Dimensional Sphere Research Articles

Rockfall analysis considering coefficients of restitution based on three-dimensional sphere discontinuous deformation analysis

Rockfall analysis considering coefficients of restitution based on three-dimensional sphere discontinuous deformation analysis

On Knots with Cyclic Symmetries

This review paper investigates the relationship between symmetries of knots and links in the three-dimensional sphere, with a focus on cyclic symmetries, and their associated polynomial invariants. It examines the behavior of these polynomials in the case where the knot is set-wise fixed by the action of finite cyclic group on the 3-sphere. The study highlights how these invariants can obstruct the existence of such symmetries, providing valuable insights into the topological properties of these knots. The paper reviews established results on polynomial criteria for periodicity and their extensions to freely periodic links. It also explores generalizations to study the symmetries of virtual knots and spatial graphs.

Bistable Perception Discriminates Between Depressive Patients, Controls, Schizophrenia Patients, and Their Siblings.

Individuals with schizophrenia have less priors than controls, meaning they rely less upon their prior experiences to interpret the current stimuli. These differences in priors are expected to show as higher alternation rates in bistable perception tasks like the Structure-from-Motion (SfM) paradigm. In this paradigm, continuously moving dots in two dimensions are perceived subjectively as traveling along a three-dimensional sphere, which results in a direction of motion (left or right) that shifts approximately every few seconds. Here, we tested healthy controls, patients with schizophrenia, siblings of patients with schizophrenia, and patients with depression with both the intermittent and continuous variants of the SfM paradigm. In the intermittent variant of the SfM paradigm, depressive patients exhibited the lowest alternation rate, followed by unaffected controls. In contrast, patients with schizophrenia and their unaffected siblings displayed significantly higher alternation rates. In the continuous variant of the SfM paradigm, patients with schizophrenia showed the lowest mean percept durations, while there were no differences between the other three groups. The intermittent SfM paradigm is a candidate endophenotype for schizophrenia. The aberrant processing in the patients may stem from alterations in adaptation and/or cross-inhibition mechanisms leading to changes in priors, as suggested by current models in the field. The intermittent SfM paradigm is, hence, a trait marker that offers the great opportunity to investigate perceptual abnormalities across the psychiatry spectrum, ranging from depression to psychosis.

Unstable Regions of Anisotropic Relativistic Spheres in Higher-Dimensions

Abstract In this work, we consider the collapse of a $\mathbb{D}$-dimensional sphere in the framework of a higher dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the $\mathbb{D}$-dimensional modified term.
This work investigates the criteria for dynamical instability of
anisotropic relativistic sphere systems with
$\mathbb{D}$-dimensional modified gravity. The certain conditions are
applied that lead to the collapse equation and their effects on
adiabatic index $\Gamma$ in both Newtonian (N) and Post-Newtonian
(PN) regimes by using a perturbation scheme. The study explores that
the $\Gamma$ plays a crucial role in determining the degree of
dynamical instability. This index characterizes the fluid's
stiffness and has a significant i7mpact on defining the ranges of
instability. This systematic investigation demonstrates the
influence of various material properties such as anisotropic
pressure, kinematic quantities, mass function, $\mathbb{D}$-dimensional modified gravity parameters, and the radial profile of energy density on the
instability of considered structures during their evolution. This
work also displays the dynamical behavior of spherically symmetric
fluid configuration via graphical approaches.

Numerical evaluation of orientation averages and its application to molecular physics.

In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modeling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely related to integration over two- or three-dimensional unit spheres, a common problem discussed in numerical analysis. The computational cost of the integration depends significantly on the quadrature method, making the selection of an appropriate method crucial for the feasibility of simulations. After reviewing several classes of spherical quadrature methods in terms of their efficiency and error distribution, we derive guidelines for choosing the best quadrature method for orientation averages and illustrate these with three examples from chiral molecule physics. While Gauss quadratures allow for achieving numerically exact integration for a wide range of applications, other methods offer advantages in specific circumstances. Our guidelines can also be applied to higher-dimensional spherical domains and other geometries. We also present a Python package providing a flexible interface to a variety of quadrature methods.

Adjoint-based shape optimization for compressible flow based on volume penalization method

AbstractReducing the resistance of compressible flow around a blunt body is of great interest in engineering applications, while an efficient shape optimization method for compressible flows remains far from well established, especially for high Mach numbers. To this end, a volume penalization method for simulating compressible flows past a no-slip and isothermal solid is established by introducing an artificial body force and a heat sink into the governing equations. The level-set functions are introduced as design variables, and the cost functional is defined as the total drag acting on the solid. Then, a continuous adjoint-based shape optimization algorithm for drag reduction is developed by deriving the adjoint equations, the adjoint boundary conditions, and the shape update formula. Both the forward and adjoint simulations are verified by existing studies. The results show that the relative deviations of the drag coefficients obtained in the present study from those reported in the reference studies are around 5% at most, and also a comparable drag reduction rate and also optimal shapes can be reproduced by the present optimization scheme for benchmark problems at relatively low Mach numbers considered in previous studies. Finally, the present method is applied to shape optimization of an initially two-dimensional cylinder and also a three-dimensional sphere in the transonic regime of Ma∞ = 1.2. The drag reduction of over 20% is achieved for both two-dimensional and three-dimensional cases.

A nanotheranostics with hypoxia-switchable fluorescence and photothermal effect for hypoxia imaging-guided immunosuppressive tumor microenvironment modulation

Modulating the immunosuppressive tumor immune microenvironment (TIME) is considered a promising strategy for cancer treatment. However, effectively modulating the immunosuppressive TIME within hypoxic zones remains a significant challenge. In this work, we developed a hypoxia-responsive amphiphilic drug carrier using boron-dipyrromethene (BODIPY) dye-modified chitosan (CsB), and then fabricated a hypoxia-targeted nanotheranostic system, named CsBPNs, through self-assembly of CsB and pexidartinib (5-((5-Chloro-1H-pyrrolo[2,3-b]pyridin-3-yl)methyl)-N-((6-(trifluoromethyl)pyridin-3-yl)methyl), PLX3397), an immunotherapeutic drug targeting tumor-associated macrophages (TAMs), for synergistic photothermal/immunotherapy and hypoxia imaging. CsBPNs demonstrated uniform size, good stability, and hypoxia-switchable fluorescence and photothermal effects, enabling deep penetration and hypoxia imaging capacities in three-dimensional tumor cell spheres and tumor tissues. In vitro and in vivo experiments showed that CsBPNs under laser irradiation promoted TAMs repolarization, reversed the immunosuppressive TIME, and enhanced the therapeutic outcome of PLX3397 in solid tumors by facilitating deep delivery into hypoxic regions and synergistic photothermal therapy. This work provides a new strategy for detecting and modulating the immunosuppressive TIME in hypoxic zones, potentially enabling more precise and effective photo-immunotherapy in the future.

픽의 정리를 활용한 Gauss Circle Problem 해결 및 3차원 도형에서의 확장

In this study, a new solution to the Gauss Circle Problem was presented using Pick’s Theorem. The simplest polygon containing both grid points inside the circle and on the circumference was drawn, and the result was derived by applying Pick’s Theorem to the polygon instead of the circle. He analyzed the existing solution method and inductively proved using Python that the conclusion obtained through the new solution method was within the error range known through the existing solution method, revealing that the new solution method was valid. A two-dimensional circle was expanded into a three-dimensional sphere, and a new solution method was applied to three-dimensional space using Reeve’s Theorem, which extends Pick’s Theorem to three dimensions.

Construction of ultra-thin NiMo3S4 nanosheet sphere electrode for high-performance hybrid supercapacitor

The construction of electrode materials with rational morphology and structure based on bimetallic sulfides is crucial to improve the performance of supercapacitors. Ultra-thin three-dimensional nickel molybdenum sulfide nanosheet spheres (NiMo3S4 NSSs) are grown on nickel foam (NF) using a one-step hydrothermal synthesis. NiMo3S4 NSSs have a diameter of ∼ 5 μm and nanosheet thickness of 200 nm. The effects of increasing the hydrothermal synthesis time and molar concentration ratios of Ni2+ to MoO42- on the morphologies of the NiMo3S4 are investigated. Due to the synergistic effect of NiMo3S4 NSSs and bimetallic ions which can provide a larger solution contact areas and improve the redox activity, the electrode exhibits good electrochemical properties. The specific capacity of NiMo3S4 NSSs/NF electrode can reach 1002.4 C/g (1 A/g). After being assembled into a hybrid supercapacitor (HSC) with activated carbon (AC), the energy density can reach 72.1 Wh/kg at the power density of 749.9 W/kg. In addition, the HSC shows an excellent stability of 89 % after 10, 000 charge-discharge cycles (10 A/g).

Magnetically actuated cisplatin-loaded nanoparticle collectives enhance drug penetration for potentiated ovarian cancer chemotherapy

Chemotherapy is the main clinical treatment for ovarian cancer, but still faces challenges of low drug targeting efficiency and insufficient drug permeability. Drug-loaded nanoparticle collectives, which are actuated by magnetic field, could be targeted to a designated location and achieve targeted drug delivery. In this work, we report a strategy that utilizes magnetic mesoporous silica nanoparticles loaded with cis-diaminodichloroplatinum (Fe3O4@SiO2-CDDP) for targeted delivery of chemotherapeutic drugs and enhances penetration into deep tumors. The Fe3O4@SiO2-CDDP collectives actively moved to the target tumor site, and this movement was regulated by a magnetic actuation system. Under the action of a torque-force hybrid magnetic field (TFMF), Fe3O4@SiO2-CDDP could further penetrate into the interior of tumors and achieve pH-responsive drug release in the tumor environment. The feasibility of this strategy was verified in three-dimensional cell spheres in vitro and in a tumor-bearing mouse model in vivo. This magnetically actuated nanoparticle collectives enhanced drug penetration strategy provides a new paradigm for targeted drug delivery and potentiated tumor therapy.

Why the big bang never happened

<p>If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.</p>

Smoothed-Interface SPH Model for Multiphase Fluid-Structure Interaction

Numerical simulation of multiphase flows with large density ratios presents considerable challenges. Traditional Smoothed Particle Hydrodynamics (SPH) methods, while efficient in tracking multi-phase interfaces, often suffer from non-physical gaps near interfaces, compromising accuracy. In this paper, we develop an advanced multiphase model with enhanced interface continuity and stability, offering a reliable approach to both multiphase flows and fluid-structure interaction. The model employs equivalent continuity equations across different phases and refines the treatment of pressure and its gradients at interfaces through a smoothing technique, which effectively eliminates the non-physical gaps prevalent in the conventional SPH multiphase models. Moreover, an efficient and accurate method for calculating interface normal vectors and identifying interfaces is proposed. Based on the method, we introduce a series of techniques, including an improved interface force model, a particle displacement strategy, and a new particle penetration detection scheme, all of which significantly improve the interface continuity and the overall simulation accuracy of multiphase flows. Finally, the proposed multiphase SPH model is validated through several numerical examples, including two-dimensional static water, standing waves, dam break, oscillating multi-fluid, and wedge entry, as well as three-dimensional sphere entry. Comparative results with the traditional model indicate that the multiphase SPH model in this work ensures interface continuity and stability in long-period simulations, even under intense flow conditions. These results suggest that the smoothed-interface SPH multiphase model can eliminate non-physical gaps at interfaces, greatly enhancing interface continuity and stability, and highlighting its potential for accurate multiphase flow simulations.

Enlargement of the localized resonant band gap by using multi-layer structures

Multi-layer structures possess highly geometrically tunable optical resonances to change the surface plasmon frequencies in the wide range. A simple analytic model is presented to describe the plasmon hybridization of multi-layer metamaterial structures with multipole resonances. We theoretically demonstrate that the number of plasmon modes increases with the number of layers, which results in the enlargement of the localized resonant optical band gap. To explore the interaction between incident fields and multi-layer structures, we derive the closed-form perturbed field in terms of a generalized polarization matrix, whose dimension matches the number of layers. This enables us to obtain the eigenmode frequencies and their corresponding eigenfunctions for three-dimensional multi-layer concentric spheres and two-dimensional multi-layer concentric cylinders in a vacuum setting. These findings offer nanoscientists a general design principle that can be applied to facilitate the proper selection of the metamaterial parameters, thereby inducing the desired resonance and enabling customized applications to be realized.

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale nonequilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman–Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS with rotation and vibration non-equilibrium is developed based on a multiple temperature relaxation model. The real gas effect in different flow regimes has been properly captured. To capture aerodynamic heating accurately, the heat flux modifications from the rotation and vibration modes are also included in the current scheme. Unstructured discrete particle velocity space is adopted to further improve the computational performance of the AUGKS. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for nonequilibrium flow simulations, especially for the flows at low and medium speed.

Semiclassical saddles of three-dimensional gravity via holography

We find out the complex geometries corresponding to the semiclassical saddles of three-dimensional quantum gravity by making use of the known results of dual conformal field theory (CFT), which is effectively given by Liouville field theory. We examine both the cases with positive and negative cosmological constants. We determine the set of semiclassical saddles to choose from the homotopy argument in the Chern-Simons formulation combined with CFT results and provide strong supports from the minisuperspace approach to the quantum gravity. For the case of positive cosmological constant, partial results were already obtained in our previous works, and they are consistent with the current ones. For the case of negative cosmological constant, we identify the geometry corresponding a semiclassical saddle with three-dimensional Euclidean anti–de Sitter space dressed with imaginary radius three-dimensional spheres. The geometry is generically unphysical, but the fact itself should not lead to any problems as derived from consistent dual CFT. We thus find an intriguing example, where the gravity path integral is performed over unphysical geometries. Published by the American Physical Society 2024

Porous hollow sphere structure PrFeO3 as an efficient sensing material for n-butanol detection

N-butanol is a harmful volatile gas, so creating an appropriate n-butanol sensor is critical for preserving human health and the manufacturing environment. In contrast to single metal oxide semiconductors, multicomponent metal oxides, especially perovskite ternary metal oxides with the ABO3 structure, exhibit significant potential for development owing to their precise structures and diverse physicochemical properties. In this paper, three-dimensional porous hollow spheres PrFeO3 were synthesized by combining air annealing and hydrothermal techniques. The crystal structure, surface composition, chemical state, and morphology of PrFeO3 materials were evaluated using several kinds of characterization approaches. The gas sensitivity of PrFeO3 materials was also thoroughly explored. The results show that at the optimal working temperature of 280 ℃, the PrFeO3 material excels in n-butanol gas sensing, with a response of 85 for 100 ppm n-butanol. Additionally, the sensor demonstrates high selectivity for n-butanol gases, low concentration detection capability, outstanding repeatability, rapid reaction recovery time (18 s/13 s), long-term stability, and exceptional reproducibility. The unique morphology and high oxygen vacancy content of PrFeO3 provide numerous active sites on its surface, promoting the adsorption and desorption of n-butanol gas molecules and enhancing its gas-sensitive properties.

Omni-directional orientation analysis of a triplet-stator spherical piezoelectric motor system

ABSTRACT Spherical piezoelectric motors (SPMs) represent a promising actuator technology applicable to the development of motion control systems with multiple degrees of freedom. However, few SPMs have made it successfully to market, as an effective and systematic rotor orientation analysis and manipulation technique has yet to be developed. This study thus developed a novel triplet-stator SPM design that integrates electrode configuration to excite lateral vibrations and offers two fundamental rotor orientations for each set of piezoelectric plates by changing the contact position between the rotor and stator. To accomplish omnidirectional orientations for the proposed SPM system, we present a systematic orientation analysis based on spherical coordinates. We further apply the concept of vector composition to derive new composite orientations by adjusting the magnitude ratio of the provided torques between three stators. An orientation angle representation accounting for the rotor dynamics is used to validate the correctness of the synthesized orientation vectors both in simulation and experiments. The orientation analysis results in a three-dimensional sphere containing eight vector spaces corresponding to eight stator actuation modes, in which an arbitrary rotor orientation reference command can be generated under the designed actuation modes. Experimental results were well correlated with simulations, thereby verifying the effectiveness of the proposed SPM system design and orientation analysis.

Regularity of a double null coordinate system for Kerr–Newman–de Sitter spacetimes

AbstractWe construct a double null coordinate system $$(u,v,\theta _\star ,\phi _\star )$$ ( u , v , θ ⋆ , ϕ ⋆ ) for Kerr–Newman–de Sitter black hole interior spacetimes and prove that the two dimensional spheres given by the intersection of the hypersurfaces $$u=\hbox {constant}$$ u = constant and $$v=\hbox {constant}$$ v = constant are $$C^\infty$$ C ∞ in Boyer–Lindquist coordinates (including at the “poles"). The null coordinates allow one to immediately extend some results previously proven for Kerr. As an example, we illustrate how Sbierski’s result in (On the initial value problem in general relativity and wave propagation in black-hole spacetimes. Doctoral thesis, 2014. https://doi.org/10.17863/CAM.16140), for the wave equation on the black hole interior, for Reissner–Nordström and Kerr spacetimes, applies to Kerr–Newman–de Sitter spacetimes.

Three-dimensional transient multilayer heat conduction sphere comprising metallic particles

A numerical approach employing finite element methodology is utilized to analyze the thermal behavior of a three-dimensional multilayer sphere composed of copper, single-wall, and multi-wall carbon nanotubes. The study investigates the external heat flux, temperatures within the three spherical layers, and their associated contours. Notably, this research diverges from prior studies by opting for copper, single-wall, and multiwall carbon nanotubes instead of generic metallic layers. Graphs are generated to illustrate the relationships between various effects and profiles. Analysis of temperature contours and distributions under non-uniform heat flux reveals that temperatures are more concentrated towards the center when the initial temperature is non-zero compared to scenarios where the inner surface starts at zero temperature. Temperature contours at t = 2, 5, 7, 9, 11, 13, 15, 27, 35, and 45 s with non-zero initial temperature are calculated. For non-zero initial temperature contours are drawn for t = 2, 45 s temperature contours are drawn. Temperature in radial azimuthal and tangential directions for t = 1, 1.5, 2, 2.5, 3 s and steady state are drawn. The initial temperature of the ith surface is kept at fi(r,θ,ϕ), where ro≤r≤r3,0≤θ≤π,0≤ϕ≤2π. It has been concluded that for zero initial temperatures after 45 s, the temperature is at 0.005K and Temperature contours for non-zero inner layer temperature t = 5 s shows 10.7K.

Superlong cycle-life sodium-ion batteries supported by electrode/active material interaction and heteroatom doping: Mechanism and application

To achieve both the capacity and stability of metal sulfides simultaneously remains a significant challenge. In this study, we have synthesized the manganese-doped copper sulfide three-dimensional (3D) hollow flower-like sphere (M/CuS-NSC), encapsulated in a nitrogen and sulfur co-doped carbon. The hollow lamellae structure allows the rational self-aggregation process of numerous active surface area enlarged nanosheets, thereby enhancing electrochemical activity. The subsurface framework characterized by CSC bonds enhances the pseudo-capacitive properties. Furthermore, the transformation of sulfur and the isomerization of carbon contribute to the enhancement of sodium ion storage. The incorporation of Mn into CuS lattice increases the interplanar distance, providing additional space for the accommodation of sodium ions. Mn doping facilitates the localization of electrons near the Fermi level, thereby improving conductivity. Additionally, Cu foils coated with M/CuS-NSC-2 engage with the electrolyte and sulfur, initiating the reaction sequence through the formation of Cu9S8. Consequently, M/CuS-NSC-2 exhibits highly reversible capacities of 676.24 mAh g−1 after 100 cycles at 0.1 A g−1 and 511.52 mAh g−1 after 10000 cycles at 10 A g−1, with an average attenuation ratio of only 0.009 %. In this study, we propose an effective strategy that combines structural design with heteroatom doping, providing a novel approach to enhance the electrochemical performance of monometallic sulfide.