Acoustic analogue of electronic BLOCH oscillations and resonant Zener tunneling in ultrasonic superlattices

We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.     

Molecular Characteristics and Antioxidant Activity of Spruce (Picea abies) Hemicelluloses Isolated by Catalytic Oxidative Delignification

Spruce (Picea abies) wood hemicelluloses have been obtained by the noncatalytic and catalytic oxidative delignification in the acetic acid-water-hydrogen peroxide medium in a processing time of 3–4 h and temperatures of 90–100 °C. In the catalytic process, the H₂SO₄, MnSO₄, TiO₂, and (NH₄)₆Mo₇O₂₄ catalysts have been used. A polysaccharide yield of up to 11.7 wt% has been found. The hemicellulose composition and structure have been studied by a complex of physicochemical methods, including gas and gel permeation chromatography, Fourier-transform infrared spectroscopy, and thermogravimetric analysis. The galactose:mannose:glucose:arabinose:xylose monomeric units in a ratio of 5:3:2:1:1 have been identified in the hemicelluloses by gas chromatography. Using gel permeation chromatography, the weight average molar mass M_w of hemicelluloses has been found to attain 47,654 g/mol in noncatalytic delignification and up to 42,793 g/mol in catalytic delignification. Based on the same technique, a method for determining the α and k parameters of the Mark–Kuhn–Houwink equation for hemicelluloses has been developed; it has been established that these parameters change between 0.33–1.01 and 1.57–472.17, respectively, depending on the catalyst concentration and process temperature and time. Moreover, the FTIR spectra of the hemicellulose samples contain all the bands characteristic of heteropolysaccharides, specifically, 1069 cm⁻¹ (C–O–C and C–O–H), 1738 cm⁻¹ (ester C=O), 1375 cm⁻¹ (–C–CH₃), 1243 cm⁻¹ (–C–O–), etc. It has been determined by the thermogravimetric analysis that the hemicelluloses isolated from spruce wood are resistant to heating to temperatures of up to ~100 °C and, upon further heating, start destructing at an increasing rate. The antioxidant activity of the hemicelluloses has been examined using the compounds simulating the 2,2-diphenyl-2-picrylhydrazyl free radicals.     

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as , where k equals the number of used moduli. The time complexity is modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle.     

Electron Transport in Configurational Model of Ferromagnetic Fulleride with Triple Orbital Degeneracy

Abstract

Phenomenon of ferromagnetic ordering was for a long time associated exclusively with transition metal and rare-earth compounds. Nowadays this view is challenged by growing evidence that in molecular carbon-based systems the ferromagnetic alignment of spins can be observed as well. We have developed a microscopical model of a fulleride electronic subsystem taking into account triple orbital degeneracy of energy states within the configurational-operator approach. Using the Green function method the energy spectrum of the model has been calculated. Conditions for the ferromagnetic state stabilization have been determined. Static electrical conductivity and effective masses of current carriers in the system with orbitally degenerated energy band have been obtained. In the ground state and for low temperatures at different forms of unperturbed density of electronic states the concentration dependences of transport characteristics for less-then-half-filled lower quasiparticle subband have been calculated.     

On Truncated Matricial Stieltjes Type Moment Problems

We study two slightly different versions of truncated generalized matricial moment problems of Stieltjes type. A central topic is the construction and investigation of distinguished solutions of both moment problems under consideration. These solutions turn out to be nonnegative Hermitian Borel measures on the real axis which are concentrated on a finite number of points. Our approach is mainly algebraic. It is based on the use of particular matrix polynomials constructed from a nonnegative Hermitian block Hankel matrix.     

Diastereoselective Coupling of Chiral Acetonide Trisubstituted Radicals with Alkenes

The stereochemical outcome of reactions of chiral nucleophilic trisubstituted acetonide radicals with electron‐deficient alkenes is dictated by a delicate balance between destabilizing non‐bonding interactions and stabilizing hydrogen‐bonding between substituents on the α and β carbons.     

Why Does the Geometric Product Simplify the Equations of Physics?

In the last decades it was observed that Clifford algebras and geometric product provide a model for different physical phenomena. We propose an explanation of this observation based on the theory of bounded symmetric domains and the algebraic structure associated with them. The invariance of physical laws is a result of symmetry of the physical world that is often expressed by the symmetry of the state space for the system implying that this state space is a symmetric domain. For example, the ball of all possible velocities is a bounded symmetric domain. The symmetry on this ball follow from the symmetry of the space-time transformations between two inertial systems, which fixes the so-called symmetric velocity between them. The Lorenz transformations acts on the ball Sof symmetric velocities by conformal transformations. The ball Sis a spin ball (type IV in Cartan's classification). The Lie algebra of this ball is defined a triple product that is closely related to geometric product. The relativistic dynamic equations in mechanics and for the Lorenz force is described by this Lie algebra and the triple product.     

Geometric nature of the environment-induced Berry phase and geometric dephasing

We investigate the geometric phase or Berry phase acquired by a spin half which is both subject to a slowly varying magnetic field and weakly coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original Berry phase (for an isolated system) is the flux of a monopole field through the loop traversed by the magnetic field, the environment-induced modification of the phase is the flux of a quadrupolelike field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the Berry phase, this geometric dephasing is gauge invariant for open paths of the magnetic field.