Spherical Density Research Articles

Analytical solution of the electro-magneto-elasto-hydrothermal coupling problem of rotating functionally graded piezoelectric/piezomagnetic hollow spheres under a hydrothermal environment

Functionally graded piezoelectric/piezomagnetic (FGPEPM) materials in a hygrothermal environment exhibit complex multi-physical field coupling effects when subjected to various loads such as mechanical, electric, magnetic, temperature, and moisture concentration. In this paper, a theoretical analysis of the electro-magneto-elasto-hygrothermal (EMEHT) coupling effects for a rotating FGPEPM hollow sphere is presented. By assuming that the properties of hygrothermo, electro-magneto-elastic, hygrothermal expansion, and density of the FGPEPM sphere obey different power laws along the thickness direction, the distributions of temperature, moisture, magnetic potential, radial displacement, electric potential, and stresses within the rotating FGPEPM sphere are determined. The present theoretical solutions are verified with existing analytical solutions for some related simplified problems. The FGPEPM hollow sphere exhibits complex multi-physical field coupling effects, containing positive/inverse piezoelectric, positive/inverse piezomagnetic, positive/inverse magnetoelectric, thermal/moist stress, pyroelectric/pyromagnetic, and hydroelectric/hydromagnetic effects under a hygrothermal environment. The influence of gradient parameters and other material properties on these EMEHT coupling effects is also investigated for FGPEPM hollow spheres under various types of loads. This theoretical research provides some reference for the optimal design for this type of functionally gradient multifield coupling material.

Freely rising or falling of a sphere in a square tube at intermediate Reynolds numbers

The motion of a sphere freely rising or falling in a 5d (d is the diameter of the sphere) square tube was numerically studied for the sphere-to-fluid density ratio ranging from 0.1 to 2.3 (0.1 ≤ ρs/ρ ≤ 2.3, ρs is the density of spheres and ρ the fluid density) and Galileo number from 140 to 230 (140 ≤ Ga ≤ 230). We report that Hopf bifurcation occurs at Gacrit ≈ 157, where both the heavy and light spheres lose stability. The helical motion is widely seen for all spheres at Ga > 160 resulting from a double-threaded vortex interacting with the tube walls, which becomes irregular at Ga ≥ 190 where heavy spheres act differently from their counterparts; that is, heavy spheres change their helical directions alternately while light spheres exhibit helical trajectories with jaggedness in connection with the shedding of the double-threaded vortices. This is because of the difference in inertia between the heavy and light spheres. We also checked the oscillation periods for the helical motion of the spheres. They show opposite variations with ρs/ρ for the two types of spheres. Light spheres (ρs/ρ ≤ 0.7) reach a zigzagging regime at Ga ≥ 200 where a vortex loop (hairpin-like vortical structure) is formed which may develop into a vortex ring downstream at small ρs/ρ. This might be the first time a transition from the helical motion to the zigzagging motion for heavy spheres (ρs/ρ ≥ 1.8) has been reported. Finally, we examined the dependence of both the terminal Reynolds number and the drag coefficient of the spheres on the Galileo number.

Sphere Coverage in n Dimensions

This paper presents some theoretical results on the sphere coverage problem in the n-dimensional space. These results refer to the minimal number of spheres, denoted by Nk(a), to cover a cuboid. The first properties outline some theoretical results for the numbers Nk(a), including sub-additivity and monotony on each variable. We use then these results to establish some lower and upper bounds for Nk(a), as well as for the minimal density of spheres to achieve k-coverage. Finally, a computation is proposed to approximate the Nk(a) numbers, and some tables are produced to show them for 2D and 3D cuboids.

A “turn-on” polymer nanothermometer based on aggregation induced emission for intracellular temperature sensing

Temperature measurements at the nanoscale facilitate the understanding of physiological processes related to heat in cells. Herein, we prepare a tetraphenylethylene-functionalized fluorophore (TPPEBr) with dual characteristics of twisted intramolecular charge transfer (TICT) and aggregation induced emission (AIE). It is polymerized with a thermo-responsive unit NIPAM to construct a fluorescent polymer nanothermometer (PNIPAM-TPPEBr). The phase transition behavior of PNIPAM from dispersed chains to dense spheres in aqueous media promotes the aggregation of TPPEBr fluorophores, which makes the fluorescence of PNIPAM-TPPEBr enhance with increasing temperature. Furthermore, the phase transition of PNIPAM is accompanied by a significant decrease in the polarity of the microenvironment, resulting in a blue shift in the emission wavelength of TPPEBr. Varying the ratio of NIPAM and TPPEBr can regulate the thermo-responsiveness of PNIPAM-TPPEBr in the physiological temperature range (31–38 °C), and the maximum relative thermal sensitivity reaches 13.2 % °C−1. The thermo-responsive performance of this nanothermometer is independent of the intracellular microenvironment, and it is successfully applied in the temperature imaging of A549 cells. Under the stimulation of ionomycin and oxidative phosphorylation inhibitor, the cell temperature increased by ca. 1.5 °C and ca. 1.0 °C, respectively.

Cost-effective production of density-controllable monodisperse spheres for experiments in fluids

Cost-effective production method for making density-controllable monodisperse spheres is demonstrated. A sodium alginate aqueous solution containing gelatin is emulsified with canola oil. The droplet surface is covered with a calcium alginate membrane by dropping the emulsion into a calcium lactate aqueous solution. The content of the canola oil can control the sphere's density. To demonstrate the applicability of the spheres to experimental research, rheological measurements of the suspensions of the spheres were performed. The effective viscosity agrees with the theoretical formula at volume fractions of 0.7%–11.7%. The demonstration highlights that the spheres can function as neutrally buoyant solid particles in studies for the physics of fluids.

Formation of Nanodiamonds during Pyrolysis of Butanosolv Lignin.

The preparation of artificial diamonds has a long history driven by decreased costs compared to naturally occurring diamonds and ethical issues. However, fabrication of diamonds in the laboratory from readily available biomass has not been extensively investigated. This work demonstrates a convenient method for producing nanodiamonds from biopolymer lignin at ambient pressure. Lignin was extracted from Douglas Fir sawdust using a butanosolv pretreatment and was pyrolyzed in N2 at 1000 °C, followed by a second thermal treatment in 5% H2/Ar at 1050 °C, both at ambient pressure. This led to the formation of nanodiamonds embedded in an amorphous carbon substrate. The changes occurring at various stages of the pyrolysis process were monitored by scanning electron microscopy, Fourier transform infrared spectroscopy, and nuclear magnetic resonance spectroscopy. High resolution transmission electron microscopy revealed that nanodiamond crystallites, 4 nm in diameter on average, formed via multiple nucleation events in some carbon-containing high density spheres. It is proposed that highly defected graphene-like flakes form during the pyrolysis of lignin as an intermediate phase. These flakes are more deformable with more localized π electrons in comparison with graphene and join together face-to-face in different manners to form cubic or hexagonal nanodiamonds. This proposed mechanism for the formation of nanodiamonds is relevant to the future fabrication of diamonds from biomass under relatively mild conditions.

From Hard to Soft Dense Sphere Packings: The Cohesive Energy of Barlow Structures Using Exact Lattice Summations for a General Lennard-Jones Potential.

There are infinitely many distinguishable dense sphere packings in dimension three (Barlow structures) with maximum packing density of ρ = π/√18. While Hales [Hales, T. C. Ann. Math. 2005, 162, 1065-1185.] proved that the packing density of the most dense cubic packing cannot be surpassed, it is currently not known how the infinite possibilities of densely packed Barlow structures with different sequences of hexagonal close packed layers are energetically related compared to the well-known face centered cubic (fcc) and hexagonal close packed (hcp) structures. We demonstrate that, for a general Lennard-Jones potential, which includes the hard-sphere model as a limiting case, Barlow packings lie energetically between fcc and hcp. Exceptions to this energy sequence only occur when fcc and hcp are energetically quasi-degenerate.

New Functional Orbital-free Within DFT for Metallic Systems

I present the continuation of a study on Laplacian Level Kinetic Energy (KE) functionals applied to metallic nanosystems. The development of novel Kinetic Energy functionals is an important topic in density functional theory (DFT). The nanoparticles are patterned using gelatin spheres of different sizes, background density and number of electrons. To reproduce the correct kinetic and potential energy density of the various nanoparticles, the use of semilocal descriptors is necessary. Need an explicit density functional expression for the kinetic energy of electrons, including the first e second functional derivative, i.e. the kinetic potential and the kinetic kernel, respectively. The exact explicit form of the non interacting kinetic energy, as a functional of the electron density, is known only for the homogeneous electron gas (HEG), i.e., the Thomas-Fermi (TF) local functional and for 1 and 2 electron systems, i.e., the von Weizsacker (VW) functional. In between these two extreme cases, different semilocal or non local approximations were developed in recent years. Most semilocal KE functionals are based on modifications of the second-order gradient expansion (GE2) or fourth-order gradient expansion (GE4). I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles. I propose a new LAP2 semilocal functional which, better than the previous ones, allows us to obtain fewer errors both of energy and potential. More details of the previous calculations can be found in my 2 previous works which will be cited in the text.

Fabrication and performance characterization of NTO/HMX spherical composite explosives with improved safety performance.

AbstractImproving the energy density and safety of explosives are crucial for developing composite energetic materials. In this study, a facile and continuous spray drying granulation technique was used to obtain NTO/HMX composite explosives with insensitive NTO as coating material. The micro‐morphology, particle size, crystallographic structure, exothermic decomposition, impact sensitivity, and detonation performance of NTO/HMX composite explosives with different NTO contents were investigated by various experimental methods. The test results indicate that the higher the NTO content, the better the crystal integrity of HMX and the lower the mechanical sensitivity of NTO/HMX composite explosives. When the mass ratio of NTO and HMX is 25 : 75, NTO/HMX composite explosives have a good spherical density structure formed by the aggregation of nanoparticles, small particle sizes with a median size of 1.22 μm, and a uniform distribution of particle sizes in the range of 0.3–2.8 μm. The addition of NTO not only enhances the thermal decomposition of HMX but also significantly decreases mechanical sensitivity. The composite explosives had not altered the raw NTO and HMX crystallographic structures (β‐type). With the same ratio (25 : 75), NTO/HMX composite explosives (25 : 75) possess higher impact energy and friction force, better safety, and better thermal stability than physical mixtures. Additionally, the high‐energy insensitive composite microspheres preserve the important high‐energy properties of HMX while effectively enhancing its safety characteristics, which have the advantages of controllable crystallographic micromorphology, high energy, and excellent impact sensibility and could be broadly applicable in the field of munitions.

Hirshfeld atom refinement and dynamical refinement of hexagonal ice structure from electron diffraction data.

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural parameters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O-H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O-H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled - with extinction correction or with dynamical refinement. The latter led to an improvement of the O-H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

Compression and self-compression of frequency modulated spherical photon density waves in anisotropic scattering media

We report on the results of a simulation of the photon density waves with pulse amplitude modulation by a complex frequency modulated signal. The problem is considered for the optical properties typical for sea water with anisotropy factor values varying from 0.75 to 0.93 at source-detector distances up to 120 m. It is shown that multiple scattering in a medium does not prevent effective compression of a signal registered using matched detection. Two competing phenomena affecting the detected pulse duration and depending on the central frequency of the modulation signal are discussed. The effect of faster attenuation of high harmonics in a complexly modulated signal leads to the detected signal duration increase as a consequence of multiple scattering. On the other hand, anomalous dispersion of photon density waves in media with scattering anisotropy leads to the pulse self-compression. The simulation results presented in the paper demonstrate the prevalence of different phenomena depending on the central frequency of the modulation signal resulting in a pulse duration decrease or increase in different frequency ranges covering the band from 107 to 2⋅109 Hz. The effect of the phase function shape on the observed effect is also discussed.

Effect of arrangement patterns of spheres encapsulating phase change material in packed beds on thermal performance

The NaNO3-KNO3 salt has the disadvantage of poor heat transfer capacity and low heat transfer efficiency in single-tank heat storage systems. However, molten salt can be used as phase change materials (PCM) and encapsulated with highly conductive sphere-shaped metals as PCM spheres. Arranging these spheres can appropriately change the situation. In this study, a heat storage system of a multilayer packed bed of PCM spheres consisting of NaNO3-KNO3 salt and type 316 stainless steel sphere shell was designed. This system's heat transfer and heat storage performance were also investigated using CFD simulation. For the same sphere diameter, the heat storage efficiency of hexagonal close packing (HCP) was 1.1 times that of cubic close packing (CCP). With the same porosity, the heat charging efficiency for the case using the 47.5 mm sphere diameter was the highest, at 99.3 %. When the number of layers of spheres was increased from 3 to 7, the heat flux through the sphere wall and the heat storage density of PCM spheres decreased from 40.8 kW and 67.3 × 105 kJ/m3 to 35.7 kW and 59.2 × 105 kJ/m3, respectively. Therefore, the heat charging efficiency of HCP was better than that of CCP. Reducing sphere size could shorten the heat transfer time and improve the heat storage efficiency. These numerical simulation results are consistent with the commonly known fact that the volumetric heat transfer intensity in the porous media is proportional to the reciprocal particle size since the smaller the particle size, the larger the contact area between the packing and the fluid. The conclusion drawn from the present findings provides an idea for designing a PCM heat storage system with high temperature and high efficiency of molten salt. The idea could also be used as a reference for the optimal design of a packed bed reactor.

Theoretical investigation of the electronic and second-order non-linear optical properties of [n]helicene derivatives

Designing and synthesizing nonlinear optical materials with excellent performance has always been a persistent goal pursued by material chemists. In paper, based on the reported [6]heliceno-bis(naphthalimides) 2, four new molecules are designed by introducing 2-dicyanomethylene-1,3-dithiole on the two middle benzene rings of the naphthalimide unit and replacing CH3 units on the R1 and R2 substituents with NH2/NO2 moieties, or their combination. The electronic spectra, reorganization energy and second-order nonlinear optical properties of the reported derivatives 1 and 2, as well as four newly designed derivatives, have been systematically investigated by means of (time-dependent) density functional theory calculations. Frontier molecular orbital analysis, electron excitation analysis, reorganization energy, and the calculation of the static and dynamic first hyperpolarizability all indicate that the studied system is greatly influenced by the number of benzene rings in helicene core and the terminal substituents attached at both ends of helicene core. Further analysis of depolarization, hyperpolarizability density and unit sphere representation reveals the nature of the nonlinear optical response of the studied system. Considering that the studied derivatives all have large static first hyperpolarizabilities (e.g., 210 × 10-30 esu for derivative 5) and small reorganization energy (e.g., 0.092 eV of hole reorganization energy and 0.118 eV of electron reorganization energy for derivative 3), they are expected to become potential nonlinear optical materials with excellent performance and bipolar transport materials. This work contributes to the rational design of high-performance molecules based on [n]helicenes derivatives and further explores their potential applications in optical materials.

Sonochemical synthesis of hollow mesoporous silica spheres (HMSSs) and its effective utilization for one-step synthesis of curcumin-loaded HMSSs

Herein, HMSSs were successfully synthesized using the sonochemical method. Compared with a conventional synthesis under continuous stirring, HMSSs synthesized under ultrasound irradiation were uniform hollow spheres with a thinner mesoporous shell, resulting in higher pore volumes and larger specific surface areas. The hollow cores were acquired without the templates but from ethanol droplets generated in situ by ultrasound. The ethanol/water volume ratio (E/W) affected the structures of sonochemical synthesized particles, i.e., mesoporous silica particles were obtained at low E/W before transforming to HMSSs under moderate E/W and dense silica spheres at high E/W. Varying [NH4OH] base catalysts in an aqueous phase altered the core structure of HMSSs from hollow cores at high [NH4OH] to partial-filled cores at a moderate concentration and non-hollow cores at low [NH4OH]. Ultrasound was effectively utilized to prepare curcumin-loaded HMSSs in a single step. Stable ethanol droplets containing curcumin were produced from the ultrasound's homogenizing effect, leading to curcumin's encapsulation within HMSSs. While the cavitation induced the chemical effect, reducing the reaction time. The encapsulation of curcumin and the formation of HMSSs could occur concurrently; thus, not only is the drug loading step unnecessary, but the efficiency of loading drugs inside HMSSs is also enhanced.

Enhancement of ionospheric heating effect by chemical release

The ionosphere can be artificially modified by employing ground-based high-power high-frequency electromagnetic waves to irradiate the ionosphere. This modification is achieved through the nonlinear interaction between the electromagnetic waves and the ionospheric plasma, leading to changes in the physical properties and structure of the ionosphere. The degree of artificial modification of the ionosphere is closely related to the heating energy density of high-frequency pump waves. Due to the high density of neutral constituents in the lower ionosphere and the high frequency of electron-neutral collisions, the energy of heating pump waves will be absorbed and attenuated during the penetration of the low ionosphere, seriously affecting the heating effect. This paper proposes a method to reduce the absorption of ionospheric heating pump waves by releasing electron attachment chemicals into low ionosphere to form a large-scale electron density hole. A model for mitigating pump waves absorption based on SF6 release is established, and the absorption at different frequencies is quantitatively calculated. The propagation characteristics of high-frequency signals in ionospheric holes are studied using a three-dimensional ray tracing method, and the results demonstrate that the chemical release method not only reduces the absorption attenuation of heating pump waves but also forms spherical electron density holes, which exhibit a focusing effect on the heating beam and enhance the heating effect. The results are of great significance for understanding the nonlinear interaction between electromagnetic wave and ionospheric plasma and improving the ionospheric heating efficiency.

Spatial distribution of reduced density of hard spheres near a hard-sphere dimer: Results from three-dimensional Ornstein–Zernike equations coupled with several different closures and from grand canonical Monte Carlo simulation

We calculated the spatial distribution function, which is the one-body reduced density distribution of solvent particles around a nonspherical solute, using the three-dimensional Ornstein–Zernike equations coupled with closures. The solvent was a hard-sphere fluid, and the contact dimer of the solvent particles was the nonspherical solute. Two traditional closures, the Percus–Yevick and hypernetted-chain approximations, and three closures with bridge functions (BFs) were examined. These spatial distribution functions were compared with the results obtained by grand canonical Monte Carlo (GCMC) simulations. Three closures with BFs, such as the modified hypernetted-chain (MHNC) closure using a bridge function proposed by Kinoshita, gave precise spatial distribution functions. These results were much more accurate than those obtained by the traditional closures. The deviations from the spatial distribution function obtained by the GCMC simulation appeared only near the concave surface of the solute dimer. However, the deviations were minor compared with those between the simulation and the predictions of the two traditional closures. By contrast, the three-body correlation functions for the closures with BFs were not more accurate than those obtained by the traditional closures.

Non-symmetric stable processes: Dirichlet heat kernel, Martin kernel and Yaglom limit

We study a d-dimensional non-symmetric strictly α-stable Lévy process X, whose spherical density is bounded and bounded away from the origin. First, we give sharp two-sided estimates on the transition density of X killed when leaving an arbitrary κ-fat set. We apply these results to get the existence of the Yaglom limit for arbitrary κ-fat cone. In the meantime we also obtain the spacial asymptotics of the survival probability at the vertex of the cone expressed by means of the Martin kernel for Γ and its homogeneity exponent. Our results hold for the dual process X̂, too.

Three-Dimensional Modeling and Inversion of Gravity Data Based on Topography: Urals Case Study

In this paper, the derivation of a concise closed form for the gravitational field of a polyhedron is presented. This formula forms the basis of the algorithm for calculating the gravitational field of an arbitrary shape body with high accuracy. Based on this algorithm, a method for gravity data inversion (creating density models of the Earth’s crust) has been developed. The algorithm can accept either regular or irregular polyhedron discretization for density model creation. The models are approximated with dense irregular grids, elements of which are polyhedrons. When performing gravity data inversion, we face three problems: topography with large amplitude, the sphericity of the planet, and a long computation time because of the large amount of data. In our previous works, we have already considered those problems separately but without explaining the details of the computation of the closed-form solution for a polyhedron. In this paper, we present for the first time a performance-effective numerical method for the inversion of gravity data based on topography. The method is based on closed-form expression for the gravity field of a spherical density model of the Earth’s crust with the upper topography layer, and provides great accuracy and speed of calculation. There are no restrictions on the model’s geometry or gravity data grid. As a case study, a spherical density model of the Earth’s crust of the Urals is created.

Theoretical investigation of the free fall of a spherical particle in a viscous fluid using continuous piecewise linearization method

This article presents a theoretical investigation of the problem of free fall of a spherical particle in a viscous fluid. The classic Boussinesq-Basset-Oseen (BBO) model for particle motion in laminar flow was modified for generalized flow by using a drag law that is applicable for 0<Re≤2.0×105. By assuming that the acceleration in the Basset force integral is constant, the Basset force effect was approximated to form an integrated added mass coefficient. Consequently, the integro-differential equation of the BBO model was transformed to a first-order nonlinear ordinary differential equation that accounts for the Basset force effect and was solved using the continuous piecewise linearization method (CPLM). The CPLM algorithm was developed based on the jerk-velocity relationship and is applicable to zero and non-zero initial conditions, steady motion, increasing or decreasing velocities and the corresponding acceleration and jerk responses. The CPLM algorithm was shown to predict published experimental results accurately and compared very well with numerical solutions and existing analytical solutions. Examination of the fall response under varying parameters showed that the fall distance, fall time and terminal velocity depend strongly on the sphere diameter, sphere density, and the density and viscosity of the fluid medium. Also, an analytical solution for the power dissipated in the fluid medium as the sphere falls to reach its terminal velocity was derived. The power dissipated was found to increase exponentially as the initial velocity deviates positively from the terminal velocity.

Galaxy cluster mass bias from projected mass maps

The determination of the mass of galaxy clusters from observations is subject to systematic uncertainties. Beyond the errors due to instrumental and observational systematic effects, in this work we investigate the bias introduced by modelling assumptions. In particular, we consider the reconstruction of the mass of galaxy clusters from convergence maps employing spherical mass density models. We made use of THE THREE HUNDRED simulations, selecting clusters in the same redshift and mass range as the NIKA2 Sunyaev-Zel’dovich Large Programme sample: 3 ≤ M500/1014 M⊙ ≤ 10 and 0.5 ≤ z ≤ 0.9. We studied different modelling and intrinsic uncertainties that should be accounted for when using the single cluster mass estimates for scaling relations. We confirm that the orientation of clusters and the radial ranges considered for the fit have an important impact on the mass bias. The effect of the projection adds uncertainties to the order of 10–16% to the mass estimates. We also find that the scatter from cluster to cluster in the mass bias when using spherical mass models is less than 9% of the true mass of the clusters.