Symmetrization and Amplification of Germicidal Radiation Flux Produced by a Mercury Amalgam UV Lamp in Cylindrical Cavity with Diffusely Reflective Walls

The study focused on increasing the efficiency of germicidal UV radiation by using highly diffuse reflective materials such as PTFE in irradiated cavities of UV air purifiers. In a conventional cylindrically symmetric cavity with a linear amalgam mercury lamp as UV-radiation source on the axis UV-radiation, flux directed from the lamp to the walls dropped from the axis to the periphery. To increase the UV irradiation, the walls are often made mirror-reflective, but the radiation flux distribution remained radially symmetric with a maximum on the source emitting surface in this case as well. When most of the emitted light is returned to the source after one reflection, the conditions of its operation are disturbed. If the walls are made of highly diffuse reflective materials, the radiation flux density inside the cavity increases on average, and its distribution becomes uniform and highly symmetric. Thus, the effect of amplification of the radiation flux due to the highly diffuse reflectivity of the walls increases with radius and reaches a maximum at the wall. Experiments were performed to demonstrate increasing amplification of germicidal UV radiation flux with a diffuse reflection coefficient in cylindrical cavities with walls of PTFE and ePTFE. The irradiation of the cavity wall was observed to increase up to 20 times at the resonant mercury line of 253.7 nm and up to 40 times at some non-resonant lines of the visible range due to highly diffuse reflectivity of the cavity walls. The flux amplification effect was limited by the diffuse reflectivity value of the walls and absorption coefficient of the radiation emitting surface. A formula for calculating the radiation flux amplification factor in a diffusely reflecting cylindrically symmetric cavity was derived for the case of Lambertian source and reflector, including wall reflectivity and source surface absorption coefficients. The effects of heating and cooling of the mercury lamp amalgam directly affected the amplification, and symmetrization of germicidal irradiation was observed and is discussed in the paper. Numerical calculations were performed by the ray tracing method. The calculated model was verified by comparing the numerical results with those of both the approximate theoretical consideration and experiments. The promising use of diffusely reflecting cylindrical cavities for UV air purifiers is discussed. Designs of air inlet and outlet ports that allow effective locking of germicidal radiation inside the UV air purifiers were considered. The results of this work may be of interest for further developments in the UV disinfection technique.

On some smooth symmetric transonic flows with nonzero angular velocity and vorticity

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic–hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli’s function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second-order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.

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.

New static cylindrical symmetric solutions in GR for unfamiliar EoS parameter values via Noether symmetry

The solutions for the field equations of f(R) gravity are investigated in static cylindrically symmetric space-time. Conserved quantities of the system, as well as unknown functions, can be determined with the help of the Noether symmetry method. In this article, some unknown values of the equations of state parameter (EoS) have emerged as a result of the constraints obtained by analyzing the Noether symmetry equations for the $$f(R)=f_0 R$$ f ( R ) = f 0 R case. Consequently, several new exact solutions have been found for cases of General Relativity in static cylindrically symmetrical space-time for the non-dust matter.

Spin Current in BF Theory

In this paper, a current that is called spin current and corresponds to the variation of the matter action in BF theory with respect to the spin connection A which takes values in Lie algebra so(3,C), in self-dual formalism is introduced. For keeping the 2-form Bi constraint (covariant derivation) DBi=0 satisfied, it is suggested adding a new term to the BF Lagrangian using a new field ψi, which can be used for calculating the spin current. The equations of motion are derived and the solutions are dicussed. It is shown that the solutions of the equations do not require a specific metric on the 4-manifold M, and one just needs to know the symmetry of the system and the information about the spin current. Finally, the solutions for spherically and cylindrically symmetric systems are found.

Linear Energy Density and the Flux of an Electric Field in Proca Tubes

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field.

Semiclassical Phase Analysis for a Trapped-Atom Sagnac Interferometer

A Sagnac atom interferometer can be constructed using a Bose–Einstein condensate trapped in a cylindrically symmetric harmonic potential. Using the Bragg interaction with a set of laser beams, the atoms can be launched into circular orbits, with two counterpropagating interferometers allowing many sources of common-mode noise to be excluded. In a perfectly symmetric and harmonic potential, the interferometer output would depend only on the rotation rate of the apparatus. However, deviations from the ideal case can lead to spurious phase shifts. These phase shifts have been theoretically analyzed for anharmonic perturbations up to quartic in the confining potential, as well as angular deviations of the laser beams, timing deviations of the laser pulses, and motional excitations of the initial condensate. Analytical and numerical results show the leading effects of the perturbations to be second order. The scaling of the phase shifts with the number of orbits and the trap axial frequency ratio are determined. The results indicate that sensitive parameters should be controlled at the 10−5 level to accommodate a rotation sensing accuracy of 10−9 rad/s. The leading-order perturbations are suppressed in the case of perfect cylindrical symmetry, even in the presence of anharmonicity and other errors. An experimental measurement of one of the perturbation terms is presented.