Symplectic Geometry of Quantum Noise

We discuss a quantum counterpart, in the sense of the Berezin–Toeplitz quantization, of certain constraints on Poisson brackets coming from “hard” symplectic geometry. It turns out that they can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics. Our findings include various geometric mechanisms of quantum noise production and a noise-localization uncertainty relation. The methods involve Floer theory and Poisson bracket invariants originated in function theory on symplectic manifolds.     

Carbon nanocones/discs – a new type of filler to improve the thermal and mechanical properties of polymer films

The mechanical characteristics and thermal properties of composite films based on the thermally stable aromatic polyimide (PI) (PMDA‐ODA) and carbon nanocones/discs (CNC) were studied. The introduction of CNC to PMDA‐ODA leads to the substantial increase of film stiffness. The Young's modulus values of the composite films are somewhat higher than those of the previously characterized composite films of this PI filled with nanoclay, carbon nanofibers, and asbestos‐like hydrosilicate nanotubes. The introduction of CNC into PMDA‐ODA (concentrations of CNC were up to 15 vol%) does not cause any marked aggregation of nanoparticles. The presence of CNC in the PI matrix does not affect the glass transition temperature of the polymer but hinders chain mobility at temperatures above T_g. This behavior makes it possible to increase the working temperature range of the composite films containing more than 5 vol% of CNCs, up to the temperature of thermal decomposition. The introduction of CNC into PMDA‐ODA leads to dramatic (～12 orders of magnitude) increase of active electrical conductivity of the material. Copyright © 2011 John Wiley & Sons, Ltd.     

Parameterization of electrostatic interactions for molecular dynamics simulations of heterocyclic polymers

The paper focuses on the problem of electrostatic interactions in molecular dynamics simulations of thermal properties of heterocyclic polymers. The study focuses on three thermoplastic polyimides synthesized on the basis of 1,3‐bis‐(3′,4‐dicarboxyphenoxy)benzene (dianhydride R) and three diamines: 4,4′‐bis‐(4″‐aminophenoxy) diphenylsulfone (diamine BAPS), 4,4′‐bis‐(4″‐aminophenoxy) biphenyl (diamine BAPB), and 4,4′‐bis‐(4''‐aminophenoxy) diphenyloxide (diamine BAPO). In the molecular dynamics simulations these polyimides were described by the Gromos53a5 force field. To parameterize the electrostatic interactions four methods of calculating the partial atomic charges were chosen: B3LYP/6–31G*(Mulliken), AM1(Mulliken), HF/6–31G*(Mulliken), and HF/6–31G*(ChelpG). As our parameterization is targeted to reproduce thermal properties of the thermoplastic polyimides, the choice of proper partial charges was finalized on a basis of the closest match between computational and experimental data for the thermal expansion coefficients of the polyimides below glass transition temperatures. Our finding clearly show that the best agreement with experimental data is achieved with the Mulliken partial atomic charges calculated by the Hartree‐Fock method with 6–31G* basis set. Furthermore, in addition to the thermal expansion coefficients this set of partial atomic charges predicts an experimentally observed relationship between glass transition temperatures of the three polyimides under study: . A mechanism behind the change in thermal properties upon the change in the chemical structure in considered polyimides may be related to an additional spatial ordering of sulfone groups due to dipole‐dipole interactions. Overall, the modified force‐field is proved to be suitable for accurate prediction of thermal properties of thermoplastic polyimides and can serve as a basis for building up atomistic theoretical models for describing other heterocyclic polymers in bulk. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 912–923     

Regioselective synthesis of 2-unsubstituted 1-aryl-4- and 1-aryl-5-acylimidazoles

An efficient and simple method for the synthesis of 2-unsubstituted 1-aryl-4- and 1-aryl-5-acylimidazoles has been developed. It consists in the condensation of α-diketone monooximes with aromatic amines and formaldehyde on the presence of boron trifluoride etherate, leading to the formation of stable boron trifluoride complexes of N-oxides. Further reduction of these complexes led to the corresponding imidazoles. This method permits broad variations of substituents in the aryl part of these compounds.     

Eigenvalues of a One-Dimensional Dirac Operator Pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a non-trivial square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.     

Symplectic packings and algebraic geometry

Oblatum 9-XI-1992 & 17-VI-1993     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.