Symmetry of electrostatic interaction between pyrophosphate DNA molecules

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.     

Coulomb effects in a ballistic one-channel S-S-S device

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E _C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q _x =CV _g . Zh. éksp. Teor. Fiz. 114, 640–653 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

Mechanism of three-dimensional polymerization of fullerite C60 at high pressures

A series of polycrystalline phases corresponding to different stages of three-dimensional polymerization and destruction of C₆₀ molecules has been synthesized by heating fullerite C₆₀ under a pressure P=12.5 GPa. The structure of the phases can be identified as fcc, and the lattice period decreases with increasing heating temperature. A model of three-dimensional polymerization in which the lattice parameter is a continuous function of the fraction of covalently bonded molecules is proposed. The model makes it possible to estimate the number of atoms in the sp ³ state. The hardness of the polymerized fcc phases is studied on the basis of percolation of rigidity. It is shown experimentally that the period a≈13.8 Å is the threshold for the formation of a three-dimensionally rigid C₆₀ polymer. It is found that the thermal stability of the strongly and weakly polymerized phases is qualitatively different. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 755–759 (10 December 1996)     

Thermodynamic parameters of diffuse phase transitions in Ag2Te

A differential thermal analysis in vacuum and studies of the coefficients of electrical conductivity and thermal conductivity, and of the thermal emf are made in Ag₂Te in the neighborhood of the structural phase transition. It is shown that these data can be used to calculate the switching factor L(T), determine the region in which the phases coexist within the transition, and calculate the thermodynamic parameters. Prior to and after the main phase transition, additional displacement transitions are observed. It is found that the phase transition takes place roughly according to the scheme α _{385 K}→α′_{405 K}→β′_{420 K}→β _{440 K}. The specific heat C _p, changes in entropy ΔS and transition enthalpy ΔH, as well as the minimum phase fluctuation volume V, and the heat Q of the phase transition are determined. It is shown that excesses of Te and Ag have almost no effect on the transition temperatures T ₀, but have a substantial effect on the thermodynamic parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1693–1697 (September 1998)     

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.     

Analytic properties of different unitarization schemes

The analytic properties of the eikonal and U-matrix unitarization schemes are examined. It is shown that the basic properties of these schemes are identical. Both can fill the full circle of unitarity, and both can lead to standard and non-standard asymptotic relations for σ _el/σ _tot. The relation between the phases of the unitarised amplitudes in each scheme is examined, and it is shown that demanding equivalence of the two schemes leads to a bound on the phase in the U-matrix scheme.     

Noncommutative electromagnetism as a large <Emphasis Type="Italic">N</Emphasis> gauge theory

We map noncommutative (NC) U(1) gauge theory on ℝ _C ^d ×ℝ _NC ²ⁿ to U(N→∞) Yang–Mills theory on ℝ _C ^d , where ℝ _C ^d is a d-dimensional commutative spacetime while ℝ _NC ²ⁿ is a 2n-dimensional NC space. The resulting U(N) Yang–Mills theory on ℝ _C ^d is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang–Mills theory onto ℝ _C ^d . We show that the gauge-Higgs system (A _μ ,Φ ^a ) in the U(N→∞) Yang–Mills theory on ℝ _C ^d leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4{\mathcal{N}}=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A _μ ,Φ ^a ) in half-BPS configurations describes self-dual Einstein gravity.     

Dynamical Lie algebra method for highly excited vibrational state of asymmetric linear tetratomic molecules

The highly excited vibrational states of asymmetric linear tetratomic molecules are studied in the framework of Lie algebra. By using symmetric groupU ₁(4)U ₂(4)⊗U ₃(4), we construct the Hamiltonian that includes not only Casimir operators but also Majorana operators M₁₂, M₁₃ and M₂₃, which are useful for getting potential energy surface and force constants in Lie algebra method. By Lie algebra treatment, we obtain the eigenvalues of the Hamiltonian, and make the concrete calculation for molecule C₂HF.     

An image processing study of a reentrant discotic cholesteric – biaxial cholesteric phase transition

In this work, we study and characterize the cholesteric sequence of phases (Ch_Dr ? Ch_B ? Ch_D), where the first Ch_Dr is the reentrant cholesteric discotic phase, Ch_B is the cholesteric biaxial phase and the second Ch_D is the cholesteric discotic phase. This sequence of phases is studied through polarized light microscopy and image processing technique, where, for the first time, the domains and borders of these transitions are established and characterized. They are also investigated and optically characterized throughout their textures.     

Dissociation energy of diatomic molecules

The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D _e[[1−exp{−b(r−r _e)}]/ [1−Cexp{−b(r−r _e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD _e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω _ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.     

Electron-driven processes for furan,tetrahydrofuran and 2, 5-dimethylfuran

We present the study of electron-induced processes for biomolecules, furan (C₄H₄O) and tetrahydrofuran (C₄H₈O) as well as an industrial relevant molecule 2, 5-dimethylfuran (C₆H₈O) through various total cross sections for impact energies from threshold to 5 keV. We have employed spherical complex optical potential to calculate total cross sections Q_T and total elastic cross sections Q_el. Since these molecules are complex molecules, we have used the group additivity rule which incorporates molecular properties as well as geometry of the target to evaluate these cross sections. Dependence of Q_T and Q_el on number of electrons and correlation of dipole polarisability (α) and ionisation potential (I) with peak of total ionisation cross sections Q_ion is studied and important inferences are noted. The present results for these applied molecules are compared with previous data wherever available. This is the maiden attempt to report Q_el and Q_T for 2, 5-dimethylfuran.     

Synchronization of high-frequency vibrations of slipping phase centers in a tin whisker under microwave radiation

Current-voltage characteristics of a system with a variable number of slipping phase centers resulting from phase separation in a tin whisker under external microwave field with a frequency Ω/2π≅35–45 GHz have been studied experimentally. Emergence and disappearance of steps with zero slope in a whisker’s current-voltage characteristic at U _m/n =(m/n)U _Ω, where m and n are integers and U _Ω is determined by Josephson’s formula _ℏΩ=2eU _Ω, have been investigated. Microwave field generated by slipping phase centers is nonharmonic, and the system of slipping phase centers permits synchronization of internal oscillations at a microwave frequency by an external field with a frequency which is the n-th harmonic of internal oscillations. The estimated microwave power generated by a whisker is 10⁻⁸ W. Stimulation of superconductivity in a current-carrying whisker has been detected. Zh. éksp. Teor. Fiz. 113, 1364–1375 (April 1998)     

Some new four-parameter potentials and their use in the study of vibrational thermodynamical quantities of diatomic molecules

Three four-parameter potentials,U _I,U _II andU _III have been proposed and their accuracy has been demonstrated by finding the mean square deviation from the true RKR potential curve for 15 electronic states of 12 diatomic molecules. Their percentage average mean square deviations from RKR curve have been found to be 1.45, 1.86 and 2.89, respectively. These compare favourably with the value 2.67 for the recently suggested four-parameter potential of Wei Hua which itself yields better results than the commonly employed three-parameter potentials. The superiority of the new potentials (especially ofU _I andU _II has been further established by using these potentials to calculate the molecular constants α_e and ω_ex_e following Dunham’s method. The corresponding percentage average mean deviations, for α_e, turn out to be 3.75, 5.13 and 15.43 and for ω_ex_e 8.73, 17.23 and 27.49, respectively, against the respective values of 7.97 and 18.88 with Wei Hua’s four-parameter potential. Also included are the values of dissociation energy determined with these potentials and these too corroborate the better performance ofU _I andU _II. The relative worth of various potential functions has been further tested by carrying out numerical study of vibrational partition function (evaluated by sum over states method), entropy and thermal capacity for the ground state of 7 molecules and comparing these with the corresponding findings based on the RKR data.     

Non-Standard Schwinger Fermionic Representation of Unitary Group

The non-standard Schwinger fermionic representation of the unitary group is studied by using n-fermion operators. One finds that the Schwinger fermionic representation of the U(n) group is not unique when n≥3. In general, based on n-fermion operators, the non-standard Schwinger fermionic representation of the U(n) group can be established in a uniform approach, where all the generators commute with the total number operators. The Schwinger fermionic representation of U(C _n ^m ) group is also discussed.     

Identification of the polymerized orthorhombic phase of C60 fullerene

It is established by x-ray diffraction and Raman scattering that the polymerization of C₆₀ fullerene at 1.5 GPa and 723 K leads to the formation of an orthorhombic phase that is different from the previously identified high-pressure orthorhombic phase. It is determined by a calculation of the optimal packing of linear C₆₀ polymers by the method of atom-atom potentials that the energetically favorable structure of the orthorhombic phase belongs to the space group P n n m and not the previously proposed group I m m m. The computed value of the rotation angle of the polymer chains that corresponds to the minimum packing energy was equal to 61°. The mechanisms leading to the formation of the polymerized phases are discussed on the basis of the results obtained. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 2, 110–114 (25 July 1997)     

Imma phase of Si: phase transitions and stability

First principles calculations of the total energy of Imma states have found instabilities in states near the β-Sn phase and in states near the simple hexagonal (sh) phase of Si crystal. In agreement with experiment the two instability ranges narrow the stable range between them and also in agreement with experiment the instabilities force first-order transitions to both the β–Sn and sh phases when the pressure is held constant, the experimental condition. The transition pressures to the β-Sn and sh phases for a non-vibrating crystal model are found to be 96 and 110 kbar respectively. These pressure values are considerably lower than the experimental values, but we show that lattice vibrations will increase the equilibrium-state pressures. We find widespread occurrence of instability in the equilibrium states of the three phases and show the presence of three kinds of instability. Near and up to the sh phase structure we find the unusual case of stability at constant volume, but, as observed, instability at constant pressure p. Two special computational procedures are discussed, which locate the unstable ranges of structure. One is based on finding phases from minima of total energy E at constant V and the other finds phases from minima of the Gibbs free energy G at constant p. When the minima cease to exist the Imma phase is unstable.     

q-Fuzzy Spheres and Quantum Differentials on Bq[SU2] and Uq(su2)

We provide a new unified construction of the two-parameter Podleś two-spheres as characterised by a projector e with trace _q (e) = 1 + λ. In our formulation the limit in which q → 1 with λ fixed is the fuzzy sphere, while the limit λ → 0 with q fixed is the standard q-deformed sphere. We show further that the non-standard Podleś spheres arise geometrically as ‘constant time slices’ of the unit hyperboloid in q-Minkowski space viewed as the braided group B _q [SU ₂]. Their localisations are then isomorphic to quotients of U _q (su ₂) at fixed values of the q-Casimir precisely q-deforming the fuzzy case. We also use transmutation and twisting theory to introduce a C_q[G_\mathbb C]{C_q[G_\mathbb {C}]} -covariant differential calculus on general B _q [G] and U _q (g), with Ω(B _q [SU ₂]) and Ω(U _q (su ₂) given in detail. To complete the picture, we show how the covariant calculus on the 3D bicrossproduct spacetime arises from Ω(C _q [SU ₂]) prior to twisting.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002