Saturation of Turbulent Drag Reduction in Dilute Polymer Solutions

Drag reduction by polymers in turbulent wall-bounded flows exhibits universal and non-universal aspects. The universal maximal mean velocity profile was explained in a recent theory. The saturation of this profile and the crossover back to the Newtonian plug are non-universal, depending on Reynolds number Re, concentration of polymer $c_p$ and the degree of polymerization $N_p$. We explain the mechanism of saturation stemming from the finiteness of extensibility of the polymers, predict its dependence on $c_p$ and $N$ in the limit of small $c_p$ and large Re, and present the excellent comparison of our predictions to experiments on drag reduction by DNA.Comment: 4 pages, 4 figs., included, PRL, submitte

Nonlinear Diffusion Through Large Complex Networks Containing Regular Subgraphs

Transport through generalized trees is considered. Trees contain the simple nodes and supernodes, either well-structured regular subgraphs or those with many triangles. We observe a superdiffusion for the highly connected nodes while it is Brownian for the rest of the nodes. Transport within a supernode is affected by the finite size effects vanishing as $N\to\infty.$ For the even dimensions of space, $d=2,4,6,...$, the finite size effects break down the perturbation theory at small scales and can be regularized by using the heat-kernel expansion.Comment: 21 pages, 2 figures include

On the segmentation and classification of hand radiographs

This research is part of a wider project to build predictive models of bone age using hand radiograph images. We examine ways of finding the outline of a hand from an X-ray as the first stage in segmenting the image into constituent bones. We assess a variety of algorithms including contouring, which has not previously been used in this context. We introduce a novel ensemble algorithm for combining outlines using two voting schemes, a likelihood ratio test and dynamic time warping (DTW). Our goal is to minimize the human intervention required, hence we investigate alternative ways of training a classifier to determine whether an outline is in fact correct or not. We evaluate outlining and classification on a set of 1370 images. We conclude that ensembling with DTW improves performance of all outlining algorithms, that the contouring algorithm used with the DTW ensemble performs the best of those assessed, and that the most effective classifier of hand outlines assessed is a random forest applied to outlines transformed into principal components

Free and self-interacting scalar fields in the presence of conical singularities

Free and self-interacting scalar fields in the presence of conical singularities are analized in some detail. The role of such a kind of singularities on free and vacuum energy and also on the one-loop effective action is pointed out using $\zeta$-function regularization and heat-kernel techniques.Comment: 20 Pages, RevTex, UTF30

Chronology Protection in Generalized Godel Spacetime

The effective action of a free scalar field propagating in the generalized Godel spacetime is evaluated by the zeta-function regularization method. From the result we show that the renormalized stress energy tensor may be divergent at the chronology horizon. This gives a support to the chronology protection conjecture.Comment: Latex 6 pages, typos correcte

Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence

The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered in the mid-twentieth century that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this colloquium review we first summarize the phenomenology of drag reduction by polymers, stressing both its universal and non-universal aspects, and then proceed to review a recent theory that provides a quantitative explanation of all the known phenomenology. We treat both flexible and rod-like polymers, explaining the existence of universal properties like the Maximum Drag Reduction (MDR) asymptote, as well as non-universal cross-over phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally we also discuss other agents for drag reduction with a stress on the important example of bubbles.Comment: Invited Colloquium Paper for Reviews of Modern Physics, 24 pages, 18 Figs., submitte

Получение фталатзамещенного вторичного полиэтилентерефталата и изучение его изотермической кристаллизации

Objects. Due to the polymer waste accumulation, the search for new directions for their utilization is urgent. Chemical recycling methods are of considerable interest, which allow one to obtain the original monomers or change the compositions of the copolymers. From the point of view of building a circular economy, a promising material is polyethylene terephthalate (PET), on the basis of which amorphous copolyesters can be obtained. The study aimed to analyze the simultaneous glycolysis and interchain exchange reactions of PET in the presence of the oligoethylene phthalate modifier with hydroxyl end groups and the study of isothermal crystallization of poly(ethylene phthalate-co-terephthalates) with different phthalate contents obtained in this way.Methods. Oligoethylene phthalate is synthesized by polycondensation. Poly(ethylene phthalateco-terephthalates) were obtained by the interaction of post-consumer PET with oligoethylene phthalate. The composition of the oligomer and copolymers was confirmed using Fourier-transform infrared spectroscopy, thermal characteristics and crystallization half-times were determined by differential scanning calorimetry.Results. In this work, the use of the post-consumer PET chemical recycling process, aimed at obtaining copolyesters under the influence of small modifier amounts was proposed. The process consisted in carrying out the combined interchain exchange and degradation with a complex oligoester different from PET. Poly(ethylene phthalate-co-terephthalate) copolymers were obtained via reaction of post-consumer poly(ethylene terephthalate) flakes and synthesized oligoethylene phthalate resin in the melt phase in the absence of catalyst. The effect of phthalate concentration in polymer on the isothermal crystallization of phthalate substituted poly(ethylene terephthalate) was estimated.Conclusions. The hypothesis about the possibility of using an oligoester modifier to obtain the PET-based copolymer at the high rate and without reducing the molecular weight to values characteristic of a monomer or oligomer has been confirmed. The process can be used to obtain random copolyesters based on post-consumer PET. The phthalate unit concentration increase is followed by decrease in the glass transition temperature, temperature and heat of fusion, and increase in crystallization half-times. Phthalate has a better ability to retard PET crystallization than 2-methyl-1,3-propanediol or furandicarboxylic acid, but is inferior to some of the other modifiers known.Цели. Накопление полимерных отходов в последнее время обуславливает поиск новых подходов к их утилизации. Значительный интерес представляют химические способы вторичной переработки, которые позволяют получить исходные мономеры или изменить составы сополимеров. С точки зрения построения экономики замкнутого цикла перспективным материалом является полиэтилентерефталат (ПЭТ), из которого в процессе химического рециклинга получают аморфные сополиэфиры. Работа посвящена исследованию одновременного протекания реакций гликолиза и межцепного обмена ПЭТ в присутствии модификатора олигоэтиленфталата с гидроксильными концевыми группами и изучению изотермической кристаллизации поли(этилен фталат-со-терефталатов) с разным содержанием фталата, полученных таким способом.Методы. Олигоэтиленфталат синтезирован поликонденсацией. Поли(этилен фталат-со-терефталаты) получены взаимодействием вторичного ПЭТ с олигоэтиленфталатом. Состав олигомера и сополимеров был подтвержден с использованием ИК-Фурье спектроскопии, термические характеристики и полупериоды кристаллизации определяли методом дифференциальной сканирующей калориметрии.Результаты. Разработан процесс получения сополиэфиров, основанный на химическом рециклинге вторичного ПЭТ под действием малых количеств модификатора. Отличительной особенностью процесса является одновременное протекание реакций межцепного обмена и деструкции сложным олигоэфиром, отличным по природе от ПЭТ. Реакцией в расплаве вторичного ПЭТ и синтезированного олигоэтиленфталата в отсутствие катализатора были получены поли(этилен фталат-со-терефталаты). Изучено влияние концентрации фталата в полимере на температуру стеклования, температуру и теплоту плавления, изотермическую кристаллизацию фталатзамещенного ПЭТ.Выводы. Подтверждена гипотеза о возможности использовани олигоэфирного модификатора для получения сополимера на основе ПЭТ с высокой скоростью и без снижения молекулярной массы до значений, характерных для мономера или олигомера. Процесс может быть использован для получения статистических сополиэфиров на основе вторичного ПЭТ. С увеличением концентрации звеньев фталата происходит снижение температуры стеклования, температуры и теплоты плавления, увеличение полупериодов кристаллизации. Фталат обладает лучшей способностью замедлять кристаллизацию ПЭТ, чем 2-метил-1,3-пропандиол или фурандикарбоновая кислота, но уступает некоторым другим известным модификаторам

Massive scalar field in multiply connected flat spacetimes

The vacuum expectation value of the stress-energy tensor $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as $R^3 \times S^1$, $R^2 \times T^2$, $R^1 \times T^3$, the M\"{o}bius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.Comment: 19 pages, REVTeX, 5 figures in separate uuencoded compressed fil

Hot Gauge Theories and ZNZ_{N} Phases

In this paper the several aspects of the $Z_{N}$ symmetry in gauge theories at high temperatures are discussed. The metastable $Z_{N}$ bubbles in the $SU(N)$ gauge theories with fermions may have, generically, unacceptable thermodynamic behavior. Their free energy $F \propto T^4$ with a positive proportionality constant. This leads not only to negative pressure but also to negative specific heat and, more seriously, to negative entropy. We argue that although such domains are important in the Euclidean theory, they cannot be interpreted as physical domains in Minkowski space. The related problem is connected with the analysis of the high-temperature limit of the confining phase. Using the two-dimensional QCD with adjoint fermions as a toy model we shall demonstrate that in the light fermion limit in this theory there is no breaking of the $Z_{N}$ symmetry in the high-temperature limit and thus there are no $Z_{N}$ bubbles.Comment: preprint PUPT-1415, 21

Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review