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Showing papers on "Spherical shell published in 2020"


Journal ArticleDOI
TL;DR: In this article, the heat transfer in phase change materials (PCM) during constrained melting, unconstrained (unfixed) melting and solidification, and phase change in finned shells are analyzed.
Abstract: To date, numerous phase change materials (PCM) have been developed for application in latent heat storage systems. There are many issues in the process from the development of PCM to using them in storage systems, which should be resolved. The problem of heat transfer in PCMs during the phase change process is the most important one. Latent heat storage containers usually have simple geometrical forms such as a sphere, cylinder, cylindrical annulus, rectangular enclosure, etc. A large number of papers were published on melting and solidification processes in PCMs. Therefore, there is a pressing necessity for generalizing the art of the state in this field and establish how accumulated knowledge meets practical requirements. The present review considers the current state in investigations of heat transfer in a spherical shell. Heat transfer in PCMs during constrained melting (solid PCM fixed inside the vessel), unconstrained (unfixed) melting and solidification, and phase change in finned shells are analyzed. It is shown that currently, there is no satisfactory description of the constrained melting process. For unconstrained melting and solidification, some correlations are suggested, describing these processes. The applicability range of the proposed correlations, as well as their accuracy were investigated and established. To intensify the process of phase change inside the spherical container, the use of orthogonal fins is appropriate option compared to the employ of circumferential fins.

84 citations


Journal ArticleDOI
TL;DR: In this article, the authors address the localization of the deformation due to buckling that occurs immediately following the onset of bifurcation in the axisymmetric buckling of a perfect spherical elastic shell subject to external pressure.
Abstract: This paper addresses localization of the deformation due to buckling that occurs immediately following the onset of bifurcation in the axisymmetric buckling of a perfect spherical elastic shell subject to external pressure. The localization process is so abrupt that the buckling mode of the classical eigenvalue analysis, which undulates over the entire shell, becomes modified immediately after bifurcation transitioning to an isolated dimple surrounded by an unbuckled expanse of the shell. The paper begins by revisiting earlier attempts to analyze the initial post-buckling behavior of the spherical shell, illustrating their severely limited range of validity. The unsuccessful attempts are followed by an approximate Rayleigh-Ritz solution which captures the essence of the localization process. The approximate solution reveals the pathway that begins at bifurcation from the classical mode shape to the localized dimple buckle. The second part of the paper presents an exact asymptotic expansion of the initial post-buckling behavior which accounts for localization and which further exposes the analytic details of the abruptness of the transition.

40 citations


Journal ArticleDOI
TL;DR: In this article, a spherical stator multi-DOF ultrasonic motor using in-plane non-axisymmetric mode was proposed, which adopts the pair combination of three orthogonal in-planar non-axis symmetric modes to generate three types of elliptical motions at eight driving feet, which can rotate the rotor around X, Y and Z axes.

33 citations


Journal ArticleDOI
TL;DR: In this paper, a thin-walled shell-of-revolution assembly comprising a deep spherical shell dome axisymmetrically and tangentially joined to a steep-sided conical shell, the whole being a closed shell structure intended for stationary deployment beneath the surface of the sea in relatively shallow water.
Abstract: Thin shells are increasingly finding new applications under the sea. In this study, we consider a thin-walled shell-of-revolution assembly comprising a deep spherical shell dome (deeper than a hemisphere) axisymmetrically and tangentially joined to a steep-sided conical shell, the whole being a closed shell structure intended for stationary deployment beneath the surface of the sea in relatively shallow water. The closed shell structure, which might serve as an underwater observatory, is intended to operate at a constant depth, anchored to the seabed against flotation forces, with the thin steel shell walls being required to withstand the external hydrostatic pressure of the surrounding water. We use shell theory to investigate the discontinuity stresses that occur at the junction of the spherical shell and the conical shell, and employ FEM to explore the buckling behaviour of the thin shell. While discontinuity stresses are relatively small, they may influence the lower buckling modes of the shell, which are found to be largely confined to the region of the cone that is adjacent to the junction. Considerations are extended to a doubly-curved variant of the cone in the form of a paraboloid of revolution. As expected, double curvature enhances buckling capacity and also influences the mode shapes.

24 citations


Journal ArticleDOI
Ming Yang1, Shaoqiong Yang1, Yanhui Wang1, Yan Liang1, Shuxin Wang1, Lianhong Zhang1 
TL;DR: In this article, a multiple intersecting spheres (MIS) pressure hull is designed to provide neutral buoyancy for underwater gliders, based on which the optimization is carried out by combining the penalty function method (PFM) and multiple population genetic algorithm (MPGA).

23 citations


Journal ArticleDOI
TL;DR: In this paper, variable-stiffness composites offer opportunities to tune structural dynamic responses, such as mass and stiffness distribution, for thin-walled structures, and variable stiffness composites can be used to tune the structural dynamic response.
Abstract: The dynamic response of thin-walled structures is driven by mass and stiffness distribution. As such, variable-stiffness (VS) composites offer opportunities to tune structural dynamic responses. To...

22 citations


Journal ArticleDOI
TL;DR: In this article, a progressive analytical model of doubly curved shells is presented and applied to a delaminated spherical shell, where the equations are derived using an improved version of the Sanders shell theory and the System of Exact Kinematic Conditions (SEKC).
Abstract: The estimation of the critical buckling loads and eigenfrequencies are among the most common problems of mechanical engineering. These parameters are very important measures to avoid the loss of stability of the designed structures. In this work a progressive analytical model of doubly curved shells will be presented and applied to a delaminated spherical shell. The equations are derived using an improved version of the Sanders shell theory and the System of Exact Kinematic Conditions (SEKC). The solution method is based on the Levy formulation. With this method the governing partial differential equation (PDE) can be reduced to an ordinary differential equation (ODE) with the use of Fourier-series. The resulting set of equations are solved using a variant of the state-space method which is able to solve systems with non-constant system matrix.

19 citations


Journal ArticleDOI
TL;DR: In this article, the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain are characterized by the boundary local time on that subset.
Abstract: We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently proposed approach to express the joint probability density of the particle position and of its multiple boundary local times via a multi-dimensional Laplace transform of the conventional propagator satisfying the diffusion equation with mixed Robin boundary conditions. In the particular cases of an interval, a circular annulus and a spherical shell, this representation can be explicitly inverted to access the statistics of two boundary local times. We provide the exact solutions and their probabilistic interpretation for the case of an interval and sketch their derivation for two other cases. We also obtain the distributions of various associated first-passage times and discuss their applications.

19 citations


Journal ArticleDOI
TL;DR: In this paper, the authors presented the study of elastoplastic deformation in an orthotropic spherical shell subjected to a temperature gradient by using Seth's transition theory, and they used the transition theory to analyze the deformation of the shell.
Abstract: The objective of this research paper is to present the study of elastoplastic deformation in an orthotropic spherical shell subjected to a temperature gradient by using Seth’s transition theory. Se...

18 citations


Journal ArticleDOI
TL;DR: In this paper, nonlinear free vibrations of porous functionally graded (FG) annular spherical shell segments surrounded by elastic medium and reinforced by circumferential stiffeners are investigated for the first time.
Abstract: This article investigates nonlinear free vibrations of porous functionally graded (FG) annular spherical shell segments surrounded by elastic medium and reinforced by circumferential stiffeners. Po...

17 citations


Journal ArticleDOI
28 Jul 2020
TL;DR: In this article, the authors demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic liquid crystal (LC) shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127.
Abstract: When an orientationally ordered system, like a nematic liquid crystal (LC), is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically on how the LC is aligned in the shell. We demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic LC shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127. Deep in the nematic phase, the director (the average molecule orientation) is tangential to the interface, but upon approaching the temperature TNI of the nematic– isotropic transition, the director realigns to normal. We link this to a delicate interplay between an interfacial tension that is nearly independent of director orientation, and the configurationdependent elastic deformation energy of an LC confined in a shell. The process is primarily triggered by the heating-induced reduction of the nematic order parameter, hence realignment temperatures differ by several tens of degrees between LCs with high and low TNI , respectively. The temperature of realignment is always lower on the positive-curved shell outside than at the negative-curved inside, yielding a complex topological reconfiguration on heating. Complementing experimental investigations with mathematical modeling and computer simulations, we identify and investigate three different trajectories, distinguished by their configurations of topological defects in the initial tangential-aligned shell. Our results uncover a new aspect of the complex response of LCs to curved confinement, demonstrating that the order of the LC itself can influence the alignment and thereby the topology of the system. They also reveal the potential of amphiphilic block copolymer stabilizers for enabling continuous tunability of LC shell configuration, opening doors for in-depth studies of topological dynamics as well as novel applications in, e.g., sensing and programmed soft actuators.

Journal ArticleDOI
TL;DR: In this article, the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain are characterized by the boundary local time on that subset.
Abstract: We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently proposed approach to express the joint probability density of the particle position and of its multiple boundary local times via a multi-dimensional Laplace transform of the conventional propagator satisfying the diffusion equation with mixed Robin boundary conditions. In the particular cases of an interval, a circular annulus and a spherical shell, this representation can be explicitly inverted to access the statistics of two boundary local times. We provide the exact solutions and their probabilistic interpretation for the case of an interval and sketch their derivation for two other cases. We also obtain the distributions of various associated first-passage times and discuss their applications.

Journal ArticleDOI
TL;DR: It is shown that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvature can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e., a strengthening factor.
Abstract: In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e., a strengthening factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that nonmechanical stimuli can have on modifying the membrane state of stress in a thin shell.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the problem of tension of a spherical shell reinforced by a flexible coating and weakened by a meridional crack and determined the stressed state near the crack tip and the distribution of the hinge reaction over the coating.
Abstract: We study the problem of tension of a spherical shell reinforced by a flexible coating and weakened by a meridional crack. The coating is modeled by a hinge connecting the faces of the cut on one of the face surfaces of the shell. The stressed state near the crack tips and the distribution of the hinge reaction over the coating are determined by the method of singular integral equations. The limit state of the shell is analyzed with regard for the bounded strength of the coating.

Journal ArticleDOI
TL;DR: The proxy-SU(3) approximation within the shell model is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations as discussed by the authors.
Abstract: The Nilsson orbitals used in the substitutions occurring in the proxy-SU(3) scheme, which are the orbitals bearing the maximum value of total angular momentum in each shell, have an extremely simple structure in the shell model basis $$|N l j \Omega \rangle $$ , with each Nilsson orbital corresponding to a single-shell model eigenvector. This simple structure is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations. Nilsson 0[110] pairs are found to correspond to $$|1 1 1 0\rangle $$ pairs in the spherical shell model basis, paving the way for using the proxy-SU(3) approximation within the shell model.

Journal ArticleDOI
TL;DR: In this paper, a model describing the displacement of a linearly elastic flexural shell subjected to given dynamic loads from the computational point of view is presented, and the model under consideration is analyzed.
Abstract: In this paper, we study a model describing the displacement of a linearly elastic flexural shell subjected to given dynamic loads from the computational point of view. The model under consideration...

Journal ArticleDOI
TL;DR: In this article, an economical conformal subgridding scheme is proposed to model the object with concave and convex surfaces accurately, and double conforming procedure with coarse grid (CG) and fine grid (FG) guarantees the modeling accuracy.
Abstract: To model the object with concave and convex surfaces accurately, an economical conformal subgridding scheme is proposed in this article. Its double conforming procedure with coarse grid (CG) and fine grid (FG) guarantees the modeling accuracy. Fast linear interpolation effectively exchanges electromagnetic fields information on the interface between grids of two sizes. One-step leapfrog alternating direction implicit (ADI) finite-difference time-domain (FDTD) method overcomes the Courant stability condition in FG region; meanwhile, conventional FDTD ensures the efficiency of simulation in CG region. While we concern the unconditionally stable method, there is not any grid omitted in our irregularly profiled fine region and any extra time wasted in solving small-scale tridiagonal matrixes cell by cell. To verify our codes, a 2-D arc component has been simulated first. Then the performance of a probe-fed normal one-eighth spherical dielectric resonator antenna (DRA), a new designed conformal-microstrip-fed one-eighth spherical shell DRA, and a four-element array with the spherical shell DRAs connected by a T-shaped power divider has been calculated by our codes. Satisfactory performance of the antenna has been obtained in return loss and radiation patterns, which are verified by measured results. The shell antenna features smaller size, lighter weight, and more convenience in conforming to the corners of the instrument housing, even with different dimensions. Most particularly, the proposed conformal subgridding scheme and its hybrid FDTD implementation perform outstandingly in simulating the thin shell antenna in terms of computer memory, CPU time, as well as accuracy.

Journal ArticleDOI
TL;DR: The numerical tests reveal that the polar singularity problems do not occur for the magnetic quantity including the newly derived MC ‘inherit’ the same numerical properties as the corresponding gravitational functional.
Abstract: In recent years, the gravitational curvatures, the third-order derivatives of the gravitational potential (GP), of a tesseroid have been introduced in the context of gravity field modeling Analogous to the gravity field, magnetic field modeling can be expanded by magnetic curvatures (MC), the third-order derivatives of the magnetic potential (MP), which are the change rates of the magnetic gradient tensor (MGT) Exploiting Poisson’s relations between $$(n+1)$$ th-order derivatives of the GP and nth-order derivatives of the MP, this paper derives expressions for the MC of a uniformly magnetized tesseroid using the fourth-order derivatives of the GP of a uniform tesseroid expressed in terms of the Cartesian kernel functions Based on the magnetic effects of a uniform spherical shell, all expressions for the MP, magnetic vector (MV), MGT and MC of tesseroids have been examined for numerical problems due to singularity of the respective integral kernels (ie, near zone and polar singularity problems) For this, the closed analytical expressions for the MP, MV, MGT and MC of the uniform spherical shell have been provided and used to generate singularity-free reference values Varying both height and latitude of the computation point, it is found numerically that the near zone problem also exists for all magnetic quantities (ie, MP, MV, MGT and MC) The numerical tests also reveal that the polar singularity problems do not occur for the magnetic quantity as a result of the use of Cartesian as opposed to spherical integral kernels This demonstrates that the magnetic quantity including the newly derived MC ‘inherit’ the same numerical properties as the corresponding gravitational functional Possible future applications (eg, geophysical information) of the MC formulas of a uniformly magnetized tesseroid could be improved modeling of the Earth’s magnetic field by dedicated satellite missions

Journal ArticleDOI
TL;DR: In this article, the existence of stable and thin spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime has been shown.
Abstract: Shells of matter sources with zero thickness play an important role in both electromagnetism and general relativity. They provide a useful laboratory for the exploration of new phenomena while at the same time they approximate smooth solutions such as domain walls . Thin shells are also useful in describing gravitational collapse or in constructing spherically symmetric vacuum solutions that avoid the presence of singularities. We demonstrate the existence of static, stable and thin spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime. This provides us with an alternative to the well-known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In constrast, when it comes to the SRAdS spacetime, the repulsion that leads to stability of the shell comes from a negative Rindler term while the Schwarzschild and anti-de Sitter terms are attractive. We demonstrate the existence of such stable spherical shells for three cases of fluid shells with the appropriate equations of state, i.e. vacuum shell, stiff matter shell, and dust shell. To do so, we also identify the metric parameter conditions that need to be satisfied in order to have shell stability in each case. The vacuum stable shell solution in the SRAdS spacetime is consistent with previous studies by two of the authors that demonstrated the existence of stable spherical scalar field domain walls in the SRAdS spacetime.

Journal ArticleDOI
TL;DR: By combining Flugge's thin shell theory and energy method, a generalized approach to investigate vibration characteristic of truncated spherical shell subjected to various edge constraints is proposed in this article, where the truncated shell is devided into different sections along the meridian line, in which the displacement function of truncation along meridian and circumferential line are respectively represented by Jacobi polynomials and Fourier series.
Abstract: By means of combining Flugge's thin shell theory and energy method, a generalized approach to investigate vibration characteristic of truncated spherical shell subjected to various edge constraints is proposed. The truncated spherical shell is devided into different sections along the meridian line, in which the displacement function of truncated spherical shell along meridian and circumferential line are respectively represented by Jacobi polynomials and Fourier series. Various edge constraints can be simulated on the basis of virtual spring stiffness method in the current research. Finally, the solutions can be derived by meand of Ritz method. The dependability and exactness of current method have been proved by the comparison between current method, FEM and related literatures. The dimensionless frequency parameters of different truncated spherical shell under various edge constraints are displayed. In addition, the influence of geometric dimensions and boundary constraints on frequency parameters are also discussed.

Journal ArticleDOI
TL;DR: In this paper, experimental characterisation and modelling of micro-capsules for self-sensing polymer composites are presented, where Melamine-formaldehyde microcapsules were selected for this purpose.
Abstract: Results of experimental characterisation and modelling of mechanical behaviour of microcapsules for self-sensing polymer composites are presented Melamine–formaldehyde microcapsules were selected for this purpose The average diameter, size distribution, and shell thickness of microcapsules were evaluated from scanning electron microscopy images Compressive properties of the shell material were evaluated in several ways AFM measurements allowed estimating stiffness and strength of a single microcapsule In parallel, modelling of the mechanical behaviour of a single microcapsule was performed Buckling of a thin-walled spherical shell under external pressure was considered and closed-form solution in a linear statement was obtained The results of analytical calculations were compared with FEM modelling Two demonstrator thin-shells with the radius of centimetre scale, hollow and filled with water, were tested in compression between two rigid plates The results of their numerical analysis obtained by FEM models developed are in good agreement with experimental results

Journal ArticleDOI
TL;DR: Details of a mechanical design to improve walking performance and development of the QRoSS V prototype model are reported, which discusses the rising operation and performance of climbing over a high vertical step.
Abstract: We have proposed and developed a new quadruped walking robot with a spherical shell, called “QRoSS”. QRoSS is a transformable robot that can store its legs in the spherical shell. The shell not only absorbs external forces from all directions, but also improves mobile performance because of its round shape. In rescue operations at a disaster site, carrying robots into a site is dangerous for operators because doing so may result in a second accident. If QRoSS is used, instead of being carried in, robots are thrown in, making the operation safe and easy. We developed the QRoSS series and conducted basic experiments to verify performance, which includes landing, rising and walking through a series of movements. This paper reports details of a mechanical design to improve walking performance and development of the QRoSS V prototype model. We discuss the rising operation and performance of climbing over a high vertical step.

Book ChapterDOI
01 Jan 2020
TL;DR: In this article, a second-order Godunov-type finite volume method (FVM) to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time has been implemented into a numerical code.
Abstract: A second-order Godunov-type finite volume method (FVM) to advance the equations of single-fluid solar wind plasma magnetohydrodynamics (MHD) in time has been implemented into a numerical code. This code operates on a three-dimensional (3D) spherical shell with both non-staggered and staggered grids on the overlapping grid system with hexahedral cells of quadrilateral frustum type. By merging geometrical factors in spherical coordinates into the reformulation of fluxes, flux evaluation is made easy to achieve, and thus many numerical schemes with the total variation diminishing (TVD) slope limiters and approximate Roe solvers intended for Cartesian case can follow in the present context of spherical grid described here. At the same time, alternative strategies to ensure a solenoidal magnetic field, such as projection Poisson (PP) solver, hyperbolic divergence cleaning (HDC) method derived from generalized Lagrange multiplier (GLM) formulation of MHD system and constrained transport (CT) method, are employed. In this chapter, an FVM is described exemplarily on a six-component composite grid system by using a minmod limiter for oscillation control. Additionally, an implicit dual time-stepping technique is demonstrated to model the steady state solar wind ambient. Being of second order in space and time, this model is written in FORTRAN language with Message Passing Interface (MPI) parallelization, and validated in modeling the large-scale structure of solar wind from the Sun to Earth process (hereafter called Sun-to-Earth Process MHD model, also STEP-MHD model for brief). To demonstrate the suitability of our code for the simulation of solar wind ambient from the Sun to Earth, selected results from Carrington rotations (CR) during different solar activity phases are presented to show its capability of producing structured solar wind in agreement with observations.

Journal ArticleDOI
TL;DR: In this article, it was shown that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z projections of angular momenta and spin remain unchanged.
Abstract: The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit--Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.

Journal ArticleDOI
TL;DR: An analytical model is presented to calculate the low frequency magnetic shielding effective (SE) of the spherical shell with a circular aperture and finite conductivity, which shows that increasing the depth has similar effect on SE like reducing aperture radius.
Abstract: In this paper, an analytical model is presented to calculate the low frequency magnetic shielding effective (SE) of the spherical shell with a circular aperture and finite conductivity. This model is obtained by the combination of two submodels: the finite conductivity shell without the aperture, and the perfect conductor shell with the aperture. Both the submodels have existing analytical solutions. The first submodel represents the diffusion effect of magnetic field penetration through the conducting shell, and the second one denotes the aperture effect of magnetic field leakage through the aperture. The total magnetic field is the superposition of these from the two submodels. Calculation results are provided for an aluminum spherical shell of radius 0.1m for frequencies between 10Hz and 1MHz. The results are in good agreement with these form 2D axisymmetric finite element simulations. It is shown that there is a critical frequency. Below this frequency, the diffusion effect is dominant and the SE enhances with the increase of frequency. Above this frequency, the aperture effect is dominant and the SE keeps unchanged with the variation of frequency. In addition, the phase shift characteristics are also analyzed for the two effects respectively, and are employed to elucidate the mechanism of the resonance phenomenon of the SE around the critical frequency. Further, the effect of aperture depth is investigated numerically, which shows that increasing the depth has similar effect on SE like reducing aperture radius.

Journal ArticleDOI
TL;DR: In this paper, the authors consider a nonholonomic system that describes the rolling without slipping of a spherical shell inside which a frame rotates with constant angular velocity, and prove the absence of an additional integral in this system and the existence of chaotic trajectories.
Abstract: We consider a nonholonomic system that describes the rolling without slipping of a spherical shell inside which a frame rotates with constant angular velocity (this system is one of the possible generalizations of the problem of the rolling of a Chaplygin sphere). After a suitable scale transformation of the radius of the shell or the mass of the system the equations of motion can be represented as a perturbation of the integrable Euler case in rigid body dynamics. Using this representation, we explicitly calculate a Melnikov integral, which contains an isolated zero under some restrictions on the system parameters. Thereby we prove the absence of an additional integral in this system and the existence of chaotic trajectories. We conclude by presenting numerical experiments that illustrate the system dynamics depending on the behavior of the Melnikov function.


Journal ArticleDOI
TL;DR: In this paper, it was shown that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z projections of angular momenta and spin remain unchanged.
Abstract: The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit–Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x–y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.

Journal ArticleDOI
TL;DR: It was found that the surface morphology transitions from initial delamination sites and that the buckles propagate on the entire surface of the sphere, dependent on the surface strain distribution, i.e., radial strain and circumferential strain.
Abstract: This study aims to provide a fundamental understanding of the morphological transition of film buckling-delamination in an elastomeric bilayer spherical shell system. We developed an experimental system in which surface delamination buckles emerge because of biaxial compression of the elastomeric bilayer spherical shell driven by an air-pressured (pneumatic) device. A flat PDMS plate was first isotropically expanded and shaped into a hemisphere by air pressure. Subsequently, the hemisphere substrate was covered with a thin PDMS film. By releasing the air pressure, the substrate contracts and the outer film surface were subjected to biaxial compression; this resulted in various surface patterns of film buckling-delamination. It was found that the surface morphology transitions from initial delamination sites and that the buckles propagate on the entire surface of the sphere. This pattern formation is dependent on the surface strain distribution, i.e., radial strain and circumferential strain. In order to control the surface pattern, we systematically changed the material and system parameters such as film thickness, Young's modulus, and interfacial adhesion condition. In addition, finite element (FEM) computation was carried out to simulate the surface pattern and to elucidate the mechanism of buckling-delamination morphological transition.

Journal ArticleDOI
TL;DR: This paper examined the effect of a large lateral variation in heat flux at the outer boundary in cylindrical annulus experiments that achieve approximate geostrophy of the convection as well as in rapidly rotating spherical shell simulations.