Non-integrability of density perturbations in the FRW universe

We investigate the evolution equation of linear density perturbations in the Friedmann-Robertson-Walker universe with matter, radiation and the cosmological constant. The concept of solvability by quadratures is defined and used to prove that there are no "closed form" solutions except for the known Chernin, Heath, Meszaros and simple degenerate ones. The analysis is performed applying Kovacic's algorithm. The possibility of the existence of other, more general solutions involving special functions is also investigated.Comment: 13 pages. The latest version with added references, and a relevant new paragraph in section I

Many-body aspects of positron annihilation in the electron gas

We investigate positron annihilation in electron liquid as a case study for many-body theory, in particular the optimized Fermi Hypernetted Chain (FHNC-EL) method. We examine several approximation schemes and show that one has to go up to the most sophisticated implementation of the theory available at the moment in order to get annihilation rates that agree reasonably well with experimental data. Even though there is basically just one number to look at, the electron-positron pair distribution function at zero distance, it is exactly this number that dictates how the full pair distribution behaves: In most cases, it falls off monotonously towards unity as the distance increases. Cases where the electron-positron pair distribution exhibits a dip are precursors to the formation of bound electron--positron pairs. The formation of electron-positron pairs is indicated by a divergence of the FHNC-EL equations, from this we can estimate the density regime where positrons must be localized. This occurs in our calculations in the range 9.4 <= r_s <=10, where r_s is the dimensionless density parameter of the electron liquid.Comment: To appear in Phys. Rev. B (2003

Testing and selection of cosmological models with (1+z)6(1+z)^6 corrections

In the paper we check whether the contribution of $(-)(1+z)^6$ type in the Friedmann equation can be tested. We consider some astronomical tests to constrain the density parameters in such models. We describe different interpretations of such an additional term: geometric effects of Loop Quantum Cosmology, effects of braneworld cosmological models, non-standard cosmological models in metric-affine gravity, and models with spinning fluid. Kinematical (or geometrical) tests based on null geodesics are insufficient to separate individual matter components when they behave like perfect fluid and scale in the same way. Still, it is possible to measure their overall effect. We use recent measurements of the coordinate distances from the Fanaroff-Riley type IIb (FRIIb) radio galaxy (RG) data, supernovae type Ia (SNIa) data, baryon oscillation peak and cosmic microwave background radiation (CMBR) observations to obtain stronger bounds for the contribution of the type considered. We demonstrate that, while $\rho^2$ corrections are very small, they can be tested by astronomical observations -- at least in principle. Bayesian criteria of model selection (the Bayesian factor, AIC, and BIC) are used to check if additional parameters are detectable in the present epoch. As it turns out, the $\Lambda$CDM model is favoured over the bouncing model driven by loop quantum effects. Or, in other words, the bounds obtained from cosmography are very weak, and from the point of view of the present data this model is indistinguishable from the $\Lambda$CDM one.Comment: 19 pages, 1 figure. Version 2 generally revised and accepted for publicatio

Rendezvous of Distance-aware Mobile Agents in Unknown Graphs

We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree $\Delta$, the rendezvous time can be exponential in $\Delta$ in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every step. We show that these \emph{distance-aware} agents are able to rendezvous in any unknown graph, in time polynomial in all the local parameters such the degree of the nodes, the initial distance $D$ and the size of the smaller of the two agent labels $l = \min(l_1, l_2)$. Our algorithm has a time complexity of $O(\Delta(D+\log{l}))$ and we show an almost matching lower bound of $\Omega(\Delta(D+\log{l}/\log{\Delta}))$ on the time complexity of any rendezvous algorithm in our scenario. Further, this lower bound extends existing lower bounds for the general rendezvous problem without distance awareness

Model and experiments to determine lubricant film formation and frictional torque in aircraft landing gear pin joints

Pin joints are found in many large articulating structures. They tend to be under high load and articulate slowly; so, the joints typically operate in the boundary or mixed lubrication regimes. This means that the operating torque depends on the respective proportions of liquid and solid contact between the joint mating faces. In this article, a mixed lubrication model of a grease-lubricated landing gear joint is established to determine a theoretical Stribeck curve, frictional torque and lubricant film thickness under different loads. Parameters describing pin joint working conditions, geometry, lubricant properties and pin/bush texture are used. The model can also predict the proportion of the load that is supported by contacting asperities and lubricant film. The changing proportions of these two parts indicate transformations between different lubrication regimes. Experiments on an instrumented pin joint have been carried out to compare with the predicted friction and torque performance. Theoretical calculation results show good consistency with experimental plots at high load. But under low load, the real friction between pin and bush is significantly lower than theoretical predictions

Low-temperature thermal conductivity of solid carbon dioxide

Preliminary results of the thermal conductivity measurements performed in the temperature range 1.5-35 K on pure carbon dioxide are presented. The data below 25 K have been obtained for the first time. The thermal conductivity coefficient reaches very high value, of about 700 W/(m×K), unusual for simple molecular crystal. Straightforward analysis applied to the data indicates the case of large-grained sample

The peculiarities of heat transfer in CO₂ and N₂O solids at low temperatures

The thermal conductivities of CO₂ and N₂O solids have been investigated in the low-temperature range 1–40 K. The thermal conductivities of CO₂ and N₂O are large compared with those of simple molecular crystals such as N₂, CO, or O₂ in the whole investigated temperature range. Analysis of the experimental data by the Callaway method shows that relatively large size of crystalline grains, low density of dislocations and weak phonon–phonon interaction might be the reasons for the good thermal conduction in these crystals at temperatures near the maxima. A comparison between calculated values of the intensity of normal phonon scattering processes and experiment gives evidence that in N₂O there is an additional (in comparison with CO₂) giant scattering of phonons. This scattering is described in the frameworks of soft potential model by the resonance phonon scattering on tunnel states and low-energy vibratons

The influence of the disordered dipole subsystem on the thermal conductivity of the CO solid at low temperatures

The thermal conductivity of solid CO was investigated in the temperature range 1–20 K. The experimental temperature dependence of thermal conductivity of solid CO was described using the time-relaxation method within the Debye model. The comparison of the experimental temperature dependences of the thermal conductivity of N₂ and CO shows that in the case of CO there is an additional large phonon scattering at temperatures near the maximum. The analysis of the experimental data indicates that this scattering is caused by the frozen disordered dipole subsystem similar to a dipole glass. The scattering is described by the resonant phonon scattering on tunnelling states and on low-energy quasi-harmonic oscillations within the soft potential model

Heat transfer in Ar and N₂ doped solid CO

The measurements of thermal conductivity coefficient of a solid carbon monoxide crystal containing argon and nitrogen admixtures at different concentrations (1.5, 3, 6, 12.5, 25% for N2 and 0.5, 1, 1.25, 2, 4% for Ar) were performed in the temperature range from 1.5 to 40 K by steady-state heat flow method. For analysis of the experimental data the Callaway method in the framework of the Debye model was used. The contribution of various mechanisms of phonon scattering, including scattering by disordered dipoles of the CO matrix, to the thermal conductivity of CO–N₂ and CO–Ar solid solutions were taken into account