validation of sophisticated numerical treatments. Classical thin-shell theories for axisymmetric domes predict a global buckling mode, but observations from experimental tests show that failure in concrete spherical caps is usually localised within a relatively small region and at a load significantly less than the classical buckling load. An investigation of the non-linear behaviour of thin-walled concrete spherical caps is currently being carried out both experimentally and theoretically at The University of New South Wales. As part of this study, an approach based on limit analysis has been developed on the basis of a local failure model and it is used for analysis of concrete/mortar spherical caps described in the published literature. The ultimate bending strength of a unit width of a spherical shell section is derived from a typical non-linear concrete stress-strain relationship and the in-plane thrust from shell membrane theory. The analytical results based on a local failure yield line model are compared with the available experimental results in the literature as well as with classical theoretical buckling results.