'Lock and key' control of optical properties in a push-pull system

We report the modulation of the absorbance of a flavin push-pull derivative through specific recognition by a complementary diamidopyridine (DAP), shifting the flavin intramolecular charge transfer band by approximately 30 nm.     

Forces between surfaces across nanoparticle solutions: role of size, shape, and concentration

Using a surface force apparatus, we have measured the normal forces between mica surfaces across various types of nanoparticles consisting of ZnS cores coated with a monolayer of physisorbed surfactant, dispersed in organic solvents. We focused on the effects of nanoparticle size, shape, and concentration on the force-distance profiles. Forces were exponentially repulsive when the surfactant layers were strongly bound to the nanoparticles and were roughly linear when there was adhesion between the nanoparticle cores, i.e., when the surfactant layers detached from the nanoparticles. In both cases, the range and magnitude of the forces were dependent upon the particle size, shape, and solution concentration. Fine details in the otherwise smooth force-distance profiles indicate specific effects due to particle chemistry and geometry and the existence of first-order disorder-order phase transitions upon confinement. Small amounts of water in the (hydrophobic) organic solvents had dramatic effects on the measured forces. Understanding and controlling the effects of particle shape, size, and concentration and the presence of water (or other surface-active solutes) on particle-particle and particle-surface interactions are important for the processing of nanoparticles into ordered superstructured materials.     

Controlling liposomal drug release with low frequency ultrasound: mechanism and feasibility

The ability of low-frequency ultrasound (LFUS) to release encapsulated drugs from sterically stabilized liposomes in a controlled manner was demonstrated. Three liposomal formulations having identical lipid bilayer compositions and a similar size ( approximately 100 nm) but differing in their encapsulated drugs and methods of drug loading have been tested. Two of the drugs, doxorubicin and methylpredinisolone hemisuccinate, were remote loaded by transmembrane gradients (ammonium sulfate and calcium acetate, respectively). The third drug, cisplatin, was loaded passively into the liposomes. For all three formulations, a short exposure to LFUS (<3 min) released nearly 80% of the drug. The magnitude of drug release was a function of LFUS amplitude and actual exposure time, irrespective of whether irradiation was pulsed or continuous. Furthermore, no change in liposome size distribution or in the chemical properties of the lipids or of the released drugs occurred due to exposure to LFUS. Based on our results, we propose that the mechanism of release is a transient introduction of porelike defects in the liposome membrane, which occurs only during exposure to LFUS, after which the membrane reseals. This explains the observed uptake of the membrane-impermeable fluorophore pyranine from the extraliposomal medium during exposure to LFUS. The implications of these findings for clinical applications of controlled drug release from liposomes are discussed.     

The action of a few permutations on r-tuples is quickly transitive

We prove that for every r and d≥2 there is a C such that for most choices of d permutations π₁, π₂,…,π_d of S_n, the following holds: for any two r-tuples of distinct elements in {1,…,n}, there is a product of less than C log n of the π_is which map the first r-tuple to the second. Although we came across this problem while studying a rather unrelated cryptographic problem, it belongs to a general context of which random Cayley graph quotients of S_n are good expanders. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12: 335–350, 1998     

Mixing Time of Critical Ising Model on Trees is Polynomial in the Height

In the heat-bath Glauber dynamics for the Ising model on the lattice, physicists believe that the spectral gap of the continuous-time chain exhibits the following behavior. For some critical inverse-temperature β _c , the inverse-gap is O(1) for β < β _c , polynomial in the surface area for β = β _c and exponential in it for β > β _c . This has been proved for \mathbbZ²{\mathbb{Z}^2} except at criticality. So far, the only underlying geometry where the critical behavior has been confirmed is the complete graph. Recently, the dynamics for the Ising model on a regular tree, also known as the Bethe lattice, has been intensively studied. The facts that the inverse-gap is bounded for β < β _c and exponential for β > β _c were established, where β _c is the critical spin-glass parameter, and the tree-height h plays the role of the surface area. In this work, we complete the picture for the inverse-gap of the Ising model on the b-ary tree, by showing that it is indeed polynomial in h at criticality. The degree of our polynomial bound does not depend on b, and furthermore, this result holds under any boundary condition. We also obtain analogous bounds for the mixing-time of the chain. In addition, we study the near critical behavior, and show that for β > β _c , the inverse-gap and mixing-time are both exp[Θ((β − β _c )h)].     

Chelating alkylidene ligands as pacifiers for ruthenium catalysed olefin metathesis

Olefin metathesis catalysed by ruthenium has emerged at the frontier of modern synthetic chemistry. The desire to enhance catalyst stability, gain control over the catalytic process and deepen the understanding of the mechanisms of metathesis has yielded a class of latent ruthenium precatalysts of delayed initiation and with switchable activity. One of the main methodologies developed for this purpose has been the introduction of tethered carbene ligands. Herein we track the evolution of ruthenium based metathesis catalysts bearing chelated alkylidenes, from the early oxygen Hoveyda type benzylidenes to the latent sulphur containing complexes.     

On Coulomb drag in double layer systems

We argue, for a wide class of systems including graphene, that in the low temperature, high density, large separation and strong screening limits the drag resistivity behaves as d(-4), where d is the separation between the two layers. The results are independent of the energy dispersion relation, the dependence on momentum of the transport time, and the electronic wave function structure. We discuss how a correct treatment of the electron-electron interactions in an inhomogeneous dielectric background changes the theoretical analysis of the experimental drag results of Kim et?al (2011 Phys. Rev. B 83 161401). We find that a quantitative understanding of the available experimental data (Kim et?al 2011 Phys. Rev. B 83 161401) for drag in graphene is lacking.     

Convolutions of cantor measures without resonance

Denote by µ _a the distribution of the random sum \((1 - a)\sum\nolimits_{j = 0}^\infty {{w_j}{a^j}} \), where P(ω _j = 0) = P(ω _j = 1) = 1/2 and all the choices are independent. For 0 < a < 1/2, the measure µ _a is supported on C _a , the central Cantor set obtained by starting with the closed united interval, removing an open central interval of length (1 ? 2a), and iterating this process inductively on each of the remaining intervals. We investigate the convolutions µ _a * (µ _b ° S _λ ^?1 ), where S _λ (x) = λx is a rescaling map. We prove that if the ratio log b/ log a is irrational and λ ≠ 0, then

$D({\mu _a} * ({\mu _b} \circ S_\lambda ^{ - 1})) = \min ({\dim _H}({C_a}) + {\dim _H}({C_b}),1)$

, where D denotes any of correlation, Hausdorff or packing dimension of a measure.

We also show that, perhaps surprisingly, for uncountably many values of λ the convolution µ_1/4* (µ_1/3 ° S _λ ^?1 ) is a singular measure, although dim _H (C _1/4) + dim _H (C _1/3) > 1 and log(1/3)/ log(1/4) is irrational.     

A dimension gap for continued fractions with independent digits

Kinney and Pitcher (1966) determined the dimension of measures on [0, 1] which make the digits in the continued fraction expansion i.i.d. variables. From their formula it is not clear that these dimensions are less than 1, but this follows from the thermodynamic formalism for the Gauss map developed by Walters (1978). We prove that, in fact, these dimensions are bounded by 1−10⁻⁷. More generally, we considerf-expansions with a corresponding absolutely continuous measureμ under which the digits form a stationary process. Denote byE _δ the set of reals where the asymptotic frequency of some digit in thef-expansion differs by at leastδ from the frequency prescribed byμ. ThenE _δ has Hausdorff dimension less than 1 for anyδ>0.