A Very Smooth Ride in a Rough Sea

It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time Serfati (C. R. Acad. Sci. Paris Série I 320:175–180, 1995), Shnirelman (Glob. Stoch. Anal., http://arxiv.org/abs/1205.5837v1, 2012). Here an elementary derivation is given, based on Cauchy’s form of the Euler equations in Lagrangian coordinates. This form implies simple recurrence relations among the time-Taylor coefficients of the Lagrangian map, used here to derive bounds for the C ^1,γ Hölder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C ^1,γ.     

Cyto-mechanoresponsive polyelectrolyte multilayer films

Cell adhesion processes take place through mechanotransduction mechanisms where stretching of proteins results in biological responses. In this work, we present the first cyto-mechanoresponsive surface that mimics such behavior by becoming cell-adhesive through exhibition of arginine-glycine-aspartic acid (RGD) adhesion peptides under stretching. This mechanoresponsive surface is based on polyelectrolyte multilayer films built on a silicone sheet and where RGD-grafted polyelectrolytes are embedded under antifouling phosphorylcholine-grafted polyelectrolytes. The stretching of this film induces an increase in fibroblast cell viability and adhesion.     

Turbulence in noninteger dimensions by fractal Fourier decimation

Fractal decimation reduces the effective dimensionality D of a flow by keeping only a (randomly chosen) set of Fourier modes whose number in a ball of radius k is proportional to k(D) for large k. At the critical dimension D(c)=4/3 there is an equilibrium Gibbs state with a k(-5/3) spectrum, as in V. L'vov et al., Phys. Rev. Lett. 89, 064501 (2002). Spectral simulations of fractally decimated two-dimensional turbulence show that the inverse cascade persists below D=2 with a rapidly rising Kolmogorov constant, likely to diverge as (D-4/3)(-2/3).     

The Application of Ultrasound in Honey: Antioxidant Activity,Inhibitory Effect on α-amylase and α-glucosidase,and In Vitro Digestibility Assessment

In the present study, the effects of ultrasound (10, 20, and 30 min) on the bioactive compounds, antioxidant capacity, enzymatic inhibition, and in vitro digestion of six honey extracts from the Oaxaca state, Mexico, were analyzed. Significant differences were found in each honey extract with respect to the ultrasonic treatment applied (p < 0.05). In the honey extract P-A1 treated with 20 min of ultrasound, the phenols reached a maximum concentration of 29.91 ± 1.56 mg EQ/100 g, and the flavonoids of 1.92 ± 0.01 mg EQ/100 g; in addition, an inhibition of α-amylase of 37.14 ± 0.09% was noted. There were also differences in the phases of intestinal and gastric digestion, presenting a decrease in phenols (3.92 ± 0.042 mg EQ/100 g), flavonoids (0.61 ± 0.17 mg EAG/100 mg), antioxidant capacity (8.89 ± 0.56 mg EAG/100 mg), and amylase inhibition (9.59 ± 1.38%). The results obtained from this study indicate that, in some honeys, the processing method could increase the concentration of bioactive compounds, the antioxidant capacity, and the enzymatic inhibition; however, when subjected to in vitro digestion, the properties of honey are modified. The results obtained could aid in the development of these compounds for use in traditional medicine as a natural source of bioactive compounds.     

Finding cliques using few probes

Consider algorithms with unbounded computation time that probe the entries of the adjacency matrix of an n vertex graph, and need to output a clique. We show that if the input graph is drawn at random from (and hence is likely to have a clique of size roughly ), then for every δ<2 and constant ?, there is an α<2 (that may depend on δ and ?) such that no algorithm that makes n^δ probes in ? rounds is likely (over the choice of the random graph) to output a clique of size larger than .     

Contemporary Photoligation Chemistry: The Visible Light Challenge

Catalyst-free and bond-forming light-induced reactions have seen an unprecedented renaissance in the realm of soft matter materials science due to their efficiency, spatio-temporal controllability and, sometimes, photoreversible nature. However, many of these reactions rely on the application of high energy UV light that can cause photo-degradation and is inapplicable in biological environments. If up-conversion systems or two-photon processes are to be avoided, strategies for red-shifting catalyst-free ligation technology are critically required. This Concept article introduces the reader to recent methods that lead to efficient, catalyst-free visible-light-induced ligation chemistry based on polyaromatic substituted photoreactive compounds—pyrene and anthracene—and, furthermore, emphasizes the broad and facile applicability of these molecules in polymeric material design. Concomitantly, we highlight that a careful action plot analysis of photochemical reactivity can provide deep insights into reactivity patterns, far beyond those suggested by the absorption spectrum. Indeed, we suggest that an action plot analysis is necessary for the evaluation of any photochemical system and its response to structural chemical changes.     

Static and Time Dependent Density Functional Theory with Internal Degrees of Freedom: Merits and Limitations Demonstrated for the Potts Model

We present an extension of the density-functional theory (DFT) formalism for lattice gases to systems with internal degrees of freedom. In order to test approximations commonly used in DFT approaches, we investigate the statics and dynamics of occupation (density) profiles in the one-dimensional Potts model. In particular, by taking the exact functional for this model we can directly evaluate the quality of the local equilibrium approximation used in time-dependent density-functional theory (TDFT). Excellent agreement is found in comparison with Monte Carlo simulations. Finally, principal limitations of TDFT are demonstrated.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Anomalous scaling in systems partially controlled by diffusion

We study the nature of anomalous scaling in several systems partially controlled by diffusion. We quantify the departure from Fickian scaling by means of an apparent exponent governing the scaling of long-time behavior with system size. We find that anomalous scaling should be expected whenever complex geometries, higher dimensionality, or time-dependent boundary conditions are encountered.     

Model reactions for crosslinking polydiacetylene materials

A series of reactions are presented which allowed us to crosslink polydiacetylenes containing carbamate groups in the side chain without attacking the triple bond. These reactions involved syntheses of carbamates and allophanates from butyl alcohol and phenyl isocyanate with metal and tertiary amine catalysts using a model compound, 2,4,7,9-tetramethyl-5-decyn-4,7-diol. Elemental analysis, IR and UV spectroscopy, and high performance liquid chromatography (HPLC) were used as analytical tools. Metal catalysts were found to favor the formation of allophanates in higher yields and purity as compared to tertiary amine catalysts.