What is the Partition Bundle?

Six-dimensional (2, 0) theory can be defined on a large class of six-manifolds endowed with some additional topological and geometrical data. We discuss the nature of the object in such a theory that generalizes the partition function of a more conventional quantum field theory.     

What is the role of chaotic scattering in irreversible processes?

We study kinetic properties of simple mechanical models of deterministic diffusion like the scattering of a point particle in a billiard of Lorentz type and the multibaker area-preserving map. We show how dynamical chaos and, in particular, chaotic scattering are related to the transport property of diffusion. Moreover, we show that the Liouvillian dynamics of the multibaker map can be decomposed into the eigenmodes of diffusive relaxation associated with the Ruelle resonances of the Perron-Frobenius operator.     

What is the Relativistic Volterra Lattice?

We develop a systematic procedure of finding integrable 6ldquo;relativistic” (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First, for a given system one finds a local discretization living in the same hierarchy. Second, one considers this discretization as a particular Cauchy problem for a certain 2-dimensional lattice equation, and then looks for another meaningful Cauchy problem, which can be, in turn, interpreted as a new discrete time system. Third, one has to identify integrable hierarchies to which these new discrete time systems belong. These novel hierarchies are called then “relativistic”, the small time step $h$ playing the role of inverse speed of light. We apply this procedure to the Toda lattice (and recover the well-known relativistic Toda lattice), as well as to the Volterra lattice and a certain Bogoyavlensky lattice, for which the “relativistic” deformations were not known previously. Received: 1 April 1998 / Accepted: 21 July 1998     

What is the Cause of Inertia?

The question of the cause of inertial reaction forces and the validity of Mach's principle are investigated. A recent claim that the cause of inertial reaction forces can be attributed to an interaction of the electrical charge of elementary particles with the hypothetical quantum mechanical zero-point fluctuation electromagnetic field is shown to be untenable. It fails to correspond to reality because the coupling of electric charge to the electromagnetic field cannot be made to mimic plausibly the universal coupling of gravity and inertia to the stress-energy-momentum (i.e., matter) tensor. The gravitational explanation of the origin of inertial forces is then briefly laid out, and various important features of it explored in the last half-century are addressed.     

What is in a pebble shape?

We propose to characterize the shapes of flat pebbles in terms of the statistical distribution of curvatures measured along the pebble contour. This is demonstrated for the erosion of clay pebbles in a controlled laboratory apparatus. Photographs at various stages of erosion are analyzed, and compared with two models. We find that the curvature distribution complements the usual measurement of aspect ratio, and connects naturally to erosion processes that are typically faster at protruding regions of high curvature.     

What is the origin of chirality in the cholesteric phase of virus suspensions?

We report a study of the cholesteric phase in monodisperse suspensions of the rodlike virus fd sterically stabilized with the polymer polyethylene glycol (PEG). After coating the virus with neutral polymers, the phase diagram and nematic order parameter of the fd-PEG system then become independent of ionic strength. Surprisingly, the fd-PEG suspensions not only continue to exhibit a cholesteric phase, which means that the grafted polymer does not screen all chiral interactions between rods, but paradoxically the cholesteric pitch of this sterically stabilized fd-PEG system varies with ionic strength. Furthermore, we observe that the cholesteric pitch decreases with increasing viral contour length, in contrast to theories which predict the opposite trend. Different models of the origin of chirality in colloidal liquid crystals are discussed.     

What is the direction followed by a beam in a photonic medium?

The direction of propagation followed by a monochromatic beam in a periodic structure is generally deduced from the isofrequency diagram, which is related to the group velocity. However, the group velocity is the derivative of omega with respect to the wavenumber, while the behavior of the beam should depend on omega only. In the subwavelength regime, a method for choosing the relevant branch of the isofrequency diagram and relying on the behavior of the system at omega only is described.     

What precision in the Digital Terrain Model is required for noise mapping?

The Digital Terrain Model is the most basic and cumbersome element of any large-scale mapping projects. Accurate assessment of Digital Terrain Model data is an intricate but vital process. The impact of its accuracy on noise mapping has not been fully researched. The aim of this research on a specific case study is to analyse the differences in noise mapping results obtained from acoustic simulations carried out with different accuracies in Digital Terrain Model data. It seems that mapping with a 0.5 m degree of accuracy in elevation is sufficient for acoustic simulation, apart from the fact that it is easily achievable with current available techniques. In contrast, it can be concluded that mapping with 5 m accuracy in elevation is insufficient and may drastically change the evaluation of the percentage of people affected by noise.     

What is the ground-state structure of the thinnest Si nanowires?

Pristine silicon whiskers are compared through energy analysis by separating the surface, edge, and bulk contributions, and by energy computation for a variety of structures and diameters d. It is shown that for d<6 nm a polycrystalline wire of five-fold symmetry, rather than single-crystal types, represents the ground state. It remains stable in molecular dynamics tests up to approximately 1000 K. Its specific surface reconstruction also stands out in that it favors kinetics of whisker growth and thus appears potentially realizable.     

What is measured in the scanning gate microscopy of a quantum point contact?

The conductance change due to a local perturbation in a phase-coherent nanostructure is calculated. The general expressions to first and second order in the perturbation are applied to the scanning gate microscopy of a two-dimensional electron gas containing a quantum point contact. The first-order correction depends on two scattering states with electrons incoming from opposite leads and is suppressed on a conductance plateau; it is significant in the step regions. On the plateaus, the dominant second-order term likewise depends on scattering states incoming from both sides. It is always negative, exhibits fringes, and has a spatial decay consistent with experiments.