Continuum modelling of spherical and spheroidal carbon onions

Carbon nanostructures are of considerable interest owing to their unique mechanical and electronic properties. Experimentally, a wide variety of different shapes are obtained, including both spherical and spheroidal carbon onions. A spheroid is an ellipsoid with two major axes equal and the term onion refers to a multi-layered composite structure. Assuming structures of either concentric spherical or ellipsoidal fullerenes comprising n layers, this paper examines the interaction energy between adjacent shells for both spherical and spheroidal carbon onions. The Lennard-Jones potential together with the continuum approximation is employed to determine the equilibrium spacing between two adjacent shells. We also determine analytical formulae for the potential energy which may be expressed either in terms of hypergeometric or Legendre functions. We find that the equilibrium spacing between shells decreases for shells further out from the inner core owing to the decreasing curvature of the outer shells of a concentric structure.     

Wrinkling of pressurized elastic shells

We study the formation of localized structures formed by the point loading of an internally pressurized elastic shell. While unpressurized shells (such as a ping-pong ball) buckle into polygonal structures, we show that pressurized shells are subject to a wrinkling instability. We study wrinkling in depth, presenting scaling laws for the critical indentation at which wrinkling occurs and the number of wrinkles formed in terms of the internal pressurization and material properties of the shell. These results are validated by numerical simulations. We show that the evolution of the wrinkle length with increasing indentation can be understood for highly pressurized shells from membrane theory. These results suggest that the position and number of wrinkles may be used in combination to give simple methods for the estimation of the mechanical properties of highly pressurized shells.     

The effect of negative-energy shells on the Schwarzschild black hole

We construct Penrose diagrams for Schwarzschild spacetimes joined by massless shells of matter, in the process correcting minor flaws in the similar diagrams drawn by Dray and ’t Hooft (Commun Math Phys 99:613–625, 1985), and confirming their result that such shells generate a horizon shift. We then consider shells with negative energy density, showing that the horizon shift in this case allows for travel between the heretofore causally separated exterior regions of the Schwarzschild geometry. These drawing techniques are then used to investigate the properties of successive shells, joining multiple Schwarzschild regions. Again, the presence of negative-energy shells leads to a causal connection between the exterior regions, even in (some) cases with two successive shells of equal but opposite total energy.     

Mass differences and neutron pairing in Ca,Sn and Pb isotopes

Various estimates of the even-odd effect of the mass shell of atomic nuclei are considered.Based on the experimental mass values of the Ca,Sn,and Pb isotopes,the dependence of the energy gap on the neutron number is traced and the relationship of this characteristic to the properties of external neutron subshells is shown.In nuclei with closed proton shells,effects directly related to neutron pairing and effects of nucleon shells are discussed.     

Damping properties of layered cylindrical shells,vibrating in axially symmetric modes

The damping of cylindrical shells coated with unconstrained layers of viscoelastic material either on one side of the shell (inside or outside) or on both sides is estimated. The basic equations of motion are derived which describe harmonic forced flexural damped vibrations in axisymmetric modes. For pure sinusoidal modes expressions for the overall loss factors are given. The damping properties of cylindrical shells of finite length, coated on the inside or outside, or on both sides (symmetrically or unsymmetrically) are compared. Classical thin shell theory is used for the analysis. It is shown how two-layered damped shells differ from two-layered damped beams. The extent of damping reduction in shells resulting from the fact that the shell cross-section is closed is discussed.     

Structural response of cylindrically curved laminated composite shells subjected to blast loading

This paper is concerned with the theoretical analysis and correlation with the numerical results of the displacement time histories of the cylindrically curved laminated composite shells exposed to normal blast shock waves. The laminated composite shell is clamped at its all edges. The dynamic equation of the cylindrical shell used in this study is valid under the assumptions made in Love's theory of thin elastic shells. The constitutive equations of laminated composite shells are given in the frame of effective modulus theory. The governing equation of the cylindrical shell is solved by the Runge-Kutta method. In addition, a finite element modeling and analysis are presented and compared with the theoretical results. The peak deflections and response frequencies obtained from theoretical and numerical analyses are in agreement. The effects of material properties and geometrical properties are examined on the dynamic behaviour.     

Buckling of 2D-FG Cylindrical Shells under Combined External Pressure and Axial Compression

This paper presents the stability of two-dimensional functionally graded (2D-FG) cylindrical shells subjected to combined external pressure and axial compression loads, based on classical shell theory. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and determined by the rule of mixture. The Euler's equation is employed to derive the stability equations, which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells. The effects of shell geometry, the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM. The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.     

Mass Ratios and Proton Pairing for Isotones with <Emphasis Type="Italic">N</Emphasis> = 20, 50, and 82

Different estimates of the even–odd effect for the nuclear mass surface are discussed. The proton-number dependence of the energy gap is derived from the measured masses of the N = 20, 50, and 82 isotones with closed neutron shells. Its interrelation with the properties of external proton shells is demonstrated, and the effects of proton pairing are considered along with the microscopic nuclear structure.     

The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure

In this paper, the vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure are studied. At first, the basic relations have been obtained for orthotropic truncated conical shells, Young's moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method to the foregoing equations, the buckling pressure and frequency parameter of truncated conical shells are obtained from these equations. Finally, carrying out some computations, the effects of the variations of conical shell characteristics, the effects of the non-homogeneity and the orthotropy on the critical dimensionless hydrostatic pressure and lowest dimensionless frequency parameter have been studied, when Young's moduli and density vary together and separately. The results are presented in tables, figures and compared with other works.     

Enormous enhancement of ZnO nanorod photoluminescence

ZnO nanorod arrays were grown on quartz slices in the aqueous solution of zinc acetate and hexamethylenetetramine at 90 °C. Then ZnO:Mg shells were epitaxially grown on the nanorods to form core/shell structures in the aqueous solution of zinc acetate, magnesium acetate and hexamethylenetetramine at the same temperature. Effects of the shells and UV laser beam irradiation on the crystal structure and photoluminescence properties of ZnO nanorods were studied. ZnO:Mg shells suppress the green emission and enhance the UV emission intensity of the nanorods by 38 times. Enhancement of the UV emission depends on the Mg content in the shells. Short time UV laser beam irradiation could improve ZnO nanorod emission efficiently. The UV emission intensity of ZnO nanorods is enhanced by 71 times by capping and subsequent UV laser beam irradiation.     

Nonideal regimes of deflagration and detonation of black powder

The explosive and deflagration properties of black powder differ significantly from those of modern propellants and compositions based on ammonium nitrate or ammonium perchlorate. Possessing a high combustibility, black powder is capable of maintaining stable combustion at high velocities in various shells, be it steel shells or thin-walled plastic tubes, without experiencing deflagration-to-detonation transition. It is extremely difficult to detonate black powder, even using a powerful booster detonator. The results of numerical simulations of a number of key experiments on the convective combustion and shock initiation of black powder described in the literature are presented. The calculations were performed within the framework of a model developed previously for describing the convective combustion of granulated pyroxylin powders, with small modifications being introduced to allow for the specific properties of black powder. The thermophysical properties of the products of combustion and detonation and the parameters of the equation of state of black powder were determined from thermodynamic calculations. The calculation results were found to be in close agreement with the experimental data. The simulation results were used to analyze the regularities of the wave processes in the system and their relation to the properties of black powder and the experimental conditions. It was demonstrated that the effects observed could be explained by a weak dependence of the burning rate of black powder on the pressure.     

Luminescence Quantum Yield and Recombination Constants in Colloidal Core/Shell Ag2S/ZnS and Ag2S/SiO2 Quantum Dots

Optics and Spectroscopy - The luminescence properties of colloidal Ag2S quantum dots (QDs) with ZnS or SiO2 shells coated with thioglycolic or 2-mercaptopropionic acids are comparatively analyzed....     

Motion correction properties of the shells k-space trajectory

The feasibility of a k-space trajectory that samples data on a set of 3D shells is demonstrated with phantom and volunteer experiments. Details of an interleaved multi-shot, helical spiral pulse sequence and a gridding reconstruction algorithm that uses Voronoi diagrams are provided. The motion-correction properties of the shells k-space trajectory are described. It is shown that when used in conjunction with three point markers, k-space data acquired with the shells trajectory provide a generalization of the RINGLET method, allowing for correction of arbitrary rigid-body motion with six degrees of freedom. Use of dedicated navigator echoes or redundant acquisitions of k-space data are not required. Retrospective motion correction is demonstrated with controlled phantom experiments and with seven healthy human volunteers. The motion correction is shown to improve the images, both qualitatively and quantitatively with a metric calculated from image entropy. Advantages and challenges of the shells trajectory are discussed, with particular attention to acquisition efficiency.     

The coulomb glory effect in collisions of antiprotons with heavy ions

The Coulomb glory effect in the back scattering of antiprotons with energies of from 100 eV to 3 keV from a bare nucleus of uranium and from uranium ions with closed shells is considered in terms of nonrelativistic and relativistic quantum theory. The appearance of Coulomb glory in collisions with multiply charged ions is caused by nucleus charge screening by filled electron shells. In scattering from a bare nucleus, the effect appears because of the screening properties of the vacuum polarization potential.     

Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method

The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It’s found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy.     

Ultrasonic investigation of magnetic nanoparticles suspension with PEG biocompatible coating

Water suspension of nanoparticles was studied by ultrasound spectroscopy. Nanoparticles have a core-shell structure with magnetic core Fe₃O₄ and surfactant shells. The surface of magnetic particles was coated with oleate sodium as the primary layer and polyethylene glycol as the secondary layer. The acoustic properties of suspensions, such as velocity and attenuation of ultrasonic waves, have been measured. From experimental data mechanical properties have been determined. Adiabatic compressibility of nanoparticles suspension decreased with increase of temperature. The changes of ultrasonic wave attenuation under the influence of the external magnetic field, show that magnetic liquids with high concentration of magnetic material (despite two surfactant shells) show tendency to aggregate.     

Structure and magnetic properties of nanoparticles encapsulated in carbon shells

Ni₂Y and Nd–Fe–Nb–B catalysts were used for the processing of nanoparticles by arc discharge between graphite electrodes. The products were collected from the cathode (deposit and collar) and reactor walls (soot). The ferromagnetic nanoparticles have size in the range of 10–50 nm and are encapsulated in carbon shells. The chemical composition, structure and magnetic properties of the nanoparticles have been studied. For the Ni₂Y catalyst we found that the arc discharge results in decomposition of the intermetallic Ni₂Y phase and formation of Ni nanoparticles encapsulated in carbon shells in the collar and soot, whereas yttrium oxide was found in the deposit. For the Nd–Fe–Nb–B catalysts the magnetic properties depend on the collection place and erosion rate. Fe and Fe–Nd–Nb nanoparticles were found in the soot and deposit, respectively.     

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.     

Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition

Linear thermal buckling and free vibration analysis are presented for functionally graded cylindrical shells with clamped-clamped boundary condition based on temperature-dependent material properties. The material properties of functionally graded materials (FGM) shell are assumed to vary smoothly and continuously across the thickness. With high-temperature specified on the inner surface of the FGM shell and outer surface at ambient temperature, 1D heat conduction equation along the thickness of the shell is applied to determine the temperature distribution; thereby, the material properties based on temperature distribution are made available for thermal buckling and free vibration analysis. First-order shear deformation theory along with Fourier series expansion of the displacement variables in the circumferential direction are used to model the FGM shell. Numerical studies involved the understanding of the influence of the power-law index, r/h and l/r ratios on the critical buckling temperature. Free vibration studies of FGM shells under elevated temperature show that the fall in natural frequency is very drastic for the mode corresponding to the lowest natural frequency when compared to the lowest buckling temperature mode.     

Vibrations of segmented cylindrical shells by a fourier series component mode method

The vibrations of a multi-segment cylindrical shell with a common mean radius are studied. The shell is uniform for any segment but the material and geometric properties may vary from segment to segment. The solution is based on the component mode method coupled with Fourier series and Lagrange multipliers. It is shown that a single segment shell with boundary conditions of free support without tangential constraint is sufficient for an arbitrary shell with arbitrary boundary conditions. Results are presented for simply supported shells and clamped-free shells for two segments with different length and thickness.