Unitary dynamics of spherical null gravitating shells

The dynamics of a thin spherically symmetric shell of zero-rest-mass matter in its own gravitational field is studied. A form of action principle is used that enables the reformulation of the dynamics as motion on a fixed background manifold. A self-adjoint extension of the Hamiltonian is obtained via the group quantization method. Operators of position and of direction of motion are constructed. The shell is shown to avoid the singularity, to bounce and to re-expand to that asymptotic region from which it contracted; the dynamics is, therefore, truly unitary. If a wave packet is sufficiently narrow and/or energetic then an essential part of it can be concentrated under its Schwarzschild radius near the bounce point but no black hole forms. The quantum Schwarzschild horizon is a linear combination of a black and white hole apparent horizons rather than an event horizon.     

On chaotic behavior of gravitating stellar shells

Motion of two gravitating spherical stellar shells around a massive central body is considered. Each shell consists of point particles with the same specific angular momenta and energies. In the case when one can neglect the influence of gravitation of one ("light") shell onto another ("heavy") shell ("restricted problem") the structure of the phase space is described. The scaling laws for the measure of the domain of chaotic motion and for the minimal energy of the light shell sufficient for its escape to infinity are obtained.     

Embedding variables in the canonical theory of gravitating shells

A thin shell of light-like dust with its own gravitational field is studied in the special case of spherical symmetry. The action functional for this system due to Louko, Whiting, and Friedman is reduced to Kuchař form: the new variables are embeddings, their conjugate momenta, and Dirac observables. The concepts of background manifold and covariant gauge fixing, that underlie these variables, are reformulated in a way that implies the uniqueness and gauge invariance of the background manifold. The reduced dynamics describes motion on this background manifold.     

Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C_s/epsilon and C_b/epsilon where C_s and C_b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C_s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2–3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.     

Relativistic dynamics of spherical timelike shells

The dynamics of general relativistic timelike spherically symmetric thin shells of matter is considered, putting special emphasis on the physical interpretation of the models and, therefore, on the dependence of the dynamical behavior upon then the choice of the equation of state. From this point of view the general formalism is reviewed both in the Israel’s and in the canonical (Lagrangian and Hamiltonian) approach. Known exact solutions corresponding to closed equations of state are reviewed as well, and a new, wide class of nonlinear barotropic solutions is introduced and discussed in detail.     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

Dynamics of a vortex pair in radial flow

The problem of vortex pair motion in two-dimensional radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of a corotating vortex pair in a quiescent environment transforms into motion along a logarithmic spiral in radial flow. The problem may have applications in astrophysics and geophysics.     

Axisymmetric vibration of continuous shallow spherical shells

The axisymmetric vibration of shallow spells supported along the outer periphery r = a and along an intermediate circle of radius r = b is considered. Shear deformation effects are included in the differential equations. This makes the analysis of higher modes more meaningful. Results are presented for three cases: (a) fixed edge condition at r = a; (b) simply supported condition at r = a; (c) free edge condition at r = a.     

Dynamics of a coupled pair of two-level tunnelling systems

An exact solution for the dynamics of a coupled pair of symmetric two-level-systems is given by calculating the resolvent of the Liouvillian and the statistical operator of the problem. At low temperatures interference effects between the two systems turn out to be of major importance. Depending on the value and the sign of the interaction parameter the susceptibility of the pair increases or decreases compared to the situation of isolated systems. For high temperatures the interference contributions disappear.     

Hydrothermal convection in moderately thin spherical shells

Hydrothermal convection of pore water with a temperature-dependent viscosity within a permeable, internally heated, moderately thin spherical shell is investigated by both a perturbation analysis and a direct numerical simulation. The analysis and simulation are mainly focused on a thin spherical shell in that convective instabilities are characterized by the spherical harmonic degree l=6 with a 13-fold mathematical degeneracy. Four different three-dimensional analytical solutions of convection are derived by removing the degeneracy through the nonlinear effect. A direct numerical simulation of the nonlinear problem is also carried out, showing satisfactory agreement between the analytical solutions and the numerical simulations.     

Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells

Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.     

Calculation of pair potentials for systems with filled shells

The possibility of calculating homoatomic and heteroatomic pair potentials for systems with filled shells by a density-functional method in which the parameters of the Hartree-Fock electron density of the isolated atoms are found by the Ritz variational method is discussed.Kabardino-Balkarian State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 6, pp. 3–8, June, 1994.     

Dynamics of coupled vortices in a pair of ferromagnetic disks

We here experimentally demonstrate that gyration modes of coupled vortices can be resonantly excited primarily by the ac current in a pair of ferromagnetic disks with variable separation. The sole gyration mode clearly splits into higher and lower frequency modes via dipolar interaction, where the main mode splitting is due to a chirality sensitive phase difference in gyrations of the coupled vortices, whereas the magnitude of the splitting is determined by their polarity configuration. These experimental results show that the coupled pair of vortices behaves similar to a diatomic molecule with bonding and antibonding states, implying a possibility for designing the magnonic band structure in a chain or an array of magnetic vortex oscillators.     

Coherent information processing by a pair of lenses in spherical wave illumination

A coherent optical information system has been analysed using the Fresnel diffraction theory. Considering the spherical wave illumination, the same system is used for spatial filtering and subsequent reimaging. The conditions for locating the spatial frequency plane and the image plane have been pointed out. The scale of the Fourier transform can be controlled by three degrees of freedom. The final image formed is inverted and magnified with respect to the input signal. The present analysis has been compared with those of Pernick and Moharir. Aberrations involved have also been discussed.     

毫米量级TMPTA空心泡沫微球的微流控法制备

利用微流控技术实现了毫米量级多元丙烯酸酯(TMPTA)空心泡沫微球的制备。通过对微流体通道的设计与流场分析,获得了具有最佳流场均匀性分布的Y型微流控通道;利用软模板技术实现了Y型通道微流控芯片的组装,并开展了TMPTA泡沫微球的结构控制研究。研究结果表明:在模板尺寸一定的情况下,能够通过调节各相流速实现对微球壁厚和直径的有效控制;微球壳层密度可通过控制单体浓度来调节。通过优化控制条件,实现了密度20~100mg/cm3、直径大于3mm的空心泡沫微球的制备。