Corrections to scaling in the q-state Potts model within Gaussian closure approximation

Corrections to scaling in the q-state Potts model due to departures of the initial condition from scaling morphology are studied at zero temperature in phase-ordering kinetics within Gaussian closure approximation. When the corrections to scaling are included, the equal time correlation function has the form G(r,t) = g₀(r/L)+L^-ωg₁(r/L) + ..., where L is the coarsening length scale. Both the correction-to-scaling exponent ω and the correction-to-scaling function g₁(x) are calculated for different values of q. The correction-to-scaling exponent ω is found to be nontrivial and depends on q. The corrections to scaling are found to be large (relative to scaling function g₀(x) itself) at large scaling variable x.     

The corrections to scaling within Mazenko’s theory in the limit of low and high dimensions

We consider corrections to scaling within an approximate theory developed by Mazenko for nonconserved order parameter in the limit of low (d → 1) and high (d → ∞) dimensions. The corrections to scaling considered here follows from the departures of the initial condition from the scaling morphology. Including corrections to scaling, the equal time correlation function has the form: C(r, t) = f ₀(r/L)+L ^−ω f ₁(r/L)+…, where L is a characteristic length scale (i.e. domain size). The correction-to-scaling exponent ω and the correction-to-scaling functions f ₁(x) are calculated for both low and high dimensions. In both dimensions the value of ω is found to be ω = 4 similar to 1D Glauber model and OJK theory (the theory developed by Ohta, Jasnow and Kawasaki).     

On the decayK L 0 →l + l −

Using one of the models of Gell-Mannet al. the intermediate vector meson mass is estimated by using the upper limit for the decay of theK _L ^Emphasis>/0 meson into a lepton pair. This mass turns out to be very large. Therefore only the leading terms are taken into account.     

The equivalent vector boson approximation for intermediate mass Higgs boson production

We consider the equivalent vector boson approximation (EVBA) for the processqq→qqWW→qqH andqq→qqZZ→qqH. It is shown that the contributions σT and σL, of the transversely and longitudinally polarized vector bosonsV respectively, are comparable with each other for intermediate values ofm _H viz. 0.3 TeV to 0.6 TeV. σT can be as large as 1.5–2 times σL in this mass range. As a result the leading EVBA for σ=σL+σT overestimates the exact total cross-section by a factor, upto 2–3 even, at high energies. σT is negligible with respect to the leading contribution σL only form _H≧0.6 TeV, where EVBA is correct within 15–20%. Further the effect of the corrections to EVBA, which are naively of nonleading order, on these conclusions in the framework of the EVBA is discussed.     

Low temperature behaviour of the blackbody radiation energy in the infinite slab resonator

The total radiation energy between two infinite extended metallic plates with distance L is studied. A low temperature representation of the energy is calculated the leading term of which is proportional to T³.For L·;T < 0.1 cmK this term is the dominant one and all other contributions may be neglected.     

Short-distance CP-violating contributions to the KL→π0e+e− decay

New constributions to the K_L→π⁰e⁺e⁻ amplitude are presented. Short-distance penguin induced diagrams for the s→dγ¹ transition supplement the previously considered electromagnetic penguin. The new CP-violating amplitude corresponds to a new piece of the relevant anomalous dimension matrix. Strong interaction corrections to the new part of the effective hamiltonian are calculated in the leading logarithmic approximation. The role of subleading terms is also discussed.     

On pion condensation in finite nuclei

The critical pionic state leading to pion condensation is investigated for finite nuclear systems. The threshold density for light nuclei, including⁴He, is found to be close to that of nuclear matter. For¹⁶O and⁴⁰Ca, the angular momenta of the most critical states areL=0 andL=2.     

Phase separation of binary systems

In this paper, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the sign of a nondimensional parameter K such that if K>0, the transition is first order with latent heat and if K<0, the transition is second order. Here the parameter K is defined in terms of the coefficients in the quadratic and cubic nonlinear terms of the Cahn-Hilliard equation and the typical length scale of the container. Second, a phase diagram is derived, characterizing the order of phase transitions, and leading in particular to a prediction that there is only a second-order transition for molar fraction near 1/2. This is different from the prediction made by the classical phase diagram. Third, a TL-phase diagram is derived, characterizing the regions of both homogeneous and separation phases and their transitions.     

Can presentF 2 andR=σ L /σ T data unravel power corrections?

We analyse the QCD non-singlet leading order prediction ofR=σ _L /σ _L using the results of the EMCF ₂ fits to proton, deuterium and iron data and we examine in detail its compatibility withR from SLAC. Least squares fits to combined EMC and SLACF ₂ andR proton data are carried out at leading order in the non-singlet case. Incompatibilities have been confirmed which, in spite of present uncertainties, require the consideration of power corrections.     

Necessary and sufficient conditions for the existence of a Lagrangian in field theory II. Direct analytic representations of tensorial field equations

By using a characterization of the concept of analytic representation and a variational approach to self-adjointness introduced in a preceding paper, we prove a theorem, according to which a necessary and sufficient condition for a class $\text{C}$², regular, tensorial, quasi-linear system of field equations to admit an ordered direct analytic representation in terms of the Lagrange equations in a region R of its variables is that the system is self-adjoint in R. We point out as a first corollary that if the ordering requirement is removed from the definition of analytic representation, then the condition of self-adjointness of the field equations is only sufficient for the existence of a Lagrangian density. We then provide as a second corollary a methodology for the computation of the Lagrangian density for the representation of self-adjoint quasi-linear tensorial field equations. This methodology is also particularized for ordinary semilinear systems of tensorial field equations through a third corollary. The above results are interpreted from the viewpoint of interactions. We first recover, through a fourth corollary, the conventional structure of the total Lagrangian density L_Tot = Σ_{1 a}ⁿL_Free^(a) + L_Int for the semilinear form of the field equations, and then introduce through a fifth corollary a generalized structure of the type L_Tot = Σ_{1 a}ⁿL_{Int, I}^(a)L_Free^(a) + L_Int.II for t representations of the field equations in the quasi-linear form. Therefore, our analysis seems to indicate that a general form of representing interacting fields is characterized by (n+1)-interaction terms in the Lagrangian: n multiplicative terms and one additive term to the Lagrangian for the free fields.     

On the derivation and analysis of the spin S XY-model susceptibility series expansions

We have derived 10th order series expansions for the free energy and 9th order ones for the fluctuation of the order parameter in the spin-SXY-model on the f.c.c. lattice for S = $\text{1}\text{2}$, 1, $\text{3}\text{2}$, 2, 3, 4, 6 and 8. Confluent singularity analyses of the fluctuation series confirm the universality hypothesis, with critical exponent γ₁ = 1.33±0.02 and correction-to-scaling exponent Δ₁ = 0.6±0.2. These values also agree with the results for S = ∞.     

Quark-lepton symmetry and B − L as the U(1) generator of the electroweak symmetry group

We seek an interpretation of the U(1) part of the electroweak symmetry group in terms of the quantum number B ? L. We show that the electroweak symmetry group, for which U(1) can be interpreted as a local B ? L symmetry, is the left-right symmetry group SU(2)_L × SU(2)_R × U(1)_L+R. The equating of U_L+R(1) to U_B?L(1) should lead to physical consequences which are not shared by standard gauge theory. B ? L may also help to explain the inversion of quark and lepton mass spectra.     

Flame acceleration and DDT in large-scale obstructed channels filled with methane-air mixtures

We study the evolution of premixed methane-air flames in large-scale obstructed channels using reactive CFD simulations. We vary the channel height d, the blockage ratio br, and the scaled distance between obstacles L/d to study their effects on the distance to DDT, L_DDT, and the distance to the shock-flame complex, L_SF. The results of simulations show two main effects. On one hand, the increase of br and decrease of L/d promote the flame acceleration and reduce L_SF and L_DDT. On the other hand, some configurations with higher br and smaller L/d prevent the detonation development. As a result, the leading shock and the flame never merge, and continue to propagate as a quasi-steady-state shock-flame complex. A collision of this complex with solid structures generates high pressures and strong reflected shocks that can ignite a detonation. This detonation would propagate in a shock-compressed material and result in extremely high pressures exceeding pressures of a regular detonation. Thus, the distance L_SF at which the shock-flame complex forms provides an important measure of a destructive potential in addition to L_DDT. This is particularly relevant for channels with high br where L_SF can be significantly shorter than L_DDT.     

Derivation of the effective pion-nucleon Lagrangian within heavy baryon chiral perturbation theory

We develop a method for constructing the heavy baryon chiral perturbation theory (HBChPT) Lagrangian, to a given chiral order, within HBChPT. We work within SU(2) theory, with only the pion field interacting with the nucleon. The main difficulties, which are solved, are to develop techniques for implementing charge conjugation invariance, and for taking the nucleon on shell, both within the non-relativistic formalism. We obtain complete lists of independent terms in L_HBChPT through O(q³) for off-shell nucleons. Then, eliminating equation-of-motion (e.o.m.) terms at the relativistic and non-relativistic level (both within HBChPT), we obtain L_HBChPT for on-shell nucleons, through O(q³). The extension of the method (to obtain on-shell L_HBChPT within HBChPT) to higher orders is also discussed.     

Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.     

Precision measurement of L X-ray wavelenghts and line widths for 74 ≦ Z ≦ 95 and their interpretation in terms of nuclear perturbations

Techniques for the precision measurement of x-ray lines using the two-crystal spectrometer are discussed, and then applied to measurement of the L x-ray spectra of the transuranic elements uranium, neptunium plutonium, and americium. In all, 52 emission lines and 4 L_III absorption edges were measured, all of them with higher precision than has heretofore been obtained and many of them for the first time. Using these data, the binding energies of the electrons for these atoms were computed. The L_II-L-_III level splitting was computed and compared with theory and it was found that current theory is not sufficient to account quantitatively for the observed data. Certain features of the emission line widths are discussed and given qualitative explanations in terms of the Coster-Kronig transition L_III-L_IIIM_V and hyperfine structure. The observed hyperfine structure is due to the large magnetic moment of Np²³⁷ which leads to increased widths of certain of the Np lines. It is believed that this is the first experimental observation of hyperfine structure in x-ray spectra.     

Phase Coexistence in Nanoscopically Thin Films Confined by Asymmetric Walls

Thin Ising films with nearest-neighbor ferromagnetic exchange in a bulk magnetic field H are studied in a L×L×D geometry, where at the opposite walls, given by the L×L surfaces, local magnetic fields H ₁, and H _D act. While in previous work, the symmetric case H ₁=H _D (leading to “capillary condensation”, when one applies the lattice gas terminology) as well as the antisymmetric case H ₁=?H _D (leading to “interface localization transitions”) were studied, we focus here on the general ‘asymmetric’ case. Monte Carlo simulations are carried out and analyses based on thermodynamic integration methods are used to establish the phase diagrams and study the properties of the coexisting phases. A discussion is given why for the range of thicknesses that is explored (16≤D≤80 lattice spacings) this is the most suitable methodology. Restricting attention to cases where in the semi-infinite system a first-order wetting transition occurs, it is shown that the latter, due to confinement, is turned in a thin-film triple point. Above the triple point, narrow two-phase coexistence curves are found, which are the analog of prewetting transitions in the semi-infinite system. A comparison to related results for (symmetrical) polymer blends and (asymmetric) colloid-polymer mixtures is made.