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.     

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 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.     

Electron-pair resonance in the coulomb blockade

We study many-body corrections to the cotunneling current via a localized state with energy epsilon(d) at large bias voltages V. We show that the transfer of electron pairs, enabled by the Coulomb repulsion in the localized level, results in ionization resonance peaks in the third derivative of the current with respect to V, centered at eV=+/-2epsilon(d)/3. Our results predict the existence of previously unnoticed structure within Coulomb-blockade diamonds.     

Design of Selective Adiabatic Inversion Pulses Using the Adiabatic Condition

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in the presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion along it. In this paper, we describe a method by which optimized modulation functions can be constructed to render insensitivity toB₁inhomogeneity over a predeterminedB₁range and over a wide band of frequencies. This is accomplished by requiring that the optimized pulse fulfill the adiabatic condition over this range ofB₁inhomogeneity and over the desired frequency band for the complete duration of the pulse. A trajectory similar to the well-known sech/tanh adiabatic pulse, i.e., a half-ellipse, is used. The optimization process improves the slice profile by optimizing the rate of motion along this trajectory. The optimized pulse can be tailored to the specific design requirements; in particular, the transition sharpness may be traded off against the inverted bandwidth. Two design examples, including experimental results, demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse: in the first example, a large frequency band is to be inverted using a weak RF amplitude in a short time. In the second example, a pulse with a very sharp transition is required.     

Direct determination of interlaminar stresses in polymeric adhesive layer

A method for direct measurement of shear and normal displacements, and a simple way of determining the distribution of the respective average stresses along an interlaminar adhesive layer (IAL), were successfully examined on a symmetrical doubler model. Experimental data proved to be in agreement with available analytical solutions for this model in the elastic stage. The method was also examined beyond the elastic linear range and may be used to follow up the initiation of delamination.