Screening of magnetic fields by superconducting and hybrid shields with circular cross-section

The use of superconducting (SC) materials is crucial for shielding quasi-static magnetic fields. However, the frequent requisite of space-saving solutions with high shielding performance requires the development of a 3D modelling procedure capable of predicting the screening properties for different orientations of the applied field. In this paper, we exploited a 3D numerical model based on a vector potential formulation to investigate the shielding ability of SC screens with cylindrical symmetry and a height/diameter aspect ratio close to unity, without and with the superimposition of a ferromagnetic (FM) circular shell. The chosen materials were MgB2 and soft iron. First, the calculation outcomes were compared with the experimental data obtained on different shielding arrangements, achieving a notable agreement in both axial-field (AF) and transverse-field (TF) orientations. Then, we used the thus validated modelling approach to investigate how the magnetic mitigation properties of a cup-shaped SC bulk can be improved by the superimposition of a coaxial FM cup. Calculations highlighted that the FM addition is very efficient in enhancing the shielding factors (SFs) in the TF orientation. Assuming a working temperature of 30 K and using a layout with the FM cup protruding over the SC one, shielding factors up to 8 times greater than those of the single SC cup were attained at low applied fields, reaching values equal or higher than 102 in the inner half of the shield. In the AF orientation, the same FM cup addition costs a modest worsening at low fields, but at the same time, it widens the applied field range, where SF ≥ 104 occurs near the close extremity of the shield, up over 1 T.

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

Static cylindrical symmetric solutions in the Einstein-Aether theory

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 [Formula: see text] of the aether field. The circular geodesics are the same of the GR theory, no matter the values of [Formula: see text]. However, the radial and [Formula: see text]-direction geodesics are allowed only for certain values of [Formula: see text] and [Formula: see text]. The [Formula: see text]-direction geodesics are restricted to an interval of [Formula: see text] 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 [Formula: see text], when the cylindrical symmetry is preserved, this spacetime is singular at the axis [Formula: see text], although for [Formula: see text] exists interval of [Formula: see text] where the spacetime is not singular, which is completely different from that one obtained with the GR theory, where the axis [Formula: see text] is always singular.

A Look at the Spatial Confining Effect on the Molecular Electrostatic Potential (MEP)—A Case Study of the HF and BrCN Molecules

In this theoretical study, we report on the molecular electrostatic potential (MEP) of titled molecules confined by repulsive potentials of cylindrical symmetry mimicking a topology. Our calculations show that the spatial restriction significantly changes the picture of the MEP of molecules in a quantitative and qualitative sense. In particular, the drastic changes in the MEP as a function of the strength of spatial confinement are observed for the BrCN molecule. This preliminary study is the first step in the investigation of the behavior of the MEP of molecular systems under orbital compression.

Qualitative properties of singular solutions to fractional elliptic equations

In this paper, by the moving spheres method, Caffarelli-Silvestre extension formula and blow-up analysis, we study the local behaviour of nonnegative solutions to fractional elliptic equations \begin{align*} (-\Delta)^{\alpha} u =f(u),~~ x\in \Omega\backslash \Gamma, \end{align*} where $0<\alpha <1$ , $\Omega = \mathbb {R}^{N}$ or $\Omega$ is a smooth bounded domain, $\Gamma$ is a singular subset of $\Omega$ with fractional capacity zero, $f(t)$ is locally bounded and positive for $t\in [0,\,\infty )$ , and $f(t)/t^{({N+2\alpha })/({N-2\alpha })}$ is nonincreasing in $t$ for large $t$ , rather than for every $t>0$ . Our main result is that the solutions satisfy the estimate \begin{align*} f(u(x))/ u(x)\leq C d(x,\Gamma)^{{-}2\alpha}. \end{align*} This estimate is new even for $\Gamma =\{0\}$ . As applications, we derive the spherical Harnack inequality, asymptotic symmetry, cylindrical symmetry of the solutions.

Symmetry resolved atomic photoionization phase shift by attosecond coincidence metrology

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics from gas to condensed phase with attosecond temporal resolution. It has, however, not yet been able to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy to reveal their roles from the angle-resolved photoionization phase shifts in rare gas atoms. By scanning the relative polarization angle between an extreme-ultraviolet attosecond pulse train and a phase-locked near-infrared laser field serving as a partial wave meter, we break the cylindrical symmetry and observe an emission direction dependent phase shift in the photoionized electron momenta. The experimental observations are well supported by numerical simulations using the R-matrix with time-dependence method, and by analytical analysis using the soft-photon approximation. Our symmetry-resolved, partial-wave analysis identifies the transition rate and phase shifts of each individual ionization pathway in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics, thereby offer new perspectives for the control, manipulation, and exploration of ultrafast electron dynamics in complex systems.

Oscillations of elastic plate, located at the end of semi-infinite cylindrical acoustic waveguide

Получено точное аналитическое решение задачи о гармонических изгибных колебаниях тонкой круглой упругой пластины, расположенной в торце полубесконечного цилиндрического акустического волновода. Кромка пластины жестко заделана в стенку волновода. Волновод с жестким корпусом заполнен идеальной сжимаемой акустической средой. Колебания пластины возбуждаются набегающими на неё нормальными волнами волновода, распределение акустического давления для которых имеет цилиндрическую симметрию. Проведено численное исследование смещения пластины на разных частотах возбуждения. Показано, что наличие сжимаемой среды существенно влияет на форму колебаний пластины. Совместные колебания акустической среды и упругой пластины носят резонансный характер. На резонансных частотах имеет место значительное увеличение амплитуды колебаний пластины. На форму колебания пластины влияют как распространяющиеся, так и неоднородные нормальные волны в волноводе, что приводит к увеличению узловых линий в распределении смещения пластины. An exact analytical solution to the problem of harmonic bending oscillations of a thin round elastic plate located at the end of a semi-infinite cylindrical acoustic waveguide has been obtained. Plate edge is rigidly embedded in waveguide wall. The waveguide with rigid housing is filled with an ideal compressible acoustic medium. The plate oscillations are excited by the normal waveguide waves running to the plate. The distribution of acoustic pressure for waves has cylindrical symmetry. Numerical study of plate displacement at different excitation frequencies was carried out. It has been shown that the presence of a compressible medium significantly affects the waveform of the plate oscillation. Joint oscillations of acoustic medium and elastic plate are resonant. There is a significant increase in amplitude of plate oscillations at resonant frequencies. The waveform of the plate oscillation is influenced by both propagating and inhomogeneous normal waves in the waveguide, which leads to an increase in the nodal lines in the displacement distribution of the plate.

Look at the Spatial Confining Effect on the Molecular Electrostatic Potential (Mep). A Case Study of the Hf and Brcn Molecules

In this theoretical study we report on molecular electrostatic potential (MEP) of titled molecules confined by repulsive potentials of cylindrical symmetry mimicking a topology. Our calculations show that the spatial restriction significantly changes the picture of MEP of molecules in quantitative and qualitative sense. In particular, the drastic changes of MEP as a function of the strength of spatial confinement are observed for the BrCN molecule. This preliminary study is the first step in the investigations of the behavior of MEP of molecular systems under the orbital compression.

Cylindrical Gravitational Wave: Source and Resonance

Gravitational waves are regarded as linear waves in the weak field approximation, which ignores the spacetime singularity. In this paper, we analyze singularities in exact gravitational wave solutions. We provide an exact general solution of the gravitational wave with cylindrical symmetry. The general solution includes some known cylindrical wave solutions as special cases. We show that there are two kinds of singularities in the cylindrical gravitational wave solution. The first kind of singularity corresponds to a singular source. The second kind of singularity corresponds to a resonance between different gravitational waves. When two gravitational waves coexist, the interference term in the source may vanish in the sense of time averaging.