Institute for Problems in Mechanics

Abstract (by translator) A detailed report is given here of the general investigations carried out by the authors in the field of relativistic cosmology during the past years. The paper consists of two parts. The first part is devoted to a study of the singularities of the cosmological solutions of the gravitational equations. An attempt is made to provide an answer to one of the principal questions of modern cosmology: ‘does the general solution of the gravitational equations have a singularity?’ The authors give a negative answer to this question. The study carried out leads, in fact, to the general conclusion that the presence of a singularity with respect to time is not a necessary property of cosmological models of the general theory of relativity, and that the general case of an arbitrary distribution of matter and gravitational field does not lead to the appearance of a singularity. This result, however, does not exclude the possibility of the existence of more restricted classes of cosmological solutions of the gravitational equations which possess a true singularity. The search for such solutions, carried out by the authors, gives them reasons to believe that the possible types of such solutions are exhausted by those to which one is naturally led by the arguments given in §§ 3, 4 and Appendices C, G. As far as the solution corresponding to the real universe is concerned, its choice is connected with some deep physical requirements, which cannot be established on the basis of only the existing theory of gravitation. Only after establishing these requirements could it be determined whether or not the solution which satisfies them possesses a singularity. The second part of the paper contains an investigation of the gravitational stability of the isotropic model. There are grounds to believe that this model gives an adequate description of the present-day state of the universe considered on a large scale. The behaviour in time of various kinds of small perturbations to the isotropic model is studied. It is shown that perturbations which do not disturb the uniformity of the distribution of matter are either damped with time or remain constant. Perturbations which involve changes in the density of matter behave differently in expanding and contracting universes. In an expanding universe the changes in the density of matter grow slowly with time for long wavelength perturbations and decrease, with time for short wavelength perturbations. The contracting universe, however, is essentially unstable against such perturbations. The entire study is carried out on the basis of the Einstein equations in their classical form, without the ‘cosmological term’, in which form they follow logically from the general foundations of the theory of relativity.

What's Happening in the Heliosphere The influence of the Sun is felt well beyond the orbits of the planets. The solar wind is a stream of charged particles emanating from the Sun that carves a bubble in interstellar space known as the heliosphere and shrouds the entire solar system. The edge of the heliosphere, the region where the solar wind interacts with interstellar space, is largely unexplored. Voyager 1 and 2 crossed this boundary in 2004 and 2007, respectively, providing detailed but only localized information. In this issue (see the cover), McComas et al. (p. 959 , published online 15 October), Fuselier et al. (p. 962 , published online 15 October), Funsten et al. (p. 964 , published online 15 October), and Möbius et al. (p. 969 , published online 15 October) present data taken by NASA's Interstellar Boundary Explorer (IBEX). Since early 2009, IBEX has been building all-sky maps of the emissions of energetic neutral atoms produced at the boundary between the heliosphere and the interstellar medium. These maps have unexpectedly revealed a narrow band of emission that bisects the two Voyager locations at energies ranging from 0.2 to 6 kiloelectron volts. Emissions from the band are two- to threefold brighter than outside the band, in contrast to current models that predict much smaller variations across the sky. By comparing the IBEX observations with models of the heliosphere, Schwadron et al. (p. 966 , published online 15 October) show that to date no model fully explains the observations. The model they have developed suggests that the interstellar magnetic field plays a stronger role than previously thought. In addition to the all-sky maps, IBEX measured the signatures of H, He, and O flowing into the heliosphere from the interstellar medium. In a related report, Krimigis et al. (p. 971 , published online 15 October) present an all-sky image of energetic neutral atoms with energies ranging between 6 and 13 kiloelectron volts obtained with the Ion and Neutral Camera onboard the Cassini spacecraft orbiting Saturn. It shows that parts of the structure observed by IBEX extend to high energies. These data indicate that the shape of the heliosphere is not consistent with that of a comet aligned in the direction of the Sun's travel through the galaxy as was previously thought.

Abstract As a result of development of optics during many centuries the concept was formed that a medium can strongly influence on the light propagation, but the light itself cannot have backward influence on the medium. That concept was refuted only with appearing of coherent and high power radiation of lasers, see, e.g., Nobel Lecture by N. Bloembergen in 1981. A new field in physics–nonlinear optics—formed as a result. The main part of laser investigations concerns with nonlinear optical phenomena, nowadays. First of all these phenomena are of extraordinary interest and beauty and provide for new methods of physical investigations. Secondly, the knowledge of laws governing the interaction of a powerful light with a medium is necessary for the correct utilization of laser beams. Finally, a great number of devices of up-to-date laser optics is totally based on utilization of nonlinear optical effects; generation of higher harmonics of light, stimulated scattering of light, optical phase conjugation, self-focusing and optical bistability are amongst. To realize the nonlinear optical effects, however, it was nearly always necessary to use powerful lasers pulses.

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics,

As the Sun moves through the local interstellar medium, its supersonic, ionized solar wind carves out a cavity called the heliosphere. Recent observations from the Interstellar Boundary Explorer (IBEX) spacecraft show that the relative motion of the Sun with respect to the interstellar medium is slower and in a somewhat different direction than previously thought. Here, we provide combined consensus values for this velocity vector and show that they have important implications for the global interstellar interaction. In particular, the velocity is almost certainly slower than the fast magnetosonic speed, with no bow shock forming ahead of the heliosphere, as was widely expected in the past.

A simple two-stage technique for producing turbostratic carbon nanotubes via the co-electrospinning of two polymer solutions is described. These strong carbon nanotubes (see Figure) can be produced in lengths of the order of 10 cm while still maintaining submicrometer inner and outer diameters. They can be used in numerous applications, such as in drug delivery, hydrogen storage, and microfluidics. Supporting information for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2089/2006/c1153_s.pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

The density of wave-front dislocations for optical fields as a function of radiation parameters is investigated both theoretically and experimentally. A field with dislocations cannot be conjugated by means of flexible adaptive mirrors.

Abstract A review of the electronic properties of pure bismuth is given. Theoretical ideas on the band structure of bismuth and the dispersion relation for electrons near the bottom of the conduction band are briefly outlined. The experiments considered are those which give the most precise information on the Fermi surface (quantum effects in conductivity, cyclotron resonance, size effects, magnetoplasma waves, etc.) and on the electron energy spectrum near the bottom of the conduction band (studies in the quantum limit, infra-red magneto-reflection). The validity of the Cohen model as a first approximation to the electron spectrum in bismuth is established, and deviations from this model are described. Experiments are proposed which may give additional information on electrons in bismuth.

A coordinated effort to combine all three methods that are used to determine the physical parameters of interstellar gas in the heliosphere has been undertaken. In order to arrive at a consistent parameter set that agrees with the observations of neutral gas, pickup ions and UV backscattering we have combined data sets from coordinated observation campaigns over three years from 1998 through 2000. The key observations include pickup ions with ACE and Ulysses SWICS, neutral atoms with Ulysses GAS, as well as UV backscattering at the He focusing cone close to the Sun with SOHO UVCS and at 1 AU with EUVE. For the first time also the solar EUV irradiance that is responsible for photo ionization was monitored with SOHO CELIAS SEM, and the He I 58.4 nm line that illuminates He was observed simultaneously with SOHO SUMER. The solar wind conditions were monitored with SOHO, ACE, and WIND. Based on these data the modeling of the interstellar gas and its secondary products in the heliosphere has resulted in a consistent set of interstellar He parameters with much reduced uncertainties, which satisfy all observations, even extended to earlier data sets. It was also established that a substantial ionization in addition to photo ionization, most likely electron impact, is required, with increasing relative importance closer to the Sun. Furthermore, the total combined ionization rate varies significantly with solar latitude, requiring a fully three dimensional and time dependent treatment of the problem.

Herschel–Bulkley fluids are materials that behave as rigid solids when the local stress τ is lower than a finite yield stress τ0, and flow as nonlinearly viscous fluids for τ>τ0. The flow domain then is characterized by two distinct areas, τ<τ0 and τ>τ0. The surface τ=τ0 is known as the yield surface. In this paper, by using analytic solutions for antiplane shear flow in a wedge between two rigid walls, we discuss the ability of regularized Herschel–Bulkley models such as the Papanastasiou, the bi-viscosity and the Bercovier and Engelman models in determining the topography of the yield surface. Results are shown for different flow parameters and compared to the exact solutions. It is concluded that regularized models with a proper choice of the regularizing parameters can be used to both predict the bulk flow and describe the unyielded zones. The Papanastasiou model predicts well the yield surface, while both the Papanastasiou and the bi-viscosity models predict well the stress field away from τ=τ0. The Bercovier and Engelman model is equivalent to the Papanastasiou model provided a proper choice of the regularization parameter δ is made. It is also demonstrated that in some cases the yield surface can be effectively recovered using an extrapolation procedure based upon an analytical representation of the solution.

We present a new kind of UV-cured holographic grating that consists of polymer slices alternated with pure nematic films. By preventing the appearance of the nematic phase during the curing process, it is possible to avoid the formation of liquid-crystal droplets and obtain a sharp and uniform morphology, which reduces scattering losses and increases diffraction efficiency.

Rotating superfluid $^{3}\mathrm{He}$-$B$ is found to possess a new contribution to the NMR frequency shift, which changes sign on reversal of either the angular velocity of rotation or the magnetic field. For $p=29.3$ bars this gyromagnetic effect shows a discontinuity in magnitude at the first-order phase-transition temperature $\frac{T}{{T}_{c}}=0.6$, at which a change in the vortex-core structure takes place. These observations support the conclusion that the vortex core possesses a spontaneous intrinsic magnetization.

The Interstellar Boundary Explorer (IBEX) has been directly observing neutral atoms from the local interstellar medium for the last six years (2009–2014). This paper ties together the 14 studies in this Astrophysical Journal Supplement Series Special Issue, which collectively describe the IBEX interstellar neutral results from this epoch and provide a number of other relevant theoretical and observational results. Interstellar neutrals interact with each other and with the ionized portion of the interstellar population in the "pristine" interstellar medium ahead of the heliosphere. Then, in the heliosphere's close vicinity, the interstellar medium begins to interact with escaping heliospheric neutrals. In this study, we compare the results from two major analysis approaches led by IBEX groups in New Hampshire and Warsaw. We also directly address the question of the distance upstream to the pristine interstellar medium and adjust both sets of results to a common distance of ∼1000 AU. The two analysis approaches are quite different, but yield fully consistent measurements of the interstellar He flow properties, further validating our findings. While detailed error bars are given for both approaches, we recommend that for most purposes, the community use "working values" of ∼25.4 km s−1, ∼757 ecliptic inflow longitude, ∼ −51 ecliptic inflow latitude, and ∼7500 K temperature at ∼1000 AU upstream. Finally, we briefly address future opportunities for even better interstellar neutral observations to be provided by the Interstellar Mapping and Acceleration Probe mission, which was recommended as the next major Heliophysics mission by the NRC's 2013 Decadal Survey.

The dynamics of propagation and disintegration of laminar liquid jets moving in air has been investigated theoretically. It is assumed that the jet is thin, i.e. the ratio of the characteristic transverse size to the longitudinal one is small. It is assumed also that the lateral surface of the jet is free of shearing forces and is ‘almost free’ of normal ones in the sense that the normal tractions other than isotropic pressure are small in comparison with the internal stresses acting in the jet cross-section. Asymptotic quasi-one-dimensional equations of the continuity, momentum and moment of momentum of liquid motion in the jet have been derived. These equations were used as a basis for studying the process of growth of long-wave bending (transverse) disturbances of high-velocity jets of circular cross-section during their motion through air. The instability condition has been obtained and the growth rate of small bending disturbances of the jet has been found; the evolution of the jet shape at the stage of finite disturbances is investigated.

This paper provides a detailed description of the latest version of our model of the solar wind (SW) interaction with the local interstellar medium (LISM). This model has already been applied to the analysis of Lyman-alpha absorption spectra toward nearby stars and for analyses of Solar and Heliospheric Observatory/SWAN data. Katushkina et al. (this issue) used the model results to analyze IBEX-Lo data. At the same time, the details of this model have not yet been published. This is a three-dimensional (3D) kinetic-magnetohydrodynamical (MHD) model that takes into account SW and interstellar plasmas (including $\alpha$ particles in SW and helium ions in LISM), the solar and interstellar magnetic fields, and the interstellar hydrogen atoms. The latitudinal dependence of SW and the actual flow direction of the interstellar gas with respect to the Sun are also taken into account in the model. It was very essential that our numerical code had been developed in such a way that any numerical diffusion or reconnection across the heliopause had not been allowed in the model. The heliospheric current sheet is a rotational discontinuity in the ideal MHD and can be treated kinematically. In the paper, we focus in particular on the effects of the heliospheric magnetic field and on the heliolatitudinal dependence of SW.

Recently Lallement et al. (2005, Science, 307, 1447) reported that the direction of the flow of interstellar neutral hydrogen in the heliosphere is deflected by ~4° from the direction of the pristine local interstellar gas flow. The most probable physical phenomenon responsible for such a deviation is the interstellar magnetic field inclined to the direction of the interstellar gas flow. In this case the flow of the interstellar charged component is asymmetric and distorted in the region of the solar wind interaction with the local interstellar medium, which is called the heliospheric interface. The interstellar H atoms pass through the heliospheric interface and interact with the plasma component by charge exchange. Some imprints of the asymmetry of the heliospheric plasma interface should be seen in the distribution of the interstellar H atom component. In this letter we explore this scenario quantitatively and demonstrate that our new self-consistent 3D kinetic-MHD model of the solar wind interaction with the magnetized interstellar plasma is able to produce the measured deviation in the case of a rather strong interstellar magnetic field of ~2.5 μG inclined by ~45° to the direction of interstellar flow.

We present a new model of the heliospheric interface – the region of the solar wind interaction with the local interstellar medium. This new model performs a multi-component treatment of charged particles in the heliosphere. All charged particles are divided into several co-moving types. The coldest type, with parameters typical of original solar wind protons, is considered in the framework of fluid approximation. The hot pickup proton components created from interstellar H atoms and heliospheric ENAs by charge exchange, electron impact ionization and photoionization are treated kinetically. The charged components are considered self-consistently with interstellar H atoms, which are described kinetically as well. To solve the kinetic equation for H atoms we use the Monte Carlo method with splitting of trajectories, which allows us 1) to reduce statistical uncertainties allowing correct interpretation of observational data; 2) to separate all H atoms in the heliosphere into several populations depending on the place of their birth and on the type of parent protons.

A wide class of two-dimensional and three-dimensional steady-state and non-steady-state flows of a viscous incompressible fluid is considered. It is assumed that the components of the velocity of a fluid linearly depend on two spatial coordinates. The three-dimensional Navier-Stokes equations in this case are reduced to a closed determining system that consists of six equations with partial derivatives of the third and second orders. A brief review of the known exact solutions of this system and the respective flows of a fluid (Couette-Poiseuille, Ekman, Stokes, Karman, and other flows) is given. The cases of reducing a determining system to one or two equations are described. Many new exact solutions of two-dimensional and three-dimensional nonstationary Navier-Stokes equations containing arbitrary functions and arbitrary parameters are derived. Periodic (both in spatial coordinates and in time) and some other solutions that are expressed in terms of elementary functions are described. The problems of the nonlinear stability of solutions are studied. A number of new hydrodynamic problems are considered. A general interpretation of the solutions as the main terms of the Taylor series expansion in terms of radial coordinates is given.

We present new kinetic-gasdynamic model of the solar wind interaction with the local interstellar medium. The model incorporates several processes suggested by McComas et al. (2009) for the origin of the heliospheric ENA ribbon -- the most prominent feature seen in the all sky maps of heliospheric ENAs discovered by the Interstellar Boundary Explorer (IBEX). The ribbon is a region of enhanced fluxes of ENAs crossing almost the entire sky. Soon after the ribbon's discovery it was realized (McComas et al., 2009) that the enhancement of the fluxes could be in the directions where the radial component of the interstellar magnetic field around the heliopause is close to zero (Schwadron et al., 2009). Our model includes secondary charge exchange of the interstellar H atoms with the interstellar pickup protons outside the heliopause and is a further advancement of the kinetic-gasdynamic model by Malama et al. (2006) where pickup protons were treated as a separate kinetic component. Izmodenov et al. (2009) have shown in the frame of Malama's model that the interstellar pickup protons outside the heliopause maybe a significant source of ENAs at energies above 1 keV. The difference between the current work and that of Izmodenov et al. (2009) is in the assumption of no-scattering for newly created pickup protons outside the heliopause. In this limit the model produces a feature qualitatively similar to the ribbon observed by IBEX.

In this paper, a capsule type robot is designed. The motion is described. The robot has no moving part outside its body, no legs, no wheel. Its motion is purely based on its internal force and friction with the environments. A four step motion pattern is proposed. A minimal energy solution is derived. A prototype capsule robot, consisting a plastic tube with a copper coil and a NiFeB magnet rod which can slide inside the tube, is built. It is essentially a motion magnet linear motor. The motion generation results are verified experimentally