On the eigenvalue spacing distribution for a point scatterer on the flat torus

We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the 2-dimensional case, we show that in the weak coupling regime the eigenvalue spacing distribution coincides with that of the spectrum of the Laplacian (ignoring multiplicties), by showing that the perturbed eigenvalues generically clump with the unperturbed ones on the scale of the mean level spacing. We also study the three dimensional case, where the situation is very different.Comment: 25 page

Quantification of trypsin with a radioimmunoassay in herring larvae (Clupea harengus) compared with a highly sensitive fluorescence technique to determine tryptic enzyme activity

Enzymatic activity and quantity of the protease trypsin were measured in individual herring larvae (Clupea harengus L.). The enzymatic activity assay was done using a fluorescence technique, and a radioimmunoassay was used for quantification of trypsin. The results are compared and the differences between the techniques discussed. Both methods gave similar results, as high or low values in trypsin quantity were reflected in high or low values of tryptic activity. Quantity and activity were linearly and positively correlated, but small differences between methods were found at the lowest detection limits. Both techniques reflect high variability between individual larvae

Measuring every particle's size from three-dimensional imaging experiments

Often experimentalists study colloidal suspensions that are nominally monodisperse. In reality these samples have a polydispersity of 4-10%. At the level of an individual particle, the consequences of this polydispersity are unknown as it is difficult to measure an individual particle size from microscopy. We propose a general method to estimate individual particle radii within a moderately concentrated colloidal suspension observed with confocal microscopy. We confirm the validity of our method by numerical simulations of four major systems: random close packing, colloidal gels, nominally monodisperse dense samples, and nominally binary dense samples. We then apply our method to experimental data, and demonstrate the utility of this method with results from four case studies. In the first, we demonstrate that we can recover the full particle size distribution {\it in situ}. In the second, we show that accounting for particle size leads to more accurate structural information in a random close packed sample. In the third, we show that crystal nucleation occurs in locally monodisperse regions. In the fourth, we show that particle mobility in a dense sample is correlated to the local volume fraction.Comment: 7 pages, 5 figure

The effect of food availability, age or size on the RNA/DNA ratio of individually measured herring larvae: laboratory calibration

RNA/DNA ratios in individual herring (Clupea harengus) larvae (collected from Kiel Bay, Baltic Sea, in 1989) were measured and proved suitable for determining nutritional status. Significant differences between fed and starving larvae appeared after 3 to 4 d of food deprivation in larvae older than 10 d after hatching. The RNA/DNA ratio showed an increase with age or length of the larvae and was less pronounced in starving larvae compared to fed larvae. The individual variability of RNA/DNA ratios in relation to larval length of fed larvae and of larvae deprived of food for intervals of 6 to 9 d is presented. Based on the length dependency and the individual variability found within the RNA/DNA ratios, a laboratory calibration is given to determine whether a larva caught in the field has been starving or not. An example for a field application is shown

Multifractal eigenfunctions for a singular quantum billiard

Whereas much work in the mathematical literature on quantum chaos has focused on phenomena such as quantum ergodicity and scarring, relatively little is known at the rigorous level about the existence of eigenfunctions whose morphology is more complex. Quantum systems whose dynamics is intermediate between certain regimes—for example, at the transition between Anderson localized and delocalized eigenfunctions, or in systems whose classical dynamics is intermediate between integrability and chaos—have been conjectured in the physics literature to have eigenfunctions exhibiting multifractal, self-similar structure. To-date, no rigorous mathematical results have been obtained about systems of this kind in the context of quantum chaos. We give here the first rigorous proof of the existence of multifractal eigenfunctions for a widely studied class of intermediate quantum systems. Specifically, we derive an analytical formula for the Renyi entropy associated with the eigenfunctions of arithmeti

Multifractal eigenfunctions for a singular quantum billiard

Whereas much work in the mathematical literature on quantum chaos has focused on phenomena such as quantum ergodicity and scarring, relatively little is known at the rigorous level about the existence of eigenfunctions whose morphology is more complex. Quantum systems whose dynamics is intermediate between certain regimes—for example, at the transition between Anderson localized and delocalized eigenfunctions, or in systems whose classical dynamics is intermediate between integrability and chaos—have been conjectured in the physics literature to have eigenfunctions exhibiting multifractal, self-similar structure. To-date, no rigorous mathematical results have been obtained about systems of this kind in the context of quantum chaos. We give here the first rigorous proof of the existence of multifractal eigenfunctions for a widely studied class of intermediate quantum systems. Specifically, we derive an analytical formula for the Renyi entropy associated with the eigenfunctions of arithmeti

Digestive response and rates of growth in pre-leptocephalus larvae of the Japanese eel (Anguilla japonica) reared on artificial diets

As food protein digestion is instrumental for promoting growth, the main protease in young marine fish larvae, trypsin, was studied in pre-leptocephalus larvae of Anguilla japonica. Tryptic enzyme activity was monitored until day 24 and rates of growth until day 36 after hatch in larval A. japonica derived from artificially matured parent fish. Tryptic activity increased with larval age and developmental stage until day 16, after which tryptic levels stabilized. In start-feeding larvae, tryptic activities increased after ingestion of an artificial diet, but elevated tryptic activities could also be found in larvae with guts void of prey, possibly due to intestinal retention of trypsin secreted in response to ingestion of a previous meal. Gut retention time for trypsin was estimated to be at least 15 h. The gut evacuation time for the artificial diet depended on the meal size and was in the range of 1-5.5 h. Rates of larval growth in length were ca. 5% day-1 during the yolk-sac stage, declining to ca. 1% day-1 in older larvae. Vision was highly important for initiation of feeding. Results provide the first quantitative information on aspects of protein digestion in eel larvae. 2003 Elsevier Science B.V. All rights reserved