Field theory onR×S 3 topology. III: The Dirac equation

A Dirac-type equation on R×S ³ topology is derived. It is a generalization of the previously obtained Klein-Gordon-type, Schrödinger-type, and Weyl-type equations, and reduces to the latter in the appropriate limit. The (discrete) energy spectrum is found and the corresponding complete set of solutions is given as expansions in terms of the matrix elements of the irreducible representations of the group SU ₂ . Finally, the properties of the solutions are discussed.     

Synthesis of 2-Chloromethyl-5-aryl-, 2-Chloromethyl-5-(5-methyl-2-furyl)-, and 2-Chloromethyl-5-(1,5-dimethyl-2-pyrrolyl)-1,3,4-oxadiazoles from Tetrazole Derivatives

Acetylation of 5-aryltetrazoles, 5-(5-methyl-2-furyl)tetrazole, and 5-(1,5-dimethyl-2-pyrrolyl)tetrazole with chloroacetyl chloride was studied.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 5, 2005, pp. 787–789.Original Russian Text Copyright © 2005 by Baranov, Tsypin, Malin, Laskin.     

Field theory onR×S 3 topology. VI: Gravitation

We extend to curved space-time the field theory on R×S³ topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU₂ gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.On leave from the Center for Theoretical Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.     

Molecular modeling of interfaces between cellulose crystals and surrounding molecules: Effects of caprolactone surface grafting

A technical problem in cellulosic nanocomposite materials is the weak interaction between hydrophilic cellulose and hydrophobic polymer matrices. One approach to solve this difficulty is to chemically graft monomers of the matrix polymer onto the cellulose surface. An important question is to understand the effect such surface modification has on the interfacial properties. Semi-empirical approaches to estimate work of adhesion based on surface energies do not provide information on specific molecular interactions. Details about these interactions were obtained using molecular dynamics (MD) simulation. Cellulose interfaces with water and caprolactone medium were modeled with different amounts of grafted caprolactone. The modification lead to an increased work of adhesion between the surface and its surrounding medium. Furthermore, the MD simulations showed that the interaction between cellulose, both modified and non-modified, and surrounding medium is dominated by Coulomb interactions, predominantly as hydrogen bonds.     

Amended Formula for the Decay of Radioactive Material for Cosmic Times

An amended formula for the decay of radioactivematerial is presented. It is a modification of thestandard exponential formula. The new formula appliesfor long cosmic times comparable to the Hubble time. It reduces to the standard formula for shorttimes. It is shown that the material decays faster thanexpected. The application of the new formula to directmeasurements of the age of the universe and its implications are briefly discussed.     

Investigation of the combustion of fumes of organochlorine wastes in oxygen environment

An experimental study of the kinetic stage of combustion fumes of organochlorine wastes. We obtained the data on the normal speed of propagation of the flame, and other parameters of the flame front. Also we found an effective constant of the reaction rate and determined requirements for reactors of a high-temperature oxidation of organochlorine waste.     

Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry

We discuss the conditions for additional supersymmetry and twisted super-symmetry in N = (2, 2) supersymmetric nonlinear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show that these solutions correspond to a bi-hermitian metric of signature (2, 2) and a pseudo-hyperkähler geometry of the target space.     

Quantum states and potentialities of quantum systems

In a previous article it was shown that in general quantum states represent perspectives on the potentialities of quantum systems, rather than the potentialities themselves. In the present paper the following questions are investigated in the context of this result: (1) How do quantum states which undergo collapse transform under pure translations? (2) Under what conditions do quantum states represent the potentialities themselves? Two alternatives are presented in response to the first question: (1) Quantum states are scalars under translations. (2) The collapse of a quantum state propagates between frames of reference at the speed of light. The advantages and disadvantages of the two alternatives are discussed. The response to the second question is shown to depend on the chosen alternative. In addition, the second alternative is shown to lead to a consistent view of quantum states as “potential perspectives on potentialities.”     

An investigation of the internal structure of shock profiles for shock capturing schemes

The theoretical understanding of discrete shock transitions obtained by shock capturing schemes is very incomplete. Previous experimental studies indicate that discrete shock transitions obtained by shock capturing schemes can be modeled by continuous functions, so called continuum shock profiles. However, the previous papers have focused on linear methods. We have experimentally studied the trajectories of discrete shock profiles in phase space for a range of different high resolution shock capturing schemes, including Riemann solver based flux limiter methods, high resolution central schemes and ENO type methods. In some cases, no continuum profiles exists. However, in these cases the point values in the shock transitions remain bounded and appear to converge toward a stable limit cycle. The possibility of such behavior was anticipated in Bultelle, Grassin and Serre, 1998, but no specific examples, or other evidence, of this behavior have previously been given. In other cases, our results indicate that continuum shock profiles exist, but are very complicated. We also study phase space orbits with regard to post shock oscillations.