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In this paper, we investigate the analytical solutions to the cylindrically symmetric compressible Navier–Stokes equations with density-dependent viscosity and vacuum free boundary. The shear and bulk viscosity coefficients are assumed to be a power function of the density and a positive constant, respectively, and the free boundary is assumed to move in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. We obtain a global analytical solution by using some ansatzs and reducing the original partial differential equations into a nonlinear ordinary differential equation about the free boundary. The free boundary is shown to grow at least sub-linearly in time and not more than linearly in time for the analytical solution by using a new averaged quantity. [ABSTRACT FROM AUTHOR]

In this paper, we study the analytical solutions to the compressible Euler equations with cylindrical symmetry and free boundary. We assume that the free boundary is moving in the radial direction with the radial velocity, which will affect the angular velocity but does not affect the axial velocity. By using some ansatzs, we reduce the original partial differential equations into an ordinary differential equation about the free boundary. We prove that the free boundary grows linearly in time by constructing some new physical functionals. Furthermore, the analytical solutions to the compressible Euler equations with time-dependent damping are also considered and the spreading rate of the free boundary is investigated according to the various sizes of the damping coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we consider Einstein–Hilbert gravity in the presence of cosmological constant with cylindrical symmetry to introduce the black hole solution of this model. Here, we solve the Einstein's vacuum field equation, and then we calculate the appropriate metric for this problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weighted integral system with negative exponents on the upper half space $ \mathbb{R}^{n+1}_+ $ as follows$ \begin{equation*} \begin{cases} u(X) = \displaystyle{\int}_{\mathbb{R}^{n+1}_+}\frac{f(u, v)(Y)}{t^\alpha z^\beta|X-Y|^\lambda}dY, &X\in\mathbb{R}^{n+1}_+, \\ v(X) = \displaystyle{\int}_{\mathbb{R}^{n+1}_+}\frac{g(u, v)(Y)}{ t^\beta z^\alpha|X-Y|^\lambda}dY, &X\in\mathbb{R}^{n+1}_+, \end{cases} \end{equation*} $where $ \alpha, \beta\le0 $, $ \lambda<0 $ and $ X = (x, t), \, Y = (y, z). $ Under the natural conditions on $ f $ and $ g $, we obtain the classification and symmetry of positive solutions by the method of moving spheres in integral forms. Moreover, we generalize our results to integral system on $ \mathbb{R}^{n+m} $. [ABSTRACT FROM AUTHOR]

We look for multiple solutions U: R³ → R³ to the curl-curl problem \nabla \times \nabla \times U = h(x,U), x \in R³, with a nonlinear function h: R³ \times R³ → R³ which is critical in R³, i.e., h(x,U) = | U| 4U, or has subcritical growth at infinity. If h is radial in U and α = 1 below, then we show that the solutions to the problem above are in one-to-one correspondence with the solutions to the following Schrödinger equation: Δ u + a r² u = f(x,u), u: R³ → R, where x = (y, z) Є R² × R, r = | y|, and α ≥ 0. In the critical case, the multiplicity problem for the latter equation has been studied only in the autonomous case α = 0 and the available methods seem to be insufficient for the problem involving the singular potential, i.e., α = 0, due to the lack of conformal invariance. Therefore we develop methods for the critical curl-curl problem and show the multiplicity of bound states for both equations. In the subcritical case, instead, studying the Schrβdinger equation in higher dimensions, we find infinitely many bound states for both problems. [ABSTRACT FROM AUTHOR]

Cylindrically symmetric cholesteric liquid crystal elastomer (CLCE) fibers templated by tubular confinement are reported, displaying mechanochromic, thermochromic, and thermomechanical responses. The synthesis inside a sacrificial tube secures radial orientation of the cholesteric helix, and the ground state retroreflection wavelength is easily tuned throughout the visible spectrum or into the near‐infrared by varying the concentration of a chiral dopant. The fibers display continuous, repeatable, and quantitatively predictable mechanochromic response, reaching a blue shift of more than −220 nm for 180% elongation. The cylindrical symmetry renders the response identical in all directions perpendicular to the fiber axis, making them exceptionally useful for monitoring complex strains, as demonstrated in revealing local strain during tying of different knots. The CLCE reflection color can be revealed with high contrast against any background by taking advantage of the circularly polarized reflection. Upon heating, the fibers respond—fully reversibly—with red shift and radial expansion/axial contraction. However, there is no transition to an isotropic state, confirming a largely forgotten theoretical prediction by de Gennes. These fibers and the easy way of making them may open new windows for large‐scale application in advanced wearable technology and beyond. [ABSTRACT FROM AUTHOR]

In this paper, we present a static solution for the five-dimensional Einstein–Gauss–Bonnet (EGB) gravitational field equations with a cylindrical symmetry and an anisotropic fluid as a source. We consider whole set of equations in the interior space which sourced by static cylindrical anisotropic fluid and junction conditions required for smoothly matching with exterior space which is a cylindrical vacuum solution of five dimensional EGB equation. We achieve density and pressures as functions of cylindrical radial coordinate and give some graphically analysis under numerical solution. [ABSTRACT FROM AUTHOR]

We propose a method of analysis of spontaneous emission of a quantum emitter (an atom, a luminescence center, a quantum dot) inside or in vicinity of a cylinder. At the focus of our method are analytical expressions for the scattering matrix of the cylindrical nanoobject. We propose the approach to electromagnetic field quantization based of eigenvalues and eigenvectors of the scattering matrix. The method is applicable for calculation and analysis of spontaneous emission rates and angular dependences of radiation for a set of different systems: semiconductor nanowires with quantum dots, plasmonic nanowires, cylindrical hollows in dielectrics and metals. Relative simplicity of the method allows obtaining analytical and semi-analytical expressions for both cases of radiation into external medium and into guided modes.

Unlike the traditional multichannel synthetic aperture radar (SAR) 3-D reconstruction technology, the single-channel SAR with two synthetic apertures in the vertical and horizontal planes, realized by curved trajectory, has the advantages of requiring less acquisition data, lower device cost, and fewer limitations on trajectories. However, due to the complex aerodynamic configuration and flight characteristics, critical challenges are faced, including the mathematical model establishment, signal property analyses, and reconstruction approach design. In this article, to address these issues, a 3-D vector geometry model of the curvilinear SAR (CLSAR) system is presented and its properties, including elevation bandwidth and resolution, are studied in detail. Then, a novel 3-D reconstruction approach for a single-channel CLSAR system based on azimuth prefocusing is presented, in which the cylindrical symmetry of the SAR system is utilized to provide accurate azimuth information of targets in observing scenes. With the assisted azimuths, the scene imaged in the vertical plane can be performed, and the 3-D reconstruction of interested targets can be obtained. Numerical results using simulated data demonstrate the effectiveness of the proposed approach.

Applying a simple harmonic map method to the cylindrically symmetric Einstein-Maxwell system, we obtain exact solutions representing strong nonlinear interaction between gravitational waves and electromagnetic waves in the case without any background field. As an interesting fact, we can show that with adjusted parameters the solution represents occurrences of large conversion phenomena in the intense region of fields near the cylindrically symmetric axis. [ABSTRACT FROM AUTHOR]

Abstract Cylindrically symmetric cholesteric liquid crystal elastomer (CLCE) fibers templated by tubular confinement are reported, displaying mechanochromic, thermochromic, and thermomechanical responses. The synthesis inside a sacrificial tube secures radial orientation of the cholesteric helix, and the ground state retroreflection wavelength is easily tuned throughout the visible spectrum or into the near‐infrared by varying the concentration of a chiral dopant. The fibers display continuous, repeatable, and quantitatively predictable mechanochromic response, reaching a blue shift of more than −220 nm for 180% elongation. The cylindrical symmetry renders the response identical in all directions perpendicular to the fiber axis, making them exceptionally useful for monitoring complex strains, as demonstrated in revealing local strain during tying of different knots. The CLCE reflection color can be revealed with high contrast against any background by taking advantage of the circularly polarized reflection. Upon heating, the fibers respond—fully reversibly—with red shift and radial expansion/axial contraction. However, there is no transition to an isotropic state, confirming a largely forgotten theoretical prediction by de Gennes. These fibers and the easy way of making them may open new windows for large‐scale application in advanced wearable technology and beyond.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we study the free boundary problem of an inviscid two-phase model, where we take the pressure function as P (n , ρ) = ρ γ + n α (γ > 1 , α ≥ 1) with n and ρ being the densities of two phases. First, we construct some self-similar analytical solutions for the N -dimensional radially symmetric case by using some ansatzs, and investigate the spreading rate of the free boundary by using the method of averaged quantities. Second, we extend the results of the N -dimensional radially symmetric case to the three-dimensional cylindrically symmetric case. Third, we present some analytical solutions for the three-dimensional cylindrically symmetric model with a Coriolis force. From the analytical solutions constructed in this paper, we find that the Coriolis force can prevent the free boundary from spreading out infinitely. [ABSTRACT FROM AUTHOR]

We consider the initial-boundary value problem for the non-isentropic compressible Navier–Stokes equations with cylindrical symmetry in three dimensions. It is well known that boundary layers present when the shear viscosity vanishes. In this paper, we derive the explicit boundary layer equations of Prandtl type for each boundary with heat conductivity coefficient dependent on temperature or as a constant. Furthermore, we improve the convergence rate of the vanishing shear viscosity to O (ϵ 5 16) without any smallness assumptions for the initial and boundary data. [ABSTRACT FROM AUTHOR]

In this short review, we present some recently obtained traversable wormhole models in the framework of general relativity (GR) in four and six dimensions that somehow widen our common ideas on wormhole existence and properties. These are, first, rotating cylindrical wormholes, asymptotically flat in the radial direction and existing without exotic matter. The topological censorship theorems are not violated due to lack of asymptotic flatness in all spatial directions. Second, these are cosmological wormholes constructed on the basis of the Lemaître–Tolman–Bondi solution. They connect two copies of a closed Friedmann world filled with dust, or two otherwise distant parts of the same Friedmann world. Third, these are wormholes obtained in six-dimensional GR, whose one entrance is located in 'our' asymptotically flat world with very small extra dimensions while the other 'end' belongs to a universe with large extra dimensions and therefore different physical properties. The possible observable features of such wormholes are briefly discussed. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global solutions of the 3D compressible micropolar fluid model in the domain to a subset of R3 bounded with two coaxial cylinders that present the solid thermo-insulated walls, which is in a thermodynamical sense perfect and polytropic. Compared with the classical Navier-Stokes equations, the angular velocity w in this model brings benefit that is the damping term - uw can provide extra regularity of w. At the same time, the term uw2 is bad, it increases the nonlinearity of our system. Moreover, the regularity and exponential stability in H4 also are proved. [ABSTRACT FROM AUTHOR]

Tornado is a destructive catastrophe. We use compressible isentropic Euler equations to describe this problem. A cylindrically symmetric special solution moving with a constant velocity in R 3 is given. It depicts how the vorticity function of the flow evolves. Even if the initial inward velocity and acceleration are both very small, the inward velocity could become very large and the vorticity could increase drastically in later time, and most of mass concentrates on a neighborhood of the moving center axis at this time. For this solution, cases when γ ≠ 2 and when γ = 2 (shallow water) have some differences, while their evolution dynamics are basically the same. When γ = 2 , the initial vorticity could depend on the space variables. [ABSTRACT FROM AUTHOR]

This article argues that an efficient artificial intelligence control algorithm needs the built-in symmetries of an industrial robot manipulator to be further characterized and exploited. The product of this enhancement is a four-dimensional (4D) discrete cylindrical grid space that can directly replace complex robot models. A* is chosen for its wide use among such algorithms to study the advantages and disadvantages of steering the robot manipulator within the 4D cylindrical discrete grid. The study shows that this approach makes it possible to control a robot without any specific knowledge of the robot kinematic and dynamic models at planning and execution time. In fact, the robot joint positions for each grid cell are pre-calculated and stored as knowledge, then quickly retrieved by the pathfinding algorithm when needed. The 4D cylindrical discrete space has both the advantages of the configuration space and the three-dimensional Cartesian workspace of the robot. Since path optimization is the core of any search algorithms, including A*, the 4D cylindrical grid provides for a search space that can embed further knowledge in form of cell properties, including the presence of obstacles and volumetric occupancy of the entire industrial robot body for obstacle avoidance applications. The main trade-off is between a limited capacity for pre-computed grid knowledge and the path search speed. This innovative approach encourages the use of search algorithms for industrial robotic applications, opens up to the study of other robot symmetries present in different robot models and lays a foundation for the application of dynamic obstacle avoidance algorithms.

In this work, we present all the possible solutions for a static cylindrical symmetric spacetime in the Einstein-Aether (EA) theory. As far as we know, this is the first work in the literature that considers cylindrically symmetric solutions in the theory of EA. One of these solutions is the generalization in EA theory of the Levi-Civita (LC) spacetime in General Relativity (GR) theory. We have shown that this generalized LC solution has unusual geodesic properties, depending on the parameter c 1 4 of the aether field. The circular geodesics are the same of the GR theory, no matter the values of c 1 4 . However, the radial and z -direction geodesics are allowed only for certain values of σ and c 1 4 . The z -direction geodesics are restricted to an interval of σ different from those predicted by the GR and the radial geodesics show that the motion is confined between the origin and a maximum radius. The latter is not affected by the aether field but the velocity and acceleration of the test particles are besides, for 0 ≤ σ < 1 / 2 , when the cylindrical symmetry is preserved, this spacetime is singular at the axis r = 0 , although for σ > 1 / 2 exists interval of c 1 4 where the spacetime is not singular, which is completely different from that one obtained with the GR theory, where the axis r = 0 is always singular. [ABSTRACT FROM AUTHOR]

A hollow cylinder with thick walls is one of the most complex objects to calculate the unsteady temperature field, so this field is the least studied. However, such objects are found in many modern constructions of systems of generation and distribution of heat. In the proposed work it deals with the study of propagation of temperature waves in the wall of the hollow cylinder with harmonic temperature change of external environment arising from its diurnal fluctuations. The approximate analytical solution is presented by separation of variables in the complex domain with the use of cylindrical functions. The algorithm of calculation of temperature fields numerically is shown using an explicit finite-difference scheme of high accuracy in conditions of cylindrical symmetry with boundary conditions of the first kind. The results of calculations according to the considered algorithm, depending on the time since the start of heat exposure and their comparison with the analytic solution are given for its implementation. Calculated radial profiles of the temperature in the cylindrical wall within the temperature waves and the analytical approximation relations for the description of its damping coefficient are presented. The results are compared with the existing analytical solution in rectangular coordinates and it is marked that they have some differences but the common results are found regardless of the material and geometry of the cylinder, as well as of temperatures of inner and outer environment. Presented dependences are invited to apply for the analytical evaluation of the temperature amplitude on the inner surface of the heated cylindrical structures that will allow the use of engineering methods to verify compliance with industrial safety requirements.

Abstract In this work, the three-dimensional model for the compressible micropolar fluid flow is considered, whereby it is assumed that the fluid is viscous, perfect, and heat conducting. The flow between two coaxial thermoinsulated cylinders, which leads to a cylindrically symmetric model with homogeneous boundary data for velocity, microrotation, and heat flux, is analyzed. The corresponding PDE system is formulated in the Lagrangian setting, and it is proven that this system has a generalized solution locally in time.

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.

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.

The similarity solution for a strong cylindrical shock wave in a rarefied polyatomic gas is analyzed on the basis of Rational Extended Thermodynamics with six independent fields; the mass density, the velocity, the pressure and the dynamic pressure. A new ODE system for the similarity solution is derived in a systematic way by using the method based on the Lie group theory proposed in the context of the spherical shock wave in a rarefied monoatomic gas in Donato and Ruggeri (J Math Anal Appl 251:395, 2000). The boundary conditions are also specified from the Rankine–Hugoniot conditions for the sub-shock. The derived similarity solution is characterized by only one dimensionless parameter α related to the relaxation time for the dynamic pressure. The numerical analysis of the similarity solution is also performed. The solution agrees with the well-known Sedov–von Neumann–Taylor (SNT) solution when α is small. When α is larger, due to the presence of the dynamic pressure, the deviation from the SNT solution is evident; the strength of a peak near the shock front becomes smaller and the profile becomes broader. [ABSTRACT FROM AUTHOR]

This paper is devoted to a collection of results on nonlinear interpolation inequalities associated with Schrödinger operators involving Aharonov–Bohm magnetic potentials, and to some consequences. As symmetry plays an important role for establishing optimality results, we shall consider various cases corresponding to a circle, a two-dimensional sphere or a two-dimensional torus, and also the Euclidean spaces of dimensions 2 and 3. Most of the results are new and we put the emphasis on the methods, as very little is known on symmetry, rigidity and optimality in the presence of a magnetic field. The most spectacular applications are new magnetic Hardy inequalities in dimensions 2 and 3. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a critical Grushin-type problem. By applying Lyapunov–Schmidt reduction argument and attaching appropriate assumptions, we prove that this problem has infinitely many positive multi-bubbling solutions with arbitrarily large energy and cylindrical symmetry. Instead of estimating the corresponding derivatives of the reduced functional in locating the concentration points of the solutions, we employ the local Pohozaev identities to locate them. [ABSTRACT FROM AUTHOR]

From backgrounds of the Lorentz symmetry breaking implemented by the tensor K F μ ν α β , we analyze the effects of the Lorentz symmetry violation at a low energy scenario from a semiclassical point of view by using the Wentzel, Kramers and Brillouin approximation. We show that the interaction of a neutral particle with electric and magnetic fields in the background defined by the tensor K F μ ν α β yields attractive scalar potentials, and thus, bound state solutions to the Schrödinger equation can be obtained. [ABSTRACT FROM AUTHOR]

Static and stationary cylindrically symmetric space-times in general relativity are considered, supported by distributions of cosmic strings stretched in the azimuthal (φ), longitudinal (z) or radial (x) directions or and by pairs of mutually opposite radiation flows in any of these directions. For such systems, exact solutions are obtained and briefly discussed, except for radial strings (a stationary solution for them is not found); it is shown that static solutions with z - and φ -directed radiation flows do not exist while for z -directed strings a solution is only possible with negative energy density. Almost all solutions under discussion contain singularities, and all stationary solutions have regions with closed timelike curves, hence, most probably, only their well-behaved regions admit application to real physical situations. [ABSTRACT FROM AUTHOR]

Electrical discharge machining (EDM) is a controlled metal-removal process used to remove metal by means of electric spark erosion. In this process, a high voltage is applied between two electrodes and the breakdown of the dielectric is initiated by moving the electrode towards the work piece. This movement increases the electric field in the gap until it reaches the breakdown value. When the breakdown occurs, the voltage falls and the current rises abruptly. The presence of a current is possible at this stage because the dielectric has been ionized and a plasma channel (the bubble) has been created between the electrodes. The pre-breakdown phase in the dielectric is characterized by the generation of numerous small bubbles that promote the breakdown process. In this paper a new model for the formation of the plasma channel (bubble) is proposed. This model considers a mixture gas/steam inside the bubble, the shell of the bubble (if any), and the fluid surrounding the bubble. The gas is modeled as ideal and the bubble is initially modeled only as a cavity within the fluid. It is assumed that the bubble is cylindrically symmetric and that the bubble oscillations preserve this symmetry. This assumption is made for the case of a single bubble far from any boundaries, and in a low amplitude-driving field. In these models the center point of the bubble remains stationary at the origin because of the cylindrical symmetry about the origin. The proposed model is evaluated using experimental data and existing models. [ABSTRACT FROM AUTHOR]

In this paper, we study the initial boundary value problem for a cylindrical symmetry fluid–particle interaction system in three dimensions. The boundary layer phenomena is investigated when the shear viscosity μ = κ ρ β goes to zero. Furthermore, we establish the boundary layer thickness of the order O (κ α) for more general initial data when 0 < α < 1 2 and give the optimal boundary-layer thickness for the system with more general initial data. As a byproduct, this work improves the corresponding results in Yao et al. (2011) for isentropic compressible Navier–Stokes equations where 0 < α < 1 4 . [ABSTRACT FROM AUTHOR]

We present a class of new Gravastar solutions following the works of Mazur and Mottola for a Gravitational Bose–Einstein Condensate (GBEC) star in generalised cylindrically symmetric space–time. A stable gravastar consists of 3 distinct regions, namely: (i) an interior de-Sitter space (p = − ρ) , which exerts an outwards repulsive force at all points on the thin shell, (ii) an intermediate thin shell with a slice of finite length separating the interior and exterior regions is supposed to be consisting of an ultra-relativistic stiff fluid, with the equation of state p = ρ and (iii) an exterior vacuum region. This thin shell, which is considered as the critical surface for the quantum phase transition, replaces both the classical de-Sitter space and Schwarzschild event horizon. The new solutions are free from any singularities. The energy density, total energy, proper length, and the entropy of this shell are explored in this model. From the thin shell solution and using Lanczos equations for stress energy density, we have predicted the mass contained into the gravastar shell. The stability of the gravastar model is analysed through the consideration of gravitational surface redshift and entropy calculation. We have also obtained a constraint on the possible mass of the thin shell without violating the condition for stable gravastar configuration. All these features indicate that the present model is physically viable. [ABSTRACT FROM AUTHOR]

The well-known problem of wormholes in General Relativity (GR) is the necessity of exotic matter, violating the Weak Energy Condition (WEC), for their support. This problem looks easier if, instead of island-like configurations, one considers string-like ones, among them, cylindrically symmetric spacetimes with rotation. However, for cylindrical wormhole solutions, a problem is the lacking asymptotic flatness, making it impossible to observe their entrances as local objects in our universe. It was suggested to solve this problem by joining a wormhole solution to flat asymptotic regions at some surfaces Σ − and Σ + on different sides of the throat. The configuration then consists of three regions, the internal one containing a throat and two flat external ones. We discuss different kinds of source matter suitable for describing the internal regions of such models (scalar fields, isotropic and anisotropic fluids) and present two examples where the internal matter itself and the surface matter on both junction surfaces Σ ± respect the WEC. In one of these models, the internal source is a stiff perfect fluid whose pressure is equal to its energy density, in the other, it is a special kind of anisotropic fluid. Both models are free from closed timelike curves. We thus obtain examples of regular twice asymptotically flat wormhole models in GR without exotic matter and without causality violations. [ABSTRACT FROM AUTHOR]

In this paper we introduce an analytical approach for predicting the melting radius during powder melting in selective laser melting (SLM) with minimum computation duration. The purpose of this work is to evaluate the suggested analytical expression in determining the melt pool geometry for SLM processes, by considering heat transfer and phase change effects with density variation and cylindrical symmetry. This allows for rendering first findings of the melt pool numerical prediction during SLM using a quasi-real-time calculation, which will contribute significantly in the process design and control, especially when applying novel powders. We consider the heat transfer problem associated with a heat source of power Q' (W/m) per unit length, activated along the span of a semi-infinite fusible material. As soon as the line heat source is activated, melting commences along the line of the heat source and propagates cylindrically outwards. The temperature field is also cylindrically symmetric. At small times (i.e., neglecting gravity and Marangoni effects), when the density of the solid material is less than that of the molten material (i.e., in the case of metallic powders), an annulus is created of which the outer interface separates the molten material from the solid. In this work we include the effect of convection on the melting process, which is shown to be relatively important. We also justify that the assumption of constant but different properties between the two material phases (liquid and solid) does not introduce significant errors in the calculations. A more important result; however, is that, if we assume constant energy input per unit length, there is an optimum power of the heat source that would result to a maximum amount of molten material when the heat source is deactivated. The model described above can be suitably applied in the case of selective laser melting (SLM) when one considers the heat energy transferred to the metallic powder bed during scanning. Using a characteristic time and length for the process, we can model the energy transfer by the laser as a heat source per unit length. The model was applied in a set of five experimental data, and it was demonstrated that it has the potential to quantitatively describe the SLM process. [ABSTRACT FROM AUTHOR]

Highlights • Expressions for cylindrically symmetric eigenfunctions of polarized RTE proved. • Method of semi-analytic modelling of radiation field inside cylinder outlined. • Quadratic recurrent relations for Wigner d-functions proved. Abstract The general expressions for cylindrically symmetric eigenfunctions of polarized radiative transfer equation in homogeneous space obeying Euclidean geometry are derived and proved. The medium is assumed to be statistically homogeneously filled with polydisperse particles, the effective medium (host medium together with particles) is assumed to be isotropic, and birefringence (both linear and circular) is assumed to be negligible. [ABSTRACT FROM AUTHOR]

We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the EMT imposes three-way restrictions either on the space–time geometry or on the components of the spinor field or on both. It should be noted that the analogical situation occurs in cosmology when the nonlinear spinor field is exploited as a source of gravitational field given by the Bianchi type-I cosmological model.

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

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In recent years, phononics, that studies thermal analogs of electronic devices, has become an important subject due to the need for better use of energy resources influenced by growing demand. On developing of these analogs, for example, thermal diodes, a successful route is the design of nanostructured materials (e.g., carbon nanotubes). However, these materials entail increased costs due to the use of complex techniques/equipments, while alternative cheaper materials present nearly comparable efficiency. In this work, we investigate how a thermal diode made by an alternative material (nematic liquid crystal), confined in a conical frustum capillary, can be optimized to achieve high rectifications. In such capillary tube, the thermotropic nematic liquid crystal 5CB produces an axially anisotropic defect called escaped radial disclination. With the molecular director field of such structure, we obtain the thermal conductivity tensor of the diode and solve the steady-state regime of Laplace and Fourier equations using the finite element method. We observed the anisotropy of the system with the non-linear temperature dependences of the molecular thermal conductivities that rectify the heat flux at rates up to 1266% at room temperature. Studying the sensitivity of the system with respect to shape and molecular and thermal aspects, we found that the improved thermal diode is suitable to be miniaturized and applied on well-determined areas, and it is robust against variations of the inward pumped heat flux. This work contributes to the usage of liquid crystals in non-display devices, having potential applications on controlling the heat flux through surfaces. [ABSTRACT FROM AUTHOR]

A wide variety of semiconductor nanostructures have been fabricated and studied experimentally and alongside theoretical investigations show the great role they have in new generation opto-electronic devices. However, mathematical modeling provide important information due to their definitive goal of predicting features and understanding of such structures' behavior under different circumstances. Hence, in the current work, the effects of applied magnetic field, temperature and dimensions of the structure on the electromagnetically induced transparency (EIT) of a GaAs quantum ring are studied while both Rashba and Dresselhaus spin-orbit interactions (SOI) are taken into account. The Schrödinger equation is solved in cylindrical coordinate with axial symmetry and in order to study the EIT, the imaginary (absorption) and real (refractive index) parts of susceptibility as well as the group velocity of the probe light pulse are investigated. The absorption and refractive index plots show that, for a specific frequency of probe field the absorption vanishes and refractive index becomes unity (known as EIT) while around such frequency the group index is positive (sub-luminal probe propagation) and for higher and lower frequencies it alters to negative (super-luminal probe propagation). The numerical results reveal that the EIT frequency, transparency window and sub(super)-luminal frequency intervals shift as we change applied magnetic field, temperature and also the structure dimensions. [ABSTRACT FROM AUTHOR]

In this paper we introduce an analytical approach for predicting the melting radius during powder melting in selective laser melting (SLM) with minimum computation duration. The purpose of this work is to evaluate the suggested analytical expression in determining the melt pool geometry for SLM processes, by considering heat transfer and phase change effects with density variation and cylindrical symmetry. This allows for rendering first findings of the melt pool numerical prediction during SLM using a quasi-real-time calculation, which will contribute significantly in the process design and control, especially when applying novel powders. We consider the heat transfer problem associated with a heat source of power Q ′ ˙ ( W / m ) per unit length, activated along the span of a semi-infinite fusible material. As soon as the line heat source is activated, melting commences along the line of the heat source and propagates cylindrically outwards. The temperature field is also cylindrically symmetric. At small times (i.e., neglecting gravity and Marangoni effects), when the density of the solid material is less than that of the molten material (i.e., in the case of metallic powders), an annulus is created of which the outer interface separates the molten material from the solid. In this work we include the effect of convection on the melting process, which is shown to be relatively important. We also justify that the assumption of constant but different properties between the two material phases (liquid and solid) does not introduce significant errors in the calculations. A more important result; however, is that, if we assume constant energy input per unit length, there is an optimum power of the heat source that would result to a maximum amount of molten material when the heat source is deactivated. The model described above can be suitably applied in the case of selective laser melting (SLM) when one considers the heat energy transferred to the metallic powder bed during scanning. Using a characteristic time and length for the process, we can model the energy transfer by the laser as a heat source per unit length. The model was applied in a set of five experimental data, and it was demonstrated that it has the potential to quantitatively describe the SLM process.