Non-trivial Shape Research Articles

SIGNATURE FOR THE SHAPE OF THE UNIVERSE

If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to reveal the topological signature of any Robertson–Walker (RW) spacetime with nontrivial topology. We also show through computer-aided simulations how one can extract the topological signatures of flat, elliptic, and hyperbolic RW universes with nontrivial topology.

The energy and temperature dependence of the electron-electron scattering rate in a one-dimensional surface superlattice

Increased interest in one-dimensional surface superlattices has motivated us to study the electron-electron scattering rate in these structures. Using a single-miniband model, we show a rich dependence of the scattering rate on the position of the Fermi level. This is particularly interesting from an experimental point of view, since the Fermi level can be externally controlled. When the Fermi level lies below the top of the miniband, the scattering rate is ( is the temperature, or the electron's excess energy above the Fermi level, whichever is larger). This behaviour is similar to that of a uniform two-dimensional electron system. Near the top of the miniband, the Van Hove singularity in the energy spectrum strongly affects the scattering rate, which is . Above the top of the miniband, the non-trivial shape of the Fermi surface leads to a rich dependence of the scattering rate on the wave vector of the scattered electron. This causes the scattering rate averaged over states near the Fermi surface to be . The method described here for calculating the scattering rate can be applied to any two-dimensional electron system with an arbitrary energy spectrum.

Microstructure and microdynamics of uninterrupted traffic flow

In this paper, ``uninterrupted homogeneous traffic flow'' is viewed as a dynamic system of spontaneously aggregating and breaking clusters of cars. This approach gives qualitative and quantitative descriptions of density fluctuations and dynamics of free traffic flow in terms of car clusters, and their distributions with respect to the number of cars in a cluster. The distributions have a nontrivial shape and a nonlinear dependence on the density of cars on the expressway. Their shape and evolution as a function of car density are described adequately by a model proposed here. This one-parameter model based on a modified Smoluchowski equation predicts a critical density at which a phase transition occurs from free to synchronized traffic flow for a multilane expressway: ${\ensuremath{\rho}}_{\mathrm{cr}}=16\ifmmode\pm\else\textpm\fi{}3{\mathrm{vehicles}\mathrm{}\mathrm{km}}^{\mathrm{\ensuremath{-}}1}{\mathrm{}(\mathrm{lane})}^{\mathrm{\ensuremath{-}}1},$ and that below this critical density traffic flow can be treated as a one-dimensional system. The model may also find application in the study of the low density pneumatic transport of granular and powdered materials.

A Hamiltonian approach to the investigation of the potential motions of an ideal fluid

Canonical variables are obtained for the equations of the potential motion of an ideal fluid in arbitrary curvilinear Euler and Lagrange systems of coordinates. The boundary conditions are written in Hamiltonian form with a Hamiltonian equal to the total energy of the fluid. The main purpose of this paper is to develop a Hamiltonian approach to the investigation of non-linear wave processes in volumes of an ideal fluid of non-trivial geometrical shape.

Study of a model Lagrangian in QCD for soft bag

The effective Lagrangian of Kogut-Susskind and 't Hooft is examined in connection with interpretation of the additional scalar field as a gluon-pairing field. The pairing effect on the short distance potential is found to be small. A bag limit of the Lagrangian is investigated. Integral representations for interquark potential and nontrivial bag shape are given for heavy quark-antiquark bag states.

Embeddings of compacta with shape dimension in the trivial range

In this paper a loop condition is defined which generalizes the cellularity criterion and applies to compacta with nontrivial shape. It is shown that if X , Y ⊂ E n , n ⩾ 5 X,Y \subset {E^n},n \geqslant 5 , are compacta which satisfy this loop condition and whose shape classes include a space having dimension in the trivial range with respect to n n , then Sh ⁡ ( X ) = Sh ⁡ ( Y ) \operatorname {Sh} (X) = \operatorname {Sh} (Y) is equivalent to E n − X ≈ E n − Y {E^n} - X \approx {E^n} - Y . An application is given to compacta with the shape of a compact connected abelian topological group.