Hierarchical superstructure of alkylamine-coated ZnS nanoparticle assemblies

We describe methodology for producing highly uniform, ordered and reproducible superstructures of surfactant-coated ZnS nanorod and nanowire assemblies, and propose a predictive multiscale "packing model" for superstructure formation based on electron microscopy and powder X-ray diffraction data on the superstructure, as well as on individual components of the nanostructured system. The studied nanoparticles showed a hierarchical structure starting from the individual faceted ZnS inorganic cores, onto which the crystalline surfactant molecules are adsorbed, to the superstructure of the nanoparticle arrays. Our results point out the critical role of the surfactant headgroup and polarity in nanoparticle assembly, and demonstrate the relationship between the molecular structure of the surfactant and the resulting superstructure of the nanoparticle assemblies.     

Charge sensing amplification via weak values measurement

A protocol employing weak values (WVs) to obtain ultrasensitive amplification of weak signals in the context of a solid-state setup is proposed. We consider an Aharonov-Bohm interferometer where both the orbital and the spin degrees of freedom are weakly affected by the presence of an external charge to be detected. The interplay between the spin and the orbital WVs leads to a significant amplification even in the presence of finite temperature, voltage, and external noise.     

Unconventional Josephson signatures of Majorana bound states

A junction between two topological superconductors containing a pair of Majorana fermions exhibits a "fractional" Josephson effect, 4π periodic in the superconductors' phase difference. An additional fractional Josephson effect, however, arises when the Majorana fermions are spatially separated by a superconducting barrier. This new term gives rise to a set of Shapiro steps which are essentially absent without Majorana modes and therefore provides a unique signature for these exotic states.     

Relaxation dispersion in MRI induced by fictitious magnetic fields

A new method entitled Relaxation Along a Fictitious Field (RAFF) was recently introduced for investigating relaxations in rotating frames of rank ≥ 2. RAFF generates a fictitious field (E) by applying frequency-swept pulses with sine and cosine amplitude and frequency modulation operating in a sub-adiabatic regime. In the present work, MRI contrast is created by varying the orientation of E, i.e. the angle ε between E and the z″ axis of the second rotating frame. When ε > 45°, the amplitude of the fictitious field E generated during RAFF is significantly larger than the RF field amplitude used for transmitting the sine/cosine pulses. Relaxation during RAFF was investigated using an invariant-trajectory approach and the Bloch-McConnell formalism. Dipole-dipole interactions between identical (like) spins and anisochronous exchange (e.g., exchange between spins with different chemical shifts) in the fast exchange regime were considered. Experimental verifications were performed in vivo in human and mouse brain. Theoretical and experimental results demonstrated that changes in ε induced a dispersion of the relaxation rate constants. The fastest relaxation was achieved at ε ≈ 56°, where the averaged contributions from transverse components during the pulse are maximal and the contribution from longitudinal components are minimal. RAFF relaxation dispersion was compared with the relaxation dispersion achieved with off-resonance spin lock T(?ρ) experiments. As compared with the off-resonance spin lock T(?ρ) method, a slower rotating frame relaxation rate was observed with RAFF, which under certain experimental conditions is desirable.     

Cellulose Nanocrystals (CNCs) Induced Crystallization of Polyvinyl Alcohol (PVA) Super Performing Nanocomposite Films

This study is aimed to explore the properties of cellulose nanocrystals (CNC)/polyvinyl alcohol (PVA) composite films with and without 1,2,3,4‐butane tetracarboxylic acid (BTCA), a nontoxic crosslinker. CNC and CNC‐PVA nanocomposite films are prepared using solution‐casting technique. Differential scanning calorimetry (DSC) analyses show that crosslinking increased the glass transition temperature but reduced the melting temperature and crystallinity. Furthermore, high CNC concentrations in the PVA matrix interfere with PVA crystallinity, whereas in specific ratio between CNC and PVA, two different crystalline structures are observed within the PVA matrix. Film surfaces and fracture topographies characterized using scanning electron microscope indicate that at certain CNC‐PVA ratios, micron‐sized needle‐like crystals have formed. These crystalline structures correlate with the remarkable improvement in mechanical properties of the CNC‐PVA nanocomposite films, that is, enhanced tensile strain and toughness to 570% and 202 MJ m^?3, respectively, as compared to pristine PVA. BTCA enhances the tensile strain, ultimate tensile stress, toughness, and modulus of CNC films compared to pristine CNC films. Water absorption of crosslinked CNC and CNC‐PVA nanocomposite films is significantly reduced, while film transparency is significantly improved as a function of PVA and crosslinker content. The presented results indicate that CNC‐PVA nanocomposite films may find applications in packaging, and though materials applications.     

Block decomposition of permutations and Schur-positivity

The block number of a permutation is the maximum number of components in its expression as a direct sum. We show that, for 321-avoiding permutations, the set of left-to-right maxima has the same distribution when the block number is assumed to be k, as when the last descent of the inverse is assumed to be at position \(n - k\). This result is analogous to the Foata–Schützenberger equidistribution theorem, and implies that the quasi-symmetric generating function of the descent set over 321-avoiding permutations with a prescribed number of blocks is Schur-positive.     

Superior biolubricant from a species of red microalga

The rheological properties of the sulfated polysaccharide of the red microalga Porphyridium sp., a heteropolymer with a molecular weight of 3-5 x 10(6) Da, indicated that this material might be an excellent candidate for lubrication applications: the viscosity of the polysaccharide is stable over a range of temperatures, pH values, and salinities. In this study, various rheological and lubricant properties of the polysaccharide were evaluated in comparison with those of a widely used biolubricant, hyaluronic acid. The viscosity of the Porphyridium sp. polysaccharide remained essentially unchanged in a temperature range of 25-70 degrees C. In tribology tests on a ball-on-flat ceramic pair, the values for the friction coefficient and wear rate for the pair lubricated with polysaccharide were remarkably lower than those for hyaluronic acid, especially at high loads. In a test on a steel ring/ultrahigh-molecular-weight polyethylene (UHMWPE) block pair, the wear tracks on the surface of the UHMWPE were more pronounced for hyaluronic acid than for the polysaccharide. Atomic force microscopy showed that the polysaccharide was effectively adsorbed onto mica surfaces, forming ultrathin coating layers in the nanometer range. As is required for biolubricant applications, the polysaccharide was not degraded by hyaluronidase. The stability of the Porphyridium sp. polysaccharide to heat and to hyaluronidase combined with its ability to reduce friction and wear indicate its potential as an advantageous biolubricant.     

The time-dependence of exchange-induced relaxation during modulated radio frequency pulses

The problem of the relaxation of identical spins 1/2 induced by chemical exchange between spins with different chemical shifts in the presence of time-dependent RF irradiation (in the first rotating frame) is considered for the fast exchange regime. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame (TDRF) is presented. Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time-dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.     

The critical random graph,with martingales

We give a short proof that the largest component C ₁ of the random graph G(n, 1/n) is of size approximately n ^2/3. The proof gives explicit bounds for the probability that the ratio is very large or very small. In particular, the probability that n ^−2/3|C ₁| exceeds A is at most e ^{- cA3}{e^{ - c{A^3}}} for some c > 0.     

Scaling limits for internal aggregation models with multiple sources

We study the scaling limits of three different aggregation models on ℤ ^d : internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; and the divisible sandpile, in which each site distributes its excess mass equally among its neighbors. As the lattice spacing tends to zero, all three models are found to have the same scaling limit, which we describe as the solution to a certain PDE free boundary problem in ℝ ^d . In particular, internal DLA has a deterministic scaling limit. We find that the scaling limits are quadrature domains, which have arisen independently in many fields such as potential theory and fluid dynamics. Our results apply both to the case of multiple point sources and to the Diaconis-Fulton smash sum of domains.