Dimensional Sphere Research Articles

Analytic weakly mixing diffeomorphisms on odd dimensional spheres

We present an approximation by conjugation scheme to obtain real-analytic diffeomorphisms of odd dimensional spheres that are weakly mixing with respect to the volume.

An Index Theorem for Quarter-Plane Toeplitz Operators via Extended Symbols and Gapped Invariants Related to Corner States

In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg–Kreĭn theory for matrix factorizations, we extend the symbols defined originally on a two-dimensional torus to some three-dimensional sphere and derive a formula to express their Fredholm indices through extended symbols. Variants for families of (self-adjoint) Fredholm quarter-plane Toeplitz operators and those preserving real structures are also included. For some bulk-edge gapped single-particle Hamiltonians of finite hopping range on a discrete lattice with a codimension-two right angle corner, topological invariants related to corner states are provided through extensions of bulk Hamiltonians.

An Improved Chimp-Inspired Optimization Algorithm for Large-Scale Spherical Vehicle Routing Problem with Time Windows.

The vehicle routing problem with time windows (VRPTW) is a classical optimization problem. There have been many related studies in recent years. At present, many studies have generally analyzed this problem on the two-dimensional plane, and few studies have explored it on spherical surfaces. In order to carry out research related to the distribution of goods by unmanned vehicles and unmanned aerial vehicles, this study carries out research based on the situation of a three-dimensional sphere and proposes a three-dimensional spherical VRPTW model. All of the customer nodes in this problem were mapped to the three-dimensional sphere. The chimp optimization algorithm is an excellent intelligent optimization algorithm proposed recently, which has been successfully applied to solve various practical problems and has achieved good results. The chimp optimization algorithm (ChOA) is characterized by its excellent ability to balance exploration and exploitation in the optimization process so that the algorithm can search the solution space adaptively, which is closely related to its outstanding adaptive factors. However, the performance of the chimp optimization algorithm in solving discrete optimization problems still needs to be improved. Firstly, the convergence speed of the algorithm is fast at first, but it becomes slower and slower as the number of iterations increases. Therefore, this paper introduces the multiple-population strategy, genetic operators, and local search methods into the algorithm to improve its overall exploration ability and convergence speed so that the algorithm can quickly find solutions with higher accuracy. Secondly, the algorithm is not suitable for discrete problems. In conclusion, this paper proposes an improved chimp optimization algorithm (MG-ChOA) and applies it to solve the spherical VRPTW model. Finally, this paper analyzes the performance of this algorithm in a multi-dimensional way by comparing it with many excellent algorithms available at present. The experimental result shows that the proposed algorithm is effective and superior in solving the discrete problem of spherical VRPTW, and its performance is superior to that of other algorithms.

Lung Organoids for Hazard Assessment of Nanomaterials

Lung epithelial organoids for the hazard assessment of inhaled nanomaterials offer a promising improvement to in vitro culture systems used so far. Organoids grow in three-dimensional (3D) spheres and can be derived from either induced pluripotent stem cells (iPSC) or primary lung tissue stem cells from either human or mouse. In this perspective we will highlight advantages and disadvantages of traditional culture systems frequently used for testing nanomaterials and compare them to lung epithelial organoids. We also discuss the differences between tissue and iPSC-derived organoids and give an outlook in which direction the whole field could possibly go with these versatile tools.

A threshold search-based population algorithm for the sphere packing problem

Cutting and packing problems occur in various real-world applications, like manufacturing, production process, automated planning, logistics, and material industries. Most of these problems are NP-hard combinatorial optimization problems and their resolution is computationally challenging. In this paper, we study a problem belonging to this family, namely the three-dimensional sphere packing problem. We propose to solve it with a population-based method, where both a reference set of solutions cooperates with a threshold operator for guiding the search process. The reference set tries to maintain the diversity of the solutions reached throughout an iterative procedure while the threshold operator tries to highlight the quality of the solutions throughout the search process. The performance of the proposed method is evaluated on benchmark instances of the literature, where its provided results are compared to those reached by some available methods in the literature. The designed method seems competitive, where it is able to achieve new bounds for several tested instances.

Texture-Aware Spherical Rotation for High Efficiency Omnidirectional Intra Video Coding

To adapt to the existing video coding standards, omnidirectional videos are usually projected from Three-Dimensional (3D) sphere to Two-Dimensional (2D) plane. However, this projection will cause geometrical stretching distortion and boundary discontinuity, which may degrade coding efficiency. In this paper, we present a Spherical Rotation based Omnidirectional Video Coding (SROVC) method, which exploits the textural properties of omnidirectional videos with spherical rotation. Firstly, SROVC framework is presented and Full-traversal Spherical Rotation (FSR) is developed to derive the optimal rotation angle with frame-level Rate Distortion Optimization (RDO). Secondly, to achieve comparable coding gains and lower computational complexity when compared with FSR, a Texture-aware Spherical Rotation (TSR) method is proposed to predict the rotation angle. Finally, to further reduce complexity and maintain coding efficiency, a Group-oriented TSR (G-TSR) approach is presented, in which the group length is statistically determined. Extensive experiments demonstrate that the proposed TSR and G-TSR schemes can achieve bit rate reductions up to 4.38%, 0.94% and 0.89% on average for CubeMap Projection (CMP) based high efficiency omnidirectional video coding. Additionally, the TSR scheme achieves bit rate saving from 0.91% to 1.19% on average under three more CMP-based projection formats, and 1.89% for joint rotation of X, Y, and Z axes.

Supercapacitor application of a three-dimensional carbon sphere–intercalated porous carbon fabricated using a hard template and a biomass material

A combination strategy involving the use of a hard template and a biomass material was employed to prepare carbon sphere–intercalated porous carbon with a hierarchical structure for application in a high-performance supercapacitor. The preparation of the microporous activated carbon first involved the carbonization and chemical activation of golden shower tree seeds and potassium ferrate. The activated carbon was then modulated through anchoring with hard-template-derived mesoporous carbon spheres (HMCSs). The obtained porous carbon had a high surface area (1446 m2 g−1), a high pore volume (1.29 cm3 g−1), a low proportion of micropores (Smicro/SBET = 8.4 %), and mesopores, indicating the successful development of carbon sphere–intercalated heterostructural architectures. It displayed a specific capacitance (154 F g−1 at a scan rate of 5 mV s−1) in 6 M KOH aqueous electrolyte. Considering the pore structure, this study employed the LiPF6 electrolyte, which has a larger ionic size, in assembling a supercapacitor. The device exhibited excellent capacitive properties, with a peak energy density of 19.16 mWh cm−3 and a peak power density of 3.25 W cm−3.

Superposition of Wave Functions in the G-Qubit Theory

Quantum computing rests upon two theoretical pillars: superposition and entanglement. But some physicists say that this is a very shaky foundation and quantum computing success will have to be based on a different theoretical foundation. The g-qubit theory supports that point of view. Current article is the first one of two and about the superposition principle. Quantum superposition principle states that any two quantum wave functions can be superposed, and the result be another valid wave function. It specifically refers to linearity of the Schrodinger equation. In the g-qubit theory quantum wave functions are identified by points on the surface of three-dimensional sphere . That gives different, more physically feasible, not mysterious, explanation of what the superposition is.

Hierarchical refinement in isogeometric analysis for flexible multibody impact simulations

Detailed impact simulations in flexible multibody systems can be simulated based on reduced isogeometric analysis (IGA) models. However, a precise simulation of an impact requires a high element resolution in the contact area. Usually in IGA, global refinement methods are used, which are easy to implement. However, in the literature, also the use of hierarchical local refinement is proposed. The local refinement generates fewer countable degrees of freedom compared to an equivalent global refinement. Numerous application areas can be found in the literature, such as contact simulations, where the computational effort is reduced by local refinement. In this work, we introduce the inclusion of hierarchically refined IGA models within the floating frame of reference formulation. Thereby, the hierarchically refined IGA model is reduced and applied in impact simulations. In two application examples, we simulate the impact of two- and three-dimensional spheres and compare with an analytical solution. The focus here is on the comparison of calculation times and accuracy of globally and locally refined reference models. The third application example consists of two flexible double pendulums and is devoted to systems in which the bodies undergo both arbitrary rigid body motions and small elastic deformations.

Polydopamine nanomotors loaded indocyanine green and ferric ion for photothermal and photodynamic synergistic therapy of tumor

The limited penetration depth of nanodrugs in the tumor and the severe hypoxia inside the tumor significantly reduce the efficacy of photothermal-photodynamic synergistic therapy (PTT-PDT). Here, we synthesized a methoxypolyethylene glycol amine (mPEG-NH2)-modified walnut-shaped polydopamine nanomotor (PDA-PEG) driven by near-infrared light (NIR). At the same time, it also loaded the photosensitizer indocyanine green (ICG) via electrostatic/hydrophobicinteractions and chelated with ferric ion (Fe3+). Under the irradiation of NIR, the asymmetry of PDA-PEG morphology led to the asymmetry of local photothermal effects and the formation of thermal gradient, which can make the nanomotor move autonomously. This ability of autonomous movement was proved to be used to improve the permeability of the nanomotor in three-dimensional (3D) tumor sphere. Fe3+ can catalyze endogenous hydrogen peroxide to produce oxygen, so as to overcome the hypoxia of tumor microenvironment and thereby generate more singlet oxygen to kill tumor cells. Animal experiments in vivo confirmed that the nanomotors had a good PTT-PDT synergistic treatment effect. The introduction of nanomotor technology has brought new ideas for cancer optical therapy.

Hierarchical Nitrogen-Doped Graphitic Carbon Spheres Anchored with Amorphous Cobalt Nanoparticles as High-Performance and Ultrastable Anode for Potassium-Ion Batteries

As one of the most promising electrochemical energy-storage devices after lithium-ion batteries, potassium-ion batteries (KIBs) have been restricted by the limited capacity of carbon-based anodes. Herein, we design and prepare three-dimensional nitrogen-doped graphitic carbon spheres anchored with cobalt nanoparticles (CoNC) via self-sacrifice template method. The CoNC spheres exhibit a uniform spherical morphology with an inner hierarchical structure. The final calcination temperature is changed to obtain CoNC-700, CoNC-800, and CoNC-900, in which CoNC-700 is verified to combine amorphous cobalt nanoparticles with graphitic carbon spheres successfully and presents excellent rate capability and good potassium-storage performance. Nitrogen-doping and amorphous cobalt nanoparticle-loading can effectively introduce rich defects to the CoNC electrode, enhance electrical conductivity, and accelerate potassium-storage kinetics, which leadto a reversible specific capacity of 382 mA h g–1 at a current density of 0.5 A g–1 and 330 mA h g–1 at a current density of 1 A g–1 after 1000 cycles, suggesting the potential of the high-capacity, ultrastable anode for potassium-ion batteries.

Estimates for Distributions of Suprema of Spherical Random Fields

Bounds for distributions of suprema of $\varphi$-sub-Gaussian random fields defined over the $N$-dimensional unit sphere are stated. Applications of the results to the spherical fractional Brownian motion, isotropic Gaussian fields and some other models are presented.

Spheres and Tori as Elliptic Linear Weingarten Surfaces

The linear Weingarten condition with ellipticity for the mean curvature and the extrinsic Gaussian curvature on a surface in the three-sphere can define a Riemannian metric which is called the elliptic linear Weingarten metric. We established some local characterizations of the round spheres and the tori immersed in the 3-dimensional unit sphere, along with the Laplace operator, the spherical Gauss map and the Gauss map associated with the elliptic linear Weingarten metric.

The Application of Fast Multipole Boundary Element Method to the Calculation of Slamming Load of Three-Dimensional Elastic Sphere

An efficient fluid-structure interaction (FSI) method is established to quickly and accurately calculate the fluid load of three-dimensional (3D) elastic structure in the process of water slamming. In this method, the boundary element method (BEM) and computational structural dynamics (CSD) are coupled by thin plate spline (TPS) interpolation method and flow field reconstruction. In order to improve the calculation efficiency, the fast multipole algorithm is introduced into the BEM, the finite element mesh of the wetted part of the structure is directly used as the flow field boundary, and the structural dynamic response is analyzed by the direct integration method of state equation based on modal superposition. The numerical results are compared with the results of Nisewanger’s sphere water entry test and the existing literature, which proves the accuracy of the numerical calculation method established in this paper. The effects of time-domain iteration step size, mesh size, slamming velocity, fluid density and structural elastic effect on water slamming load are studied. The results show that the slamming velocity and fluid density have a great influence on the simulation results; the iteration step size has little influence on the accuracy of simulation calculation, and the mesh size has a certain influence on the accuracy of simulation calculation; elastic effect reduces the peak value of slamming load, considering elastic effect is necessary for accurate calculation of slamming load.

Formation of Three-Dimensional Spheres Enhances the Neurogenic Potential of Stem Cells from Apical Papilla.

Three-dimensional SCAP spheres were first generated in a 256-well agarose microtissue mold. The spheres and single cells were individually cultured on collagen I-coated μ-slides. Cell morphological changes, neural marker expression, and neurite outgrowth were evaluated by confocal microscope, ELISA, and RT-qPCR. Pronounced morphological changes were noticed in a time-dependent manner. The migrating cells' morphology changed from fibroblast-like cells to neuron-like cells. Compared to the 2D culture, neurite length, number, and the expression of multiple progenitors, immature and mature neural markers were significantly higher in the 3D spheres. BDNF and NGF-β may play a significant role in the neural differentiation of SCAP spheres. The formation of 3D spheres enhanced the neurogenic potential of SCAPs, suggesting the advantage of using the 3D spheres of SCAPs for treating neural diseases.

Radiation Treatment Timing and Dose Delivery: Effects on Bladder Cancer Cells in 3D in Vitro Culture

While radical cystectomy remains the primary treatment of choice for bladder cancer, increased evidence supports the use of bladder-preservation strategies based on adjuvant radiotherapy. This highlights the need for a better understanding of bladder cancer radiosensitivity to different types of treatment deliveries. The purpose of this study is to analyze the effect of treatment time, dose and fractionation on the number and sizes of grown three-dimensional (3D) bladder cancer spheres, and to assess the capacity of the linear-quadratic model in describing the response of cells cultured in 3D. 3D MatrigelTM-based cultures were employed to enrich for cancer stem cells (CSCs) from three human bladder cancer cell lines, RT4, T24 and UM-UC-3. Three single dose radiation treatments were performed at different time points after plating, and sphere number and sizes were assessed. Anti-CD44 immunofluorescence, clonogenic assay and anti-γH2AX staining were also performed to analyze the cell lines’ radiosensitivity. The radiosensitivity of spheres was dependent on the treatment timing after plating. Current linear quadratic dose fractionation models were shown to over-estimate radiosensitivity in 3D models. Our results showed the importance of treatment timing on the radio-response of bladder cancer spheres. We also demonstrated that bladder cancer spheres are more resistant to dose-fractionation than the estimation from the theoretical linear-quadratic model.

Dynamical mass generation for ferromagnetic skyrmions in two dimensions

Magnetic skyrmions are topological magnetization textures that are characterized by the homotopy group of two dimensional spheres. Despite years of intensive research on skyrmions, the fundamental problem of the inertia of a skyrmion in driven motion remains unresolved. By properly taking into account a direct coupling between skyrmion motion and the correspondingly excited magnons, we identify a dynamical mass for the skyrmion in motion. The direct coupling between skyrmion motion and magnons can be employed to engineer skyrmion dynamics with magnons through ingenious material and geometry design.

Variance Estimates in Linnik’s Problem

Abstract We evaluate the variance of the number of lattice points in a small randomly rotated spherical ball on a surface of 3-dimensional sphere centered at the origin. Previously, Bourgain, Rudnick, and Sarnak showed conditionally on the Generalized Lindelöf Hypothesis that the variance is bounded from above by $\sigma (\Omega ){N_n}^{1+\varepsilon }$, where $\sigma (\Omega )$ is the area of the ball $\Omega $ on the unit sphere and $N_n$ is the total number of solutions of Diophantine equation $x^2 + y^2 + z^2 = n$. Assuming the Grand Riemann Hypothesis and using the moments method of Soundararajan and Harper, we establish the upper bound of the form $c\sigma (\Omega ) N_n$, where $c$ is an absolute constant. This bound is of the conjectured order of magnitude.

Modified Thirring model beyond the excluded-volume approximation

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a modified version of the Thirring model for self-gravitating systems with attractive and repulsive long-range interactions in which particles are treated as hard spheres in dimension d = 1, 2, 3. Equilibrium states of the model are studied under completely open conditions, in the unconstrained ensemble, by means of both Monte Carlo simulations and analytical methods and are compared with the corresponding states at fixed number of particles, in the isothermal-isobaric ensemble. Our theoretical description is performed for an arbitrary local equation of state, which allows us to examine the system beyond the excluded-volume approximation. The simulations confirm the theoretical prediction of the possible occurrence of first-order phase transitions in the unconstrained ensemble. This work contributes to the understanding of long-range interacting systems exchanging heat, work and matter with the environment.

Convergence of the Free Energy for Spherical Spin Glasses

We prove that the free energy of any spherical mixed $p$-spin model converges as the dimension $N$ tends to infinity. While the convergence is a consequence of the Parisi formula, the proof we give is independent of the formula and uses the well-known Guerra-Toninelli interpolation method. The latter was invented for models with Ising spins to prove that the free energy is super-additive and therefore (normalized by $N$) converges. In the spherical case, however, the configuration space is not a product space and the interpolation cannot be applied directly. We first relate the free energy on the sphere of dimension $N+M$ to a free energy defined on the product of spheres in dimensions $N$ and $M$ to which we then apply the interpolation method. This yields an approximate super-additivity which is sufficient to prove the convergence.