Nonlinear systems with fast and slow motions. Changes in the probability distribution for fast motions under the influence of slower ones

The influence of slow processes on the probability distribution of fast random processes is investigated. By reviewing four examples we show that such influence is apparently of a universal character and that, in some cases, this universality is of multifractal form. As our examples we consider theoretically stochastic resonance, turbulent jets with acoustic forcing, and two problems studied experimentally by Shnoll on the influence of the Earth’s slow rotation on the probability distribution for the velocities of model Brownian particles and on alpha decay. In the case of stochastic resonance, the slow process is a low frequency, harmonic, external force. In the case of turbulent jets, the slow process is acoustic forcing. In the models based on Shnoll’s experiments, the slow processes are inertial forces arising from the rotation of the Earth, both about its own axis and about the Sun. It is shown that all of these slow processes cause changes in the probability distributions for the velocities of fast processes interacting with them, and that these changes are similar in form.     

Modal resonant ultrasound spectroscopy for ferroelastics

Recent experimental and theoretical improvements of resonant ultrasound spectroscopy (RUS) are summarized to investigate elastic constants of phases in shape memory alloys. The proposed inversion procedure, described in this work, is particularly suitable to reliable evaluation of the temperature dependence of elastic constants of low-symmetry ferroelastic materials which may be strongly elastically anisotropic and tend to exist in twinned forms. The method is applicable even for the evaluation of single-crystal elastic constants from RUS measurements on microtwinned crystals, since it involves a homogenization algorithm based on the macroscopic deformation response of the layered structure. This potentially allows performing meaningful acoustic studies on samples with a general submicron-size layered structure.     

Mimicking DNA stretching with the Static Mode method: Shear stress versus transverse pulling stress

DNA sequencing using nanopores is closer than ever to become a reality, but further research and development still need to be done, especially to unravel the atomic-scale mechanisms of induced DNA stretching. At this level, molecular modeling and simulation are essential to investigate DNA conformational flexibility and its response to the forces involved. In this work, through a "Static Mode" approach, we present a directed exploration of the deformations of a 27-mer subjected to externally imposed forces, as it could be in a nanopore. We show how the DNA sugar-phosphate backbone undergoes the majority of the induced deformation, before the base pairing is affected, and to what extent unzipping initiation depends on the force direction.     

Changes in the Effective Parameters of Averaged Motion in Nonlinear Systems Subject to Noise

We discuss how the effective parameters characterising averaged motion in nonlinear systems are affected by noise (random fluctuations). In this approach to stochastic dynamics, the stochastic system is replaced by its deterministic equivalent but with noise-dependent parameters. We show that it can help to resolve certain paradoxes and that it has a utility extending far beyond its usual application in passing from the microscopic equations of motion to the macroscopic ones. As illustrative examples, we consider the diode-capacitor circuit, a Brownian ratchet, and a generic stochastic resonance system. In the latter two cases we calculate for the first time their effective parameters of averaged motion as functions of noise intensity. We speculate that many other stochastic problems can be treated in a similar way. PACS: 05.10.Gg, 05.40.-a, 05.40.Jc     

Bond relaxation phenomenon and impurity modes frequencies in III–V compounds

In regard with very recent studies which evidence the bond relaxation phenomenon in III–V solid solutions, a new approach is proposed to determine theoretically the isoelectronic impurity modes frequencies. It is based on an embedded molecular unit model which accounts for the relaxation in the neighboring of the substituted atom and so avoids both the single-site and virtual crystal approximations. The results obtained for GaAs in some III–V compounds are compared with the experimental available data.     

Pseudopotential study of the thermodynamic characteristics of supercooled Mg and Zn melts

We use a pseudopotential and thermodynamic perturbation theory to study the thermodynamic characteristics of metallic Mg and Zn melts. A system of solid spheres is selected, to be the ground state. Our calculations of the melting temperature, entropy, and volume are in good agreement with experiment, and the calculated results are insensitive to the choice of pseudopotential. As the temperature is lowered the diameter of the solid spheres and the packing density increase. In addition, there is a marked decrease in the melt's self diffusion coefficient, reflecting the possibility of forming an amorphous structure.Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 4, pp. 20–24, April, 1984.     

A strategy for the asymmetric aminohomologation of alpha, beta-dihydroxy aldehydes: application to the synthesis of the southwest tripeptide segment of echinocandin B

The synthesis of the (2S,3S,4S)-3,4-dihydroxyhomotyrosine amino acid segment, present in echinocandin B, in its activated form ready for peptide coupling is described. The key steps of the approach are the enantioselective AD reaction of 4-methoxycinnamic acid methyl ester, a completely diastereoselective [2 + 2] hydroxyketene-imine cycloaddition, and the TEMPO-assisted cycloexpansion of the resulting 3-hydroxy beta-lactam to the corresponding alpha-amino acid N-carboxy anhydride (NCA). The smooth opening of the latter upon treatment with L-Thr(OSi(t)BuPh(2))OMe and further acylation with the N-Cbz protected L-4-tert-butyldiphenylsilyloxy proline rendered the southwest portion of echinocandin B.     

Alkylation of chiral alpha-hydroxy ketones derived from (1R)-(+)-camphor. An asymmetric variant of the classical acetylene route to carbonyl compounds

[reaction: see text]. The asymmetric version of the traditional route for transforming acetylene into alpha-branched carbonyl compounds is now feasible for the first time. The method involves the temporary attachment of camphor to acetylene and gives a remarkably high diastereo- and enantioselectivity.     

Knoevenagel Condensation Catalyzed by a Mexican Bentonite Using Infrared Irradiation

Diethyl malonate undergoes condensation with aromatic aldehydes without solvents. in the presence of a Mexican bentonite using infrared irradiation as the energy source, to give the benzylidenemalonate compounds in fair yield.