Thin Spherical Layer Research Articles

Proton quantal delocalization and H/D translocations in (MeOH)nH+ (n = 2, 3).

In this study, we present results from path integral molecular dynamics simulations that describe the characteristics of the quantum spatial delocalizations of protons participating in OH bonds in (MeOH)2H+ and in (MeOH)3H+. The characterization was carried out by examining the overall structures of the corresponding isomorphic polymers. To introduce full flexibility in the force treatment, we have adopted a neural network fitting procedure based on second-order Møller-Plesset perturbation theory predictions. For the dimer case, we found that the spatial extent of the shared connective proton can be portrayed in terms of a prolate-like structure with typical dimensions of ∼0.1 Å. On the other hand, the dangling polymers lie confined within a thin spherical layer, spread over length scales of the order of ∼0.25 Å. In contrast, connective protons in (MeOH)3H+ exhibit larger delocalizations along the O-H bond and more localized ones along perpendicular directions, compared to their dangling counterparts. We also examined the characteristics of the relative propensities of H and D isotopes to be localized in dangling and connective positions. Physical interpretations of the different thermodynamic trends are provided in terms of the local geometrical characteristics and of the strengths of the corresponding intermolecular connectivities.

Disjoining Pressure in Thin Spherical Liquid Films and Vapor Layers with Molecular Correlations Included

Disjoining Pressure in Thin Spherical Liquid Films and Vapor Layers with Molecular Correlations Included

Second-Harmonic Generation in a Thin Spherical Layer with a Small Radius by Coherent Sources of Elliptically Polarized Radiation

Second-Harmonic Generation in a Thin Spherical Layer with a Small Radius by Coherent Sources of Elliptically Polarized Radiation

SECOND-HARMONIC GENERATION IN A THIN SPHERICAL LAYER OF A SMALL RADIUS BY COHERENT SOURCES OF ELLIPTICALLY POLARIZED RADIATION

Explicit forms of the power density and the total radiation power of the second-harmonic generation in a thin spherical layer of a small radius are determined. The conditions for a maximal total power of the second harmonic and the direction of observation of the maximum intensity of the second harmonic are found analytically for special cases of the second-order dielectric susceptibility tensor. A numerical maximization of the energy characteristics of the second-harmonic generated radiation is carried out using one and two coherent sources with the same ellipticity of radiation. The advantage of using several coherent sources compared to a single source of initial radiation is shown.

Circulating light at continuous electrical current

The most famous object in the world of circulating light is ball lightning (BL). In our opinion, BL is a thin spherical layer of highly compressed air, in which ordinary white light circulates in all possible directions. The refractive index of a spherical shell in a form of highly compressed air is greater than that of the surrounding space and the shell is a non-zero curvature light guide that prevents light from being radiated into free space. At the same time, there are other objects in which circulating light is present and determines their anomalous properties. These are liquid balls of silicon that can bounce on a sheet of paper dozens of times. This is a ball periodically flashing in cold water under the action of a standing spherical acoustic wave. These are luminous objects produced by an erosive gas discharge that can burn through the thin foil. However, the lifetime of such objects is, at best, a few seconds. At the same time, luminous objects have been known for more than a century that arise from a continuous electric current between damp electrodes. These objects exist indefinitely as long as there is a continuous electrical current. We analyze the properties of these objects for the presence of circulating light in them.

Unknown features of a behavior of the circulating light

The term "circulating light" encompasses a set of objects with anomalous properties in which circulating light is the cause of these anomalies. Such objects include natural ball lightning, luminous objects arising from attempts to obtain artificial ball lightning in the laboratory, as well as objects responsible for the phenomenon of sonoluminescence and cavitation. We represent natural ball lightning in the form of ordinary white light, which circulates in all possible directions in the shell in the form of a thin spherical layer of highly compressed air, which is compressed by the same light. The density of light energy in such an object is extremely high. As a result, it is subject to the action of optically induced forces. The magnitude of these forces is negligible at ordinary light intensity but increases by billion times at an interaction with the circulating light. Using the well-known laws of optics and physics and taking into account the action of these forces, all the features of the behavior of ball lightning, which were reported by eyewitnesses, were explained. Now we explain the behavior of the circulating light in situations that is not acceptable for direct observation. These are the properties of large ball lightning, the behavior of ball lightning inside a tornado, and its behavior in pipelines through which gases are pumped.

Steady states and stability of the circulating light in the air atmosphere

We show that the necessary conditions are met for the existence of stable circulating light in the ordinary atmosphere of the earth. Circulating light is a thin spherical layer of highly compressed air in which intense white light circulates in all possible directions. The reflective index of highly compressed air is increased compared to that of the surrounding area. In this case, a thin layer of highly compressed air is a spherical light guide, which prevents the circulating light from being radiated into the surrounding space. In turn, the circulating light provides excess air pressure in the spherical layer. It is shown that the circulating light is stable when the air is compressed approximately 1000 times, at which its pressure is several Gigapascals. In this case, the energy density of the circulating light exceeds the energy density of air by about 10–20 times. Previously, it was shown that the behavior of such a circulating light in the earth's atmosphere completely coincides with the mysterious and intriguing behavior of natural ball lightning. Therefore, we consider such a circulating lightning as an experimental proof of the existence of circulating light in nature.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое. II. Анализ диаграмм направленности

The solution to the problem of second harmonic–sum frequency generation by two coherent plane electromagnetic waves with elliptical polarizations and equal frequencies in a thin spherical layer is analyzed graphically. Asymmetries are introduced that quantitatively describe the shape of three-dimensional directivity patterns (spatial distribution of the power density of second harmonic–sum frequency radiation). Three-dimensional directivity patterns and asymmetries are analyzed for various combinations of the parameters: ratio of the complex amplitudes of the incident waves, angle between the wave vectors of the incident waves (the opening angle), ellipticities, orientations of polarization ellipses, spherical particle size. It is found that, at small particle sizes, each anisotropy type corresponds to its own individual directivity pattern. It is revealed that, for one of the anisotropy types, the shape of the directivity pattern almost does not change for nearly all possible ranges of the above parameters.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое. I. Аналитическое решение

The problem of the simultaneous second–harmonic and sum–frequency generation by two coherent plane electromagnetic waves with elliptical polarizations and equal frequencies in a thin spherical layer is solved in the Rayleigh–Gans–Debye model. The second–order dielectric susceptibility tensor is chosen in a form containing four independent components (including one chiral component). Fundamental differences are shown between the problem statements as well as between solutions to the problem of second–order nonlinear generation by several coherent electromagnetic waves and the problem of sum–frequency generation in the limiting case of equality of the frequencies of the incident waves. Combinations of parameters are determined at which the spatial distribution of the radiation generated as a result of incidence of two plane waves coincides with the distribution of second–harmonic radiation generated by one plane wave. The limiting cases of the obtained solution are considered: small and large radii of the spherical particle. In these cases the contributions of the chiral and non-chiral anisotropy coefficients to the generated radiation are determined.

Генерация второй гармоники-суммарной частоты в тонком сферическом слое. IV. Оптимизационный анализ

A numerical maximization of the intensity of the generated radiation of second harmonic–sum frequency from a thin spherical layer is carried out. It is found that, for all the considered anisotropy types and any size of the spherical layer, the maximum of the intensity is observed at the same parameters of the problem, and an increase in the particle size leads to an increase in generated spatial power density. It is shown that, for large particle sizes, the intensity of the generated radiation is proportional to the fourth power of the particle radius. The distribution law of the generated power density is found analytically for one of the anisotropy types in the case of codirectional incidence of waves on a spherical particle of small radius.

Point vortices dynamics on a rotating sphere and modeling of global atmospheric vortices interaction

It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of antipodal point vortices (APVs), in contrast to the stream function of a single point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing the well-known nonlinear problem of a point vortices interaction with a regular vorticity field, and an exact solution for the APV dynamics problem on a rotating sphere is obtained. Due to this, a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures, such as atmospheric centers of action.

Physical and optical laws responsible for existence and abnormal behavior of ball lightning

Earlier in numerous publications, we showed that ball lightning is mainly an optical phenomenon. This is a symbiosis of two elements: light and air. Intense light circulates in a thin spherical layer of highly compressed air and compresses this air, since the total energy of light and compressed air is minimal in this case. In turn, the thin layer of highly compressed air has an increased refractive index and can be considered as a planar thin-film lightguide, the curvature of which is nonzero in two mutually perpendicular directions. The intensity of the circulating light in a spherical waveguide increases by 109 times compared with the intensity of the same light that propagates rectilinearly. As a result, the forces arising at an interaction between light and the optical medium increase 109 times and exceed other types of forces. It is these forces that determine the anomalous properties and the mysterious behavior of ball lightning in the earth's atmosphere. In numerous publications, we have explained almost all the puzzles in the behavior of ball lightning. Therefore, there is no reason to doubt that the optical nature of ball lightning is true. In this article, we list those phenomena that are responsible for the existence and abnormal behavior of circulating light.

Dynamic Deformation Effects During Compression and Drain of Asymptotically Thin Perfectly Rigid Plastic Spherical Layer

The present article deals with a solution of an analogue of the Prandtl problem on compression and drain (spreading) of a perfectly rigid plastic material in an asymptotically thin spherical layer by taking into account inertial effects. Various compression modes that characterize the transition from a quasistatic process to a dynamic one are considered.

Simple explanation of physical nature of ball lightning

Now above 500 different theories on the ball lightning nature are known. We believe that a correct theory should explain anomalous behavior of ball lightning in an atmosphere. A single theory that satisfies this requirements is the optical theory where ball lightning consists of the conventional white light that we see and the air that we breathe. It is a symbiosis of a thin spherical layer of strongly compressed air and the intensive light that circulates in the layer in all possible directions. They help each other. The thin layer of the strongly compressed air is the light guide that prevents radiation of the light in surrounding space. In turn, the intense circulating light compresses the air due to the phenomenon of the electrostriction pressure. White light fells into a trap that it created for himself.The intensity of the circulating light in the sphere of 10 cm diameter increases by about one billion times as compared with that of the light propagating in a straight line. The forces arising at an interaction of the light and an inhomogeneous optical medium increases by billion times also. These forces surpass other known forces and determine a behavior of the sphere of light in the air atmosphere. Now we presents in a popular form an explanation of the most known and intriguing puzzles of ball lightning behavior. We consider this explanation as the decisive argument in the correctness of the optical theory of the ball lightning nature.

Modeling the F Layer of the Earth’s Ionosphere: Solution of the Ambipolar Diffusion Equations

The paper presents the problem formulation and methods of numerical solution for a dynamical global model of the F layer of the Earth’s ionosphere (altitude 100–500 km), which is a computational unit of the coupled thermosphere–ionosphere model. The model is based on a system of equations of the global ionospheric formation and dynamics in a spherical geomagnetic coordinate system in the approximation of a thin spherical layer. The features of the formulated system of equations are investigated and the methods for its solution are proposed based on the method of splitting them by physical processes. In this paper we present the results of a single step of the splitting method—the solution of equations which describe the ambipolar diffusion of ions along the magnetic field lines and the gravitational settling of ions, as well as the plasma–chemical transformations. The accuracy of the proposed algorithms is investigated based on the prescribed analytical solution, which qualitatively correctly describes the real ionospheric electron distribution. The results of the numerical experiments on studying the sensitivity of the solution to perturbations of the ion flow at the upper boundary are provided.

Robin-type boundary conditions in transition from reaction-diffusion equations in 3D domains to equations in 2D domains

We consider a singular limit of diffusion equations in 3D domains of thickness converging to zero. In the 2D limit the resulting reaction-diffusion equation has a source term resulting from the Robin-type boundary conditions imposed on boundaries of the original 3D domain. The proposed approach can be applied to constructing approximate solutions of diffusion problems in thin planar, cylindrical, or spherical layers between two membranes. As an example we refer to the problem of activation of B lymphocytes, which typically have large nuclei and a thin cytoplasmic layer which can be considered as a spherical shell. For this example, assuming additionally axial symmetry we provide a rigorous convergence theorem in the language of semigroups of operators.

Design and test of a compact and high-resolution time-of-flight measurement device for cold neutron beams

A time-of-flight device was developed to characterize wavelength distribution and uniformity of a cold neutron beam. This device is very compact---the distance of flight is 60 cm---but achieves very high resolution---the intrinsic resolution $\mathrm{\ensuremath{\Delta}}\ensuremath{\lambda}/\ensuremath{\lambda}=2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at $\ensuremath{\lambda}=0.89\text{ }\text{ }\mathrm{nm}$. The time-of-flight device is composed of a fixed slit, a disk rotating up to 216 Hz, and a neutron detector with a thin spherical conversion layer with the chopper slit in its focus. The device accepts the complete angular divergence of the initial neutron beam. The efficiency of neutron detection is constant over the detector area. Systematic corrections caused by neutron scattering in air are minimized due to the reduction of the time-of-flight length. Measurements have been performed on the beamline of the GRANIT experiment at ILL (part of the H172 beamline) on level C, and the first order diffraction peak of the crystal monochromator used for the GRANIT beamline was found to be at $\ensuremath{\lambda}=0.8961(11)\text{ }\text{ }\mathrm{nm}$, and having a width of $\ensuremath{\sigma}=0.0213(13)\text{ }\text{ }\mathrm{nm}$.

New type of centrifugal instability in a thin rotating spherical layer

We numerically model the instability of viscous incompressible fluid flows caused by torsional oscillations of the inner sphere in a thin spherical layer with respect to the state of rest. We show that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to the structures, which were not previously observed. The revealed instability is found in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.

Instability of the Flow in a Spherical Layer under Torsional Oscillations of the Inner Boundary

The instability of viscous incompressible fluid flows caused in a thin spherical layer by torsional oscillations of the inner sphere in a thin spherical layer with respect to the sate of rest is studied numerically. It has been established that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to structures not observed earlier. The revealed instability is observed in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.

Sum-Frequency Generation from a Thin Spherical Layer: I. Analytical Solution

We have analyzed the influence of the angle between the wave vectors of two incident waves (the opening angle) and of the type of the anisotropy of a nonlinear layer on the shape of the directivity pattern of a sum-frequency harmonic generated by the two plane elliptically polarized electromagnetic waves from a thin spherical optically nonlinear layer deposited on the surface of a dielectric spherical particle placed in a dielectric. Our analysis has shown that, if the radius of the thin spherical nonlinear layer is small, the shape of the directivity pattern will change significantly with increasing opening angle only for some types of anisotropy: the main lobes shift toward the direction that is opposite to the direction of the sum of the wave vectors of the incident waves. For three types of anisotropy, the directivity patterns have similar shapes. We have also found that, for one of the types of the anisotropy, the shape of the directivity pattern remains unchanged upon a change in the opening angle. The mathematical properties of functions describing the spatial distribution of the generated harmonic have been determined. In particular, it has been found that, upon incidence of linearly polarized waves on a thin nonlinear spherical layer that possesses either solely chiral or solely nonchiral nonlinear properties, linearly polarized radiation of the sum-frequency harmonic is generated.