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

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

Mid-Lift-to-Drag Ratio Rigid Vehicle Control System Design and Simulation for Human Mars Entry

The Mid-Lift-to-Drag Ratio Rigid Vehicle (MRV) is a proposed candidate in the NASA Evolvable Mars Campaign's (EMC) Pathfinder Entry, Descent, and Landing (EDL) architecture study. The purpose of the study is to design a mission and vehicle capable of transporting a 20mt payload to the surface of Mars. The MRV is unique in its rigid, asymmetrical lifting-body shape which enables a higher lift-to-drag ratio (L/D) than the typical robotic Mars entry capsule vehicles that carry much less mass. This paper presents the formulation and six-degree-of-freedom (6DOF) performance of the MRV's control system, which uses both aerosurfaces and a propulsive reaction control system (RCS) to affect longitudinal and lateral directional behavior

Effect of three common SNPs in 5′-flanking region of LEP and ADIPOQ genes on their expression in Polish obese children and adolescents

Genes encoding adipokines are considered as candidates for human obesity. In this study we analyzed the expression of leptin (LEP) and adiponectin (ADIPOQ) genes in relation to common 5′-flanking or 5′UTR variants: -2548G>A (LEP), 19A>G (LEP) and -11377C>G (ADIPOQ) in Polish obese children and adolescents. Relative transcription levels in the subcutaneous adipose tissue (real time RT–PCR) and serum protein concentrations (RIA) were measured in 48 obese subjects with known genotypes at three polymorphic sites and in five non-obese controls. None of the studied polymorphisms altered significantly the expression. Significantly elevated relative transcription levels of the LEP gene (P < 0.05) and serum leptin concentrations (P < 0.01) were recorded in obese patients, when compared with the non-obese controls, but such differences were not found for the ADIPOQ gene. Interestingly, the leptin to adiponectin protein concentration ratio (L/A) was approximately sevenfold higher in obese children and adolescents when compared with the non-obese controls (P < 0.001). Taking into consideration the observed relationship between the genotypes and the gene expression level we suggest that these SNPs are not conclusive markers for predisposition to obesity in Polish children and adolescents. On the other hand, we confirmed that the leptin to adiponectin gene expression ratio (L/A) is an informative index characterizing obesity

Universe from vacuum in loop-string cosmology

In this paper we study the description of the Universe based on the low energy superstring theory modified by the Loop Quantum Gravity effects.This approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007) 103531. We show that in the contrast with the string motivated pre-Big Bang scenario, the cosmological realisation of the $t$-duality transformation is not necessary to avoid an initial singularity. In the model considered the universe starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase the scale factor $a\to 0$, energy density $\rho \to 0$ and coupling of the interactions $g^2_s \to 0$. After this stage the universe evolves to the non-singular hot Big Bang phase $\rho \to \rho_{\text{max}} < \infty$. Then the standard classical universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the universe starts the evolution from the asymptotically free vacuum phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.Comment: JHEP3 LaTeX class, 19 pages, 9 figures, v2: added some comments and references, v3: new numerical result added, new figure

Excess thermal resistivity in N₂–CO solid solution at low carbon monoxide concentration

The results of measurements of the thermal conductivity of pure and carbon-monoxide-doped nitrogen crystals, for samples containing up to 0.7% of CO molecules, in the temperature range 1.2–26 K are presented. From the preliminary analysis it results that the interaction of phonons with admixture molecule featuring the same mass, as the host molecule, is relatively weak and depends weakly on the admixture concentration within investigated range of carbon monoxide in nitrogen crystal

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio