Generalized Bethe ansatz solution of a one-dimensional asymmetric exclusion process on a ring with blockage

We present a model for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of lengthL with a single defect, across which they move with probability 0 p 1. This model is equivalent to a two-dimensional, six-vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions. We solve this model with a Bethe ansatz generalized to this kind of boundary condition. We discuss in detail the steady state and derive exact expressions for the currentj, the density profilen(x), and the two-point density correlation function. In the thermodynamic limitL the phase diagram shows three phases, a low-density phase, a coexistence phase, and a high-density phase related to the low-density phase by a particle-hole symmetry. In the low-density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale . On the phase transition line diverges and the currentj approaches its critical valuej _c = p as a power law,j _c – j ^–1/2. In the coexistence phase the width of the interface between the high-density region and the low-density region is proportional toL ^1/2 if the density f 1/2 and=0 independent ofL if = 1/2. The (connected) two-point correlation function turns out to be of a scaling form with a space-dependent amplitude n(x₁, x₂) =A(x₂)A ^Ke^–r/ withr = x ₂ –x ₁ and a critical exponent = 0.     

Franck-Condon matrix elements for bound-continuum vibrational transitions calculated by numerical integration and basis set expansion techniques

Franck-Condon factor distributions for bound-to-continuum transitions of one-dimensional vibrational states are calculated by a) using numerical integration, b) employing a finite number of square integrable harmonic oscillator functions. The methods are generally applicable to any kind of bound or repulsive potential involved. Results are presented and compared to model potential calculations previously reported by Krüger [1].     

Radiationless transitions in trivalent lanthanide ions embedded in solids

Radiationless transitions in lanthanide ions embedded in glassy and crystalline hosts have been briefly reviewed. The correlations of multiphonon relaxation rates with energy gaps, vibrational frequencies, temperatures and electronic symmetries have been discussed. The essence of various theories, such as Nth order methods, non-adiabatic Hamiltonian method, dynamic coupling model has also been presented.     

“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

Phase Transition and Crystal Structure of the Monomeric Europium(II) Thiolate Eu(SC36H49)2

Single crystal X‐ray diffraction of Eu(SC₃₆H₄₉)₂ has revealed a first order phase transition at a temperature of 119 K, that involves a reduction of the specific volume by 1 %. The transition corresponds to a doubling of the unit cell, as it is the result from reorientations of isopropyl groups that appear at peripheral sites of the organic ligands. It is argued that a denser packing is achieved at the expense of a less favourable conformation of one of the two crystallographically‐independent complexes in the low‐temperature phase. The Bond‐Valence method is used to show that interactions of equal strengths are present between europium and both sulphur atoms and both coordinating phenyl rings.     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Clathrate formation and phase transitions in β-hydroquinone

Clathrate thermodynamic stability conditions and the phase transitions associated with either the orientational ordering of the guest molecules or with the condensation of the guest molecules in the host lattice are investigated by means of the common microscopic model. The theory proposed describes the thermodynamic properties of -hydroquinone (Q ) clathrates. The dielectric constant (T) was measured experimentally inQ ·CH₃OH andQ ·SO₂ in the temperature range from 4.2 to 300 K and the phase transitions were found. It is shown that the theory qualitatively explains the experimental data obtained.Dedicated to Professor H. M. Powell.     

Thermal behavior of selected ferroelectric liquid crystals

Thermal properties of three ferroelectric liquid crystals, namely: 3-octyloxy-6-[2-fluor-4-(fluoroctyloxy)phenyl]-pyridine (FFP), 3-(3-fluor-nonyl)-6[4-heptyloxyphenyl]-pyridine (FNHPh-P), 4-[(S,S)-2,3-epoxyhexyloxy]phenyl 4-(decyloxy)benzoate (EHPhDB) were studied using heat flux differential scanning calorimetry method. All the transitions expected in this compounds, except the SmC^*-SmA^* and SmC^*-S₃ transitions, were detected in the DSC curves. The temperatures of the phase transitions and the enthalpy changes associated with them were determined. The transition from the liquid crystalline to the crystalline state showed significant hysteresis for all three compounds studied. The following transitions: SmA^*-Is, SmG^*-SmC^* for FNHPh-P, N^*-Is for EHPhDB, N^*-Is and SmC^*-N^* for FFP also showed a small hysteresis basing on which first-order character of all the above transitions was implied. All three substances studied in this work are characterized by a complex polymorphism in the solid state.The author is grateful to Dr. Stanislaw Wróbel for his stimulating interest, valuable discussions and supplying the samples. This work has been done in the framework of the KBN grant 2 P302 139 07.     

Non-solvated aluminum hydride. Crystallization from diethyl ether-benzene solutions

Crystallization of non-solvated aluminum hydride from a diethyl ether-benzene mixed solvent was studied. The desolvation of AlH₃·(Et₂O)_x etherate in solution and the crystallization of α-AlH₃ during polythermal heating of the solution occur only in the presence of ≥10 wt.% LiAlH₄. The process is multistage, and the crystallization begins with the formation of the AlH₃·0.25Et₂O solvate, which recrystallizes in the solid phase into γ-AlH₃ and then α-AlH₃. Four crystalline modifications of aluminum hydride were characterized by X-ray diffraction and electron microscopy. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1259–1265, July, 2007.     

Polymer drying. VI. EPR spin-probe studies on swelled poly(styrene-co-divinylbenzene)

The electron paramagnetic resonance (EPR) signal and the residual number (α_t) of volatile molecules per phenyl group of poly(styrene-co-divinylbenzene) in samples that had been swelled to saturation in a dilute solution of a nitroxide spin-probe (TEMPO or 4-oxo-TEMPO), dissolved in a volatile liquid, were monitored simultaneously as the system containing excess liquid was allowed to evaporate to dryness. The results showed that the characteristic motionally narrowed three-line EPR spectrum began to change when α_t became equal to α_g (the number of sorbed molecules per phenyl group of polymer at liquid-saturation). The ratio of the intensity of the low-field and high-field hyperfine peaks relative to the middle peak decreased monotonically to an asymptotic limit that was attained when α_t became equal to α_g (the number of residual adsorbed molecules per phenyl group of polymer at completion of the transition from the rubbery state to the glassy state). The EPR hyperfine pattern, from which the rotational correlation times were estimated, changed most significantly as α_t decreased from α_G to α_g while exhibiting inflections at about α′_s and α′_g the compositions that mark, respectively, incipient desorption of adsorbed molecules and incipient transition from the rubbery state to the glassy state. The pattern between these inflections points, however, varied with the affinity of the solvent for the polymer.