Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion

I explain the geometric basis for the recently-discovered nonholonomic mapping principle which permits deriving laws of nature in spacetimes with curvature and torsion from those in flat spacetime, thus replacing and extending Einstein's equivalence principle. As an important consequence, it yields a new action principle for determining the equation of motion of a free spinless point particle in such spacetimes. Surprisingly, this equation contains a torsion force, although the action involves only the metric. This force makes trajectories autoparallel rather than geodesic, as a manifestation of inertia. A generalization of the mapping principle transforms path integrals from flat spacetimes to those with curvature and torsion, thus playing the role of a quantum equivalence principle. This generalization yields consistent results only for completely antisymmetric or for gradient torsion.     

Diagram of State of Stiff Amphiphilic Macromolecules

Summary: We studied coil-globule transitions in stiff-chain amphiphilic macromolecules via computer modeling and constructed phase diagrams for such molecules in terms of solvent quality and persistence length. We showed that the shape of the phase diagram essentially depends on the macromolecule degree of polymerization. Relatively short amphiphilic molecules always form a spherical globule in a poor solvent, and the coil-globule transition includes one or two intermediate conformations, depending on the chain's stiffness. These are a disk-like globule in case of high enough Kuhn segment length, and a pearl necklace-like structure of spherical micelles and a disk-like globule in case of relatively flexible chains. The phase diagram of a long stiff amphiphilic chain was found to be more complex still. Thus three specific regions can be distinguished in the poor solvent region, depending on the chain stiffness. These correspond to a cylindrical globule without any specific backbone ordering, a cylindrical globule containing blobs with collagen-like ordering of the chain, and co-existence of collagen-like and toroidal globules. In the intermediate transition region in this case, apart from the pearl necklace-like conformations with spherical micelles, necklace conformations can be also observed where the polymeric chain has collagen-like ordering within each bead.     

Jeffreys fluids in forced elongation

In this paper we study existence, uniqueness and regularity of solutions for the equations governing the forced elongation of fluids with differential constitutive law of Jeffreys type. These equations consist of nonlinear first-order hyperbolic equations in one spatial dimension. Forced elongation is imposed through velocity boundary conditions at the domain entry and exit. The existence result is based on the Schauder fixed point theorem and energy methods in the space of boundary-regular functions.     

Standard single-mode fibers as convenient means for the generation of ultrafast high-pulse-energy super-continua

High-pulse-energy super-continua featuring an M² of one were generated in standard single-mode fibers. The highest pulse energy achieved was ∼600 nJ and the pulse duration was ∼1 ps. The spectral width of the generated continua extended over up to 35% of the pump wavelength. PACS 42.65.-k; 42.81.-i; 42.79.Nv     

Classical solutions of quasilinear parabolic systems on two dimensional domains

Using results on abstract evolutions equations and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems admit a local, classical solution in the space of p–integrable functions, for some p greater than 1, over a bounded two dimensional space domain. The treatment of such equations in a space of integrable functions enables us to define the normal component of the current across the boundary of any Lipschitz subset. As applications we have in mind systems of reaction diffusion equations, e.g. van Roosbroeck’s system.     

Numerical calculation of current density distributions in high temperature superconducting tapes with finite thickness in self field and external field

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of J_c is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.     

Synthesis of analogs of D-Ala-D-Ala as potential inhibitors of bacterial cell wall biosynthesis

The syntheses of the L,L- and D,D-stereoisomers of N- phenoxyacetyl -X-alanine in which X = Ser, Ala( beta Cl ) or Arg, are described. The antibacterial activity of these peptides and some of their synthetic intermediates has been examined. Four of the intermediates in which X = Ala( beta Cl ) and Arg(NO2), which possess C-terminal benzyl ester groups, were active against viridans streptococci and Streptococcus agalactiae. The D,D-enantiomers were more active than the corresponding L,L-isomers. None of the compounds were active against beta-lactamase producing bacteria or acted as beta-lactamase inhibitors.     

Ueber die Best?ndigkeit einiger Explosivstoffe

Ohne Zusammenfassung     

Exceptional Modules for Tubular Canonical Algebras

Let Λ be a tubular canonical algebra of quiver type over a field. We show that each exceptional Λ-module can be exhibited by matrices involving as coefficients 0, 1 and –1 if Λ is of type (3,3,3), (2,4,4) or (2,3,6) and by matrices involving as coefficients 0, 1, –1, λ, –λ and λ–1 if Λ is of type (2,2,2,2) and defined by a parameter λ. Presented by Claus M. Ringel.     

Electrochemical properties of a proton conducting polymer

Electrochemical, optical and thermal characterisation of a proton conducting polymer system based on poly(2-acrylamido-2 methyl-propane-sulfonic acid) (Poly-AMPS) for use in electrochromic windows is reported. The polymer electrolyte has been obtained by cross-linking branched poly(ethylene imine) with the 2-acrylamido-2 methyl-propane-sulfonic acid. The conductivity of the poly-AMPS films is influenced by the water content in the membrane and can vary between 10⁻⁴ and 10⁻⁷ Ω⁻¹ cm⁻¹. A minimum activation energy of 17±3 kJ/mol is estimated by a simple Arrhenius model. Poly-AMPS is very sensitive to the humidity in the surroundings and electrochromic windows should be sealed if poly-AMPS is used. Temperatures above 45–50 °C give increasing cracks in the polymer and loss of adhesion to the electrode surface. Paper presented at the 4th Euroconference on Solid State Ionics, Renvyle, Galway, Ireland, Sept. 13–19, 1997