Boundary critical behaviour at mm-axial Lifshitz points: the special transition for the case of a surface plane parallel to the modulation axes

The critical behaviour of $d$-dimensional semi-infinite systems with $n$-component order parameter $\bm{\phi}$ is studied at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the $m$ potential modulation axes, with $0\leq m\leq d-1$, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent $\eta_\|^{\rm sp}$, the surface crossover exponent $\Phi$ and related ones are determined to first order in \epsilon=4+\case{m}{2}-d. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, $\Phi$ is $m$-dependent already at first order in $\epsilon$. The \Or(\epsilon) term of $\eta_\|^{\rm sp}$ is found to vanish, which implies that the difference of $\beta_1^{\rm sp}$ and the bulk exponent $\beta$ is of order $\epsilon^2$.Comment: 21 pages, one figure included as eps file, uses IOP style file

The target asymmetry in hard vector-meson electroproduction and parton angular momenta

The target asymmetry for electroproduction of vector mesons is investigated within the handbag approach. While the generalized parton distribution (GPD) H is taken from a previous analysis of the elctroproduction cross section, we here construct the GPD E from double distributions and constrain it by the Pauli form factors of the nucleon, positivity bounds and sum rules. Predictions for the target asymmetry are given for various vector mesons and discussed how experimental data on the asymmetry will further constrain E and what we may learn about the angular momenta the partons carry.Comment: 24 pages, 11 figures, late

Generalized parton distributions in the deuteron

We introduce generalized quark and gluon distributions in the deuteron, which can be measured in exclusive processes like deeply virtual Compton scattering and meson electroproduction. We discuss the basic properties of these distributions, and point out how they probe the interplay of nucleon and parton degrees of freedom in the deuteron wave function

Logarithmic corrections in the two-dimensional Ising model in a random surface field

In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour.Comment: 10 pages, 4 figures, extended version with one new sectio

Compton telescope with coded aperture mask: Imaging with the INTEGRAL/IBIS Compton mode

Compton telescopes provide a good sensitivity over a wide field of view in the difficult energy range running from a few hundred keV to several MeV. Their angular resolution is, however, poor and strongly energy dependent. We present a novel experimental design associating a coded mask and a Compton detection unit to overcome these pitfalls. It maintains the Compton performance while improving the angular resolution by at least an order of magnitude in the field of view subtended by the mask. This improvement is obtained only at the expense of the efficiency that is reduced by a factor of two. In addition, the background corrections benefit from the coded mask technique, i.e. a simultaneous measurement of the source and background. This design is implemented and tested using the IBIS telescope on board the INTEGRAL satellite to construct images with a 12' resolution over a 29 degrees x 29 degrees field of view in the energy range from 200 keV to a few MeV. The details of the analysis method and the resulting telescope performance, particularly in terms of sensitivity, are presented

Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions

The critical dynamics of relaxational stochastic models with nonconserved $n$-component order parameter $\bm{\phi}$ and no coupling to other slow variables ("model A") is investigated in film geometries for the cases of periodic and free boundary conditions. The Hamiltonian $\mathcal{H}$ governing the stationary equilibrium distribution is taken to be O(n) symmetric and to involve, in the case of free boundary conditions, the boundary terms $\int_{\mathfrak{B}_j}\mathring{c}_j \phi^2/2$ associated with the two confining surface planes $\mathfrak{B}_j$, $j=1,2$, at $z=0$ and $z=L$, where the enhancement variables $\mathring{c}_j$ are presumed to be subcritical or critical. A field-theoretic RG study of the dynamic critical behavior at $d=4-\epsilon$ bulk dimensions is presented, with special attention paid to the cases where the classical theories involve zero modes at $T_{c,\infty}$. This applies when either both $\mathring{c}_j$ take the critical value $\mathring{c}_{\text{sp}}$ associated with the special surface transition, or else periodic boundary conditions are imposed. Owing to the zero modes, the $\epsilon$ expansion becomes ill-defined at $T_{c,\infty}$. Analogously to the static case, the field theory can be reorganized to obtain a well-defined small-$\epsilon$ expansion involving half-integer powers of $\epsilon$, modulated by powers of $\ln\epsilon$. Explicit results for the scaling functions of $T$-dependent finite-size susceptibilities at temperatures $T\ge T_{c,\infty}$ and of layer and surface susceptibilities at the bulk critical point are given to orders $\epsilon$ and $\epsilon^{3/2}$, respectively. For the case of periodic boundary conditions, the consistency of the expansions to $O(\epsilon^{3/2})$ with exact large-$n$ results is shown.Comment: Latex file with 8 eps files included; text added in conclusions and abstract, typos correcte

Integration of CasADi and JModelica.org

This paper presents the integration of two open source softwares: CasADi, which is a framework for efficient evaluation of expressions and their derivatives, and the Modelica-based platform JModelica.org. The integration of the tools is based on an XML format for exchange of DAE models. The JModelica.org platform supports export of model in this XML format, whereas CasADi supports import of models expressed in this format. Furthermore, we have carried out comparisons with ACADO, which is a multiple shooting package for solving optimal control problems. CasADi, in turn, has been interfaced with ACADO Toolkit, enabling users to define optimal control problems using Modelica and Optimica specifications, and use solve using direct multiple shooting. In addition, a collocation algorithm targeted at solving large- scale DAE constrained dynamic optimization problems has been implemented. This implementation explores CasADi’s Python and IPOPT interfaces, which offers a convenient, yet highly efficient environment for development of optimization algorithms. The algorithms are evaluated using industrially relevant benchmark problems

Effects of surfaces on resistor percolation

We study the effects of surfaces on resistor percolation at the instance of a semi-infinite geometry. Particularly we are interested in the average resistance between two connected ports located on the surface. Based on general grounds as symmetries and relevance we introduce a field theoretic Hamiltonian for semi-infinite random resistor networks. We show that the surface contributes to the average resistance only in terms of corrections to scaling. These corrections are governed by surface resistance exponents. We carry out renormalization group improved perturbation calculations for the special and the ordinary transition. We calculate the surface resistance exponents \phi_{\mathcal S \mathnormal} and \phi_{\mathcal S \mathnormal}^\infty for the special and the ordinary transition, respectively, to one-loop order.Comment: 19 pages, 3 figure

Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.Comment: Old paper, for archiving. 6 pages, 1 figure, IOP macro, eps

Transverse Deformation of Parton Distributions and Transversity Decomposition of Angular Momentum

Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.Comment: 12 pages, 1 figure, version to appear in PR