Synthesis of optically active 6-substituted 2-(aminomethyl)chromans

Three novel, optically active, 6-substituted 2-(aminomethyl)chromans were synthesized from readily available chroman 2-carboxylic acid precursors. These chroman-containing primary amines are useful building blocks for the synthesis of chroman-derived pharmaceutical agents.     

Affine lie algebras in massive field theory and form factors from vertex operators

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions by investigating theq1 limit of theq-deformed affine symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebrasplit into two independent affine algebras on this factorized space, each with level 1 in the anti-periodic sector, and level 0 in the periodic sector. The space of fields in the anti-periodic sector can be organized using level-1 highest weight representations if one supplements the algebra with the usual local integrals of motion. Introducing a particle-field duality leads to a new way of computing form-factors in radial quantization. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. Form-factors are computed as vacuum expectation values of vertex operators in momentum space.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 430–441, March, 1994.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Nonlinear normal modes and band zones in granular chains with no pre-compression

We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg (Adv. Appl. Mech. 9:155–242, 1966), we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances.     

Interfacial density of states in magnetic tunnel junctions

Large zero-bias resistance anomalies as well as a collapse of magnetoresistance were observed in Co/Al2O3/Co magnetic tunnel junctions with thin Cr interfacial layers. The tunnel magnetoresistance decays exponentially with nominal Cr interlayer thickness with a length scale of approximately 1 A more than twice as fast as for Cu interlayers. The strong suppression of magnetoresistance, as well as the zero-bias anomalies, can be understood by considering a strong spin-dependent modification of the density of states at Co/Cr interfaces. The role of the interfacial density of states is shown by the use of specially engineered structures. Similar effects are predicted and observed in junctions with Ru interfacial layers.     

Kondo effect in magnetic tunnel junctions

Tunneling magnetoresistance was found to be suppressed with decreasing temperature for magnetic tunnel junctions (MTJs) oxidized under high plasma power. A strong temperature dependence of the junction resistance was observed, along with zero-bias anomalies of dynamic resistance at low temperatures. Resistance shows a logarithmic dependence on temperature, and resistance versus temperature exhibits a scaling behavior. Our experimental data can be explained in a consistent way by the Kondo effect in the MTJs with the Kondo temperature TK=20-30 K.     

Energy Transfers in a System of Two Coupled Oscillators with Essential Nonlinearity: 1:1 Resonance Manifold and Transient Bridging Orbits

The purpose of this study is to highlight and explain the vigorous energy transfers that may take place in a linear oscillator weakly coupled to an essentially nonlinear attachment, termed a nonlinear energy sink. Although these energy exchanges are encountered during the transient dynamics of the damped system, it is shown that the dynamics can be interpreted mainly in terms of the periodic orbits of the underlying Hamiltonian system. To this end, a frequency-energy plot gathering the periodic orbits of the system is constructed which demonstrates that, thanks to a 1:1 resonance capture, energy can be irreversibly and almost completely transferred from the linear oscillator to the nonlinear attachment. Furthermore, it is observed that this nonlinear energy pumping is triggered by the excitation of transient bridging orbits compatible with the nonlinear attachment being initially at rest, a common feature in most practical applications. A parametric study of the energy exchanges is also performed to understand the influence of the parameters of the nonlinear energy sink. Finally, the results of experimental measurements supporting the theoretical developments are discussed. This study was carried out while the author was a postdoctoral fellow at the National Technical University of Athens and at the University of Illinois at Urbana-Champaign.     

Computing the endomorphism ring of an ordinary elliptic curve over a finite field

We present two algorithms to compute the endomorphism ring of an ordinary elliptic curve E defined over a finite field Fq. Under suitable heuristic assumptions, both have subexponential complexity. We bound the complexity of the first algorithm in terms of , while our bound for the second algorithm depends primarily on log|DE|, where DE is the discriminant of the order isomorphic to End(E). As a byproduct, our method yields a short certificate that may be used to verify that the endomorphism ring is as claimed.     

Studies on the stereoselective synthesis of C-allyl glycosides

An investigation was carried out to explore the use of sulfoxide donors as common precursors to stereoisomeric C-glycoconjugates of glycoprotein and glycolipid tumor antigens. A study focusing on the effects of reaction conditions and substrate structure on the stereoselectivity of allylation was carried out. Although conditions were realized to selectively afford alpha-allylation products in good to excellent yields, the search for conditions favoring beta-selectivity proved less successful.