A classical theorem of Simonovits from the 1980s asserts that every graph $G$ satisfying ${e(G) \gg v(G)^{1+1/k}}$ must contain $\gtrsim \left(\frac{e(G)}{v(G)}\right)^{2k}$ copies $C_{2k}$. Recently, Morris and Saxton established a balanced version Simonovits' theorem, showing such has $C_{2k}$, which are `uniformly distributed' over edges $G$. Moreover, they used this result to obtain sharp b...

This paper introduces nucleation theory applied to crystallizing protein solutions. It is shown that the classical approach explains the available nucleation data under most conditions used for growing protein crystals for structural studies and for industrial crystallization. However, it fails to explain most experimental data on the structure of the critical clusters. It is also shown that fo...

Abstract The paper presents a practical control approach, which can be used to directly design the shape of a crystal size distribution, to robustly achieve desired product properties. The control approach is implemented in a hierarchical structure where on the lower level a model-free crystallization control methodology, the supersaturation control, drives the system in the phase diagram, rath...

The counterdiffusion of gases across a composite layer can lead to supersaturation and development of bubbles within the layer. A physicochemical model has been derived to predict the extent of such supersaturation; experiments with inert liquid layers confirm predictions. These findings explain the evolution of cutaneous lesions observed in man during simulated deep-sea dives and the cutaneous...

Supersaturation etching starts with Cl insertion into Si-Si bonds of Si 100 and leads to the desorption of SiCl2 pairs. During etching, insertion occurs through a Cl2 dissociative chemisorption process mediated by single dangling bond sites created by phonon-activated electron-stimulated desorption of atomic Cl. Based on scanning tunneling microscopy results, we identify a surface species, desc...

24 We have addressed the need for improved measurements of cloud condensation nuclei 25 (CCN) by developing a continuous-flow instrument that provides in situ measurements of CCN. 26 The design presented in this paper can operate between 0.1% and 3% supersaturation, at 27 sampling rates sufficient for airborne operation. The design constitutes a cylindrical continuous28 flow thermal-gradient di...

OBJECTIVE To evaluate the effect of dietary supplementation with sodium chloride (NaCl) on urinary calcium excretion, urine calcium concentration, and urinary relative supersaturation (RSS) with calcium oxalate (CaOx). ANIMALS 6 adult female healthy Beagles. PROCEDURE By use of a crossover study design, a canned diet designed to decrease CaOx urolith recurrence with and without supplemental...

The aim of this study was to establish the relative effects of dietary calcium and oxalate (in the form of oxalic acid) on the composition of urine produced by healthy adult Cairn Terriers and Miniature Schnauzers. A nutritionally complete dry dog food was fed to 7 dogs (4 Cairn terriers and 3 Miniature schnauzers) for 24 weeks. The dogs were fed the diet alone, or supplemented with six differe...