Feeble forces and gravity

We develop a scenario in which feeble intermediate range forces emerge as an effect resulting from the compactification (à la Kaluza-Klein) of multidimensional theories. These feeble forces compete with gravity and in general permit different bodies to fall to earth with different accelerations. We show that these feeble forces are mediated by vectors (V) and/or scalars (S), whose dimensionless coupling constants are typically of order g_v g_s 10^–10 Under certain plausible assumptions the ranges of these feeble forces are expected to be of order 1 m to 1 km. It is conjectured that the general strategy will prove applicable to realistic multidimensional theories such as the 10-dimensional superstring theories. We speculate that deviations from the standard gravitational force-similar to the ones reported recently as a fifth force-may be interpreted as evidence for higher dimensions.This essay received the second award from the Gravity Research Foundation for the year 1986.Supported by the U.S. Department of Energy under grant # DE-FG03-84ER-40168.     

Anionic polymerization and copolymerization of p-bromostyrene

Monodispersed poly(4-bromostyrenes) (PBs) and their block copolymers with styrene, isoprene, and 3-methylbutene were prepared and characterized by GPC and NMR. Polystyryl and α-methylstyryl carbanions act as effective initiators of the anionic polymerization of Bs in THF. The undersirable side reactions, due to thermally or photochemically induced decomposition of the bromostyryl carbanions, PBs^?, may be eliminated by conducting the reaction at ?78°C and in the dark. Under such conditions, the rate constant of propagation, k_p (?78°), is 1.5 × 10³ M^?1 s^?1. Radical anions, \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm Bs}^{\mathop - \limits_ \cdot} $\end{document}, formed as result of electron transfer from sodium naphthalenide to Bs, may eject spontaneously bromine ions. This step and reactions involving the respective phenyl radicals compete at ?78°C with the addition steps leading to polymer formation. Electron affinity of Bs seems to be much higher than that of styrene or isoprene, and PBs^? carbanions do not add to the latter monomers. Addition of Bs to polyisoprenyl carbanions leads to formation of the BsIBs block copolymers. BsIBs, prepared in THF, may be converted by preferential hydrogenation of the 1–2 adducts into block copolymers of Bs with poly(2-methylbutene) and isoprenyl segments. The effectiveness of Bs as a flame retarding constituent of polymeric systems seems to be much more pronounced when it is incorporated in a “block” than in a random fashion. A considerably larger fraction of PBs is required to achieve the same LOI value when the respective homopolymers are blended. Spatial distribution of the easily charred microdomains in the block copolymers is believed to be responsible for this phenomenon.     

Perturbations of molecular extravalence excitations by rare-gas fluids

In this paper we report the results of an experimental study of the vacuum ultraviolet absorption spectra of molecular impurity states of methyl iodide in Ar (density range ? = 0–1.4 g cm^?3) and in Kr (? = 0–2.3 g cm^?3), of carbon disulphide in Ar (? = 0–1.4 g cm^?3) and of formaldehyde in Ar (? = 0–1.25 g cm^?3). The experimental results provide new information regarding medium perturbations of intravalenc transitions, of the lowest extravalence transitions and of transitions to mixed valence—Rydberg configurations, which serve as a diagnostic tool to distinguish between different types of electronic excitations. All the lowest extravalence molecular excitations exhibit appreciable blue spectral shifts at moderate and at high fluid densities, intravalence transitions are practically insensitive to medium effects, while excitations to mixed valence—Rydberg configurations are characterized by a moderate blue spectral shift. New information has been obtained concerning the energetics of molecular ionization processes in a dense fluid. The high n = 2–5 Rydberg states of CH₃l exhibit a large red shift at moderate (? = 0–0.5 cm^?3) Ar densities. The ionization potential E_g and the effective Rydberg constant G for CH₃I in Ar was found to decrease from G = 13.6 eV and E_g = 9.55 eV at ? = 0 and E_g = 9.08 eV and constant G for CH₃l in Ar was found to decrease from G = 13.6 eV and E_g = 9.55eV at ? = 0 and E_g = 9.08 eV and G ≈ 7.15 eV at ? = 0.5 g cm^?3. Experimental evidence was obtained for the identification of n = 2 molecular Wannier impurity states of CH₃I and of CH₂O in liquid Ar. These spectroscopic data result in E_g ≈ 8.6 eV for CH₃I in liquid Ar and E_g ≈ 10.2 eV for CH₂O in liquid Ar.     

Is there a unique consistent theory of quantum gravity?

Superstrings have been proposed as a quantum-theoretical framework for unifying all the fundamental forces, including gravity. We consider the question of whether there might be more general supersymmetric possibilities, based on higher extended objects such as membranes, jellies, etc. We argue that all the possible extended objects in all possible spacetime dimensions are quantummechanically inconsistent except for the 10-dimensional superstring and the 11-dimensional supermembrane. These are also the only two such theories that contain massless gravitons and, thus, that can describe gravity at low energies. It is remarkable that the range of possibilities can be narrowed down to this extent. Whether these can be further narrowed down to just one consistent theory remains open to further research.This essay received the first award from the Gravity Research Foundation for the year 1988.-Ed.     

Noise in a Small Genetic Circuit that Undergoes Bifurcation

Based on the consideration of Boolean dynamics, it has been hypothesized that cell types may correspond to alternative attractors of a gene regulatory network. Recent stochastic Boolean network analysis, however, raised the important question concerning the stability of such attractors. In this paper a detailed numerical analysis is performed within the framework of Langevin dynamics. While the present results confirm that the noise is indeed an important dynamical element, the cell type as represented by attractors can still be a viable hypothesis. It is found that the stability of an attractor depends on the strength of noise related to the distance of the system to the bifurcation point and it can be exponentially stable depending on biological parameters.     

Extension of the static shakedown theorems to softening materials

A generalization of the static shakedown theorems for elastic plastic hardening solids with isotropic [Mech. Res. Commun. 29 (2002) 159] and anisotropic [Acta Mechanica, 2004] damage accounting for the possibility of material softening is proposed.     

The effect of velocity on rigid wheel performance

A simulation model to predict the effect of velocity on rigid-wheel performance for off-road terrain was examined. The soil–wheel simulation model is based on determining the forces acting on a wheel in steady state conditions. The stress distribution at the interface was analyzed from the instantaneous equilibrium between wheel and soil elements. The soil was presented by its reaction to penetration and shear. The simulation model describes the effect of wheel velocity on the soil–wheel interaction performances such as: wheel sinkage, wheel slip, net tractive ratio, gross traction ratio, tractive efficiency and motion resistance ratio. Simulation results from several soil-wheel configurations corroborate that the effect of velocity should be considered. It was found that wheel performance such as net tractive ratio and tractive efficiency, increases with increasing velocity. Both, relative wheel sinkage and relative free rolling wheel force ratio, decrease as velocity increases. The suggested model improves the performance prediction of off-road operating vehicles and can be used for applications such as controlling and improving off-road vehicle performance.     

Duality in non-additive expected utility theory

Some duality problems in expected utility theory, raised by the introduction of non-additive probabilities, are examined. These problems do not arise if the probability measure is symmetric; i.e. has the property of complementary additivity. Additional, mild properties of coherence of conditional probabilities imply full additivity of the unconditional measure.