Cylindrical Symmetry Research Articles

A Second-order Modified Ghost Fluid Method (2nd-MGFM) with Discontinuous Galerkin Method for 1-D compressible Multi-medium Problem with Cylindrical and Spherical Symmetry

A Second-order Modified Ghost Fluid Method (2nd-MGFM) with Discontinuous Galerkin Method for 1-D compressible Multi-medium Problem with Cylindrical and Spherical Symmetry

Three-Dimensional Coordinate Extraction Based on Radargrammetry for Single-Channel Curvilinear SAR System

With the rapid development of high-resolution synthetic aperture radar (SAR) systems, the technique that utilizes multiple two-dimensional (2-D) SAR images with different view angles to extract three-dimensional (3-D) coordinates of targets has gained wide concern in recent years. Unlike the traditional multi-channel SAR utilized for 3-D coordinate extraction, the single-channel curvilinear SAR (CLSAR) has the advantages of large variation of view angle, requiring fewer acquisition data, and lower device cost. However, due to the complex aerodynamic configuration and flight characteristics, important issues should be considered, including the mathematical model establishment, imaging geometry analysis, and high-precision extraction model design. In this paper, to address these challenges, a 3-D vector model of CLSAR was presented and the imaging geometries under different view angles were analyzed. Then, a novel 3-D coordinate extraction approach based on radargrammetry was proposed, in which the unique property of the SAR system, called cylindrical symmetry, was utilized to establish a novel extraction model. Compared with the conventional approach, the proposed one has fewer constraints on the trajectory of radar platform, requires fewer model parameters, and can obtain higher extraction accuracy without the assistance of extra ground control points (GCPs). Numerical results using simulated data demonstrated the effectiveness of the proposed approach.

Underexpanded gas jets of Mach 2: the changing physical structure and power transmission

ABSTRACT Supersonic jets with excess gas pressure are associated with many phenomena including radio galaxies, protostars, volcanic plumes, rocket exhausts, and champagne cork popping. Some common properties are derived here based on steady uniform hydrodynamic flow from a circular orifice. We present a systematic numerical study over a wide range of parameters for Mach 2 jets, concentrating on simulations of jets with pressures exceeding the ambient pressure. With cylindrical symmetry, we show how the location of the stand-off and following downstream shocks depend not only on the overpressure but also on the density due to a feedback loop, which results in an oscillatory flow pattern. We conclude that rapidly varying and gradually evolving shock patterns arise even from steady uniform jets. This can take the form of turbulent plumes at high overpressures and regular oscillations at low overpressures. We identify where this screeching contributes to noise and sound wave generation, which may aid the regulation of star and galaxy formation. However, the main effect for such low Mach number jets is to drive a circulatory motion in which the ambient medium is driven out along the axial direction while mass and energy flow laterally inwards, setting up a large advection pattern. Once the initial bow shock has propagated out, the noise from the jet is insufficient to significantly alter the environment. High Mach number jets do not follow these conclusions and will be treated separately.

Electromagnetic waves in lossy conductive media: cylindrical and spherical symmetry cases

It was recently demonstrated that surface electromagnetic waves can propagate inside stratified lossy conductive media. Here we consider electromagnetic waves in lossy conductive media in the cylindrical and spherical symmetry cases. We demonstrate that low loss electromagnetic waves may also propagate along cylindrical channels inside lossy media. Applications of these cylindrical waves may include active communication through plasma, search for underground cables, and propagation of electromagnetic signals along bones and nerves inside biological tissues. On the other hand, consideration of the spherical symmetry case indicates the possibility of deeply subwavelength ‘hot spots’ inside highly lossy biological tissues.

Using Cylindrical and Spherical Symmetries in Numerical Simulations of Quasi-Infinite Mechanical Systems

The application of cylindrical and spherical symmetries for numerical studies of many-body problems is presented. It is shown that periodic boundary conditions corresponding to formally cylindrical symmetry allow for reducing the problem of a huge number of interacting particles, minimizing the effect of boundary conditions, and obtaining reasonably correct results from a practical point of view. A physically realizable cylindrical configuration is also studied. The advantages and disadvantages of symmetric realizations are discussed. Finally, spherical symmetry, which naturally realizes a three-dimensional system without boundaries on its two-dimensional surface, is studied. As an example, tectonic dynamics are considered, and interesting patterns resembling real ones are found. It is stressed that perturbations of the axis of planet rotation may be responsible for the formation of such patterns.

Hydrodynamic Impacts of Short Laser Pulses on Plasmas

We determine conditions allowing for simplification of the description of the impact of a short and arbitrarily intense laser pulse onto a cold plasma at rest. If both the initial plasma density and pulse profile have plane symmetry, then suitable matched upper bounds on the maximum and the relative variations of the initial density, as well as on the intensity and duration of the pulse, ensure a strictly hydrodynamic evolution of the electron fluid without wave-breaking or vacuum-heating during its whole interaction with the pulse, while ions can be regarded as immobile. We use a recently developed fully relativistic plane model whereby the system of the Lorentz–Maxwell and continuity PDEs is reduced into a family of highly nonlinear but decoupled systems of non-autonomous Hamilton equations with one degree of freedom, the light-like coordinate ξ=ct−z instead of time t as an independent variable, and new a priori estimates (eased by use of a Liapunov function) of the solutions in terms of the input data (i.e., the initial density and pulse profile). If the laser spot radius R is finite and is not too small, the same conclusions hold for the part of the plasma close to the axis z→ of cylindrical symmetry. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons.

Service Limits for Metal Oxide Varistors Having Cylindrical Symmetry as Function of the Ambient Temperature

This article presents an original experimental method applied to assess the stability limits of a given Metal Oxide Varistor (MOV), with cylindrical symmetry (cylinder or disk shape), as a direct relation between the ambient temperature and the service rated voltage, in the permanent operational regime. As the crossing current of a certain varistor is heavily influenced by its physical temperature, we must find an empirical relationship between these two parameters for a symmetrical configuration. Each ambient temperature can increase the temperature reference and any higher voltage will also produce an increased current, causing a uncontrolled runaway heating process, in an avalanche model. We tried to eliminate any references to technical dimensions or device values, focusing on material parameters. In the case of a symmetric MOV, we will consider the load coefficient, which is the ratio between the service DC voltage and the nominal DC opening voltage. By using experimental measurements and a simple mathematical model, we will establish the relation between the critical load coefficient and the ambient temperature in the case of symmetrical MOVs. This procedure could be applied to the design of more performant and safe surge arrester devices using existing MOVs, for all voltage levels and symmetrical configurations.

Efficient and Accurate Modeling of the Surface Deflection of Thin Layers on Composite Substrates with Applications to Piezoelectric Parameter Measurements

The electrical and mechanical response of multilayered structures involving a piezoelectric layer and bull’s eye shaped electrodes is investigated. A boundary element method is employed based on spectral domain Green’s functions. With this method, the electric field distribution is determined first, and the local mechanical displacement in a second step. As will be shown, this allows us to exploit cylindrical symmetry for the electric surface charge distribution, but not for the vertical surface displacements. The effect of substrate bending due to in plane-stress, introduced by the piezoelectric constant d31, and the benefits of using bull’s eye electrode geometries with thick metallic backplates intended to reduce this effect are studied. A rigorous analysis and a largely simplified, but accurate approximation are compared. The application of this technique is demonstrated on a practical example for highly efficient and accurate determination of selected piezoelectric coefficients from surface topography measurements on such structures.

Moment constraints in beams with discrete and continuous rotational symmetry

This study presents a general analysis of how the transverse rotational symmetry of a beam imposes equality constraints among transverse beam moments. Efficient analytic methods are developed to derive symmetry-imposed constraints among $k$th order moments in beams with continuous or $n$-fold rotational symmetry for arbitrary $k$ and $n$. The formalism also enables one to construct symmetry arguments based on how discrete and continuous rotational symmetries manifest themselves differently in terms of beam moments. Three case studies on beams with continuous, twofold, and threefold rotational symmetries are conducted. We prove that, regardless of their triangulation, beams with threefold rotational symmetry (e.g., from electron cyclotron resonance ion source) always have the same rms properties as beams with cylindrical symmetry. These counterintuitive results derived purely from symmetry considerations have clarified beam dynamics at the Facility for Rare Isotope Beams.

Evolution of weak shock waves in non-ideal magnetogasdynamics

Abstract In this article, a study concerning the growth and decay of weak shock waves in non-ideal magnetogasdynamic regime has been performed. One-dimensional plane and cylindrical symmetries are assumed. The flow medium is considered as a perfectly conducting non-ideal gas permeated with either axial or azimuthal magnetic field. The Generalized Wavefront Expansion (GWE) method used in this work provides a system of coupled non-linear transport equations which completely describe the evolution of weak shocks and first order discontinuities induced behind it. The solution obtained during the process agrees with the classical decay laws for weak shocks. A general criterion for steepening of compressive waves and flattening of expansion waves has been derived. Further, the effect of geometrical spreading, magnetic field, and non-idealness of the gas on steepening or flattening of waves is discussed and illustrated via figures. Also, a comparison between growth and decay of weak shocks in ideal and non-ideal magnetogasdynamic regimes has been made. It has been observed during the study that all compressive waves evolve into shock regardless of their initial strength, and expansive waves decay and damp out eventually.

Ambipolar diffusion: Self-similar solutions and MHD code testing

Context. Ambipolar diffusion is a process occurring in partially ionised astrophysical systems that imparts a complicated mathematical and physical nature to Ohm’s law. The numerical codes that solve the magnetohydrodynamic (MHD) equations have to be able to deal with the singularities that are naturally created in the system by the ambipolar diffusion term. Aims. The global aim is to calculate a set of theoretical self-similar solutions to the nonlinear diffusion equation with cylindrical symmetry that can be used as tests for MHD codes which include the ambipolar diffusion term. Methods. First, following the general methods developed in the applied mathematics literature, we obtained the theoretical solutions as eigenfunctions of a nonlinear ordinary differential equation. Phase-plane techniques were used to integrate through the singularities at the locations of the nulls, which correspond to infinitely sharp current sheets. In the second half of the paper, we consider the use of these solutions as tests for MHD codes. To that end, we used the Bifrost code, thereby testing the capabilities of these solutions as tests as well as (inversely) the accuracy of Bifrost’s recently developed ambipolar diffusion module. Results. The obtained solutions are shown to constitute a demanding, but nonetheless viable, test for MHD codes that incorporate ambipolar diffusion. Detailed tabulated runs of the solutions have been made available at a public repository. The Bifrost code is able to reproduce the theoretical solutions with sufficient accuracy up to very advanced diffusive times. Using the code, we also explored the asymptotic properties of our theoretical solutions in time when initially perturbed with either small or finite perturbations. Conclusions. The functions obtained in this paper are relevant as physical solutions and also as tests for general MHD codes. They provide a more stringent and general test than the simple Zeldovich-Kompaneets-Barenblatt-Pattle solution.

On the non-isentropic compressible Navier–Stokes equations with cylindrical symmetry: boundary layers and convergence rate at vanishing shear viscosity

On the non-isentropic compressible Navier–Stokes equations with cylindrical symmetry: boundary layers and convergence rate at vanishing shear viscosity

Observable effect of quantized cylindrical gravitational waves

We investigate the response of a model gravitational wave detector consisting of two particles to the quantized cylindrical gravitational waves and obtain a relation between the standard deviation of the distance between two particles and the distance from the source to the detector. It is found that the quantum effect carried by the cylindrical gravitational wave can be observed above Planck scale even though the source is as far as the cosmological horizon. The equation of motion for the change of the distance between two particles is obtained when the cylindrical gravitational waves pass. It is surprising that the dissipative term does not exist up to the first order approximation due to cylindrical symmetry of the gravitational wave.

Graphical translators for anisotropic and crystalline mean curvature flow

In this paper we discuss existence, uniqueness and some properties of a class of solitons to the anisotropic mean curvature flow, i.e., graphical translators, either in the plane or under an assumption of cylindrical symmetry on the anisotropy and the mobility. In these cases, the equation becomes an ordinary differential equation, and this allows to find explicitly the translators and describe their main features.

Confinement-deconfinement temperature for a rotating quark-gluon plasma

Non-central heavy ion collisions lead to the production of a quark gluon plasma with angular momentum. We investigate, using holographic AdS/QCD models, how does rotation of the medium affects the confinement/deconfinement transition temperature $T_c$. In holographic models, this transition is represented by a Hawking-Page process involving two asymptotically anti-de Sitter spaces. The plasma is represented here by extending the holographic approach to anti-de Sitter spaces with cylindrical symmetry. Then, the rotation of the medium is introduced through a Lorentz boost. We consider hard and soft wall AdS/QCD models. In both cases we find it out that, as the rotational velocity $v$ increases, $T_c$ decreases, following the expression $T_c(v) = T_c(0)/\gamma(v)$, where $\gamma(v)$ is the Lorentz factor.

Optimal orientation detection of an anisotropic dipolar scatterer

The angular orientation of an anisotropic scatterer with cylindrical symmetry in a linearly polarized light field represents an optomechanical librator. Here, we propose and theoretically analyze an optimal measurement scheme for the two angular degrees of freedom of such a librator. The imprecision-backaction product of this scheme reaches the Heisenberg uncertainty limit. Furthermore, we propose and analyze a realistic measurement scheme and show that, in the absence of spinning motion around the symmetry axis, measurement-based ground-state cooling of the rotational degrees of freedom of an anisotropic point scatterer levitated in an optical trap is feasible.

Fast, semianalytical approach to obtain the stray magnetic field above a magnetic skyrmion

We present a fast, matrix-based semianalytical method to calculate the stray magnetic field and its derivative above spin textures with cylindrical symmetry. A magnetostatic Green's function approach is used to obtain accurate fields and magnetic forces, which are confirmed using micromagnetic simulations. The developed method can be used to quickly analyze and fit experimental measurements of the stray magnetic field (measured, for example, via nitrogen vacancies in diamond) or magnetic forces (measured via magnetic force microscopy) above a thin film or patterned element. Calculations for magnetic skyrmions show that these techniques have the potential to distinguish between Bloch and N\'eel walls for skyrmions in single-layer as well as in multilayer thin films where the wall structure evolves with depth.

The toroidal dipole operator in nanostructures

The parity violation in nuclear reactions led to the discovery of the new class of toroidal multipoles. Since then, it was observed that toroidal multipoles are present in the electromagnetic structure of systems at all scales, from elementary particles, to solid state systems and metamaterials. The toroidal dipole T (the lowest order multipole) is the most common. In quantum systems, this corresponds to the toroidal dipole operator Tˆ, with the projections Tˆi (i=1,2,3) on the coordinate axes. Here we analyze a quantum particle in a system with cylindrical symmetry, which is a typical system in which toroidal moments appear. We find the expressions for the Hamiltonian, momenta, and toroidal dipole operators in adequate curvilinear coordinates, which allow us to find analytical expressions for the eigenfunctions of the momentum operators. While the toroidal dipole is hermitian, it is not self-adjoint, but in the new set of coordinates the operator Tˆ3 splits into two components, one of which is (only) hermitian, whereas the other one is self-adjoint. The self-adjoint component is the one that is physically significant and represents an observable. Furthermore, we numerically diagonalize the Hamiltonian and the toroidal dipole operator and find their eigenfunctions and eigenvalues. We write the partition function and calculate the thermodynamic quantities for a system of ideal particles on a torus. Besides proving that the toroidal dipole is self-adjoint and therefore an observable, such systems open up the possibility of making metamaterials that exploit the quantization and the quantum properties of the toroidal dipoles.

A study of the optical resonances of various nanostructured silver systems with cylindrical symmetry

In the present work, the optical resonances of different silver nanoparticle systems with cylindrical symmetry are studied by using the COMSOL Multiphysics® professional package. The purpose of the research is to analyze the dependence of optical resonances on the geometry. We found a strong dependence between plasmons and geometry.

Comparison between Cylindrical, Trigonal, and General Symmetry Models for the Analysis of Polarization-Dependent Second Harmonic Generation Measurements Acquired from Collagen-Rich Equine Pericardium Samples

Polarization-dependent second harmonic generation (PSHG) microscopy is used as an innovative, high-resolution, non-destructive, and label-free diagnostic imaging tool to elucidate biological issues with high significance. In the present study, information on the structure and directionality of collagen fibers in equine pericardium tissue was collected using PSHG imaging measurements. In an effort to acquire precise results, three different mathematical models (cylindrical, trigonal, and general) were applied to the analysis of the recorded PSHG datasets. A factor called the “ratio parameter” was calculated to provide quantitative information. The implementation of the trigonal symmetry model to the recorded data led to the extraction of improved results compared with the application of the widely used cylindrical symmetry model. The best outcome was achieved through the application of the general model that does not include any kind of symmetry for the data processing. Our findings suggest that the trigonal symmetry model is preferable for the analysis of the PSHG datasets acquired from the collagenous tissues compared with the cylindrical model approach although an increased computational time is required.