Functional integral approach to the Falicov-Kimball model

Using the functional integral method of Hubbard-Stratonovich, we have studied the existence of first order phase transitions in the Falicov-Kimball model. By means of two different approximation we have obtained results at variance. The first approximation, that we called uniform, is like a mean field one; and the second, a self-consistent one, is similar to the coherent potential approximation.     

Electron spin relaxation of irradiated ferroelectric KDP: K2SeO4

Electron spin resonance relaxation times were measured for the radiation induced radical ion SeO₄^3? in selenium doped KDP single crystals. The spin-lattice relaxation time was found to obey the relation $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>R</mtext>}}{}^{\mathrm{?1}}\text{= AT + BT}{}^5\text{∫}{}_0{}^{\mathrm{<mtext>\theta </mtext><mtext>2T</mtext>}}\text{x}{}^4\text{csch}{}^2\text{x}\text{d}\text{x}$ from 7 K to 200 K except in the neighborhood of the transition temperature where the data fit the expression T₁^?1 = T_1R^?1b_±T ? T_c^m± where θ is the Debye temperature and the plus and minus signs refer to data at temperatures above and below T_c respectively.     

Kinetics in continuous flow sample processing Chemical Contributions to Dispersion in Flow-Injection Techniques

A numerical model based on a basic dispersion equation modified by simultaneous consideration of the chemical effect introduced by a chemical reaction taking place as the sample plug disperses has been tested. Computer analysis and simulation (by use of an alternating direction implicit finite difference approximation) by solving the laminar dispersion equation and the rate expression simultaneously, have been evaluated with experimental studies of a reaction of moderate speed (oxidation of ascorbic acid by dichromate ion). Theoretically generated signal profiles indicated the need for three correction factors representative of the deviation of the experimental system from ideality. The rate coefficient in the chemical kinetic term (if pseudo-first-order is assumed) appears to change in an oscillating manner reflecting the complexity of the overall kinetic process. A straight-line relationship was found between the time at peak maximum and the rate coefficient in computer-simulated curves. Such a correlation provided a way to estimate a value for the rate coefficient of the L-ascorbic acid/dichromate reaction which agreed with the one obtained from batch kinetic determinations. In some of the cases studied, the unbalanced evolution of dispersion forces resulted in chemically induced doubled-humped peaks.     

Phase transition in anisotropic coupled random walk

We have studied the continous limit of a coupled random walk including scattering anisotropy. We found a phase transition in the behaviour of the probability distribution around the isotropic critical point. We show the transient behaviour of the variance, and the power spectrum of the random forces.     

Two-dimensional Cutting Stock with Multiple Stock Sizes

In this paper an algorithm for a cutting stock problem in the wood industry is presented. Cuts are of guillotine type and requirements have to be met exactly, i.e. no over- or under-production is allowed. There are several different board sizes from which panels can be cut and the problem is to find the best mix of boards and respective cutting patterns that satisfies the demand for panels with minimum wastage. The heuristic algorithm uses a pattern-building procedure combined with an enumeration scheme for the mix of boards.     

Volumetric properties of aqueous electrolytes at high temperature. II. B(OH)3 and B(OH)3−NaB(OH)4−NaOH mixtures up to 523 K

The densities of boric acid aqueous solutions and sodium hydroxide-sodium borate mixtures were measured as a function of concentration, between 375 and 523 K at pressures close to saturation. The partial molar volumes of boric acid were obtained and it was found that they are almost independent of the concentration. The partial molar volumes of the sodium hydroxide-sodium borate mixtures were fitted to the Pitzer equation for mixtures using the known parameters for NaOH. Thus, the partial molar volume at infinite dilution and the Pitzer parameters of sodium borate could be obtained by assuming ideal mixing.     

NMR polarization echoes in a nematic liquid crystal

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.     

Mobilities and ion-pairing in LiB(OH)4 and NaB(OH)4 aqueous solutions. A conductivity study

The conductivities of aqueous solutions of sodium borate at 25°C and lithium borate at various temperatures are reported. The conductivity of the B(OH) ₄ ⁻ ion is 35.3 ±0.2 S-cm²-mole⁻¹ at 25°C. The electrolytes are both associated, the lithium salt being more associated than the sodium salt. The mobilities and association constants obtained from the conductivity data agree with a model recently proposed for the H₂O−B(OH) ₄ ⁻ interactions. A discrepancy in the reported thermodynamic behavior of NaB(OH)₄ aqueous solutions has been resolved by means of the association constants obtained in the present study. Thus the usefulness of the conductivity measurements to determine excess chemical potentials of binary electrolytes in dilute solution is again shown.     

Continuous-flow determination of reserpine by oxidation with periodate ion and catalysis by manganese(II) in solution or by an MnO2(s) reactor

The periodate ion oxidation of reserpine catalyzed by Mn(II) or Mn(IV) ions was used for the continuous-flow determination of the pharmaceutical drug. Spectrophotometric monitoring of the oxidation product, 3,4-didehydroreserpine, at 385 nm served as means of detection. The Mn(II) catalyst was used in solution and the Mn(IV) in immobilized form as crystalline MnO₂(s) was thermally embedded on the walls of Tygon tubing and incorporated in the flow system as a solid catalyst in an open-tubular reactor. The proposed methods were applied to the analyses of single tablets and of Rauwolfia serpentina standard powders.     

On the CH...Cu agostic interaction: chiral copper(II) compounds with ephedrine and pseudoephedrine derivatives

The ephedrine derivative, (H2ceph), yields [Cu(Hceph)2], showing a CH...Cu(II) agostic interaction; while in the analogous compound [Cu(Hcpse)2], with pseudoephedrine (H2cpse), that interaction is absent, despite the fact that these two diasteromers differ only in the orientation of the methyl and phenyl groups: erythro in H2ceph and threo in H2cpse. The X-ray crystal structure of [Cu(Hceph)2], indicates a Cu...HC length of 2.454 A and the theoretical study reveals the formation of a Cu...HC bond since the associated electronic density shows both a bond critical point and a bond ring critical point.