ПРИНЦИП ВОЗМОЖНЫХ ПЕРЕМЕЩЕНИЙ В МОМЕНТНОМЕМБРАННОЙ ДИНАМИЧЕСКОЙ ТЕОРИИ УПРУГИХ ТОНКИХ ОБОЛОЧЕК / The Principle of Possible Displacments in the Moment-Membrane Dynamic Theory of Elastic Thin Shells

В работе излагается моментно-мембранная динамическая теория упругих тонких оболочек на основе метода гипотез, который соответствует качественной стороне результата интегрирования трехмерной граничной задачи моментной теории упругости в тонкой области оболочки. На основе принципа возможных перемещений трехмерной моментной динамической теории упругости с независимыми полями перемещений и вращений и основных соотношений моментномембранной динамической теории упругих тонких оболочек, устанавливается принцип возможных перемещений для моментномембранной динамической теории упругих тонких оболочек./ In the present paper the moment-membrane dynamic theory of elastic thin shells is presented based on the hypotheses method, which corresponds to the qualitative side of the result of integration of the three-dimensional boundary-value problem of the moment theory of elasticity in a thin region of the shell. On the basis of the principle of possible displacements of the threedimensional moment dynamic theory of elasticity with independent fields of displacements and rotations and the basic relations of the moment-membrane dynamic theory of elastic thin shells, the principle of possible displacements for the moment-membrane dynamic theory of elastic thin shells is established.

Positive Feedback Regulation of fzd7 Expression Robustly Shapes Wnt Signaling Range in Early Heart Development

Secreted molecules called morphogens govern tissue patterning in a concentration-dependent manner. However, it is still unclear how reproducible patterning can be achieved with diffusing molecules, especially when patterning differentiation of a thin region. Wnt is a morphogen that organizes cardiac development; especially Wnt6 patterns the cardiogenic mesoderm to induce differentiation of a thin pericardium in Xenopus. It is, however, unclear how Wnt6 can pattern such a thin tissue. In this study, we reveal that a Wnt receptor, frizzled7, is expressed in a Wnt-dependent manner in the prospective heart region, and that this receptor-feedback is essential for shaping a steep gradient of Wnt. In addition, the feedback imparts robustness against fluctuations of Wnt ligand production and allows the system to reach a steady state quickly. We also found a Wnt antagonist sFRP1, which is expressed at the opposite side of Wnt source, accumulates on a novel type of heparan sulfate (HS), N-acetyl-rich HS, which is highly presented in the outer of cardiogenic mesoderm, achieving local inhibition of Wnt signaling by restricting sFRP1 spreading. These two intricate regulatory systems restrict Wnt signaling and ensure reproducible patterning of a thin pericardium tissue.

Measuring the properties of reionized bubbles with resolved Lyα spectra

ABSTRACT Identifying and characterizing reionized bubbles enables us to track both their size distribution, which depends on the primary ionizing sources, and the relationship between reionization and galaxy evolution. We demonstrate that spectrally resolved z ≳ 6 Lyman-alpha (Lyα) emission can constrain properties of reionized regions. Specifically, the distance from a source to a neutral region sets the minimum observable Lyα velocity offset from systemic. Detection of flux on the blue side of the Lyα resonance implies the source resides in a large, sufficiently ionized region that photons can escape without significant resonant absorption, and thus constrains both the sizes of and the residual neutral fractions within ionized bubbles. We estimate the extent of the region around galaxies which is optically thin to blue Lyα photons, analogous to quasar proximity zones, as a function of the source’s ionizing photon output and surrounding gas density. This optically thin region is typically ≲ 0.3 pMpc in radius (allowing transmission of flux ≳ −250 km s−1), ≲ 20 per cent of the distance to the neutral region. In a proof-of-concept, we demonstrate the z ≈ 6.6 galaxy COLA1 – with a blue Lyα peak – likely resides in an ionized region >0.7 pMpc, with residual neutral fraction <10−5.5. To ionize its own proximity zone we infer COLA1 has a high ionizing photon escape fraction (fesc > 0.50), relatively steep UV slope (β < −1.79), and low line-of-sight gas density (∼0.5 times the cosmic mean), suggesting it is a rare, underdense line-of-sight.

Improved error of electromagnetic shielding problems by a two-process coupling subproblem technique

Introduction: The direct application of the classcial finite element method for dealing with magnetodynamic problems consisting of thin regions is extremely difficult or even not possible. Many authors have been recently developed a thin shell model in order to overcome this drawback. However, this development generally neglects inaccuracies around edges and corners of thin shell, that lead to inaccuracies of the magnetic fields, eddy currents and joule power losses, specially increasing with the thickness. Methods: In this article, we propose a two-process coupling subproblem technique for improving the errors that overcome thin shell assumptions. This technique is based on the subproblem method to couple SPs in two-processes. The first scenario is an initial problem solved with coils/stranded inductors together with thin region models. The obtained solutions are then considered as volume sources for the second scenario including actual volume improvements that scope with the thin shell assumptions. The final solution is sum up of the subproblem solutions achieved from both the scenarios. The extended method is approached for the h-conformal magnetic formulation. Results: The obtained results of the method are checked/compared to be close to the reference solutions computed from the classcial finite element method and the measured results. This can be pointed out a very good agreement. Conclusion: The extended method has been also successfully applied to the practical problem (TEAM workshop problem 21, model B).

Spectropolarimetric analysis of prompt emission of GRB 160325A: jet with evolving environment of internal shocks

ABSTRACT GRB 160325A is the only bright burst detected by AstroSat CZT Imager in its primary field of view to date. In this work, we present the spectral and polarimetric analysis of the prompt emission of the burst using AstroSat, Fermi, and Niel Gehrels Swift observations. The prompt emission consists of two distinct emission episodes separated by a few seconds of quiescent/ mild activity period. The first emission episode shows a thermal component as well as a low polarization fraction of $PF \lt 37\, {{\ \rm per\ cent}}$ at $1.5\, \sigma$ confidence level. On the other hand, the second emission episode shows a non-thermal spectrum and is found to be highly polarized with $PF \gt 43\, {{\ \rm per\ cent}}$ at 1.5σ confidence level. We also study the afterglow properties of the jet using Swift/XRT data. The observed jet break suggests that the jet is pointed towards the observer and has an opening angle of 1.2° for an assumed redshift, z = 2. With composite modelling of polarization, spectrum of the prompt emission, and the afterglow, we infer that the first episode of emission originates from the photosphere with localized dissipation happening below it, and the second from the optically thin region above the photosphere. The photospheric emission is generated mainly by inverse Compton scattering, whereas the emission in the optically thin region is produced by the synchrotron process. The low radiation efficiency of the burst suggests that the outflow remains baryonic dominated throughout the burst duration with only a subdominant Poynting flux component, and the kinetic energy of the jet is likely dissipated via internal shocks which evolves from an optically thick to optically thin environment within the jet.

On-Chip Diffusion Bonding creates Stable Interconnections Usable at Temperatures over 300°C

In this paper, we present a conceptual design of an on-chip solder stack to connect silicon devices faster and more reliable. Almost all electronic devices rely on solder layers to provide electrical, mechanical, and thermal connections between components. We improve the solder connection with industry-standard solder parameters of 300°C and some minutes of soldering time. An ideal solder connection is composed of intermetallic phases (IMPs) at the interfaces between device and solder, and substrate and solder. Typically, a thin region of Sn-based solder remains between the two IMP layers at the interfaces. IMPs of copper (Cu) and tin (Sn) are Cu6Sn5 and Cu3Sn. The formation of IMPs is decisive for a good mechanical connection because of their high melting point and mechanical stability. To achieve these requirements, we implement the solder stack as a transient liquid phase bonding (TLPB) system. To realize durable interconnections, we use the diffusion of a high-melting first component in a second component, which is liquid at solder process temperature. Ongoing diffusion leads to the formation of IMPs with a melting point above process temperature, resulting in a solidification of the connection at constant temperature. By this isothermal solidification, the solder connection becomes more durable against mechanical and thermal load and is usable at temperatures exceeding 300°C.

Non–adiabatic tidal oscillations induced by a planetary companion

We calculate the dynamical tides raised by a close planetary companion on non–rotating stars of 1 M⊙ and 1.4 M⊙. Using the Henyey method, we solve the fully non–adiabatic equations throughout the star. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non–adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent with non–adiabaticity. Although this approximation generally applies in the low frequency limit, it also fails in the parts of the convection zone where the forcing frequency is small but larger than the Brunt-Väisälä frequency. We derive analytical estimates which give a good approximation to the numerical values of the magnitude of the ratio of the horizontal and radial displacements at the surface. The relative surface flux perturbation is also significant, on the order of 0.1% for a system modelled on 51 Pegasi b. Observations affected by the horizontal displacement may therefore be more achievable than previously thought, and brightness perturbations may be the result of flux perturbations rather than due to the radial displacement. We discuss the implication of this on the possibility of detecting such tidally excited oscillations, including the prospect of utilising the large horizontal motion for observations of systems such as 51 Pegasi.

Boundary Layers

It is found experimentally that all the components of fluid velocity (not just thenormal component) vanish at a wall. No matter how small the viscosity, the large velocity gradients near a wall invalidate Euler’s equations. Prandtl proposed that viscosity has negligible effect except near a thin region near a wall. Prandtl’s equations simplify the Navier-Stokes equation in this boundary layer, by ignoring one dimension. They have an unusual scale invariance in which the distances along the boundary and perpendicular to it have different dimensions. Using this symmetry, Blasius reduced Prandtl’s equations to one dimension. They can then be solved numerically. A convergent analytic approximation was also found by H. Weyl. The drag on a flat plate can now be derived, resolving d’Alembert’s paradox. When the boundary is too long, Prandtl’s theory breaks down: the boundary layer becomes turbulent or separates from the wall.

Interaction between mountain waves and shear flow in an inertial layer

Mountain-generated inertia–gravity waves (IGWs) affect the dynamics of both the atmosphere and the ocean through the mean force they exert as they interact with the flow. A key to this interaction is the presence of critical-level singularities or, when planetary rotation is taken into account, inertial-level singularities, where the Doppler-shifted wave frequency matches the local Coriolis frequency. We examine the role of the latter singularities by studying the steady wavepacket generated by a multiscale mountain in a rotating linear shear flow at low Rossby number. Using a combination of Wentzel–Kramers–Brillouin (WKB) and saddle-point approximations, we provide an explicit description of the form of the wavepacket, of the mean forcing it induces and of the mean-flow response. We identify two distinguished regimes of wave propagation: Regime I applies far enough from a dominant inertial level for the standard ray-tracing approximation to be valid; Regime II applies to a thin region where the wavepacket structure is controlled by the inertial-level singularities. The wave–mean-flow interaction is governed by the change in Eliassen–Palm (or pseudomomentum) flux. This change is localised in a thin inertial layer where the wavepacket takes a limiting form of that found in Regime II. We solve a quasi-geostrophic potential-vorticity equation forced by the divergence of the Eliassen–Palm flux to compute the wave-induced mean flow. Our results, obtained in an inviscid limit, show that the wavepacket reaches a large-but-finite distance downstream of the mountain (specifically, a distance of order$(k_{\ast }\unicode[STIX]{x1D6E5})^{1/2}\unicode[STIX]{x1D6E5}$, where$k_{\ast }^{-1}$and$\unicode[STIX]{x1D6E5}$measure the wave and envelope scales of the mountain) and extends horizontally over a similar scale.