N-string vertex,canonical forms and bosonization

We give the field representation of the canonical forms for the operators which generate the projective transformation. This representation is also applicable in formulating the N-string vertex of Lovelace and Olive. It shows that they have the properties of a transition operator. Requiring the same properties for the ghost sector in bosonized form we construct the BRST invariant canonical form and the N-string vertex. We consider the (N − 3) b-ghost insertion. We show that the resulting vertex with (N − 3) parameters corresponding to the location of the ghosts is symmetric with respect to the N strings and it gives the proper integration measure.     

Adjacency networks

We consider a finite set S={x₁,…,x_r} and associate to each element x_i a probability p_i. We then form sequences (N-strings) by drawing at random N elements from S with respect to the probabilities assigned to them. Each N-string generates a network where the elements of S are represented as vertices and edges are drawn between adjacent vertices. These structures are multigraphs having multiple edges and loops. We show that the degree distributions of these networks are invariant under permutations of the generating N-strings. We describe then a constructive method to generate scale-free networks and we show how scale-free topologies naturally emerge when the probabilities are Zipf distributed.     

N-string vertex and loop calculation in the bosonic string

We construct a BRST invariant twisted propagator and discuss different forms of the N-string vertex. We then use them for constructing loop diagrams in the bosonic string.     

A simple expression for the multiloop amplitude in the bosonic string

Using the previously constructed new N-string vertex and BRST invariant twisted propagator we obtain a simple and explicit expression for the multiloop partition function of the bosonic string. We construct also the two-loop amplitude with N external tachyons and give the recipe for writing the amplitude at any perturbative order.     

Covariant loop calculus for the neveu-schwarz string

We derive the g-loop, N-string amplitude (density) of the (closed) NS-string in an explicit parametrization of super moduli space for a subset of 2^g even spinstructures.     

BRST invariant mixed string vertex for the bosonic string

We construct a BRST invariant (N + M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain a BRST invariant vertex for the open-closed string transition.     

Noncritical holographic QCD in external electric field

We investigate behavior of a noncritical model in external electric field and explore its phase structure in the quenched approximation Nf?Nc. We compute the conductivity of QCD plasma in this model and compare it with the predictions of Sakai-Sugimoto model, D3-D7 system and lattice simulations. We find that, while the behavior of conductivity in noncritical model as a function of temperature and baryon density is similar to those of D3-D7 system, the phase diagram of noncritical model resembles the phase diagram of Sakai-Sugimoto model.     

N-Superstring vertex and the vertex operator for the emission of the superstring

The BRST invariant, supersymmetric N-string vertex which applies to both, the Neveu-Schwarz and Ramond sector of the superstring is formulated using the vertex operator for the emission of a superstring. It is shown that the N-superstring vertex thus obtained is cyclic symmetric when GSO projected on-shell states and operators for the external strings are applied. The constraint equations of this vertex and their singularity structure are examined and we show that this vertex also has the required property of a transition operator. We also give a proof of its BRST invariance and supersymmetry.     

N-string,g-loop vertex for the bosonic string

We construct the N-string, g-loop vertex V_N,g for the orbital degrees of freedom of the bosonic string in terms of the first abelian differentials, the period matrix and the prime form. We also build the |g> vacuum recently discussed by many people in the framework of an operator formalism on an arbitrary Riemann surface; our expression also contains the measure that takes into account the ghost contribution.     

Ghost vertices for the bosonic string using the group-theoretic approach to string theory

The N-string tree-level scattering vertices for the bosonic string are extended to include anticommuting (ghost) oscillators. These vertices behave correctly under the action of the BRST charge Q and reproduce the known results for the scattering of physical states. This work is an application of the group-theoretic approach to string theory.     

Enhancing ϕ-sensitivity of ignition delay times through dilution of fuel-air mixture

The high ϕ-sensitivity (η) of ignition delay time (τ_IDT) is one of the desirable fuel properties for the high-load extension of advanced compression ignition engine. Recent studies revealed the effectiveness of a high dilution rate (x_D) for enhancing η at the engine-relevant conditions. This study aims to quantify the effect of dilution on the η of isooctane using a combined experiment-simulation approach. The ignition delay of the isooctane/air mixture was measured with an Advanced Fuel Ignition Delay Analyzer (AFIDA) over the temperature range of 623 – 923 K at 10 bar pressure with global ϕ = 0.3 – 0.6, with and without 28.6% of additional N₂ dilution. For precise evaluation of experimental η, the facility effect of the AFIDA experiment was characterized with three-dimensional computational fluid dynamics (3-D CFD) simulation. The temperature in the combustion chamber from 3-D CFD indicated a substantial temporal dependency, varying up to ∼52 K by charge-cooling of fuel injection and heat transfer from the wall. We introduced the dimensionless number θ(t) for characterizing the temporal profile of chamber temperature. Consideration of the facility effect using θ(t) resulted in better agreement between the experimental η and zero-dimensional (0-D) kinetics simulation. The refined η were then further utilized to quantify the effectiveness of dilution to η. The extent of η enhancement with dilution strategy was maximized at the low-temperature chemistry regime, increasing η by 77% with a 28.6% dilution rate. Further analysis on the dilution effect was carried out using 0-D kinetics simulation, revealing the critical dimensionless numbers relevant to the effectiveness of dilution to η enhancement. This study is the first experiment-simulation combined research to quantify the effect of dilution on η, facilitating the kinetics model refinement for better reproduction of ϕ-sensitivity.     

Effects of large amplitude and transverse shear on vibrations of triangular plates

In this paper an analytical investigation of large amplitude free flexural vibrations of isotropic and orthotropic moderately thick triangular plates is carried out. The governing equations are expressed in terms of the lateral displacement, w, and the stress function, F, and are based on an improved non-linear vibration theory which accounts for the effects of transverse shear deformation and rotatory inertia. Solutions to the governing equations are obtained by using a single-mode approximation for w, Galerkin's method and a numerical integration procedure. Numerical results are presented in terms of variations of non-linear frequency ratios with amplitudes of vibrations. The effects of transverse shear, rotatory inertia, material properties, aspect ratios, and thickness parameters are studied and compared with available solutions wherever possible. Present results are in close agreement with those reported for thin plates. It is believed that all of the results reported here that are applicable for moderately thick plates are new and therefore, no comparison is possible.     

Formal analytical solutions for the Gross-Pitaevskii equation

Considering the Gross-Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter Φ(x) and for the chemical potential μ as a function of a unique dimensionless non-linear parameter Λ. We report solutions for different ranges of values for the repulsive and the attractive non-linear interactions in the condensate. Also, we study a bright soliton-like variational solution for the order parameter for positive and negative values of Λ. Introducing an accumulated error function we have performed a quantitative analysis with respect to other well-established methods as: the perturbation theory, the Thomas-Fermi approximation, and the numerical solution. This study gives a very useful result establishing the universal range of the Λ-values where each solution can be easily implemented. In particular, we showed that for Λ<−9, the bright soliton function reproduces the exact solution of GPE wave function.     

Magnetic susceptibility of the O(N) non-linear sigma model

We investigate a non-perturbative method suited to the study of asymptotically free theories. We apply it to the two-dimensional O(N) non-linear sigma model to extract the value of the magnetic susceptibility. This scheme is shown to be exact when N goes to infinity. We compare our results with Monte Carlo data.     

IMPROVEMENT OF THE SEMI-ANALYTICAL METHOD, FOR DETERMINING THE GEOMETRICALLY NON-LINEAR RESPONSE OF THIN STRAIGHT STRUCTURES. PART I: APPLICATION TO CLAMPED-CLAMPED AND SIMPLY SUPPORTED-CLAMPED BEAMS

In a previous series of papers (Benamar 1990 Ph.D. Thesis, University of Southampton; Benamaret al. 1991 Journal of Sound and Vibration149, 179-195;164, 399-424 [1-3]) a general model based on Hamilton's principle and spectral analysis has been developed for non-linear free vibrations occurring at large displacement amplitudes of fully clamped beams and rectangular homogeneous and composite plates. The results obtained with this model corresponding to the first non-linear mode shape of a clamped-clamped (CC) beam and to the first non-linear mode shape of a CC plate are in good agreement with those obtained in previous experimental studies (Benamaret al. 1991 Journal of Sound and Vibration 149, 179-195;164, 399-424 [2, 3]). More recently, this model has been re-derived (Azar et al. 1999 Journal of Sound and Vibration224, 377-395; submitted [4, 5]) using spectral analysis, Lagrange's equations and the harmonic balance method, and applied to obtain the non-linear steady state forced periodic response of simply supported (SS), CC, and simply supported-clamped (SSC) beams. The practical application of this approach to engineering problems necessitates the use of appropriate software in each case or use of published tables of data, obtained from numerical solution of the non-linear algebraic system, corresponding to each problem. The present work was an attempt to develop a more practical simple “multi-mode theory” based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance. The purpose was to derive simple formulae, which are easy to use, for engineering purposes. In this paper, two models are proposed. The first is concerned with displacement amplitudes of vibrationW_max /H, obtained at the beam centre, up to about 0·7 times the beam thickness and the second may be used for higher amplitudes W_max/H up to about 1·5 times the beam thickness. This new approach has been successfully used in the free vibration case to the first, second and third non-linear modes shapes of CC beams and to the first non-linear mode shape of a CSS beam. It has also been applied to obtain the non-linear steady state periodic forced response of CC and CSS beams, excited harmonically with concentrated and distributed forces.     

Counterterms in extended supergravities

Geometrical invariants respecting all necessary symmetries of the theory are shown to exist, starting from the 8th (4th) loop approximation in N = 8 (N = 4) on-shell supergravity. 3-loop counterterms are presented on a linearized level for N = 4 and N = 8 theories. The corresponding 3-loop non-linear invariants are discussed.     

Multi-grid Monte Carlo via XY embedding. General theory and two-dimensional O(N)-symmetric non-linear σ-models

We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an XY model into the target model, and we study its mathematical properties for a variety of non-linear σ-models. We then apply the method to the two-dimensional O(N)-symmetric nonlinear σ-models (also called N-vector models) with N = 3,4,8 and study its dynamic critical behavior. Using lattices up to 256 × 256, we find dynamic critical exponentsZ_int, M² 0.70 ± 0.08, 0.60 ± 0.07, 0.52 ± 0.10 for N = 3, 4, 8, respectively (subjective 68% confidence intervals). Thus, for these asymptotically free models, critical slowing down is greatly reduced compared to local algorithms, but not completely eliminated; and the dynamic critical exponent does apparently vary with N. We also analyze the static data for N = 8 using a finite-size scaling extrapolation method. The correlation length ξ agrees with the four-loop asymptotic-freedom prediction to within 1 % over the interval 12 ⪅ ξ ⪅ 650.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.