Interplay of classical noise sources in the relaxation oscillations of an Nd:YAG laser

We present an investigation of fluctuations in the start-up of a single-mode, continuous wave, Nd:YAG laser that result from the interplay of classical pump and loss rate noise. We show that the timescale of the classical fluctuations is a key factor in determining the main structural features of relaxation oscillation ensembles. We find that long-timescale pump rate fluctuations are the primary factor determining the timing jitter of the first intensity spike, but that short-timescale loss rate fluctuations are necessary to match the sloping of the peaks of corresponding intensity spikes in an ensemble.     

Hydrogen Abstraction/Acetylene Addition Revealed

For almost half a century, polycyclic aromatic hydrocarbons (PAHs) have been proposed to play a key role in the astrochemical evolution of the interstellar medium (ISM) and in the chemistry of combustion systems. However, even the most fundamental reaction mechanism assumed to lead to the simplest PAH naphthalene—the hydrogen abstraction–acetylene addition (HACA) mechanism—has eluded experimental observation. Here, by probing the phenylacetylene (C₈H₆) intermediate together with naphthalene (C₁₀H₈) under combustion‐like conditions by photo‐ionization mass spectrometry, the very first direct experimental evidence for the validity of the HACA mechanism which so far had only been speculated theoretically is reported.     

Emulsifying properties of an arabinoxylan–protein gum from distillers’ grains and the co-production of animal feed

In order to improve corn ethanol profitability and energy efficiency, a natural gum consisting of primarily arabinoxylan and crude protein (CP) was extracted from distillers’ grains (DG), a major byproduct from the dry grind corn ethanol production. DG was fractionated into an alkali-soluble gum fraction and an alkali-insoluble residue fraction by extracting with 1–5 % NaOH at 25–75 °C for 1–5 h. The extraction conditions, which significantly affect the yields and compositions of DG gum and residue, were statistically modeled to optimize yields and compositions. DG gum had 8–22 % CP, which could all be reduced to about 8 % by purification with bentonite clay. The isolated gums (purified and unpurified) were made into emulsifying agents, whereas residues were characterized as animal feed. The results demonstrated that the purification process affects the emulsifying properties of the DG gum-derived emulsifying agents. In parallel, the DG residue was found to have increased fiber digestibility and metabolizable energy compared to the original DG. An economic analysis determined that concurrent productions and utilizations of DG gum and DG residue could improve the cost and energy balance of the current corn ethanol process.     

Symmetry properties in systems of semilinear elliptic equations

We investigate symmetry properties of solutions of systems of semilinear elliptic equations. The two main tools we use consist of the maximum principle and the device of moving parallel planes to a critical position and then showing that the solution is symmetric about the limiting plane. An application to the Belousov-Zhabotinskii chemical reaction is given.     

Large amplitude periodic solutions of a system of equations derived from the Hodgkin-Huxley equations

The Hodgkin-Huxley equations form the most widely accepted model of nerve conduction in the squid axon.We make several appropriate assumptions on the functions and parameters occurring in the current clamped version of these equations. These assumptions reduce the original system of four partial differential equations to a system of three ordinary differential equations. We show that there is a range of parameters over which the reduced system has a large amplitude periodic solution.