On Auxiliary Fields in BF Theories

We discuss the structure of auxiliary fields for non-Abelian BF theories in arbitrary dimensions. By modifying the classical BRST operator, we build the on-shell invariant complete quantum action. Therefore, we introduce the auxiliary fields which close the BRST algebra and lead to the invariant extension of the classical action.Comment: 7 pages, minor changes, typos in equations corrected and acknowledgements adde

Bringing the power of dynamic languages to hardware control systems

Hardware control systems are normally programmed using high-performance languages like C or C++ and increasingly also Java. All these languages are strongly typed and compiled which brings usually good performance but at the cost of a longer development and testing cycle and the need for more programming expertise. Dynamic languages which were long thought to be too slow and not powerful enough for control purposes are, thanks to modern powerful computers and advanced implementation techniques, fast enough for many of these tasks. We present examples from the LHCb Experiment Control System (ECS), which is based on a commercial SCADA software. We have successfully used Python to integrate hardware devices into the ECS. We present the necessary lightweight middle-ware we have developed, including examples for controlling hardware and software devices. We also discuss the development cycle, tools used and compare the effort to traditional solutions

Dimensional hyper-reduction of nonlinear finite element models via empirical cubature

We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accurac

High-performance model reduction procedures in multiscale simulations

Technological progress and discovery and mastery of increasingly sophisticated structural materials have been inexorably tied together since the dawn of history. In the present era — the so-called Space Age —-, the prevailing trend is to design and create new materials, or improved existing ones, by meticulously altering and controlling structural features that span across all types of length scales: the ultimate aim is to achieve macroscopic proper- ties (yield strength, ductility, toughness, fatigue limit . . . ) tailored to given practical applications. Research efforts in this aspect range in complexity from the creation of structures at the scale of single atoms and molecules — the realm of nanotechnology —, to the more mundane, to the average civil and mechanical engineers, development of structural materials by changing the composition, distribution, size and topology of their constituents at the microscopic/mesoscopic level (composite materials and porous metals, for instance)

Nanotechnology measurements of the Young's modulus of polymeric materials

Making use of atomic force microscopy (AFM) —known as the state-of-the-art technology for handling matter on an atomic and molecular scale—, this paper describes the use of a nanotechnology technique for characterizing properties of polymeric materials. AFM measurement on two materials (polyamide and polystyrene) allowed to compare the performance of two distinct multi-asperity adhesion models based on the JKR (Johnson-Kendall-Robert) and DMT (Derajaguin- Muller-Toporov) theories, when assessing the Young’s Modulus (modulus of elasticity) of the investigated materials. Experimental results confirm that the JKR model processed through a MatLab algorithm produces more reliable results of the Young’s Modulus than the DMT model built-in in the AFM software

Continuum approach to computational multiscale modeling of propagating fracture

A new approach to two-scale modeling of propagating fracture, based on computational homogenization (FE2), is presented. The specific features of the approach are: a) a continuum setting for representation of the fracture at both scales based on the Continuum Strong Discontinuity Approach (CSDA), and b) the use, for the considered non-smooth (discontinuous) problem, of the same computational homogenization framework than for classical smooth cases. As a key issue, the approach retrieves a characteristic length computed at the lower scale, which is exported to the upper one and used therein as a regularization parameter for a propagating strong discontinuity kinematics. This guarantees the correct transfer of fracture energy between scales and the proper dissipation at the upper scale. Representative simulations show that the resulting formulation provides consistent results, which are objective with respect to, both, size and bias of the upper-scale mesh, and with respect to the size of the lower-scale RVE/failure cell, as well as the capability to model propagating cracks at the upper scale, in combination with crack-path-field and strain injection techniques. The continuum character of the approach confers to the formulation a minimal invasive character, with respect to standard procedures for multi-scale computational homogenizatio

The algebra of adjacency patterns: Rees matrix semigroups with reversion

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems.Comment: 30 pages, 9 figure