Magnetism of fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt

The magnetic moments of the fcc/fcc, hcp/hcp twin and fcc/hcp twin-like boundaries in cobalt were investigated by first-principles calculations based on density functional theory. The magnetic moments in fcc/fcc were larger than those of the bulk fcc, while the variations in the magnetic moment were complicated in hcp/hcp and fcc/hcp. The magnetovolume effect on the magnetic moment at the twin(-like) boundaries was investigated in terms of the local average atomic distance and the average deviation from equilibrium; however, the complicated variations in the magnetic moment could not be explained from the magnetovolume effect. Next, the narrowing (or broadening) of the partial density of states (PDOS) width of 3d orbitals, the number of occupied states for the spin-down channel, and the PDOS around the Fermi level were investigated. The entire variation in the magnetic moment at the twin(-like) boundaries could be understood in terms of these factors. Charge transfer occurred in hcp/hcp. In this case, the contributions of 4s and 4p electrons to the variation in the magnetic moment were relatively large.     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Study of the pion trajectory in the photoproduction of leading neutrons at HERA

Energetic neutrons produced in ep collisions at HERA have been studied with the ZEUS detector in the photoproduction regime at a mean photon–proton center-of-mass energy of 220 GeV. The neutrons carry a large fraction 0.64<x_L<0.925 of the incoming proton energy, and the four-momentum transfer squared at the proton–neutron vertex is small, |t|<0.425 GeV². The x_L distribution of the neutrons is measured in bins of t. The (1−x_L) distributions in the t bins studied satisfy a power law dN/dx_L∝(1−x_L)^a(t), with the powers a(t) following a linear function of t: . This result is consistent with the expectations of pion-exchange models, in which the incoming proton fluctuates to a neutron–pion state, and the electron interacts with the pion.     

Size effects in the melting and crystallization temperatures of copper chloride nanocrystals in glass

The size dependence of the crystallization temperature T _c and melting temperature T _m of copper chloride nanocrystals in glasses is studied in the size range R _a from 1 to 30 nm. Jumps are found in the temperature dependence of T _c at R _a =13 nm and R _a =1.8 nm, a jump is found in the temperature dependence of T _m at R _a =2.2 nm, and the supercooling of the melt is found to vanish in the case of crystallization at R _a ⩽1.4 nm. It is conjectured that the jump in T _c with large R _a occurs for a nano-crystal radius equal to that of a crystalline nucleus in the melt, and the jumps in T _c and T _m for smaller values of R _a are due to a change in the shape (faceting) of the nanocrystals. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 7, 481–486 (10 October 1997)     

Parity violation effects in hydrogen atom in forbidden magnetic-dipole transitions

General expressions for the probability of all strongly forbidden magnetic-dipole transitions between states njl and n′jl in the hydrogen atom and light hydrogen-like ions are derived in the lowest order in the parameter (αZ) in the form W _n′jl;njl ^(Ml) = D _n′n ^lj αm _e (αZ)¹⁰ (in relativistic units), where m _e is the electron mass, α is the fine-structure constant, Z is the nuclear charge, and the constants D _n′n ^lj are presented in an analytical form. Using these expressions, the dependence of the degree of parity violation on the principal quantum numbers n and n′ of the lower and upper states in the ns _1/2-n′s _1/2 and np _1/2-n′p _1/2 M1 transitions is systematically analyzed. The results obtained can be used in designing experiments on parity violation in the hydrogen atom.     

The modified Korteweg-de Vries equation on the quarter plane with t-periodic data

We study the modified Korteweg-de Vries equation posed on the quarter plane with asymptotically t-periodic Dirichlet boundary datum u(0,t) in the sense that u(0,t) tends to a periodic function g?₀ (t) with period τ as t → ∞. We consider the perturbative expansion of the solution in a small ε > 0. Here we show that if the unknown boundary data u_x(0,t) and u_xx(0,t) are asymptotically t-periodic with period τ which tend to the functions g?₁ (t) and g?₂ (t) as t → ∞, respectively, then the periodic functions g?₁ (t) and g?₂ (t) can be uniquely determined in terms of the function g?₀ (t). Furthermore, we characterize the Fourier coefficients of g?₁ (t) and g?₂ (t) to all orders in the perturbative expansion by solving an infinite system of algebraic equations. As an illustrative example, we consider the case of a sine-wave as Dirichlet datum and we explicitly determine the coefficients for large t up to the third order in the perturbative expansion.     

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R _e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR _e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR _e δR _e and δE _e in the horizon entropy S _e and enclosed energy E _e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T _e of the CEH at an arbitrary time in a flat FRW universe is E _e /S _e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T _e dS _e =PdV _e −dE _e , where V _e is the enclosed volume and P is the average cosmic pressure.     

Quadratic Actions in Dependent Fields and the Action Principle

General field theories are considered, within the functional differential formalism of quantum field theory, with interaction Lagrangian densities L _I (x;λ), with λ a generic coupling constant, such that the following expression ∂ L _I (x;λ)/∂ λ may be expressed as quadratic functions in dependent fields but may, in general, be arbitrary functions of independent fields. These necessarily include, as special cases, present renormalizable gauge theories. It is shown, in a unified manner, that the vacuum-to-vacuum transition amplitude (the generating functional) may be explicitly derived in functional differential form which, in general, leads to modifications to computational rules by including such factors as Faddeev–Popov ones and modifications thereof which are explicitly obtained. The derivation is given in the presence of external sources and does not rely on any symmetry and invariance arguments as is often done in gauge theories and no appeal is made to path integrals.     

B-decay CP-asymmetries in SUSY with a U(2)3 flavour symmetry

We study CP asymmetries in rare B decays within supersymmetry with a U(2)³ flavour symmetry, motivated by the SUSY flavour and CP problems, the hierarchies in the Yukawa couplings and the absence so far of any direct evidence for SUSY. Even in the absence of flavour-blind phases, we find potentially sizable CP violating contributions to b→s decay amplitudes. The effects in the mixing-induced CP asymmetries in B→ϕK _S and B→η′K _S , angular CP asymmetries in B→K ^∗ μ ⁺ μ ⁻ and the direct CP asymmetry in B→X _s γ can be in the region to be probed by LHCb and next generation B factories. At the same time, these effects in B decays are compatible with CP violating contributions to meson mixing, including a non-standard B _s mixing phase hinted by current tensions in the CKM fit mostly between S_yKS, e_KS_{\psi K_{S}}, \epsilon_{K} and DM_Bs/DM_Bd\Delta M_{B_{s}}/\Delta M_{B_{d}}.     

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.     

On the role of the final-state interactions in rare <Emphasis Type="Italic">B</Emphasis> decays

The effects of final-state interactions (FSI) in hadronic B decays are investigated. The model for FSI, based on Regge phenomenology of high-energy hadronic interactions, is proposed. It is shown that this model explains the pattern of phases in matrix elements of B → ππ and B → ρρ decays. These phases play an important role for CP violation in B decays. The most precise determination of the unitarity triangle angle α from B _d → ρπ decays is performed. The relation between CP asymmetries in B → Kπ decays is discussed. It is emphasized that the large-distance FSI can explain the structure of polarizations of the vector mesons in B decays and other puzzles like a very large branching ratio of the B decay to $ \bar \Xi $ \bar \Xi _c Λ _c .     

Eigenvalues of graphs with twofold symmetry

There are many cases in which the spectrum of a graph contains the complete spectrum of a smaller graph. The larger (composite) graph and the smaller (component) graph are said to be subspectral. It is shown here that whenever a composite graph G has a twofold symmetry operation which defines two equivalent sets of vertices r and s, it is possible to construct two subspectral components G ₊ and G _-, whose eigenvalues, taken jointly, comprise the full spectrum of G. The following rules are given for constructing the components. (1) Draw the r set of vertices and all the edges connecting the members of the set. Then examine in G the vertices through which r and s are connected (the so-called bridging vertices). (2) If a bridging vertex r ₁ is connected to its symmetry-equivalent partner s ₁, then r ₁ is weighted +1 in G ₊ and -1 in G _-. (3) If r ₁ is connected to a vertex s ₂ which is symmetry-equivalent to a second bridging vertex r ₂ in r, then the weight of the edge between r ₁ and r ₂ in G (+1 if they are connected, zero if they are not) is increased by one unit in G ₊ and decreased by one unit in G _-. The derivation of these rules is shown, and the relationship between the spectrum of G and the spectra of G ₊ and G _- is explained in terms of the symmetry properties of the adjacency matrix of G.     

Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings

We present exact results on the partition function of the q-state Potts model on various families of graphs G in a generalized external magnetic field that favors or disfavors spin values in a subset I _s ={1,…,s} of the total set of possible spin values, Z(G,q,s,v,w), where v and w are temperature- and field-dependent Boltzmann variables. We remark on differences in thermodynamic behavior between our model with a generalized external magnetic field and the Potts model with a conventional magnetic field that favors or disfavors a single spin value. Exact results are also given for the interesting special case of the zero-temperature Potts antiferromagnet, corresponding to a set-weighted chromatic polynomial Ph(G,q,s,w) that counts the number of colorings of the vertices of G subject to the condition that colors of adjacent vertices are different, with a weighting w that favors or disfavors colors in the interval I _s . We derive powerful new upper and lower bounds on Z(G,q,s,v,w) for the ferromagnetic case in terms of zero-field Potts partition functions with certain transformed arguments. We also prove general inequalities for Z(G,q,s,v,w) on different families of tree graphs. As part of our analysis, we elucidate how the field-dependent Potts partition function and weighted-set chromatic polynomial distinguish, respectively, between Tutte-equivalent and chromatically equivalent pairs of graphs.     

Holomorphic extension of the logistic sequence

The logistic problem is formulated in terms of the Superfunction and Abelfunction of the quadratic transfer function H(z) = uz(1 − z). The Superfunction F as holomorphic solution of equation H(F(z)) = F(z + 1) generalizes the logistic sequence to the complex values of the argument z. The efficient algorithm for the evaluation of function F and its inverse function, id est, the Abelfunction G are suggested; F(G(z)) = z. The halfiteration h(z) = F(1/2 + G(z)) is constructed; in wide range of values z, the relation h(h(z)) = H(z) holds. For the special case u = 4, the Superfunction F and the Abelfunction G are expressed in terms of elementary functions.     

Anisotropy of rotation of nitroxide probes in nematogenic liquid crystals

An electron paramagnetic resonance (EPR) line shape simulation for nitroxide spin probes in the motional narrowing region was carried out assuming axially symmetricg andA tensors and with different anisotropies of rotationN (=R _∥/R _⊥) whereR _∥ andR _⊥ are, respectively, elements of the diffusion tensor along and perpendicular to its principal axisz′. In addition, it was assumed that the principal axes of the diffusion tensor coincide with the molecular axes. Each of three casesz′=x,z′=y andz′=z, which result from cyclic permutations of the molecular axesx, y andz with thez′,y′ andx′ axes of the diffusion tensor, yields its typical EPR spectrum characterized by the relative intensities of the low-, center- and high-field lines. The parameter δ defined by and calculable from the intensities of the three lines was found to vary linearly withN for thez′=x andz′=y cases and, as anticipated, to be practically constant at a value of 1 for thez′=z case. This suggested a method for estimatingN for a probe from its EPR spectrum. Experimental spectra over a narrow temperature range (1°C) in the vicinity of the nematic-to-isotropic transition (about 34.6°C) ofN-(4-n-butylbenzilidene)-4-amino-2,2,6,6-tetramethylpiperidine-1-oxide at a mole fraction of 1·10⁻³ in 4-n-pentyl-4′-cyanobiphenyl showed a pattern of peak heights characteristic of thez′=x case with δ values that gave, neglecting effects of the mean field, higher and lowerN values in the nematic and isotropic regions, respectively. Analysis of other similar systems in the literature gave similar results.     

Singularity of the vortex density of states in d-wave superconductors

In d-wave superconductors, the electronic density of states (DOS) induced by a vortex exhibits a divergence at low energies: N _vortex(E) ∼1/|E|. This divergence is the result of gap nodes in the spectrum of excitation outside the vortex core. The heat capacity in two regimes, T ²/T _c ² ≫ B/B _c 2 and T ²/T _c ² ≪ B/B _c 2, is discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 641–645 (10 November 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation

We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationu _t =u _xx +f(u) withf(0)=f(1)=0, andf>0 in (0,1), which permits, in principle, the calculation of the exact speed for arbitraryf.     

One-dimensional Anderson model with dichotomic correlation in the presence of external electric field

A one-dimensional diagonal tight binding electronic system with dichotomic correlated disorder in the presence of external d.c field is investigated. It is found numerically that the conductance distribution obeys fairly well to log-normal distribution in weak disorder strength in localized regime, which indicates validity of single parameter scaling theory in this limit. Contrary to the universal cumulant relation C ₁ = 2C ₂ in the absence of d.c. field, we demonstrated numerically that C ₁ ≫ 2C ₂ in the presence of the field in localized regime. We interpret this result as suppression of the fluctuation effects by the external field. In addition, it is obtained that the quantity NF _c , here N is the system size and F _c is the crossover field, decreases as the as the system energy E increases. Moreover, we find numerically a simple linear relation between the average logarithm of the conductance 〈ln(g)〉 and the field strength as 〈ln(g)〉 = C(N, λ)F, here C(N, λ) is a constant for particular values of N and λ, which is the Poisson parameter of the dichotomic process.     

Self-diffusion in liquid metals

A survey is made of all published data on self-diffusion in liquid metals and an examination is carried out on the temperature-dependence of D for studies covering a wide range of temperatures. Log D versus 1/T and D versus T represent the best data equally well, while D versus T ^1/2 and D versus T ² do not. The proper functional form is taken to be D=CT experimentally, and a simple free diffusion theory is developed from the standpoint of vibrational atom motion. An equation having no adjustable parameters results (D=k ² ? _D T/hk), in which κ is the vibrational force constant. Values calculated for D at the melting point are in good agreement with experimental values for potassium, sodium, copper and silver, but are below the measured values for lead, indium, zinc and tin.     

Analysis of temperature and concentration dependence of flow stress in KCl–KBr single crystals with special reference to solute distribution

Available data on the temperature and concentration dependence of critical resolved shear stress (CRSS) of KCl–KBr solid-solution crystals containing 9, 17, 27 and 45?mol% KBr in the temperature range 77–230?K have been analyzed within the framework of the kink-pair nucleation model of plastic flow in solid- solution crystals. It is found that CRSS τ decreases with increasing temperature T in accordance with the model relation lnτ?=?A???BT, where A and B are positive constants. The CRSS τ at a given temperature depends on solute concentration c as τ?∝?c^p , where exponent p has a value between 0.33 and 0.57 as temperature T rises from 0 to 230?K. The model parameter W _o, i.e. binding energy between the edge-dislocation segment L _o involved in the unit activation process and the solute atoms close to it (T?→?0?K), which is inversely proportional to B, increases with solute concentration c monotonically as W _o?∝?c ^0.33 up to a critical value c _m?=?35?mol% KBr, which is in reasonable agreement with the model prediction W _o?∝?c ^0.25. However, W _o decreases with an increase in c beyond c _m, which indicates somewhat ordered distribution of solute in the host lattice of concentrated KCl–KBr solid solutions with c?>?c _m.