Bulk viscosity and cavitation in boost-invariant hydrodynamic expansion

We solve second order relativistic hydrodynamics equations for a boost-invariant 1+1-dimensional expanding fluid with an equation of state taken from lattice calculations of the thermodynamics of strongly coupled quark-gluon plasma. We investigate the dependence of the energy density as a function of proper time on the values of the shear viscosity η, the bulk viscosity ζ, and second order coefficients, confirming that large changes in the values of the latter have negligible effects. Varying the shear viscosity between zero and a few times s/4π, with s the entropy density, has significant effects, as expected based on other studies. Introducing a nonzero bulk viscosity also has significant effects. In fact, if the bulk viscosity peaks near the crossover temperature T c to the degree indicated by recent lattice calculations in QCD without quarks, it can make the fluid cavitate — falling apart into droplets. It is interesting to see a hydrodynamic calculation predicting its own breakdown, via cavitation, at the temperatures where hadronization is thought to occur in ultrarelativistic heavy ion collisions.United States. Dept. of Energy. Office of Nuclear Physics (Grant No. DE-FG02-94ER40818

Effect of Nutrient Supplements on Cucumber Fermentation by Lactic Acid Bacteria

Lactic acid bacteria (LAB) are important industrial microorganisms involved in fermentation of food and beverage products. The strict fermentative growth of LAB has complex requirements of various nutrients including amino acids, vitamins and minerals. Information about the effect of these nutrients on the growth of LAB in cucumber fermentation is not readily available. It is evident, from previous research that certain nutrients like; leucine, isoleucine, tryptophan, valine, biotin, nicotinic acid, pantothenic acid, riboflavin, manganese and magnesium are beneficial for LAB growth, but are not provided in sufficient quantities by the cucumber in the brine. The objective of this study was to determine the efficacy of (1) the above mentioned nutrients (2) the most effective concentrations of biotin, isoleucine and valine alone and (3) combination of biotin, isoleucine and valine with cucumber fermentation brine, on the production of LAB and lactic acid in brine. The yield of LAB was determined from microscopical counts using a hemacytometer, lactic acid concentration, dry weight and the final sugar concentration in the brine was determined. The first three trials established that biotin, valine and isoleucine improved LAB growth. Efficacy of five different concentrations each of biotin, valine and isoleucine in cucumber juice was determined in trial four. Biotin and isoleucine treatments at three different concentrations, in trial four, were equally effective on LAB growth; hence the lowest concentrations of 614 nM of biotin and 0.76 mM of isoleucine were selected; whereas valine treatments showed a relative small increase in the LAB growth with increase in concentration and 1.17 mM of valine was the most effective of all the valine treatments. These optimized concentrations of nutrients were used in trial five, in different combinations. Of these, biotin and valine treatments when used individually or in combination showed a significant increase in LAB growth and the rate of production and concentration of lactic acid in the brine. These results indicated that the addition of biotin and valine potentially increased the number of LAB. Additional research is required using whole cucumbers to develop effective treatments

Lost Relatives of the Gumbel Trick

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method re- lies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of related methods, of which the Gumbel trick is one member, and show that the new methods have superior properties in several settings with minimal additional computational cost. In particular, for the Gumbel trick to yield computational benefits for discrete graphical models, Gumbel perturbations on all configurations are typically replaced with so- called low-rank perturbations. We show how a subfamily of our new methods adapts to this set- ting, proving new upper and lower bounds on the log partition function and deriving a family of sequential samplers for the Gibbs distribution. Finally, we balance the discussion by showing how the simpler analytical form of the Gumbel trick enables additional theoretical results.Alan Turing Institute under EPSRC grant EP/N510129/1, and by the Leverhulme Trust via the CFI