Unparticles in gauge theory

A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle (“ungluon”). The model is formulated in terms of Lagrangian which features the source field S(x) which becomes a local pseudo-Goldstone field of conformal symmetry — the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by B _μ(x) ∼ ∂_μ S(x). Because the conformal sector is strongly coupled, the mode S(x) may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the “ungluon” exchange pattern — the “ungluon” propagator.     

Fredholm Modules on P.C.F. Self-Similar Fractals and Their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct non-trivial Fredholm modules on post critically finite fractals by regular harmonic structures (D, r). The modules are (d _S , ∞)–summable, the summability exponent d _S coinciding with the spectral dimension of the generalized Laplacian operator associated with (D, r). The characteristic tools of the noncommutative infinitesimal calculus allow to define a d _S -energy functional which is shown to be a self-similar conformal invariant. Thiswork has been supported by the project “Teoria ellittica e forme di Dirichlet su spazi frattali” G.N.A.M.P.A. 2008 and by the G.R.E.F.I.-G.E.N.C.O. French-Italian Research Group.     

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

Rotational excitations in muonic atom scattering by molecular hydrogen

A computational scheme based on the infinite order sudden approximation (IOS) is proposed for treating molecular and screening effects in muonic atom scattering at low energies. With this scheme the differential (dσ/dΩ(ɛj← 0|θ) and the total σ_tot(ɛ) cross-sections of muonic atom scattering on molecules of hydrogen isotopes are calculated at energies ɛ_rot=ℏω_I⩽ɛ⩽ɛ_vib= ℏω_03BD;. The IOS permits a quantitative analysis of the dependence of the differential cross-sections on the scattering angle and on the rotational excitations, particularly the rotational rainbow effects. An attractive feature of this approach is also to include the energy and the angular dependencies in the “input” cross-sections describing the muonic atom scattering on each bare nucleus of the molecule. The calculated total cross-sections ω_tot(ɛ) are in agreement with the data obtained earlier with the pseudopotential approach. This revised version was published online in August 2006 with corrections to the Cover Date.     

A model for multiparticle production in high energy hadronic collisions

A model for multiparticle production process in high-energy hadronic collisions is proposed. In the centre of mass (CM) system of colliding particles the target and the projectile are assumed to pass through each other sharing energies allowed by kinematical constraints. Thus in app collision the energy associated with each is √S/2 (S being the square of the CM energy) which is taken to be the real variable that governs the number of particles produced. In the case of hadronnucleus collisions the projectile and the target ofv nucleons lying in a (Lorentz contracted) tube pass through each other sharing energies ⋍ √S _A2, whereS _A ⋍vS. Before the final state particles emerge from these systems, the constituents of the target, i.e.,v nucleons share equally (= √S _A2v) the total energy associated with the target and become the centres from which final state particles stem out. Several results have been discussed.     

Quantum deformation of lorentz group

A one parameter quantum deformationS _μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS _μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS _μ U(2). It shows thatS _μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS _μ U(2). The same construction applied to any compact quantum groupG _c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG _d ofG _c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG _c . The theory of smooth representations ofS _μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS _μ U(2) are classified. An application to 4D ₊ differential calculus is presented. The nonsmooth case is also discussed.     

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors<Superscript>⋆</Superscript>

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from 2π exchange with excitations of virtual Δ(1232)-isobars are also taken into account in our diagrammatic calculation of the energy per particle ˉ(k _f). In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, ρ₀ ≃ 0.16fm^-3, ˉ₀ ≃ - 16MeV, is well reproduced with a monopole mass of Λ ≃ 4πf _π ≃ 1.16GeV. As in the recent approach based on the universal low-momentum NN potential V _low-k, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion exchange contributions to ˉ(k _f) on the “resolution” scale Λ can be compensated over a wide range of Λ by counterterms with two “running” contact couplings. As a further application we study the in-medium chiral condensate 〈ˉq〉(ρ) beyond the linear density approximation. For ρ ⩽ 1.5ρ₀ we find small corrections from the derivative dˉ(k _f)/dm _π, which are stable against variations of the monopole regulator mass Λ.     

Microwave dielectric characterization of binary mixture of formamide with <Emphasis Type="Italic">N,N</Emphasis>-dimethylaminoethanol

Dielectric relaxation measurements of formamide (FMD)-N,N-dimethylaminoethanol (DMAE) solvent mixtures have been carried out over the entire concentration range using time domain reflectometry technique at 25, 35 and 45°C in the frequency range of 10 MHz to 20 GHz. The mixtures exhibit a principle dispersion of the Davidson-Cole relaxation type at microwave frequencies. Bilinear calibration method is used to obtain complex permittivity ɛ*(ω) from complex reflection coefficient ρ*(ω) over the frequency range of 10 MHz to 10 GHz. The excess permittivity (ɛ ^E), excess inverse relaxation time (1/τ)^E, Kirkwood correlation factor (g ^eff), activation energy and Bruggeman factor (f _B) are also calculated to study the solute-solvent interaction.      

Effect of γ irradiation on the low-temperature electrical conductivity and dielectric properties of TlGaSe2 crystals

Electrical conductivity and dielectric properties of single-crystal TlGaSe₂ have been studied as a function of γ irradiation dose in the 100–280 K range including the existence of an incommensurate phase. Anomalies in the form of maxima have been observed in the σ=f(T), tan δ=f(T), and ɛ=f(T) curves at the points of transition from the paraphase to incommensurate (IC) phase, T _i, and from the IC to commensurate phase, T _c. The increase in the quantities σ, tan δ, and ɛ observed initially with increasing irradiation dose is followed by their strong decrease and disappearance of the anomalies. It has been established that γ irradiation does not affect the phase transition temperatures T _i and T _c. Fiz. Tverd. Tela (St. Petersburg) 40, 1328–1331 (July 1998)     

Dielectric properties and phase transitions in crystals of TlInS x Se2 − x solid solutions

This paper reports on a study of the dielectric permittivity and electrical conductivity of single-crystal TlInS _x Se_{2 − x} solid solutions as functions of temperature and composition. It has been found that the dielectric permittivity ɛ and electrical conductivity σ decrease with increasing x and increase with growing temperature. The temperature dependences ɛ = f(T) and σ = f(T) for TlInS _x Se_{2 − x} crystals have been demonstrated to reveal anomalies in the form of maxima, which suggests that these crystals undergo phase transitions. The temperatures of the phase transitions increase with increasing x.     

Electrical properties of nickel-doped arsenic trisulphide

Results of temperature and frequency dependent a.c. conductivity of pure and nickel-doped a-As₂S₃ are reported. The a.c. conductivity of pure As₂S₃ obeys a well-known relationship: σ_ac ∝ω ^s. Frequency exponents is found to decrease with increasing temperature. Correlated barrier hopping (CBH) model successfully explains the entire behaviour of a.c. conductivity with respect to temperature and frequency for pure As₂S₃. But a different behaviour of a.c. conductivity has been observed for the nickel doped As₂S₃. At higher temperatures, distinct peaks have been observed in the plots of temperature dependence of a.c. conductivity. The frequency dependent behaviour of a.c. conductivity (σ_ac ∝ω ^s) for nickeldoped As₂S₃ is similar to pure As₂S₃ at lower temperatures. But at higher temperatures, ln σ_ac vs lnf curves have been found to deviate from linearity. Such a behaviour has been explained by assuming that nickel doping gives rise to some neutral defect states (D ^0′) in the band gap. Single polaron hopping is expected to occur between theseD ^0‘ andD ⁺ states. Furthermore, allD ⁺,D ^0′ pairs are assumed to be equivalent, having a fixed relaxation time at a given temperature. The contribution of this relaxation to a.c. conductivity is found to be responsible for the observed peak in the plots of temperature dependence of a.c. conductivity for nickel-doped As₂S₃. The entire behaviour of a.c. conductivity with respect to temperature and frequency has been explained by using CBH and “simple pair” models. Theoretical results obtained by using these models, have been found to be in agreement with the experimental results.     

Electrical and magnetic properties of [(CoFeZr)x(Al2O3)1 ? x/(α-SiH)]n multilayer structures

The concentration dependences of the electrical resistivity and complex permeability of [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n multilayer structures and (Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} composites have been studied. It has been established that introduction of a semiconductor interlayer into the (Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} composites substantially decreases the electrical resistivity of [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n multilayer structures. The concentration dependences of the real and imaginary parts of the complex permeability of the [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n nanomultilayer structures substantially differ from those of the (Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} composites. The real part of the complex permeability of the [“(Co₄₅Fe₄₅Zr₁₀) _x (Al₂O₃)_{100 − x} ”/“α-Si: H”] _n nanomultilayer structures follows the curve with a minimum near the percolation threshold of the composite, and the imaginary part smoothly decreases as the ferromagnetic phase concentration increases. The results obtained are explained by the increase in the bifurcation temperature due to the conduction electrons of the semiconductor interlayer, which favor magnetic ordering of ferromagnetic grains.     

A geometric generalization of classical mechanics and quantization

A geometrization of classical mechanics is presented which may be considered as a realization of the Hertz picture of mechanics. The trajectories in thef-dimensional configuration spaceV _f of a classical mechanical system are obtained as the projections onV _f of the geodesics in an (f + 1) dimensional Riemannian spaceV _{f + 1}, with an appropriate metric, if the additional (f + 1)th coordinate, taken to be an angle, is assumed to be “cyclic”. When the additional (angular) coordinate is not cyclic we obtain what may be regarded as a generalization of classical mechanics in a geometrized form. This defines new motions in the neighbourhood of the classical motions. It has been shown that, when the angular coordinate is “quasi-cyclic”, these new motions can be used to describe events in the quantum domain with appropriate periodicity conditions on the geodesics inV _{f + 1}.     

Experimental investigation of ligand effects on the conversion electron spectrum of the 22.5 keV M1 + E2 nuclear transition in <Superscript>149</Superscript>Sm

The conversion electron spectrum of the 22.5keV M1 + E2 nuclear transition in ¹⁴⁹Sm from the electron capture decay of ¹⁴⁹Eu was experimentally studied for the “Eu₂O₃” and “EuF₃” compounds in which ¹⁴⁹Eu ions have the same assumed oxidation number +3 . While the energies of the L, M, N, O, and P₁ conversion lines for “EuF₃” were lower, on average, by 1.7(1), 2.7(2), 2.3(3), 4.1(2), and 5.7(9)eV, respectively, than those for “Eu₂O₃”, no changes between the two ligand complexes were observed for relative intensities of the conversion lines and their natural widths within the error limits.     

Couette Flows over a Rough Boundary and Drag Reduction

 We consider the Couette flow between two plates. The lower plate is fixed and has periodically placed riblets of the characteristic size ɛ on it. In the limit ɛ → 0 we find the effective Couette-Navier flow as an O(ɛ ² ) approximation for the effective mass flow and an O(ɛ ² )L ¹ -approximation for the velocity. In the effective solution the effect of roughness enters through the Navier slip condition with the matrix coefficient in front of the effective shear stress, calculated using a boundary layer problem. Furthermore, an O(ɛ ² ) approximation for the tangential drag force is found. In all estimates explicit dependence on the kinematic viscosity ν, the velocity of the upper plate and the distance between the plates L ₃ is kept. Also the uniqueness of the solution is expressed through a non-linear algebraic condition linking and L ₃ . Then the result is applied to the viscous sub-layers around immersed bodies, strictly containing the surface riblets. It is found that for the riblets of the characteristic size ɛ, being of the order smaller or equal to , the approximation obtained for the tangential drag could be applied. We compare ɛ and for realistic data and our results lead to the conclusion that the riblets reduce significantly tangential drag, which may explain their presence on the skin of Nektons. Received: 14 December 2001 / Accepted: 1 August 2002 Published online: 7 November 2002     

Quark mass and the masses of Goldstone bosons

Based on the Dyson-Schwinger Equations (DSEs) of QCD in the “rainbow” approximation, the fully dressed quark propagator S _f (p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes A _f and B _f which built up the fully dressed quark propagator, and the dynamical running masses M _f , which is defined by A _f and B _f for light quarks u, d and s, are calculated, respectively. Using the predicted current masses m _f , quark local vacuum condensates, and our predicted value of pion decay constant, the masses of Goldstone bosons K, π and η and their in-medium values are also evaluated. Our predictions fit to data and to many other different calculations quite well. The numerical results show that the mass of quark is dependent of its momentum p ². The fully dressed quark amplitudes A _f and B _f have correct behaviors and can be used for many purposes in our future researches on non-perturbative QCD.      

Flexible-to-semiflexible chain crossover on the pressure-area isotherm of a lipid bilayer

We find theoretically that competition between ∼K _f q ⁴ and ∼Qq ² terms in the Fourier-transformed conformational energy of a single-lipid chain, in combination with interchain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)∼(A−A ₀)^−α. The crossover manifests itself in the transition from α = 5/3 to α = 3. Our microscopic model represents a single-lipid molecule as a worm-like chain with a finite irreducible cross-section area A ₀, a flexural rigidity K _f , and a stretching modulus Q in a parabolic potential with the self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area A* obeys the relation Q/√K _f B(A*) ≈ 2. We predict a peculiar possibility of deducing the effective elastic moduli K _f and Q of an individual hydrocarbon chain from the analysis of the isotherm with such a crossover. Also calculated is the crossover-related behavior of the area compressibility modulus K _A , the equilibrium area per lipid A _t , and the chain order parameter S(θ). The text was submitted by the authors in English.     

Micelle-smectic phase coexistence: Origin of the maximum swelling of a mixed lamellar phase

By use of a mean-field approach the spin-wave dispersion of the Cu degrees of freedom in the undoped high-T _C material Nd₂CuO₄is investigated. The experimentally observed sharp decrease of the Cu spin-wave gap with increasing temperature in the range is explained by a paramagnetic-like susceptibility of the Nd spins which couple to the Cu subsystem. The degeneracy of the “in-plane” and “out-of-plane” polarized Cu spin-wave branches is shown to be lifted by the uniaxial anisotropy of the Cu-Cu nearest-neighbor interaction. Received: 13 August 1997 / Revised: 4 December 1997 / Accepted: 11 December 1997     

Observation of exchange bias and spin-glass-like ordering in ɛ-Fe2.8Cr0.2N nanoparticles

Nanoparticles of ɛ-Fe_2.8Cr_0.2N system exhibit the exchange bias phenomenon due to the exchange coupling of the spins of the antiferromagnetic (AF) oxide/oxynitride surface layer and the ferromagnetic (FM) nitride core. Exchange bias is observed at 10 K both in the absence and presence of cooling field. Due to the interface disorder, a mixture of parallel and anti-parallel/perpendicular coupling of the AF and FM spins is observed. The roughness of AF-FM interface induces disorder due to the random exchange anisotropy. The saturation magnetization is also found to be drastically lowered as compared to parent ɛ-Fe₃N. Below 58 K, the broad peak (T _E ≅ T _f ) in zero-field cooled (ZFC) magnetization curves indicates the presence of unidirectional anisotropy and spinglass-like ordering, that arises from the freezing of localized frustrated spins.