Most likely ensemble with a given average energy prepared by a single slit

We discuss an ensemble of particle selected by a single slit within the statistical model of quantization reported earlier. We look for the most probable distribution of the position of the particle with a given average energy by applying Jaynes’s maximum entropy principle. We first show that the most likely ensemble with the lowest possible average energy is given by the quantum mechanical ground state of a particle trapped inside the slit. We further show that in general it takes a larger energy to collect the beam of particles into a target position with a higher precision.     

Possible corrections to quantum mechanical predictions in a hidden variable model

We derive possible corrections to the statistical predictions of quantum mechanics in measurement over an ensemble of identically prepared systems based on a hidden variable model of quantization developed in the previous work. The corrections are characterized by a dimensionless parameter σ$\sigma$ and the prediction of quantum mechanics is reproduced in the formal limit σ→0$\sigma \to 0$. Quantum mechanics is argued to be reliable for a sufficiently low quantum number.     

Quantization from Hamilton–Jacobi theory with a random constraint

We propose a method of quantization based on Hamilton–Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization yet with a unique ordering of operators if the Lagrange multiplier that arises in the dynamical system with constraint can only take binary values ±?/2$\pm ?/2$ with equal probability.     

On Quantum-Classical Transition of a Single Particle

We discuss the issue of quantum-classical transition in a system of a single particle with and without external potential. This is done by elaborating the notion of self-trapped wave function recently developed by the author. For a free particle, we show that there is a subset of self-trapped wave functions which is particle-like. Namely, the spatially localized wave packet is moving uniformly with undistorted shape as if the whole wave packet is indeed a classical free particle. The length of the spatial support of the wave packet is given by the Compton wavelength so that the wave packet is more localized for particle with larger mass. Whereas for a particle of mass m in a macroscopic external potential, we show that the time needed by the corresponding self-trapped wave function to depart from a classical trajectory is of the order ∼m ² c/ℏ. We argue that it is the Compton wavelength that matters and not the de Broglie wavelength as in conventional semiclassical approach.     

Self-Assembled Graphene/MWCNT Bilayers as Platinum-Free Counter Electrode in Dye-Sensitized Solar Cells

We describe the preparation and properties of bilayers of graphene- and multi-walled carbon nanotubes (MWCNTs) as an alternative to conventionally used platinum-based counter electrode for dye-sensitized solar cells (DSSC). The counter electrodes were prepared by a simple and easy-to-implement double self-assembly process. The preparation allows for controlling the surface roughness of electrode in a layer-by-layer deposition. Annealing under N₂ atmosphere improves the electrode's conductivity and the catalytic activity of graphene and MWCNTs to reduce the I₃⁻ species within the electrolyte of the DSSC. The performance of different counter-electrodes is compared for ZnO photoanode-based DSSCs. Bilayer electrodes show higher power conversion efficiencies than monolayer graphene electrodes or monolayer MWCNTs electrodes. The bilayer graphene (bottom)/MWCNTs (top) counter electrode-based DSSC exhibits a maximum power conversion efficiency of 4.1 % exceeding the efficiency of a reference DSSC with a thin film platinum counter electrode (efficiency of 3.4 %). In addition, the double self-assembled counter electrodes are mechanically stable, which enables their recycling for DSSCs fabrication without significant loss of the solar cell performance.     

Structure determination and quantification of a new flavone glycoside with anti-acetylcholinesterase activity from the herbs of Elsholtzia ciliata

Three acacetin triglycosides (compounds 1, 2 and 3) were isolated from the herbs of Elsholtzia ciliata (Labiatae). The structure were identified as 7-O-β-D-glucopyranosyl-(1 → 2)[α-L-rhamnopyranosyl-(1 → 6)]-β-D-glucopyranoside (compound 1), 7-O-(6-O-acetyl)-β-D-glucopyranosyl-(1 → 2)[α-L-rhamnopyranosyl-(1 → 6)]-β-D-glucopyranoside (compound 2) and 7-O-(6-O-acetyl)-β-D-glucopyranosyl-(1 → 2)[(4-O-acetyl)-α-L-rhamnopyranosyl-(1 → 6)]-β-D-glucopyranoside (compound 3) of acacetin. The structures of these compounds were determined on the basis of 2D-NMR spectroscopic data. Compound 3 has not been isolated from a natural source. In addition, the three compounds were quantitatively analysed by HPLC. Acetylcholinesterase (AChE) inhibition activity was assayed to find anti-Alzheimer’s activity, since this enzyme increases the concentration of acetylcholine (ACh), a neurotransmitter, responsible for brain’s memory. Acacetin, the aglycone of the three compounds, exhibited a potent anti-cholinesterase activity (IC₅₀, 50.33 ± 0.87), though its glycosides (1, 2 and 3) were less active. HPLC analysis demonstrated that the three compounds were contained in the MeOH extract in the order of compounds 2 (12.63 mg/g extract) > 3 (3.10 mg/g) > 1 (2.92 mg/g).     

Synthesis and properties of π-extended fluoranthene derivatives from 1,2-diarylacenaphthylene derivatives

Acenaphthylene units work as a useful platform for the synthesis of polycyclic aromatic hydrocarbons (PAH). Three 1,2-diarylacenaphthylene derivatives (9-phenanthryl, 7-t-butyl-2-pyrenyl and 2-naphthyl) were prepared by Suzuki-Miyaura coupling of 1,2-dibromoacenaphthylene with the corresponding boronic acids and ester. The Scholl reaction of the phenanthryl derivative affords a donor-acceptor type fluoranthene derivative possessing a hemi-coronene structure by forming two CC bonds between phenanthryl groups. The reaction of the pyrenyl derivative allows one CC bond formation to give a helicene-type fluoranthene derivative. The reaction of the naphthyl derivative provides an asymmetric fluroranthene derivative having an anthracene unit accompanied with one CC bonding reaction, while a photochemical cyclization followed by dehydroaromatization reaction of the compound gives a symmetric fluoranthene derivative with a [5]helicene structure.     

The role of structure in the nonlinear mechanics of cross-linked semiflexible polymer networks

The microstructural basis of the characteristic nonlinear mechanics of biopolymer networks remains unclear. We present a 3D network model of realistic, cross-linked semiflexible fibers to study strain-stiffening and the effect of fiber volume-occupancy. We identify two structural parameters, namely, network connectivity and fiber entanglements, that fully govern the nonlinear response from small to large strains. The results also reveal distinct deformation mechanisms at different length scales and, in particular, the contributions of heterogeneity at short length scales.