Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.     

Linked scans of peptides and protein digests: amino acid sequence determination of components of complex mixtures

Two-sector linked-scan analysis of an unpurified proteolytic digest of a pyruvate decarboxylase enzyme (60,000 Da) has allowed the discovery and assignment of an amino-terminal post-translational modification and processing event. A difference in amino acid sequence from that predicted by a recently published nucleotide sequence has also been found. These results illustrate both the use and considerable potential of linked-scan methods for the analysis of complex biopolymer mixtures.     

Power spectra and spatial pattern dynamics of a ring laser

Experimental measurements of power spectra of a single longitudinal and transverse mode ring dye laser are presented that reveal the critical slowing down of the laser near threshold. External pump noise serves as a probe of the frequency response of the dye laser. Detailed comparisons of the spectral characteristics with computer simulations and an approximate analytic theory are given. The dynamics of spatial pattern formation in a multimode dye laser is examined through measurements of first-passage-time distributions. A comparison of the experiments with computer simulations based on a simple theoretical model of the two-mode laser shows qualitative agreement. These measurements indicate that there are a variety of complex phenomena associated with the transverse mode pattern formation dynamics that need to be addressed theoretically and studied further experimentally.     

Alpha particle and deuteron impactL-shell ionization of Ar,Cu, Ge,Br, Zr and Ag

Alpha particle and deuteron impactL-subshell ionization cross-sections of Ar, Cu, Ge, Br, Zr and Ag have been computed using Vriens’ expressions for ionization cross-section of atoms due to impact of heavy charged particles. The effects of Coulomb deflection of the projectile and increase in binding of the target electron in the presence of projectile have been incorporated. Hartree-Fock velocity distributions for the target electrons have been used in the present calculations. The simple binary encounter approximation model is found to give results which are in satisfactory agreement with those obtained from experiments and from other theories.     

Superheated drops of R114—as a neutron spectrometer

The basic principle that has been used in the application of superheated drops in neutron spectrometry is its dependence of threshold energy of nucleation on temperature. In the present work, superheated drops of R114 suspended in a visco-elastic gel were irradiated at different temperatures by neutrons obtained from an ²⁴¹Am–Be source. The temperature of the detector was converted to the energy of the incident neutrons following the method developed by us to unfold the neutron energy spectrum. The threshold energy obtained by us agrees well with other results obtained using monochromatic neutron sources, clearly demonstrating the validity of our principle of spectrometry.     

Characterization of the Hf-NTA complex

Hafnium ion forms a strong complex with nitrilotriacetic acid (NTA). But there is a controversy about the nature of the complex on whether it is a 1:1 or a 1:2 complex. We have carried out an electrophoresis experiment and supplemented data to establish the nature of the complex. Our data indicates that it is a 1:2 complex i.e. [Hf(NTA)₂]^2- in which the coordination number 8 has been satisfied for hafnium.     

Highly stereoselective approach toward the synthesis of the macrolactone core of amphidinolide W

The diastereoselective synthesis of the macrolactone core of amphidinolide W was successfully accomplished using Evans’ asymmetric alkylation, Aldol reaction, Julia-Kocienski olefination, and Kita’s macrocyclization protocol.     

Markov property of continuous dislocation band propagation

Tensile tests were carried out by deforming polycrystalline samples of substitutional Al–2.5%Mg alloy at room temperature for a range of strain rates. The Portevin–Le Chatelier (PLC) effect was observed throughout the strain rate regime. The deformation bands in this region are found to be of type A in nature. From the analysis of the experimental stress time series data we could infer that the dynamics of type A dislocation band propagation is a Markov process.