Perfect Sphere Research Articles

Dynamical clustering interrupts motility-induced phase separation in chiral active Brownian particles.

One of the most intriguing phenomena in active matter has been the gas-liquid-like motility-induced phase separation (MIPS) observed in repulsive active particles. However, experimentally, no particle can be a perfect sphere, and the asymmetric shape, mass distribution, or catalysis coating can induce an active torque on the particle, which makes it a chiral active particle. Here, using computer simulations and dynamic mean-field theory, we demonstrate that the large enough torque of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional MIPS. Multiple clusters arise from the combination of the conventional MIPS cohesion, and the circulating current caused disintegration. The nonvanishing current in non-equilibrium steady states microscopically originates from the motility "relieved" by automatic rotation, which breaks the detailed balance at the continuum level. This suggests that no equilibrium-like phase separation theory can be constructed for chiral active colloids even with tiny active torque, in which no visible collective motion exists. This mechanism also sheds light on the understanding of dynamic clusters observed in a variety of active matter systems.

Higher-Dimensional Regular Reissner–Nordström Black Holes Associated with Linear Electrodynamics

Following the interpretation of matter source that the energy-momentum tensor of anisotropic fluid can be dealt with effectively as the energy-momentum tensor of perfect fluid plus linear (Maxwell) electromagnetic field, we obtain the regular higher-dimensional Reissner–Nordström (Tangherlini–RN) solution by starting with the noncommutative geometry-inspired Schwarzschild solution. Using the boundary conditions that connect the noncommutative Schwarzschild solution in the interior of the charged perfect fluid sphere to the Tangherlini–RN solution in the exterior of the sphere, we find that the interior structure can be reflected by an exterior parameter, the charge-to-mass ratio. Moreover, we investigate the stability of the boundary under mass perturbation and indicate that the new interpretation imposes a rigid restriction upon the charge-to-mass ratio. This restriction, in turn, permits a stable noncommutative black hole only in the 4-dimensional spacetime.

The Mathematical Anti-atomism of Plato’s Timaeus

In Plato’s eponymous dialogue, Timaeus, the main character presents the universe as an (almost) perfect sphere filled by tiny, invisible particles having the form of four regular polyhedrons. At first glance, such a construction may seem close to an atomistic theory. However, one does not find any text in Antiquity that links Timaeus’ cosmology to the atomists, while Aristotle opposes clearly Plato to the latter. Nevertheless, Plato is commonly presented in contemporary literature as some sort of atomist, sometimes as supporting a form of so-called ‘mathematical atomism’. However, the term ‘atomism’ is rarely defined when applied to Plato. Since it covers many different theories, it seems that this term has almost as different meanings as different authors. The purpose of this article is to consider whether it is correct to connect Timaeus’ cosmology to some kind of ‘atomism’, however this term may be understood. Its purpose is double: to obtain a better understanding of the cosmology of the Timaeus, and to consider the different modern ‘atomistic’ interpretations of this cosmology. In short, we would like to show that such a claim, in any form whatsoever, is misleading, an impediment to the understanding of the dialogue, and more generally of Plato’s philosophy.

Spheroidal magnetic stars rotating in vacuum

Context. Gravity shapes stars to become almost spherical because of the isotropic nature of gravitational attraction in Newton’s theory. However, several mechanisms break this isotropy, such as their rotation generating a centrifugal force, magnetic pressure, or anisotropic equations of state. The stellar surface therefore slightly or significantly deviates from a sphere depending on the strength of these anisotropic perturbations. Aims. In this paper, we compute analytical and numerical solutions of the electromagnetic field produced by a rotating spheroidal star of oblate or prolate nature. This study is particularly relevant for millisecond pulsars for which strong deformations are produced by rotation or a strong magnetic field, leading to indirect observational signatures of the polar cap thermal X-ray emission. Methods. First we solve the time harmonic Maxwell equations in vacuum by using oblate and prolate spheroidal coordinates adapted to the stellar boundary conditions. The solutions are expanded in series of radial and angular spheroidal wave functions. Particular emphasis is put on the magnetic dipole radiation. Second, we compute approximate solutions by integrating the time-dependent Maxwell equations in spheroidal coordinates numerically. Results. We show that the spin-down luminosity corrections compared to a perfect sphere are, to leading order, given by terms involving (a/rL)2 and (a/R)2 where a is the stellar oblateness or prolateness, R the smallest star radius, and rL the light-cylinder radius. The corresponding perturbations in the electromagnetic field are only perceptible close to the surface, deforming the polar cap rims. At large distances r ≫ a, the solution tends asymptotically to the perfect spherical case of a rotating dipole.

Photonic Crystals with Tunable Lattice Structures Based on Anisotropic Metal–Organic Framework Particles and Their Application in Anticounterfeiting

Photonic crystals (PCs) with controllable lattice structures, photonic bandgaps, and brilliant colors are fabricated by the self‐assembly of the monodispersed anisotropic metal–organic framework (MOF) ZIF‐8 particles into long‐range ordered superstructures. The shape parameter (m) of the particles is used to quantify to what degree the particle shape has deformed from that of a perfect sphere (m = 2) and that of a perfect cube (m = ∞). It is experimentally proven that m value is the key for controlling the lattice structures. Three PCs with different m values of ZIF‐8 particles (9.7, 4.7, and 2.5) are found to be simple cubic, rhombohedral, and face‐centered‐cubic structures, respectively. Different from the conventional spherical particles‐based PCs, brilliant colors can be generated from the second‐order diffraction of the nonspherical MOFs‐based PCs. Taking advantage of this unique characteristic, a new information encryption technology is developed by combing the first‐order diffraction of rhombohedral PCs and first‐second‐order diffraction of simple‐cubic PCs. This work paves a way to explore nonspherical particle‐based PCs materials with different crystal forms and provides a new insight in novel optical characteristics of the PCs, which will promote their applications in anticounterfeiting, color displays, and printings.

Diffraction of helical x-rays by optically active achiral crystals

Four crystal classes are optically active yet not chiral (non-enantiomorphic). Corresponding Bragg diffraction patterns calculated for circularly polarized (helical) x-rays tuned to an atomic resonance prove that angular anisotropy in the distribution of electrons create spots not indexed on the chemical structure (defined by a space group derived from Thomson scattering by perfect spheres of charge). Templeton-Templeton scattering, as it is usually called, of helical x-rays is quantified in terms of a chiral signature defined as the partial diffracted intensity hallmarked by x-ray helicity. Our electric dipole - electric dipole (E1-E1) chiral signature for a space group in the optically active crystal class D2d affords a complete interpretation in terms of copper quadrupoles of diffraction data collected on copper metaborate [E. N. Ovchinnikova et al., J. Synchrotron Rad. 28, 1455 (2021)]. An example of a chiral signature derived from a parity-odd resonance event (E1-E2) is included in our study. It is firmly established that tuning the energy of x-rays to an atomic resonance enhances the intensity of inherently weak Templeton-Templeton scattering and renders space-group forbidden Bragg spots element specific. Our chiral signature as a function of rotation about the reflection vector (azimuthal-angle scan) is specific to position multiplicity, Wyckoff letter and symmetry in a favourable space group.

Implications of a Novel Biopsy Downloading System on Prostate Cancer Detection Rate, Surveillance and Focal Therapy – A Prospective Study

ObjectiveTo examine the SmartBx, a novel biopsy downloading system, allowing downloading of biopsy cores with maximal core preservation as prostate biopsy sampling lacks preservation of core configuration & orientation. MethodsWe prospectively collected cores from TRUS biopsy patients. Half were collected using the SmartBx & half using standard downloading. We measured length of the first ∼3200 cores through various pathology steps and within core cancer length in 160 SmartBx cores. We compared core length, yield (% of core available for final analysis/ original core on needle) and cancer detection rate between SmartBx and standard cores. T-test or chi-square were used for analysis. Results6014 cores were collected from 429 patients. Core length (12.3mm vs. 10mm; P<.01) and core yield (77.5% vs. 62.2%; P<.01) were significantly higher using the SmartBx compared to standard method, respectively. Cancer detection rate was significantly higher using the SmartBx for patients with PSA<10 (10.1% vs. 7.96%; n=2080 & n=2073, respectively; P<.016). Other subgroups showed non-significant higher detection rate for SmartBx cores. We noticed higher detection rate of clinically significant prostate cancer. Within core cancer length in 160 SmartBx cores was significantly lower compared to standard positive whole cores (4.45mm vs. 10.9mm; P<.001). Assuming cancer site a perfect sphere, disease volume was 11-fold lower for within core compared to entire core (46.1mm vs. 679.9mm; P<.0001). ConclusionsSmartBx results in significant higher core length, yield and cancer detection rate. Precise localization of within core tumor foci allows significant reduction in tumor volume.

Anisotropic counterpart of charged Durgapal V perfect fluid sphere

In this paper, we have developed a static charged anisotropic stellar model for a spherically symmetric spacetime geometry. For this, we have considered charged Durgapal V perfect fluid sphere and constructed its anisotropic counterpart by using gravitational decoupling through the minimal geometric deformation (MGD) approach. We have presented physical analysis of the constructed model in details by taking observational data of two different compact stars, namely, SMC X-4 and Vela X-1, into account. All the physical properties such as density, pressure, sound speeds, energy conditions, stability conditions, Tolman–Oppenheimer–Volkoff (TOV) equation, compactness factor, and redshift are found to meet the general criteria required to ensure a well-behaved stellar system.

Hollow iron submicron spheres with strong ferromagnetism

Hollow iron submicron spheres with high saturation magnetization at room temperature were successfully developed for the first time. By means of spray pyrolysis, α -Fe2O3 hollow spheres with the diameter ranging from 0.5 µm to 2.5 µm and an average shell thickness of approximately 20 nm could be obtained in large scale. In subsequent reductive annealing under dilute hydrogen atmosphere, as-synthesized α -Fe2O3 can be transformed into Fe3O4, unstable FeO, and Fe in sequence with an increase in annealing temperature from 350 °C to 600 °C. An optimal reductive temperature of 425 °C was proposed to obtain perfect iron hollow spheres showing a maximum saturation magnetization up to 184 emu/g, which is greater than literature reported values and can be ascribed to curvature effect and symmetrical structural feature.

Computing the orientational-average of diffusion-weighted MRI signals: a comparison of different techniques

Numerous applications in diffusion MRI involve computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient sampling vectors are uniformly distributed on a sphere (or ‘shell’), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres. To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its ‘isotropic part’. Here, these different methods are simulated and compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61 orientations per shell), and isotropically-distributed sampling vectors, all averaging methods give comparable results, (MAP-MRI-based estimates give slightly higher accuracy, albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give significantly higher accuracy compared with the other methods. We also apply these approaches to in vivo data where the results are broadly consistent with our simulations. A statistical analysis of the simulated data shows that the orientationally-averaged signals at each b-value are largely Gaussian distributed.

Number of independent measurements required to obtain reliable mean scattering properties of irregular particles having a small size parameter, using microwave analogy measurements

Laboratory measurements of light scattered by a cloud of randomly oriented levitating particles are often used to interpret remote sensing measurements of dust in space and in Earth's atmosphere. It is necessary to know how many particles or how many different orientations of the same particles must be considered to retrieve the mean scattering function of brightness and polarization. New laboratory measurements were conducted using the microwave analogy method between frequencies of 3 to 18 GHz, where an "analog" particle with a small size parameter in a range of 0.5-12 will have a size of several cm. Twelve such "analog" particles from compact shapes to aggregates with small fractal dimensions were fabricated by additive manufacturing (3D printing) and were studied. The number of necessary measurements to reach the mean scattering properties of a particle with an accuracy of about 5% is obtained for less than 20 different orientations. To reach a 1.5% (1-σ) error in brightness and a 0.5% (1-σ) error in polarization, the number of necessary measurements is in a range of 20 to 70, depending on the shape, fluffiness, deviation from a perfect sphere, and surface irregularities of the particle. These results show that several tens of randomly oriented particles of the same size are sufficient to retrieve the mean light scattering properties. Also, several tens of orientations of the same particles provide mean scattering properties, compared to modelling calculations using the Finite Element Method, for an aggregate composed of identical monomers.

Soot PCF: pore condensation and freezing framework for soot aggregates

Abstract. Atmospheric ice formation in cirrus clouds is often initiated by aerosol particles that act as ice-nucleating particles. The aerosol–cloud interactions of soot and associated feedbacks remain uncertain, in part because a coherent understanding of the ice nucleation mechanism and activity of soot has not yet emerged. Here, we provide a new framework that predicts ice formation on soot particles via pore condensation and freezing (PCF) that, unlike previous approaches, considers soot particle properties, capturing their vastly different pore properties compared to other aerosol species such as mineral dust. During PCF, water is taken up into pores of the soot aggregates by capillary condensation. At cirrus temperatures, the pore water can freeze homogeneously and subsequently grow into a macroscopic ice crystal. In the soot-PCF framework presented here, the relative humidity conditions required for these steps are derived for different pore types as a function of temperature. The pore types considered here encompass n-membered ring pores that form between n individual spheres within the same layer of primary particles as well as pores in the form of inner cavities that form between two layers of primary particles. We treat soot primary particles as perfect spheres and use the contact angle between soot and water (θsw), the primary particle diameter (Dpp), and the degree of primary particle overlap (overlap coefficient, Cov) to characterize pore properties. We find that three-membered and four-membered ring pores are of the right size for PCF, assuming primary particle sizes typical of atmospheric soot particles. For these pore types, we derive equations that describe the conditions for all three steps of soot PCF, namely capillary condensation, ice nucleation, and ice growth. Since at typical cirrus conditions homogeneous ice nucleation can be considered immediate as soon as the water volume within the pore is large enough to host a critical ice embryo, soot PCF becomes limited by either capillary condensation or ice crystal growth. We use the soot-PCF framework to derive a new equation to parameterize ice formation on soot particles via PCF, based on soot properties that are routinely measured, including the primary particle size, overlap, and the fractal dimension. These properties, along with the number of primary particles making up an aggregate and the contact angle between water and soot, constrain the parameterization. Applying the new parameterization to previously reported laboratory data of ice formation on soot particles provides direct evidence that ice nucleation on soot aggregates takes place via PCF. We conclude that this new framework clarifies the ice formation mechanism on soot particles in cirrus conditions and provides a new perspective to represent ice formation on soot in climate models.

EFFECTIVE STRUCTURE OF A WOODEN RESIDENTIAL BUILDING IN THE FORM OF A GEODESIC DOME WITH A UNIVERSAL CONNECTOR

Abstract. Since the middle of the twentieth century, a new architectural solution has been spherical shells broken down into elements by geodesic lines – circles with radii equal to the radius of the sphere. A geodesic dome is a dome made of a spherical polyhedron with an optimally distributed arrangement of vertices and edges tending to a perfect sphere. Using the technical capabilities of computer design, digital models of the layout and calculation of geodesic domes became available. It is possible not only to calculate multi-mesh network layouts with high accuracy, but also to automate the design. At the same time, it cannot be said that the optimal system has already been obtained and studied. The issues of optimal shaping, taking into account a simple universal connector and confirmation of theoretical results by field tests, remain not fully studied. Development of the design of a mesh wooden house in the form of a geo dome with optimal parameters of the geodetic network and nodal connections of the frame elements using a universal connector is the theme of this publication. The proposed form of division is a fullerene polyhedron describing a sphere and consisting of five and hexagonal faces. The dome polyhedron is built on the basis of the icosahedron. The number of partitions of vertices and edges that make up the split edge ‒ the frequency, is chosen equal to 3. The first class of partitioning by the "equal chords" method is adopted. The proposed universal connector for connecting parts of building structures at any angle and a method of mounting building structures using a universal connector. As a result of introduction of new technical decisions we receive essential simplification of a design, reduction of quantity of its components, at the same time increase of its manufacturability and providing an opportunity to connect details of building designs in an end face at any angle.

Thermal Nonlinear Klein-Gordon Equation for Nano-/Micro-Sized Metallic Particle-Attosecond Laser Pulse Interaction.

In this study, a rigorous analytical solution to the thermal nonlinear Klein–Gordon equation in the Kozłowski version is provided. The Klein–Gordon heat equation is solved via the Zhukovsky “state-of-the-art” mathematical techniques. Our study can be regarded as an initial approximation of attosecond laser–particle interaction when the prevalent phenomenon is photon–electron interaction. The electrons interact with the laser beam, which means that the nucleus does not play a significant role in temperature distribution. The particle is supposed to be homogenous with respect to thermophysical properties. This theoretical approach could prove useful for the study of metallic nano-/micro-particles interacting with attosecond laser pulses. Specific applications for Au “nano” particles with a 50 nm radius and “micro” particles with 110, 130, 150, and 1000 nm radii under 100 attosecond laser pulse irradiation are considered. First, the cross-section is supposed to be proportional to the area of the particle, which is assumed to be a perfect sphere of radius R or a rotation ellipsoid. Second, the absorption coefficient is calculated using a semiclassical approach, taking into account the number of atoms per unit volume, the classical electron radius, the laser wavelength, and the atomic scattering factor (10 in case of Au), which cover all the basic aspects for the interaction between the attosecond laser and a nanoparticle. The model is applicable within the 100–2000 nm range. The main conclusion of the model is that for a range inferior to 1000 nm, a competition between ballistic and thermal phenomena occurs. For values in excess of 1000 nm, our study suggests that the thermal phenomena are dominant. Contrastingly, during the irradiation with fs pulses, this value is of the order of 100 nm. This theoretical model’s predictions could be soon confirmed with the new EU-ELI facilities in progress, which will generate pulses of 100 as at a 30 nm wavelength.

A facility location model for marine applications

In any facility location problem, some measure of point-to-point distance is a fundamental consideration. The distance metric may be based on a straight line, rectilinear, great circle. Cosine or similar. Though Euclidean distance is used in most of the applications, it may not yield accurate results when the data points are located on Earth surface and are fairly separated. Great Circle Distance is used in such cases assuming the Earth as a perfect sphere, though it is not so. Vincenty’s formulae are based on an ellipsoidal model of the Earth and report better results. This paper proposes and analyses a simple model using Vincenty’s formulae and compared it with the Haversine formula which is used to calculate the great circle distance. One and two collection points are optimally located for 10 supply points using Weiszfeld iterative algorithm. Though this model can be readily applied for marine applications like oil rigs, drill ships, floating production systems and other drilling barges; they can be used on land also with suitable modifications.

Non-wetting Materials

A drop of rain falling on a surface, such as the car’s window or the palm of your hand, tends to spread over the surface and even hang onto it. But there are materials, such as the leaf of the lotus flower, from which a drop of water will roll down to the ground as an almost perfect sphere, while cleaning the material of dust particles and other pollutions. In this article, we will investigate what influences the tendency of different materials to be wetted to different extents, and how can we design and produce such materials in the lab.

The preparation of spherical metal powders using the high-temperature remelting spheroidization technology

In this paper, a novel technology to prepare spherical metal powder was proposed. Several spherical metal powders were fabricated successfully by using the high-temperature remelting spheroidization (HRS) technology. Among these powders, thorough research on copper powder spheroidization was conducted. The influence of feed rate and temperature on the properties of as-prepared HRS copper powder was investigated. The particle morphology, particle size distribution, oxygen content, bulk density, fluidity and spheroidization rate of copper powder were characterized. The results showed some unique advantages of the HRS technology in the preparation of spherical metal powders. When the temperature was 1623 K, the particles of HRS copper powder were perfect spheres with smooth surfaces and fully dense with no pores inside. The HRS technology can effectively avoid the defects in conventional methods such as satellite particle and hollow particle. The spheroidization rate of HRS copper powder was nearly 100%. The fluidity of HRS copper powder was 11.4 s/50 g, significantly increased compared to the 56.1 s/50 g of the raw powder. Regarding the settling process and heat exchange behavior of metal particles, we developed the HRS process analytical model. HRS technology is a promising method to prepare high-quality metal powder.

Dyadic Green’s Function for Electric Dipole Excitation of a Perfect Electromagnetic Conductor Sphere

In this article, we investigate the dyadic Green's function (DGF) of a perfect electromagnetic conductor sphere (PEMCS) due to electric dipoles, theoretically by employing the scattering superposition principle (SSP) and the Ohm-Rayleigh method. Then, the derived DGF is used to calculate the scattered field of a PEMCS due to an arbitrarily oriented infinitesimal electric dipole and also plane wave illumination. Numerical results are compared with those obtained by the FEKO commercial software to demonstrate the efficiency and accuracy of the proposed method. The results are in excellent agreement.

An explicit expression for the retention factor and velocity dependency of the mobile zone mass transfer band broadening in packed spheres beds used in liquid chromatography

The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (hCm) in packed bed columns. For this purpose, first high-accuracy computations of the band broadening in a perfectly ordered sphere array (fcc-arrangement, external porosity ε=0.40) were made using computational fluid dynamics (CFD), covering a broad range of zone retention factors (2≤k’’≤18) and reduced velocities (0≤νi≤48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the hCm-contribution. This fitting exercise showed the traditional literature approach, using the Wilson-Geankoplis correlation to calculate the dimensionless Sherwood (Sh) number for the mass transfer, leads to fitting errors on the hCm-term as large as 150%. Instead, a new correlation for Sh is established. In addition, we also explored the difference in fitting accuracy between hCm-expressions based on either a plug-flow or a laminar flow profile assumption. Surprisingly, no significant difference in fitting accuracy between both assumptions was observed. Finally, a best-fit analytical expression is proposed that can represent the CFD-computed band broadening data with an average absolute fitting error of Δh=0.005, corresponding to a relative error of 2.5% on the hCm-term and of only 0.3% on the total plate height in a perfectly ordered sphere packing. Defining the presently investigated fcc-ordered sphere array with external porosity=40% as the reference geometry for a perfect sphere packing, the established expression can be used as a new yardstick expression against which the degree of eddy-dispersion can be measured.

Utility of shape evolution and displacement in the classification of chronic multiple sclerosis lesions

The accurate recognition of multiple sclerosis (MS) lesions is challenged by the high sensitivity and imperfect specificity of MRI. To examine whether longitudinal changes in volume, surface area, 3-dimensional (3D) displacement (i.e. change in lesion position), and 3D deformation (i.e. change in lesion shape) could inform on the origin of supratentorial brain lesions, we prospectively enrolled 23 patients with MS and 11 patients with small vessel disease (SVD) and performed standardized 3-T 3D brain MRI studies. Bayesian linear mixed effects regression models were constructed to evaluate associations between changes in lesion morphology and disease state. A total of 248 MS and 157 SVD lesions were studied. Individual MS lesions demonstrated significant decreases in volume < 3.75mm3 (p = 0.04), greater shifts in 3D displacement by 23.4% with increasing duration between MRI time points (p = 0.007), and greater transitions to a more non-spherical shape (p < 0.0001). If 62.2% of lesions within a given MRI study had a calculated theoretical radius > 2.49 based on deviation from a perfect 3D sphere, a 92.7% in-sample and 91.2% out-of-sample accuracy was identified for the diagnosis of MS. Longitudinal 3D shape evolution and displacement characteristics may improve lesion classification, adding to MRI techniques aimed at improving lesion specificity.