Phase-shift randomness in one-dimensional disordered conductors in the quasi-metallic domain

An invariant imbedding method yields exact analytical results for the distribution of the phase theta (L) of the reflection amplitude and for low-order resistance moments (pn) for a disordered conductor of length L in the quasi-metallic regime L<

Resistance fluctuations, phase randomness and noise in one-dimensional conductors with a long-range correlated potential

When the size (L) of a one-dimensional metallic conductor is less than the correlation length λ-1 of the Gaussian random potential, one expects transport properties to show ballistic behaviour. Using an invariant imbedding method, we study the exact distribution of the resistance, of the phase θ of the reflection amplitude of an incident electron of wave number k0, and of dθ/dk0, for λL ll 1. The resistance is non-self-averaging and the n-th resistance moment varies periodically as (1 - cos 2k0L)n. The charge fluctuation noise, determined by the distribution of dθ/dk0, is constant at low frequencies.

Structure of 1 lct-Hydroxyeon-1,4,18-trienine-3-one

C21H27NO2, Mr=325.5 , orthorhombic,P21212,, a = 7.516 (2), b = 13.430 (2), c =18.047 (2) A, U= 1821.79 A 3, Z = 4, D x =1.186 Mg m -a, 2(Cu Ka) = 1.5418 A, # = 0.56 mm -1, F(000) = 704, T= 293 K, final R = 0.04 for 1892 reflections with I _> 3a(I). Ring A is planar, and rings B and C adopt a chair conformation. Rings D and E are envelopes, with C(14) and C(17) displaced from their respective planes by 0.643 (3) and 0.482 (3)A. The ring system A/B shows quasi-trans fusion, whilst ring systems B/C and C/D are trans fused about C(8)-C(9) and C(13)-C(14) respectively. The D/E junction shows cis fusion.

The structure of 11[alpha]-hydroxycon-1,4-dienine-3-one monohydrate

C22H31NO2.H2 O, M r = 359" 5, orthorhombic,P2~212 ~, a= 10.032 (1), b= 11.186 (1), C = 17.980 (1)/~,, U= 2017.48/~3, Z = 4, D x = 1.276 Mg m -a, 2(Cu Kct) = 1.5418/~, # = 0.69 mm -~,F(000) = 784, T = 293 K. Final R = 0.05 for 1972 unique reflections with I > 3o(/). Ring A is planar, and rings B and C adopt a chair conformation. Rings D and E are envelopes, with C(14) and C(20) displaced from their respective ring planes by 0-616 (2) and 0.648 (3)/~. The A/B ring junction is quasi-trans,whilst ring systems B/C and C/D are trans fused about the bonds C(8)-C(9) and C(13)-C(14) respectively.The D/E junction shows cis fusion.

Time Dependent Operator-split and Unsplit Schemes for One Dimensional Premixed Flames

This paper is concerned with a study of an operator split scheme and unsplit scheme for the computation of adiabatic freely propagating one-dimensional premixed flames. The study uses unsteady method for both split and unsplit schemes employing implicit chemistry and explicit diffusion, a combination which is stable and convergent. Solution scheme is not sensitive to the initial starting estimate and provides steady state even with straight line profiles (far from steady state) in small number of time steps. Two systems H2-Air and H2-NO (involving complex nitrogen chemistry) are considered in presentinvestigation. Careful comparison shows that the operator split approach is slightly superior than the unsplit when chemistry becomes complex. Comparison of computational times with those of existing steady and unsteady methods seems to suggest that the method employing implicit-explicit algorithm is very efficient and robust.

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of noninteracting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials and show that nonadiabatic pumping violates the simple sin phi rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time-reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and nonresonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.

Curie-temprature of a spin one xy ferromagnet with uniaxial anisotropy

A spin one XY ferromagnet with uniaxial anisotropy has been investigated, using Green's function technique in random phase approximation (RPA). The Green functions associated with the anisotropy energy are treated without decoupling. A set of coupled equations have been obtained to find the critical temperature Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc as function of the uniaxial anisotropy parameter D. Tc and left angle bracket(SZ)2right-pointing angle bracket at Tc are found to increase with D. The results are compared with the earlier results obtained in the Narath type of RPA.

On uniqueness, transfer and combination of acoustic sources in one-dimensional systems

The use of electroacoustic analogies suggests that a source of acoustical energy (such as an engine, compressor, blower, turbine, loudspeaker, etc.) can be characterized by an acoustic source pressure ps and internal source impedance Zs, analogous to the open-circuit voltage and internal impedance of an electrical source. The present paper shows analytically that the source characteristics evaluated by means of the indirect methods are independent of the loads selected; that is, the evaluated values of ps and Zs are unique, and that the results of the different methods (including the direct method) are identical. In addition, general relations have been derived here for the transfer of source characteristics from one station to another station across one or more acoustical elements, and also for combining several sources into a single equivalent source. Finally, all the conclusions are extended to the case of a uniformly moving medium, incorporating the convective as well as dissipative effects of the mean flow.

A regio and stereospecific radical annulation route to chiral tricyclo[4.3.1.o3,7]decane (isotwistane) system1 synthesis of (+)-10-α-Naphthyl-5-epi-Pupukean-9-one

Contrary to that of phenyl derivative 1 the radical 4 adds to radicophiles in an inter- followed by intra-molecular radical Michael addition (radical annulation), furnishing a novel route to chiral isotwistanes 5.

One pot synthesis of polycyclic oxygen aromatics. Part III mechanism of formation

Reaction of 6-Image -butyl-1-bromomethyl-2-(2-tetrahydropyranyloxy)-naphthalene2c with tetrachlorocatechol (TCC) in acetone in presence of K2CO3 gave diastereomers 6c and 7c. A mechanism (Scheme-1) invoking the base induced cleavage of the pyranyl ether 2 to 1,2-naphthoquinone-1-methide 8 as the first step has been postulated. The cleavage of the pyranyl ether linkage in 2 to give dimers 4 and 5 of 1,2-naphthoquinone-1-methide has been demonstrated with different bases. 1,2-Naphthoquinone-1-methide 8, thus generated, undergoes Michael addition with TCC followed by elimination of chloride ions to give a diketone, which further undergoes aldolisation with acetone to give diastereomers 6 and 7. Michael reaction of 8, generated Image from pyranyl ethers 2a-c, with tetrabromocatechol (TBC) under similar-reaction conditions gave the expected monobromo compounds 6h, 6i, 6k, 7n, 7n and 7q. The last step in the proposed mechanism, Image ., aldolisation has also been demonstrated using different ketonic solvents. Thus, reaction of 2a-c with TCC/TBC in diethyl ketone/methyl ethyl ketone under similar reaction conditions gave the expected compounds 6 and 7.

Synthesis Of (+/-)-2-Isopropyl-5,6-Dimethylbicyclo[3.2.1]Oct-6-En-8-One

Methanolic hydrogen chloride cyclization of the triketone 8, prepared from the Mannich base 7 and 2-methylcyclopentane-1,3-dione, gives ketones 9 and 10. NaBH4 reduction of 9 followed by Grignard reaction with CH3MgI affords the diol 12. Catalytic hydrogenation of 12 followed by PCC oxidation yields the ketoalcohol 13. Dehydration of 13 with SOCl2/pyridine results in a 1:1 mixture of the endo-14 and exo-15 olefins, separated by chromatography.

The identification of 14 alpha,17 beta-dihydroxyandrost-4-en-3-one monohydrate and 14 alpha,17 beta-dihydroxyandrosta-1,4-dien-3-one monohydrate, metabolites of androstenedione in Mucor piriformis

The microorganism Mucor piriformis transforms androst-4-ene-3,17-dione into a major and several minor metabolites. X-ray crystallographic analysis of two of these metabolites was undertaken to determine unambiguously their composition and chirality. Crystals belong to the orthorhombic space-group P2(1)2(1)2(1), with a = 7.199(4) angstrom and a = 6.023(3) angstrom, b = 11.719(3) angstrom and b = 13.455(4) angstrom, c = 20.409(3) angstrom and c = 20.702(4) angstrom for the two title compounds, respectively. The structures have been refined to final R values of 0.060 and 0.040, respectively.

Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).