Search Results (22)

The scattering problem of elastic waves impinging on periodic single and double arrays of parallel cylindrical defects is considered for isotropic materials. An analytic expression for the scattering matrix is obtained by means of the Lippmann–Schwinger formalism and analyzed in the long-wavelength approximation. It is proved that, for a specific curve in the space of physical and geometrical parameters, the scattering is dominated by resonances. The shear mode polarized parallel to the cylinders is decoupled from the other two polarization modes due to the translational symmetry along the cylinders. It is found that a relative mass density and relative Lamé coefficients of the scatterers give opposite contributions to the width of resonances in this mode. A relation between the Bloch phase and material parameters is found to obtain a global minimum of the width. The minimal width is shown to vanish in the leading order of the long wavelength limit for the single array. This new effect is not present in similar acoustic and photonic systems. The shear and compression modes in a plane perpendicular to the cylinders are coupled due to the normal traction boundary condition and have different group velocities. For the double array, it is proved that, under certain conditions on physical and geometrical parameters, there exist resonances with the vanishing width, known as Bound States in the Continuum (BSC). Necessary and sufficient conditions for the existence of BSC are found for any number of open diffraction channels. Analytic BSC solutions are obtained. Spectral parameters of BSC are given in terms of the Bloch phase and group velocities of the shear and compression modes. Full article

In this paper, we study inverse interface problems with unknown boundary conditions, using point observations for parabolic equations with cylindrical symmetry. In the one-dimensional, two-layer interface problem, the left interval $0<r<l_1$, i.e., the zero degeneracy, causes serious solution difficulty. For this, we investigate the well-posedness of the direct (forward) problem. Next, we formulate and solve five inverse boundary condition problems for the interface heat equation with cylindrical symmetry from internal measurements. The finite volume difference method is developed to construct second-order schemes for direct and inverse problems. The correctness of the proposed numerical solution decomposition algorithms for the inverse problems is discussed. Several numerical examples are presented to illustrate the efficiency of the approach. Full article

Sounding rockets constitute a class of rocket with a generally simple layout, being composed of a cylindrical center-body, a nosecone, a number of fins placed symmetrically around the longitudinal axis (usually three or four), and possibly a boat-tail. This type of flying craft is typically not actively controlled; instead, a passive stabilization effect is obtained through suitable positioning and sizing of the fins. Therefore, in the context of dynamic performance analysis, the margin of static stability is an index of primary interest. However, the classical approach to static stability analysis, which consists in splitting computations in two decoupled domains, namely, around the pitch and yaw axis, provides a very limited insight to the missile performance for this type of vehicle due to the violation of the classical assumptions of planar symmetry and symmetric flight conditions commonly adopted for winged aircraft. To tackle this issue, this paper introduces a method for analyzing static stability through a novel index, capable of more generally assessing the level of static stability for sounding rockets, exploiting the same information on aerodynamic coefficients typically required for more usual (i.e., decoupled) static stability analyses, and suggests a way to assess the validity and shortcoming of the method in each case at hand. Full article

The stability of astrophysical jets in the linear regime is investigated by presenting a methodology to find the growth rates of the various instabilities. We perturb a cylindrical axisymmetric steady jet, linearize the relativistic ideal magnetohydrodynamic (MHD) equations, and analyze the evolution of the eigenmodes of the perturbation by deriving the differential equations that need to be integrated, subject to the appropriate boundary conditions, in order to find the dispersion relation. We also apply the WKBJ approximation and, additionally, give analytical solutions in some subcases corresponding to unperturbed jets with constant bulk velocity along the symmetry axis. Full article

The solar sail spacecraft utilizing a hybrid approach of solar sail and solar electric propulsion in the heliocentric displaced orbit is affected by external disturbances, internal unmodeled dynamics, initial injection errors, and input saturation. To solve the station-keeping control problem under such complex conditions, an adaptive control strategy is proposed. First, the dynamical equations of the spacecraft utilizing hybrid low-thrust propulsion in the cylindrical coordinate system are derived. Second, the combined disturbance acceleration introduced by external disturbances and internal unmodeled dynamics is constructed, and a radial basis function neural network estimator is designed to estimate it online in real time. Third, an adaptive high-performance station-keeping controller based on an improved integral sliding surface and multivariate super-twisting sliding mode approaching law is designed. Then, stability analysis is conducted using Lyapunov theory, adaptive laws are designed, and the introduced virtual control accelerations are converted into actual control variables. Finally, simulations are conducted under different simulation conditions based on the disturbance sources. The results show that although the use of hybrid low-thrust propulsion breaks the symmetry of the solar sail in configuration, the proposed control strategy can effectively achieve the station-keeping and disturbance estimation of the spacecraft with only a small amount of propellant consumed and position tracking errors up to decimeters. Full article

A new approach is adopted to completely classify the Lagrangian associated with the static cylindrically symmetric spacetime metric via Noether symmetries. The determining equations representing Noether symmetries are analyzed using a Maple algorithm that imposes different conditions on metric coefficients under which static cylindrically symmetric spacetimes admit Noether symmetries of different dimensions. These conditions are used to solve the determining equations, giving the explicit form of vector fields representing Noether symmetries. The obtained Noether symmetry generators are used in Noether’s theorem to find the expressions for corresponding conservation laws. The singularity of the obtained metrics is discussed by finding their Kretschmann scalar. Full article

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. Full article

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 $\xi =ct-z$ 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 $\overrightarrow{z}$ of cylindrical symmetry. These results may help in drastically simplifying the study of extreme acceleration mechanisms of electrons. Full article

In recent years, structured laser beams for shaping inverse energy flow regions: regions with a direction of energy flow opposite to the propagation direction of a laser beam, have been actively studied. Unfortunately, many structured laser beams generate inverse energy flow regions with dimensions of the order of the wavelength. Moreover, there are significant limitations to the location of these regions. Here, we investigate the possibility of controlling inverse energy flow distributions by using the generalization of well-known cylindrical vector beams with special polarization symmetry—vector Lissajous beams (VLBs)—defined by two polarization orders (p, q). We derive the conditions for the indices (p, q) in order, not only to shape separate isolated regions with a reverse energy flow, but also regions that are infinitely extended along a certain direction in the focal plane. In addition, we show that the maximum intensity curves of the studied VLBs are useful for predicting the properties of focused beams. Full article

Two mass-accommodation methods are proposed to describe the melting of paraffin wax used as a phase-change material in a centrally heated annular region. The two methods are presented as models where volume changes produced during the phase transition are incorporated through total mass conservation. The mass of the phase-change material is imposed as a constant, which brings an additional equation of motion. Volume changes in a cylindrical unit are pictured in two different ways. On the one hand, volume changes in the radial direction are proposed through an equation of motion where the outer radius of the cylindrical unit is promoted as a dynamical variable of motion. On the other hand, volume changes along the axial symmetry axis of the cylindrical unit are proposed through an equation of motion, where the excess volume of liquid constitutes the dynamical variable. The energy–mass balance at the liquid–solid interface is obtained according to each method of conceiving volume changes. The resulting energy–mass balance at the interface constitutes an equation of motion for the radius of the region delimited by the liquid–solid interface. Subtle differences are found between the equations of motion for the interface. The differences are consistent with mass conservation and local mass balance at the interface. Stationary states for volume changes and the radius of the region delimited by the liquid–solid interface are obtained for each mass-accommodation method. We show that the relationship between these steady states is proportional to the relationship between liquid and solid densities when the system is close to the high melting regime. Experimental tests are performed in a vertical annular region occupied by a paraffin wax. The boundary conditions used in the experimental tests produce a thin liquid layer during a melting process. The experimental results are used to characterize the phase-change material through the proposed models in this work. Finally, the thermodynamic properties of the paraffin wax are estimated by minimizing the quadratic error between the temperature readings within the phase-change material and the temperature field predicted by the proposed model. Full article

In this paper, the scattering of a plane wave from a lossy Fabry–Perót resonator, realized with two equiaxial thin resistive disks with the same radius, is analyzed by means of the generalization of the Helmholtz–Galerkin regularizing technique recently developed by the author. The disks are modelled as 2-D planar surfaces described in terms of generalized boundary conditions. Taking advantage of the revolution symmetry, the problem is equivalently formulated as a set of independent systems of 1-D equations in the vector Hankel transform domain for the cylindrical harmonics of the effective surface current densities. The Helmholtz decomposition of the unknowns, combined with a suitable choice of the expansion functions in a Galerkin scheme, lead to a fast-converging Fredholm second-kind matrix operator equation. Moreover, an analytical technique specifically devised to efficiently evaluate the integrals of the coefficient matrix is adopted. As shown in the numerical results section, near-field and far-field parameters are accurately and efficiently reconstructed even at the resonance frequencies of the natural modes, which are searched for the peaks of the total scattering cross-section and the absorption cross-section. Moreover, the proposed method drastically outperforms the general-purpose commercial software CST Microwave Studio in terms of both CPU time and memory occupation. Full article

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of modern physics, astrophysics, and cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the general relativity and quantum field theories, and all that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D universe’s expansion and its following acceleration. Full article

This paper presents a new type of 2-DOF single-loop mechanism inspired by the Sarrus mechanism, and it utilizes this mechanism to construct 2-DOF cylindrical deployable mechanisms. First, the motion pattern of the single-loop mechanism is analyzed utilizing screw theory. According to the structural symmetries, the cylindrical deployable mechanisms are constructed through the linear pattern combination and circular pattern combination of the single-loop mechanisms. After the geometrical analysis and interference condition analysis, the axial, circumferential and area magnification ratios are defined and, furthermore, applied to the parameter optimization of the deployable mechanisms, forming an example surface. Finally, a simplified 1-DOF single-loop mechanism is derived from the proposed 2-DOF mechanism, which is used to construct 1-DOF cylindrical deployable mechanisms with singular free workspaces. Full article

In this paper, a solution is provided to solve the heat conduction equation in the three-dimensional cylinder region, where the laser intensity of the material irradiation surface is expressed as a Gaussian distribution. Based on the symmetry of heat distribution, firstly, the form of the heat equation in the common rectangular coordinate system is changed to another form in the two-dimensional cylindrical coordinate system. Secondly, the ADI with the backward Euler method and with Crank–Nicolson method are established to discretize the model in the cylindrical coordinate system, after which the simulation results are obtained, where the first kind of boundary value condition is used to verify the accuracy of these two algorithms. Then, the above two methods are used to solve the model with the third kind of boundary value condition. Finally, the comparison is performed with the results obtained by the MATLAB’s PDETOOL, which shows that the solution is more feasible and efficient. Full article

Background: The primary stability is a determinant clinical condition for the success of different dental implants macro-design in different bone density using a validated and repeatable in vitro technique employing solid rigid polyurethane blocks. Materials and Methods: Five implants 3.8 × 13 mm² for each macro-design (i.e., IK—tapered; IC—cylindric; and IA—active blade shape) were positioned into 20- and 30- pounds per cubic foot (PCF) polyurethane blocks. Bucco-lingual (BL) and mesial-distal (MD) implant stability quotient score (ISQ) was assessed by resonance frequency analysis while, insertion/removal torques were evaluated by dynamometric ratchet. Results: IC implants shown better primary stability in terms of ISQ compared to IA and IK in lower density block (20 PCF), while IK was superior to IA in higher density (30 PCF). IC shown higher removal torque in 30-PCF compared to IA and IC. Conclusions: The study effectiveness on polyurethane artificial bone with isotropic symmetry structure showed that the implants macro-design might represent a key factor on primary stability, in particular on low-density alveolar bone. Clinicians should consider patients features and implant geometry during low-density jaws rehabilitation. Further investigations are needed to generalize these findings. Full article