Systematic stability analysis of the renormalization group flow for the normal-superconductor-normal junction of Luttinger liquid wires

We study the renormalization group flows of the two terminal conductance of a superconducting junction of two Luttinger liquid wires. We compute the power laws associated with the renormalization group flow around the various fixed points of this system using the generators of the SU(4) group to generate the appropriate parametrization of an matrix representing small deviations from a given fixed point matrix [obtained earlier in S. Das, S. Rao, and A. Saha, Phys. Rev. B 77, 155418 (2008)], and we then perform a comprehensive stability analysis. In particular, for the nontrivial fixed point which has intermediate values of transmission, reflection, Andreev reflection, and crossed Andreev reflection, we show that there are eleven independent directions in which the system can be perturbed, which are relevant or irrelevant, and five directions which are marginal. We obtain power laws associated with these relevant and irrelevant perturbations. Unlike the case of the two-wire charge-conserving junction, here we show that there are power laws which are nonlinear functions of V(0) and V(2kF) [where V(k) represents the Fourier transform of the interelectron interaction potential at momentum k]. We also obtain the power law dependence of linear response conductance on voltage bias or temperature around this fixed point.

Reactivity of Cationic Terminal Borylene Complexes: Novel Mechanisms for Insertion and Metathesis Chemistry Involving Strongly Lewis Acidic Ligand Systems

The reactions of terminal borylene complexes of the type [CpFe(CO)(2)(BNR2)](+) (R = `Pr, Cy) with heteroallenes have been investigated by quantum-chemical methods, in an attempt to explain the experimentally observed product distributions. Reaction with dicyclohexylcarbodiimide (CyNCNCy) gives a bis-insertion product, in which 1 equiv of carbodiimide is assimilated into each of the Fe=B and B=N double bonds to form a spirocyclic boronium system. In contrast, isocyanates (R'NCO, R' = Ph, 2,6-wXy1, CY; XYl = C6H3Me2) react to give isonitrile complexes of the type [CpFe(CO)(2)(CNR')]+, via a net oxygen abstraction (or formal metathesis) process. Both carbodiimide and socyanate substrates are shown to prefer initial attack at the Fe=B bond rather than the B=N bond of the borylene complex. Further mechanistic studies reveal that the carbodiimide reaction ultimately leads to the bis-insertion compounds [CpFe(CO)(2)C(NCy)(2)B(NCY)(2)CNR2](+), rather than to the isonitrile system [CpFe(CO)(2)(CNCy)](+), on the basis of both thermodynamic (product stability) and kinetic considerations (barrier heights). The mechanism of the initial carbodiimide insertion process is unusual in that it involves coordination of the substrate at the (borylene) ligand followed by migration of the metal fragment, rather than a more conventional process: i.e., coordination of the unsaturated substrate at the metal followed by ligand migration. In the case of isocyanate substrates, metathesis products are competitive with those from the insertion pathway. Direct, single-step metathesis reactivity to give products containing a coordinated isonitrile ligand (i.e. [CpFe(CO)(2)(CNR')](+)) is facile if initial coordination of the isocyanate at boron occurs via the oxygen donor (which is kinetically favored); insertion chemistry is feasible when the isocyanate attacks initially via the nitrogen atom. However, even in the latter case, further reaction of the monoinsertion product so formed with excess isocyanate offers a number of facile (low energetic barrier) routes which also generate ['CpFe(CO)(2)(CNR')](+), rather than the bis-insertion product [CpFe(CO)(2)C(NR')(O)B(NR')(O)CNR2](+) (i.e., the direct analogue of the observed products in the carbodiimide reaction).

Helix-coil stability constants for amino acids in nonaqueous solvents. Studies of random poly(-benzyl-L-glutamate-co-L-alanine) and poly(-benzyl-L-glutamate-co-L-leucine) in a mixed solvent

The host-guest technique has been applied to the determination of the helix-coil stability constants of two naturally occurring amino acids, L-alanine and L-leucine, in a nonaqueous solvent system. Random copolymers containing L-alanine and L-leucine, respectively, as guest residues and -benzyl-L-glutamate as the host residue were synthesized. The polymers were fractionated and characterized for their amino acid content, molecular weight, and helix-coil transition behavior in a dichloroacetic acid (DCA)-1,2-dichloroethane (DCE) mixture. Two types of helix-coil transitions were carried out on the copolymers: solvent-induced transitions in DCA-DCE mixtures at 25°C and thermally induced transitions in a 82:18 (wt %) DCA-DCE mixture. The thermally induced transitions were analyzed by statistical mechanical methods to determine the Zimm-Bragg parameters, and s, of the guest residues. The experimental data indicate that, in the nonaqueous solvent, the L-alanine residue stabilizes the -helical conformation more than the L-leucine residue does. This is in contrast to their behavior in aqueous solution, where the reverse is true. The implications of this finding for the analysis of helical structures in globular proteins are discussed.

Seismic reliability assessment of external stability of reinforced soil walls using pseudo-dynamic method

The paper presents a method for the evaluation of external stability of reinforced soil walls subjected to earthquakes in the framework of the pseudo-dynamic method. The seismic reliability of the wall is evaluated by considering the different possible failure modes such as sliding along the base, overturning about the toe point of the wall, bearing capacity and the eccentricity of the resultant force. The analysis is performed considering properties of the reinforced backfill, foundation soil below the base of the wall, length of the geosynthetic reinforcement and characteristics of earthquake ground motions such as shear wave and primary wave velocity as random variables. The optimum length of reinforcement needed to maintain stability against four modes of failure by targeting various component reliability indices is obtained. Differences between pseudo-static and pseudo-dynamic methods are clearly highlighted in the paper. A complete analysis of pseudo-static and pseudo-dynamic methodologies shows that the pseudodynamic method results in realistic design values for the length of geosynthetic reinforcement under earthquake conditions.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Fast Accurate Transient Stability Simulations

The paper describes a Simultaneous Implicit (SI) approach for transient stability simulations based on an iterative technique using traingularised admittance matrix [1]. The reduced saliency of generator in the subtransient state is taken advantage of to speed up the algorithm. Accordingly, generator differential equations, except rotor swing, contain voltage proportional to fluxes in the main field, dampers and a hypothetical winding representing deep flowing eddy currents, as state variables. The simulation results are validated by comparison with two independent methods viz. Runge-Kutta simulation for a simplified system and a method based on modelling damper windings using conventional induction motor theory.

Note On The Stability Of Parallel Magnetic-Fields - Comment

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.

High temperature stability of oxysulfides containing Ce3+ and Y3+ ions

Standard Gibbs energies of formation of oxysulfides of cerium and yttrium from their respective oxedes were determined using solid oxide galvanic cells incorporating calcia-stabilized zirconia as the electrolyte in the temperature range 870–1120 K. The sulfur potential over the electrode containing the oxide and oxysulfide was fixed by a buffer mixture of Ag + Ag2S. A small amount of CaH2 was added to the buffer to generate an equilibrium ratio of H2S and H2 species in a closed system containing the buffer and the electrode. The sulfur potential is transmitted to the electrode via the gas phase. The results can be summarized by the equations 2left angle bracketCeO2right-pointing angle bracket+1/2(S2)→left angle bracketCe2O2Sright-pointing angle bracket+(O2) ΔG°=430600−109·7T(±400)J mol−1 left angle bracketY2O3right-pointing angle bracket+1/2(S2)→left angle bracketY2O2Sright-pointing angle bracket+1/2(O2) ΔG°=114780−1·45T(±200)J mol−1 The values are compared with data reported in the literature. The stability field diagram for the Ce---O---S system has been developed using the results of this study for Ce2O2S and data for other phases from the literature.

Correlation Between The Stability Of Carbonates In Ternary Ln2o3-H2o-Co2 Hydrothermal Systems And Lanthanide Systematics

Phase diagrams for ternary Ln2O3-H2O-CO2 systems for the entire lanthanide series (except promethium) were studied at temperatures in the range 100–950 °C and pressures up to 3000 bar. The phase diagrams obtained for the heavier lanthanides are far more complex, with the appearance of a number of stable carbonate phases. New carbonates isolated from lanthanide systems (Ln ≡ Tm, Yb, Lu) include Ln6(OH)4(CO3)7, Ln4(OH)6-(CO3)3, Ln2O(OH)2CO3, Ln6O2(OH)8(CO3)3 and Ln12O7(OH)10(CO3)6. Stable carbonate phases common to all the lighter lanthanides are hexagonal LnOHCO3 and hexagonal Ln2O2CO3. Ln2(CO3)3• 3H2O is stable from samarium onwards and orthorhombic LnOHCO3 is stable from gadolinium onwards. On the basis of the appearance of stable carbonates, four different groups of lanthanides were established: lanthanum to neodymium, promethium to europium, terbium to erbium and thulium to lutetium. Gadolinium is the connecting element between groups II and III. This is in accordance with the tetrad classification for f transition elements.

Stability criteria for single pulse solutions of cw passive mode-locked lasers

The stability of the steady-state solutions of mode-locking of cw lasers by a fast saturable absorber is imvestigated. It is shown that the solutions are stable if the condition (Ps/Pa) = (2/3) (P0Pa) is satisfied, where (Ps/Pa) is the steady-state la ser power, (P0/Pa) is the power at mode-locking threshold, and Pa is the saturated power of the absorber.

Stability of Slopes by Method of Characteristics

The method of characteristics with some simplifying assumptions is made applicable for analyzing a given straight slope. By assuming that the mobilized shear strength varies with depth, and treating the whole soil mass as a series of layers, factors of safety of a given slope at different heights and a series of lines with different mobilized shear strength are obtained. The results show that the factors of safety obtained by the present method are lower than those obtained by friction circle method.

nvestigations on the Stability and Extinction of a Laminar Diffusion Flame Over a Porous Flat Plate

The limits of stability and extinction of a laminar diffusion flame have been experimentally studied in a two-dimensional laminar boundary layer over a porous flat plate through which n-pentane vapour was uniformly injected. The stability and extinction boundaries are mapped on a plot of free stream oxidant velocity versus fuel injection velocity. Effects of free stream temperature and of dilution of fuel and oxidant on these boundaries have been examined. The results show that there exists a limiting oxidant flux beyond which the diffusion flame cannot be sustained. This limiting oxidant flux has been found to depend_on the free stream oxygen concentration, fuel concentration and injection'velocity of the fuel.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Stability and structural transitions of tomato aspermy virus and cucumber mosaic virus

The properties of the S-strain of cucumber mosaic virus (S-CMV) and the B-strain of tomato aspermy virus (B-TAV) have been studied with respect to their (i) size and sedimentation behavior, (ii) requirement of divalent metal ions for stability, (iii) sensitivity towards chloride salts and the anionic detergent sodium dodecyl sulfate, (iv) solubility in ammonium sulfate-containing buffers, and (v) pH-dependent structural transitions. The results indicate that the coat protein of B-TAV is more hydrophobic than the other well-studied strains of TAV and CMV. Circular dichroism and uv absorption studies reveal pH-dependent structural transitions, although these do not result in particle swelling. These transitions appear to alter the strength of protein-nucleic acid interactions in these viruses.