Fractional statistical mechanics

The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generalization of the Hamiltonian systems is discussed. Liouville and Bogoliubov equations with fractional coordinate and momenta derivatives are considered as a basis to derive fractional kinetic equations. The Fokker-Planck-Zaslavsky equation that has fractional phase-space derivatives is obtained from the fractional Bogoliubov equation. The linear fractional kinetic equation for distribution of the charged particles is considered.     

Pulsed and cw laser oscillations in LiF:F-2 color center crystal under laser diode pumping

Continuous-wave laser oscillations in LiF:F-2 crystal optically pumped by a laser diode at 970 nm were demonstrated for what is believed to be the first time. The slope efficiency of 14% and conversion efficiency of 5.5% were achieved for 80 micros pump pulse duration and 5 Hz pulse repetition rate. An efficiency twice as low was measured at a 6.25 kHz pulse repetition rate (50% off-duty factor) and in cw mode of laser operation.     

Molecular thermodynamics for micellar branching in solutions of ionic surfactants

We develop an analytical molecular-thermodynamic model for the aggregation free energy of branching portions of wormlike ionic micelles in 1:1 salt solution. The junction of three cylindrical aggregates is represented by a combination of pieces of the torus and bilayer. A geometry-dependent analytical solution is obtained for the linearized Poisson-Boltzmann equation. This analytical solution is applicable to saddle-like structures and reduces to the solutions known previously for planar, cylindrical, and spherical aggregates. For micellar junctions, our new analytical solution is in excellent agreement with numerical results over the range of parameters typical of ionic surfactant systems with branching micelles. Our model correctly predicts the sequence of stable aggregate morphologies, including a narrow bicontinuous zone, in dependence of hydrocarbon tail length, head size, and solution salinity. For predicting properties of a spatial network of wormlike micelles, our aggregation free energy is used in the Zilman-Safran theory. Our predictions are compared with experimental data for branching micelles of ionic surfactants.     

Quantum dissipation from power-law memory

A new quantum dissipation model based on memory mechanism is suggested. Dynamics of open and closed quantum systems with power-law memory is considered. The processes with power-law memory are described by using integration and differentiation of non-integer orders, by methods of fractional calculus. An example of quantum oscillator with linear friction and power-law memory is considered.     

Effect of Anion Position on the Electronic Energy Structure of CuGaS2 and AgGaS2

The effect of the anion displacement parameter (u) on the local partial and total densities of electronic states is investigated for two chalcogenides of A^IB^IIIC ₂ ^VI type: CuGaS₂ and AgGaS₂. The forbidden gap (E_g) of the compounds is estimated. The calculations were performed in the framework of the cluster version of the local coherent potential approximation. It is established that E_g is a linear function of u. The curves of the local partial densities of states permit the estimation of the dependence of the splitting of the characteristic maxima on the chosen value of u; this dependence is also linear.     

Chemical binding in ternary chalcogenides AiBIIIC 2 VI

The semiconductors a^IB^IIIc ₂ ^Vi (A^I = Cu, Ag; B111 = Ga, In; CVI = 5, Se) have found wide use in quantum electronics and nonlinear optics. Some of them show great promise as materials for solar batteries. The valence and vacant states of the components of A^IB^IIIC ₂ ^VI were studied experimentally (SK X-ray emission and absorption spectra in sulfides) and theoretically using the cluster version of the local coherent potential. For this study, experimental literature data are used. The calculations were performed with inclusion of the d states of the noble metal lying at the top of the valence band and determining the nature of the chemical bond (p— d hybridization). Also included is the structural factor (anion shift from the equilibrium positions in a sphalerite structure), whose effect on the forbidden gap E_g is comparable to that of p— d hybridization. Lattice parameters a and c and anion shifts u are calculated in terms of Jaffe and Zunger theory using Pauling's tetrahedral radii. The calculated density of state curves agree well in shape and satisfactorily in energy with the corresponding X-ray and X-ray photoelectron spectra. Our results confirm that Bragg's idea on transferability and conservation of elementary bonds is applicable to the compounds under study. The estimated forbidden gaps Eg proved to be close to the experimental ones to an accuracy of approximately 0.2 eV for all compounds A^IB^IIIC ₂ ^VI . Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, pp. 515-524, May–June, 2000.     

Display Selection of a Hybrid Foldamer–Peptide Macrocycle

Expanding the chemical diversity of peptide macrocycle libraries for display selection is desirable to improve their potential to bind biomolecular targets. We now have implemented a considerable expansion through a large aromatic helical foldamer inclusion. A foldamer was first identified that undergoes flexizyme-mediated tRNA acylation and that is capable of initiating ribosomal translation with yields sufficiently high to perform an mRNA display selection of macrocyclic foldamer–peptide hybrids. A hybrid macrocyclic nanomolar binder to the C-lobe of the E6AP HECT domain was selected that showed a highly converged peptide sequence. A crystal structure and molecular dynamics simulations revealed that both the peptide and foldamer are helical in an intriguing reciprocal stapling fashion. The strong residue convergence could be rationalized based on their involvement in specific interactions with the target protein. The foldamer stabilizes the peptide helix through stapling and through contacts with key residues. These results altogether represent a significant extension of the chemical space amenable to display selection and highlight possible benefits of inserting an aromatic foldamer into a peptide macrocycle for the purpose of protein recognition.