ANALYSIS OF WALL SHAPE IN INDOOR AIR CIRCULATION BY THE FINITE ELEMENT METHOD

The use of computational models in built environments comes from the need to deal with situations as close as possible to the reality and also to study functional spaces that could be able to provide, for example, thermal comfort. In this work we analyze some cases of indoor air circulation in built environments through a mixed stabilized finite element method, applied to the Navier-Stokes equations in velocity and pressure variables. The implemented numerical method ensures stability for the internal constraint imposed by the velocity field, and accommodates moderate to large advective effects. The obtained internal wind field allows the choice of wall shapes that increase or not the ventilation and can alter its distribution, allowing in this way a better adequacy of the built environment for the climate needs and its objectives

Nambu-Jona-Lasinio model with Wilson fermions

12 pages, 5 figuresWe present a lattice study of a Nambu Jona-Lasinio (NJL) model using Wilson fermions. Four fermion interactions are a natural part of several extensions of the Standard Model, appearing as a low energy description of a more fundamental theory. In models of dynamical electroweak symmetry breaking they are used to endow the Standard Model fermions with masses. In infrared conformal models these interaction, when sufficiently strong, can alter the dynamics of the fixed point, turning the theory into a (near) conformal model with desirable features for model building. As a first step toward the nonperturbative study of these models, we study the phase space of the ungauged NJL model

Wilson Fermions with Four Fermion Interactions

Contribution to proceedings of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe, JapanWe present a lattice study of a four fermion theory, known as Nambu Jona-Lasinio (NJL) theory, via Wilson fermions. Four fermion interactions naturally occur in several extensions of the Standard Model as a low energy parameterisation of a more fundamental theory. In models of dynamical electroweak symmetry breaking these operators, at an effective level, are used to endow the Standard Model fermions with masses. Furthermore these operators, when sufficiently strong, can drastically modify the fundamental composite dynamics by, for example, turning a strongly coupled infrared conformal theory into a (near) conformal one with desirable features for model building. As first step, we study spontaneous chiral symmetry breaking for the lattice version of the NJL model

Template Composite Dark Matter : SU(2) gauge theory with 2 fundamental flavours

Contribution to proceedings of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe, JapanWe present a non perturbative study of SU(2) gauge theory with two fundamental Dirac flavours. We discuss how the model can be used as a template for composite Dark Matter (DM). We estimate one particular interaction of the DM candidate with the Standard Model : the interaction through photon exchange computing the electric polarizability of the DM candidate. Finally, we briefly discuss the viability of the model given the present experimental constraints

Integrable and superintegrable systems with spin in three-dimensional Euclidean space

A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components of linear momentum. Several such systems are found and for one non-trivial example we show how superintegrability leads to exact solvability: we obtain exact (nonperturbative) bound state energy formulas and exact expressions for the wave functions in terms of products of Laguerre and Jacobi polynomials.Comment: 23 page

Hamiltonians separable in cartesian coordinates and third-order integrals of motion

We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy

Third order superintegrable systems separating in polar coordinates

A complete classification is presented of quantum and classical superintegrable systems in $E_2$ that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function

Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials

We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.Comment: 33 pages, references added, misprints correcte

Singlet channel scattering in a composite Higgs model on the lattice

AbstractWe present the first calculation of the scattering amplitude in the singlet channel beyond QCD. The calculation is performed in SU(2) gauge theory with $$N_f=2$$ N f = 2 fundamental Dirac fermions and based on a finite-volume scattering formalism. The theory exhibits a $$SU(4) \rightarrow Sp(4)$$ S U ( 4 ) → S p ( 4 ) chiral symmetry breaking pattern that is used to design minimal composite Higgs models currently tested at the LHC. Our results show that, for the range of underlying fermion mass considered, the lowest flavour singlet state is stable.</jats:p