Size quantization in high-temperature superconducting cuprates and a link to Einstein's diffusion law

Optimum doping of high-temperature superconductors (HTSC) defines a superconducting unit volume for each HTSC. For a single-mode HTSC, e.g., a cuprate with one CuO₂ plane, the volume is given by V_sc=cx², where c is the unit cell height and x the doping distance. The experimental resistivity at T_c is connected to the structure by ρ(exp)≈c×h/(2e²). Combining this result with the classical definition of resistivity leads to an equation similar to Einstein's diffusion law x²/(2τ)=h/(2M_eff)=D, where τ is the relaxation time, M_eff=2m_e and D the diffusion constant. It has also been shown that the mean free path d=x. The Einstein–Smoluchowski diffusion relation D=μk_BT_c provides a connection to T_c.     

Heating and acceleration of charged particles during magnetic dipolarizations

In this paper, we analyzed the thermal and energy characteristics of the plasma components observed during the magnetic dipolarizations in the near tail by the Cluster satellites. It was previously found that the first dipolarization the ratio of proton and electron temperatures (T _p/T _e) was ~6–7. At the time of the observation of the first dipolarization front T _p/T _e decreases by up to ~3–4. The minimum value T _p/T _e (~2.0) is observed behind the front during the turbulent dipolarization phase. Decreases in T _p/T _e observed at this time are associated with an increase in T _e, whereas the proton temperature either decreases or remains unchanged. Decreases of the value T _p/T _e during the magnetic dipolarizations coincide with increase in wave activity in the wide frequency band up to electron gyrofrequency f _ce. High-frequency modes can resonantly interact with electrons causing their heating. The acceleration of ions with different masses up to energies of several hundred kiloelectron-volts is also observed during dipolarizations. In this case, the index of the energy spectrum decreases (a fraction of energetic ions increases) during the enhancement of low-frequency electromagnetic fluctuations at frequencies that correspond to the gyrofrequency of this ion component. Thus, we can conclude that the processes of the interaction between waves and particles play an important role in increasing the energy of plasma particles during magnetic dipolarizations.     

The optimization of the orbital Hohmann transfer

There are four bi-impulsive distinct configurations for the generalized Hohmann orbit transfer. In this case the terminal orbits as well as the transfer orbit are elliptic and coplanar. The elements of the initial orbit a₁, e₁ and the semi-major axis a₂ of the terminal orbit are uniquely given quantities. For optimization procedure, minimization is relevant to the independent parameter e_T, the eccentricity of the transfer orbit. We are capable of the assignment of minimum rocket fuel expenditure by using ordinary calculus condition of minimization for |ΔV_A|+|ΔV_B|=S.We exposed in detail the multi-steps of the optimization procedure. We constructed the variation table of S(e_T) which proved that S(e_T) is a decreasing function of e_T in the admissible interval [e_Tmin,e_Tmax]. Our analysis leads to the fact that e₂=1 for e_T=e_Tmax, i.e. the final orbit is a parabolic trajectory.     

Organization of the on-ground data processing for remote sensing purposes using finite rings and fields concept

In most of the modern on-ground data processing systems for remote sensing the digital signal conversions, on the analogy of the analog signal, are defined over a field of complex numbers, C, as the digital signal values (as well as those of the analog one) may be regarded as a subset of the field. Such an approach requires substantial computing and hardware expenses. For a signal defined in the finite range N (N = 0, 1, …, n − 1) most of the algorithms require the number of operations proportional to log N, N, N² and even to greater powers of N. That is why the building up of the data processing system mathematical model with a minute number of computations, as well as the computations organization, is a problem of great importance. It is not always necessary to build up a model using transformations over the field C. These transformations may be also defined over some other (abstract) fields, e.g. over the finite field GF(p) or finite residue ring moduli M, Z_M. This approach gives numerous advantages. They are discussed in the presented paper along with limitations of the approach. A series of the data processing system models are described. The design concepts for the on-ground images processing equipment are also discussed.     

Families of periodic solutions in three-dimensional restricted three-body problem

Planar orbits of three-dimensional restricted circular three-body problem are considered as a special case of three-dimensional orbits, and the second-order monodromy matrices M (in coordinate z and velocity v _z ) are calculated for them. Semi-trace s of matrix M determines vertical stability of an orbit. If |s| ≤ 1, then transformation of the subspace (z, v _z ) in the neighborhood of solution for the period is reduced to deformation and a rotation through angle φ, cosφ = s. If the angle ? can be rationally expressed through 2π,φ = 2π·p/q, where p and q are integer, then a planar orbit generates the families of three-dimensional periodic solutions that have a period larger by a factor of q (second kind Poincareé periodic solutions). Directions of continuation in the subspace (z, v _z ) are determined by matrix M. If |s| < 1, we have two new families, while only one exists at resonances 1: 1 (s = 1) and 2: 1 (s = ?1). In the course of motion along the family of three-dimensional periodic solutions, a transition is possible from one family of planar solutions to another one, sometimes previously unknown family of planar solutions.     

Numerical investigation on cavity structure of solid-fuel scramjet combustor

The influences of miscellaneous combustor structures for solid fuel scramjet combustion on the performance are investigated, including a detailed interaction analysis between shocks/waves and combustion. Hydroxyl-terminated polybutadiene is chosen as the solid fuel with the non-premixed equilibrium probability density function combustion model. The results show combustion enhancement when structure of combustor is modified. The radical emphasis is to examine the sensitivity of the properties due to variations on the length-to-depth ratio of cavity, aft wall angle, and offset ratio. It is noted that there is an appropriate structure of cavity (L/D=4, θ=45°, and D_d/D_u=1.25–1.5) regarding the combustion efficiency, total pressure loss and specific impulse. The observation of function for combustor components provides instructional insight into the design considerations for a combustor of a solid-fuel scramjet.     

Definition and analysis of properties of optimal three-impulse point-to-orbit transfers under time constraint

This paper deals with energetically optimal multi-impulse transfers of a spacecraft in the central Newtonian gravitational field near a planet. The transfer from a point on initial orbit to the final orbit with the given angular momentum and energy constants is considered. The transfer time is bounded above.With the distance from spacecraft to planet limited and the time free, such parameters of given orbits are chosen that the 3-impulse apsidal transfer T_r is optimal with an intermediate impulse at the maximum distance. On the basis of necessary optimality conditions an algorithm is developed to numerically determine the desired optimal transfer trajectory T_t under time constraint, the apsidal trajectory T_r being taken as initial approach. From the geometry and energy viewpoints, both trajectories T_t and T_r are close to each other. The trajectory T_t is also 3-impulsive, all impulses on it are nonapsidal. The distance from the planet is larger and the sum of impulses is less for this trajectory than for the initial trajectory T_r with the same transfer time.The simplified solution of the problem is constructed producing good approximation to the exact numerical optimization results. The solution asymptotics is found when the transfer time tends to infinity.     

Characteristics of thermal ion outflows in the polar cap according to data of the <Emphasis Type="Italic">Interball-2</Emphasis> satellite

Characteristics of polar wind fluxes at a height of ∼20000 km measured by the Hyperboloid mass-spectrometer installed onboard the Interball-2 satellite are presented in the paper. The characteristics are presented for the upwelling flows of ionospheric ions H⁺, He⁺, and O⁺ from the sunlit polar cap in the period of solar activity minimum. Orbit segments with minimal precipitation of magnetospheric ions and electrons were preliminarily selected, and the measurements where the fluxes of ions coming from the cusp/cleft were excluded as carefully as possible. Thus, the densities, field-aligned velocities, and temperatures of ions in the regions where fluxes of polar wind could be detected with the maximal probability degree are presented in the paper. It is found that cases when only H⁺ ions are reaching the detector are with high probability the polar wind outflows. Their characteristics agree well with the Tube-7 hydrodynamic model and are as follows: n ≈ 1.5 cm⁻³, V _∥ ∼ 21 km/s; T _∥ = 3500 K, and T _⊥ = 2000 K. In cases when He⁺ and O⁺ ions are also detected, the temperatures are substantially higher than the model ones, and the measured field-aligned velocities of O⁺ fluxes are several times higher than the model ones. Moreover, it was revealed that the polar wind outflows are predominantly observed in the polar cap regions where the polar rain fluxes are very small.     

On the limiting mass of a dense stellar matter

In the present work, we have derived an expression $\text{M}{}_{\mathrm{L}}\text{? 4.738 M}{}_{\mathrm{\odot }}$ (M_⊙ = 1.985 × 10³³ g = mass of the Sun) giving the “limiting” value of the mass of a dense stellar matter, by introducing the concept of nuclear size correction in the theory of relativistic Thomas Fermi model for a compressed atom. We find that $\text{M}{}_{\mathrm{L}}\text{? 5.1571 M}{}_{\mathrm{<mtext>Ch</mtext>}}\text{and}\text{=3.2750(M}{}_{\mathrm{<mtext>O</mtext>}}\text{)}{}_{\mathrm{<mtext>Prev</mtext>}}$ [M_Ch and (M_O)_Prev denote respectively the Chandrasekhar and author's “limiting” masses]. By making a comparative study with those of previous results it has been shown that our present treatment would provide satisfactory results for the density ranges from ? ? 10⁸ up to $\text{? ? 10}{}^{11}\text{g}\text{/}\text{cm}{}^3$. Other results of cognate interest in the non-relativistic regime 10³ < ? ? 10⁵ (without the nuclear size effect) are presented. The astrophysical implications of the results are mentioned.     

Mass-, time-, and energy-characteristics of the interstellar flights during the long proper time of astronauts

The existence of extraterrestrial intelligence (ETI) and extraterrestrial scientific-technical civilization (STC) is of principal importance for CETI (communication with extraterrestrial intelligence) and SETI (search for extraterrestrial intelligence). According to Kardashev and Bracewell, the Earth-like STC in their farther development can expand to the nearby planetary systems of the Galaxy, creating galactic community (Bracewell's galactic club).In a previous paper the possibilities of the one-step relativistic rocket interstellar flight during the proper time of life of one-two generations of astronauts were analysed. The realization of such interstellar flights is very improbable, even to the nearest stars. These results could be true for the case of the comparatively short proper time of astronauts, i.e. large acceleration. But flights to the nearest stars could be realized with small and very small accelerations. In the present paper are calculated the proper times t in the reference systems connected with the astronauts (S₂), as well as the times T in the reference systems (S₁)-inertial, velocities v in S₁, mass ratios, powers and energies for various flights, exhaust velocities u and accelerations a. Results are critically discussed.     

Material performance under combined stresses in the hard space environment of the sunprobe helios-a

The Sun mission of the German-US-sunprobe HELIOS-A, the first man-made satellite which approaches the Sun as close as 0.3 AU, covers now more than half a sun-cycle.Therefore the long term behaviour of surface materials which usually are applied on spacecraft as aluminized Teflon, Second-Surface-Mirrors (SSM) made from fused silica and Solar Cells (SC), under extreme stresses and combined loads, shall be evaluated.Based upon the temperature readings of the house-keeping data from HELIOS, a semi-quantitative relationship between the different loads (e.g. radiation, solar wind) and the spacecraft response was established using the results of the first four orbits.From these temperatures, α(t, T)-values were calculated. The related changes of the absorptance values are interpreted in terms of degradation and contamination of the surface materials concerned. Here, not only physico-chemical considerations and models but also the results from thorough ground tests are used to describe the experienced effects by a semi-theoretical function.Taking the derived α(t, T)-values, temperatures are calculated and a long term prediction for 20 orbits is made. The predicted temperature values are compared with the housekeeping data of 15 orbits, i.e. until 1982; the deviations are explained and the validity of the chosen model discussed.     

Non-linear behaviour effect on Mach cone behind the body moving in rarefied ionosphere

The problem of rarefied plasma flow near the body in highly rarefied ionized planet atmosphere is considered. Plasma is supposed to be non-isothermal, T_i ? T_e. In the case of thermodynamically non-equilibrium electrons the solution of modified Korteweg-de Vries equation is estimated in the Mach cone region behind the body and it is shown that Mach cone appears to be curved.     

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

The surface temperature distributions due to thermocapillary convections in a thin liquid layer with heat fluxes imposed on the free surface are investigated. The nondimensional analysis predicts that, when convection is important, the characteristic length scale in the flow direction L, and the characteristic temperature difference ΔT₀, can be represented by and , respectively, where L_R and ΔT_T are the reference scales used in the conduction-dominant situations with A denoting the aspect ratio and Ma the Marangoni number. Having had L and ΔT₀ defined, the global surface-temperature gradient ( ), the global thermocapillary driving-force, and other interesting features can then be readily determined. Finally, numerical calculations involving a Gaussian heat flux distribution are presented to justify these two relations.     

Orbit prediction and shuttle rendezvous strategy for eureca

The European Retrievable Carrier (EURECA) is a platform to be launched, deployed and retrieved in low Earth orbit by the Space Shuttle.A newly developed analytical orbit prediction method is described which meets the severe requirements for EURECA's orbit propagation. It is based on an averaging procedure including the Earth's zonal harmonics J₂, J₃ and J₄ and a refined treatment of the air drag perturbation where EURECA's large solar panels are taken into account. Some orbit prediction results are included.In order to offer more flexibility for the Shuttle retrieval of EURECA, it is proposed to execute a part of the rendezvous manoeuvres by EURECA. A corresponding strategy is described.     

Fine structure of interplanetary shock fronts from the data of the BMSW instrument of the PLASMA-F experiment

The paper is concerned with studying the thickness of fronts of 38 interplanetary shocks detected by the BMSW instrument, which is a part of the scientific payload of the SPEKTR-R spacecraft, which was launched into a highly elliptical orbit in 2011. The main parameters of the interplanetary shocks have been calculated as follows: the ratio of thermal pressure to magnetic pressure before the front β, the angle between the shock front normal and the undisturbed magnetic field θ_Bn, the ratio of the shock propagation velocity to the magnetosonic velocity in the undisturbed region M_ms, and the shock front velocity relative to the Earth. It has been shown that the front thickness determined from the plasma parameters approximately matches the front thickness obtained from the magnetic field measurements and lies between 0.5 and 5 proton inertial lengths. In some events, the oscillations have been observed (upstream and downstream of the shock) in plasma parameters and in the magnetic field data. The length has been found to be between 0.5 and 6 proton inertial lengths for the preceding oscillations and between 0.5 and 10 proton inertial lengths for the following oscillations. The average value of the proton inertial length is 62 km.     

Numerical simulation of effects of the August 11, 1999 solar eclipse in the outer ionosphere

The results of a numerical simulation of such parameters of the topside ionosphere as concentration N _e and temperature T _e of electrons, and concentration n(H⁺) and fluxes along the magnetic field lines Φ(H⁺) of H⁺ ions at an altitude of ～2000 km for the conditions of the August 11, 1999 solar eclipse are presented. The calculations were performed using the Global Self-consistent Model of the Thermosphere, Ionosphere, and Protonosphere of the Earth (GSM TIP). It is shown that during the eclipse, in addition to a region of decreased values of T _e in the Northern Hemisphere and in the magnetically conjugate region in the Southern Hemisphere, regions of electron heating emerge in both hemispheres. Simultaneously, an extended region of decreased values of N _e comes into existence and moves behind the Moon’s shadow. Regions with decreased (down to ～30%) and enhanced (up to ～50%) concentrations of H⁺ ions are detected in the global distribution of these ions.     

Observations of corotating solar wind structures at radio sounding by signals of the <Emphasis Type="Italic">Rosetta</Emphasis> and <Emphasis Type="Italic">Mars Express</Emphasis> spacecraft

In the implementation of the space projects Rosetta and Mars Express, a large-scale series of experiments has been carried out on radio sounding circumsolar plasma by decimeter (S-band) and centimeter (X-band) signals of the Rosetta comet probe (from October 3 to October 31, 2010) and the Mars Express satellite of Mars (from December 25, 2010 to March 27, 2011). It was found that in the phase of ingress the spacecraft behind the Sun, the intensity of the frequency fluctuations increases in accordance with a power function whose argument is the solar offset distance of radio ray path, and when the spacecraft is removed from the Sun (the egress phase), frequency fluctuations are reduced. Periodic strong increases in the fluctuation level, exceeding by a factor of 3–12 the background values of this value determined by the regular radial dependences, are imposed on the regular dependences. It was found that increasing the fluctuations of radio waves alternates with the periodicity m × T or n × T, where m = 1/2, n = 1, аnd T is the synodic period of the Sun’s rotation (T ≈ 27 days). It was shown that the corotating structures associated with the interaction regions of different speed fluxes are formed in the area of solar wind acceleration and at distances of 6–20 solar radii already have a quasi-stationary character.     

An inversion approach for lunar regolith layer thickness using optical albedo data and microwave emission simulation

An approach to inversion of the lunar regolith layer thickness by using multi-channel brightness temperature observation in passive microwave remote sensing is developed. To first make simulation of brightness temperature from the lunar layered media, the lunar regolith layer thickness (d) is proposed being constructed by available lunar DEM (digital elevation mapping) and on site measurements. The physical temperature distribution (T) over the lunar surface is also empirically assumed as a monotonic function of the latitude. Optical albedo of the lunar nearside from the telescopic observation is employed to construct the spatial distribution of the FeO+TiO₂ content (S) in the lunar regolith layer. A statistic relationship between the DEM and S of the lunar nearside is further extended to construction of S of the lunar farside. Thus, the dielectric permittivity (ε) of global lunar regolith layer can then be determined. Based on all these conditions (d,T,ε), brightness temperature of the lunar regolith layer in passive microwave remote sensing, which is planned for China's Chang-E lunar project, is numerically simulated by a parallel layering model using the strong fluctuation theory of random media.Then, taking these simulations with random noise as observations, an inversion method of the lunar regolith layer thickness is developed by using three- or two-channels brightness temperatures. When the S is low, and the four channels brightness temperatures in China's Chang-E project are well distinguishable, the regolith layer thickness and physical temperature of the underlying lunar rock media can be inverted by the three-channels approach. When the S becomes high that the brightness temperature at high frequency channels such as 19.35, 37 GHz are saturated, the regolith layer thickness is alternatively inverted only by the two-channels approach.Numerical simulation and inversion approach in this paper make an evaluation of the performance for lunar passive microwave remote sensing, and for future data calibration and validation.     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

Experimental investigation of fuel regression rate in a HTPB based lab-scale hybrid rocket motor

The fuel regression rate is an important parameter in the design process of the hybrid rocket motor. Additives in the solid fuel may have influences on the fuel regression rate, which will affect the internal ballistics of the motor. A series of firing experiments have been conducted on lab-scale hybrid rocket motors with 98% hydrogen peroxide (H₂O₂) oxidizer and hydroxyl terminated polybutadiene (HTPB) based fuels in this paper. An innovative fuel regression rate analysis method is established to diminish the errors caused by start and tailing stages in a short time firing test. The effects of the metal Mg, Al, aromatic hydrocarbon anthracene (C₁₄H₁₀), and carbon black (C) on the fuel regression rate are investigated. The fuel regression rate formulas of different fuel components are fitted according to the experiment data. The results indicate that the influence of C₁₄H₁₀ on the fuel regression rate of HTPB is not evident. However, the metal additives in the HTPB fuel can increase the fuel regression rate significantly.