Velocity profiles in laminar diffusion flames

Velocity profiles in vertical laminar diffusion flames were measured by using laser Doppler velocimetry (LDV). Four fuels were used: n-heptane, iso-octane, cyclohexane, and ethyl alcohol. The velocity profiles were similar for all the fuels, although there were some differences in the peak velocities. The data compared favorably with the theoretical velocity predictions. The differences could be attributed to errors in experimental positioning and in the prediction of temperature profiles. Error in the predicted temperature profiles are probably due to the difficulty in predicting the radiative heat losses from the flame

Propagation of Errors for Matrix Inversion

A formula is given for the propagation of errors during matrix inversion. An explicit calculation for a 2 by 2 matrix using both the formula and a Monte Carlo calculation are compared. A prescription is given to determine when a matrix with uncertain elements is sufficiently nonsingular for the calculation of the covariances of the inverted matrix elements to be reliable.Comment: 18 pages, 4 figures, figure 4 contains two eps file

Determination of combustion gas temperatures by infrared radiometry in sooting and nonsooting flames

Flame temperatures in nonsooting and sooting environments were successfully measured by radiometry for pre-mixed propane-oxygen laminar flames stabilized on a water-cooled, porous sintered-bronze burner. The measured temperatures in the nonsooting flames were compared with fine-wire thermocouple measurements. The results show excellent agreement below 1700 K, and when the thermocouple measurements were corrected for radiation effects, the agreement was good for even higher temperatures. The benefits of radiometry are: (1) the flow is not disturbed by an intruding probe, (2) calibration is easily done using a blackbody source, and (3) measurements can be made even with soot present. The theory involved in the radiometry measurements and the energy balance calculations used to correct the thermocouple temperature measurements are discussed

On the rough Gronwall lemma and its applications

We present a rough path analog of the classical Gronwall Lemma introduced recently by A. Deya, M. Gubinelli, M. Hofmanov\'a, S. Tindel in [arXiv:1604.00437] and discuss two of its applications. First, it is applied in the framework of rough path driven PDEs in order to establish energy estimates for weak solutions. Second, it is used in order to prove uniqueness for reflected rough differential equations

Ground Beetles (Coleoptera: Carabidae) Inhabiting Stands of Reed Canary Grass Phalaris Arundinacea on Islands in the Lower Chippewa River, Wisconsin

We used pitfall traps to assess ground beetle diversity (Coleoptera:Carabidae) on two islands in the lower Chippewa River, Eau Claire County, Wisconsin, with rapidly expanding populations of reed canary grass, Phalaris arundinaceae. We collected 233 individuals belonging to 17 species over four, 3-9 day sampling periods, May-August 1994. All species have been documented in Wisconsin and most are considered habitat generalists. Agonum fidele, A. extensicolle, Anisodactylus harrisii and Bembidion quadrimaculatum oppositum comprised 70% of all species collected. Seven species were common to both islands, with 13 species collected on Canarygrass Island and 11 species on Ski Jump Island. Carabid species diversity (Shannon’s H=2.01) was greatest on Canarygrass Island

A 233 km Tunnel for Lepton and Hadron Colliders

A decade ago, a cost analysis was conducted to bore a 233 km circumference Very Large Hadron Collider (VLHC) tunnel passing through Fermilab. Here we outline implementations of $e^+e^-$, $p \bar{p}$, and $\mu^+ \mu^-$ collider rings in this tunnel using recent technological innovations. The 240 and 500 GeV $e^+e^-$ colliders employ Crab Waist Crossings, ultra low emittance damped bunches, short vertical IP focal lengths, superconducting RF, and low coercivity, grain oriented silicon steel/concrete dipoles. Some details are also provided for a high luminosity 240 GeV $e^+ e^-$ collider and 1.75 TeV muon accelerator in a Fermilab site filler tunnel. The 40 TeV $p \bar{p}$ collider uses the high intensity Fermilab $\bar{p}$ source, exploits high cross sections for $p \bar{p}$ production of high mass states, and uses 2 Tesla ultra low carbon steel/YBCO superconducting magnets run with liquid neon. The 35 TeV muon ring ramps the 2 Tesla superconducting magnets at 9 Hz every 0.4 seconds, uses 250 GV of superconducting RF to accelerate muons from 1.75 to 17.5 TeV in 63 orbits with 71% survival, and mitigates neutrino radiation with phase shifting, roller coaster motion in a FODO lattice.Comment: LaTex, 6 pages, 1 figure, Advanced Accelerator Concepts Workshop, Austin, TX, 10-15 June 201