Noise-induced asymptotic periodicity in a piecewise linear map

We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system.     

Additions of enantiopure alpha-sulfinyl carbanions to (S)-N-sulfinimines: asymmetric synthesis of beta-amino sulfoxides and beta-alphamino alcohols

The addition of the lithium anions derived from (R)- and (S)-methyl and -ethyl p-tolyl sulfoxides to (S)-N-benzylidene-p-toluenesulfinamide provides an easy access route to enantiomerically pure beta-(N-sulfinyl)amino sulfoxides. Stereoselectivity can be achieved when the configurations at the sulfur atoms of the two reagents are opposite (matched pair), thus resulting in only one diastereoisomer, even for the case in which two new chiral centers are created. The N-sulfinyl group primarily controls the configuration of the carbon bonded to the nitrogen, whereas the configuration of the alpha-sulfinyl carbanion seems to be responsible for the level of asymmetric induction, as well as for the configuration of the new stereogenic C-SO carbon in the reactions with ethyl p-tolyl sulfoxides. An efficient method for transforming the obtained beta-(N-sulfinyl)amino sulfoxides into optically pure beta-amino alcohols, based on the stereoselective non-oxidative Pummerer reaction, is also reported.     

Propagating fronts,chaos and multistability in a cell replication model

Numerical solutions to a model equation that describes cell population dynamics are presented and analyzed. A distinctive feature of the model equation (a hyperbolic partial differential equation) is the presence of delayed arguments in the time (t) and maturation (x) variables due to the nonzero length of the cell cycle. This transport like equation balances a linear convection with a nonlinear, nonlocal, and delayed reaction term. The linear convection term acts to impress the value of u(t,x=0) on the entire population while the death term acts to drive the population to extinction. The rich phenomenology of solution behaviour presented here arises from the nonlinear, nonlocal birth term. The existence of this kinetic nonlinearity accounts for the existence and propagation of soliton-like or front solutions, while the increasing effect of nonlocality and temporal delays acts to produce a fine periodic structure on the trailing part of the front. This nonlinear, nonlocal, and delayed kinetic term is also shown to be responsible for the existence of a Hopf bifurcation and subsequent period doublings to apparent "chaos" along the characteristics of this hyperbolic partial differential equation. In the time maturation plane, the combined effects of nonlinearity, nonlocality, and delays leads to solution behaviour exhibiting spatial chaos for certain parameter values. Although analytic results are not available for the system we have studied, consistency and validation of the numerical results was achieved by using different numerical methods. A general conclusion of this work, of interest for the understanding of any biological system modeled by a hyperbolic delayed partial differential equation, is that increasing the spatio-temporal delays will often lead to spatial complexity and irregular wave propagation. (c) 1996 American Institute of Physics.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.     

Neutron captue prompt gamma-ray activation analysis at the NIST Cold Neutron Research Facility

An instrument for neutron capture prompt gamma-ray activation analysis (PGAA) has been constructed as part of the Cold Neutron Research Facility at the 20 MW National Institute of Standards and Technology Research Reactor. The neutron fluence rate (thermal equivalent) is 1.5·10⁸ n ·cm^–2·s^–1, with negligible fast neutrons and gamma-rays. With compact geometry and hydrogen-free construction, the sensitivity is sevenfold better than an existing thermal instrument. Hydrogen background is thirtyfold lower.     

Level decay and orientational kinetics of the rhodamine B monomer and dimer

The population kinetics and the rotational diffusion of the rhodamine B monomer and dimer were measured by using picosecond pulses from a mode-locked Nd : YAG laser to induce and time resolve the concentration-dependent transient absorption saturation of various aqueous solutions of this organic dye.     

Measurability of vacuum fluctuations and dark energy

Vacuum fluctuations of the electromagnetic field induce current fluctuations in resistively shunted Josephson junctions that are measurable in terms of a physically relevant power spectrum. In this paper we investigate under which conditions vacuum fluctuations can be gravitationally active, thus contributing to the dark energy density of the universe. Our central hypothesis is that vacuum fluctuations are gravitationally active if and only if they are measurable   in terms of a physical power spectrum in a suitable macroscopic or mesoscopic detector. This hypothesis is consistent with the observed dark energy density in the universe and offers a resolution of the cosmological constant problem. Using this hypothesis we show that the observable vacuum energy density _ρvac${\rho }_{\mathit{vac}}$ in the universe is related to the largest possible critical temperature _Tc$T_c$ of superconductors through _ρvac=σ·(_kTc)⁴/?³c³${\rho }_{\mathit{vac}}=\sigma ·({\mathit{kT}}_c{)}^4/{?}^3{c}^3$, where σ$\sigma$ is a small constant of the order 10^-3${10}^{-3}$. This relation can be regarded as an analog of the Stefan–Boltzmann law for dark energy. Our hypothesis is testable in Josephson junctions where we predict there should be a cutoff in the measured spectrum at 1.7 THz if the hypothesis is true.