Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points

In this paper we analyze a two-degree-of-freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical points. In addition, the model has an index one saddle between the potential wells. We study the dynamical mechanisms underlying transport between the two potential wells, with emphasis on the role of the flat region surrounding the wells. The model allows us to probe many of the features of the “roaming mechanism” whose reaction dynamics are of current interest in the chemistry community.     

On the stability of quasipolynomials with weighted diamond coefficients

In this paper we treat the problem of robust stability of families of time delay systems with multipleinterval delays and complex weighted diamond coefficients. We provide conditions on the weights under which a simple edge-type stability criterion is available. An application of Kharitonov-Zhabko results, which requires additional restrictions on the delays and leads to a significant reduction of computational burden associated with the stability criteria. In particular, aneight-extreme-point result is derived for diamond quasipolynomials with constant delays.     

Semiclassical IVR approach to rotational excitation of non-polar diatomic molecules by non-resonant laser pulses

We apply the ‘classic’ semiclassical initial value representation (SC-IVR) approach to describe rotational excitation of non-polar diatomic molecules by intense short non-resonant laser pulses. We also investigate the applicability of the quantum mechanical sudden approximation. It is found that the SC-IVR approach gives accurate rotational excitation probabilities in regimes where the sudden approximation fails. Primitive semiclassical wavefunction propagation is used to illustrate the phenomenon of angular focussing of rotation states by strong pulses.     

Grafting of Preformed Polyethylene Oxide on Dialdehyde Starch by Acetal Formation

The acid-catalyzed reaction of dialdehyde starch with diethylene glycol and polyethylene oxide-400 under anhydrous conditions was studied as a new approach to the preparation of graft polymers of polyalkylene oxides on starch, the attachment of the side chains being through acetal linkages. The reaction was carried out in DMF in the presence of p-toluene sulfonic acid. It was found that increasing the reaction temperature, the diol concentration, or the reaction time led to an increase in the degree of grafting, as seen from the decrease in the dicarbonyl content of the products. Fusible graft polymers, soluble in water and in organic solvents, were obtained.     

Affine stratifications from finite misère quotients

Given a morphism from an affine semigroup to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof rests on mesoprimary decomposition of monoid congruences and a novel list of equivalent conditions characterizing the existence of an affine stratification. The motivating consequence of the main result is a special case of a conjecture due to Guo and the author on the existence of affine stratifications for (the set of winning positions of) any lattice game. The special case proved here assumes that the lattice game has finite misère quotient, in the sense of Plambeck and Siegel.     

On the Statistical Mechanics of Non-Hamiltonian Systems: The Generalized Liouville Equation, Entropy, and Time-Dependent Metrics

Several questions in the statistical mechanics of non-Hamiltonian systems are discussed. The theory of differential forms on the phase space manifold is applied to provide a fully covariant formulation of the generalized Liouville equation. The properties of invariant volume elements are considered, and the nonexistence in general of smooth invariant measures noted. The time evolution of the generalized Gibbs entropy associated with a given choice of volume form is studied, and conditions under which the entropy is constant are discussed. For non-Hamiltonian systems on manifolds with a metric tensor compatible with the flow, it is shown that the associated metric factor is in general a time-dependent solution of the generalized Liouville equation.     

Employment of [Amim] Cl in the effort to upgrade the properties of cellulose acetate based polymer electrolytes

Transparent thin film polymer electrolytes were prepared by solvent casting technique with the doping of environmental-friendly ionic liquid, 1-allyl-3-methylimidazolium chloride ([Amim] Cl) into the matrix formed by cellulose acetate (CA) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI). The ionic conducting nature of this system improves significantly from the order of 10^?7–10^?2 S cm^?1 upon increasing doping of [Amim] Cl content till a maximum of 4.68 × 10^?2 S cm^?1 is attained for the composition CA:LiTFSI:[Amim] Cl (14:6:80 wt%). The improving trend in ionic conductivity results from the bond weakening between the connecting atoms in the crystalline region that induces to the increase in amorphous counterpart fractions in the CA matrix. This observation was proved via the accountancies in the reduction of relative viscosity, root mean square value and increase in void as increase in [Amim] Cl doping. The resultant phase conversion hence permits immense lithium ion (Li⁺) fluidity along the polymer backbone and assisting the improvement in ionic conductivity. The thin film polymer electrolyte is found to be elastic in the presence of crystalline fraction and radically deforms upon the chains diffusion into the amorphous fraction. The linear curvatures of the Arrhenius plot justify the conductivity improvement as via the increasing frequency of Li⁺ ions hopping as the temperature increases. The increasing addition of [Amim] Cl diminishes both the heat-resistivity and thermal stability of CA:LiTFSI:[Amim] Cl matrix.     

The power of 2 dividing the class-number of a binary quadratic discriminant

In this paper we study congruence conditions on class numbers of binary quadratic discriminants d, modulo powers of 2, where d has two or three distinct prime divisors.     

Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem

Fermionic quantization, or Clifford algebra, is combined with pseudodifferential operators to simplify the proof of the Atiyah-Singer index theorem for the Dirac operator on a spin manifold.