Critical Biot Number of a Periodic Array of Rectangular Fins

We consider the heat transfer problem associated with a periodic array of rectangular fins subjected to convection heat transfer with a uniform heat transfer coefficient. Our analysis differs from the classical approach as (i) we consider two-dimensional (2D) heat conduction and (ii) the wall, to which the fins are attached, is included in the analysis

Electromagnetic form factors of the Delta baryon

We develop a methodology that enables us to extract accurately the electromagnetic Delta form factors and their momentum dependence. We test our approach in the quenched approximation as a preparation for a study using dynamical fermions. Our calculation of the four form factors covers pion masses between about 410 MeV and 560 MeV on lattices with a size of 2.9 fm and a lattice spacing 0.09 fm. From the form factors we are able to obtain estimates of the magnetic moment and the charge radius of the Delta, which we compare to existing experimental and theoretical results.Our non-zero result for the electric quadrupole form factor signals a deformation of the Delta, pointing to an oblate charge distribution

Heat transfer enhancement of a periodic array of isothermal pipes

We address the problem of two-dimensional heat conduction in a solid slab whose upper and lower surfaces are subjected to uniform convection. In the midsection of the slab there is a periodic array of isothermal pipes of general cross section. The main objective of this work is to find the optimum shapes of the pipes that maximize the Shape Factor (heat transport rate). The Shape Factor is obtained by transforming the periodic array of pipes into a periodic array of strips, using the generalized Schwarz- Christoffel transformation, and applying the collocation boundary element method on the transformed domain. Subsequently we pose the inverse problem, i.e. finding the shape that maximizes the Shape factor given the perimeter of the pipes. For large Biot number the optimum shapes are in agreement with the isothermal case, i.e. circular for sufficiently small perimeters/heat transfer, and elongated towards the surfaces of the slab for larger perimeters/heat transfer. Furthermore, for the isothermal case, we were able to discover a new family of optimum shapes for large thickness of the slab and large perimeters, which do not have their maximum width on the horizontal axis of symmetry. For small Biot number the optimum pipes are flatter than the isothermal ones for a given perimeter. The flatness becomes more apparent for larger perimeters. Most important, for large perimeters there exists a critical thickness which is characterized by maximum heat transfer rate. This is further investigated using the finite element method to obtain the critical thickness of a slab and the critical depth of the periodic array of circular pipe

The N to Δ\Delta axial transition form factors in quenched and unquenched QCD

The four N to $\Delta$ axial transition form factors are evaluated using quenched QCD, using two flavors of dynamical Wilson fermions and using domain wall valence fermions on three-flavor MILC configurations for pion masses down to 360 MeV. We provide a prediction for the parity violating asymmetry as a function of $Q^2$ and examine the validity of the non-diagonal Goldberger-Treiman relation.Comment: Normalization factor in figures 3 and 4 corrected, discussion on the evaluation of the renormalized qaurk mass included, typos corrected, 7 pages, 6 figures, talk presented at the XXIV International Symposium on Lattice Field Theory, 23rd - 28th of July, 200

A study of the N to Delta transition form factors in full QCD

The N to Delta transition form factors GM1, GE2 and GC2 are evaluated using dynamical MILC configurations and valence domain wall fermions at three values of quark mass corresponding to pion mass 606 MeV, 502 MeV and 364 MeV on lattices of spatial size $20^3$ and $28^3$. The unquenched results are compared to those obtained at similar pion mass in the quenched theory.Comment: 6 pages, 4 figures, talk presented at Lattice 2005 (Hadron spectrum), uses PoS.cl

Antiheavy-Antiheavy-Light-Light Four-Quark Bound States

We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the $\bar{b}\bar{b}us$ four-quark system with quantum numbers $J^P=1^+$ and the $\bar{b}\bar{c}ud$ four-quark systems with $I(J^P)=0(0^+)$ and $I(J^P)=0(1^+)$ utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for $\bar{b}\bar{b}us$ with $E_{\textrm{bind},\bar{b}\bar{b}us} = (-86 \pm 22 \pm 10)\,\textrm{MeV}$, but no indication for a bound state in both $\bar{b}\bar{c}ud$ channels. Moreover, we show preliminary results for $\bar{b}\bar{b}ud$ with $I(J^P)=0(1^+)$, where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in $E_{\textrm{bind},\bar{b}\bar{b}ud} =(-103 \pm 8 )\,\textrm{MeV}$.Comment: 9 pages, 3 figures, talk given at "The 39th International Symposium on Lattice Field Theory", 08th-13th August 2022, Bonn, German

Elastic Nucleon-Pion scattering amplitudes in the Δ\Delta channel at physical pion mass from Lattice QCD

We present an investigation of pion-nucleon elastic scattering in the $I\,(J^P) = \frac{3}{2}\,(\frac{3}{2}^+)$ channel using lattice QCD with degenerate up and down, strange and charm quarks with masses tuned to their physical values. We use an ensemble of twisted mass fermions with box size $L = 5.1\,\mathrm{fm}$ and lattice spacing $a = 0.08\,\mathrm{fm}$ and we consider the $\pi N$ system in rest and moving frames up to total momentum $\vec{P}^2 = 3\,(2\pi/L)^2$ = 0.17 GeV$^2$. We take into account the finite volume symmetries and $S$- and $P$-wave mixing, and use the L\"uscher formalism to simultaneously constrain the $J = 1/2,\,\ell = 0$ and $J = 3/2,\,\ell = 1$ scattering amplitudes. We estimate the $\Delta$ resonance pole in the $P$-wave channel as well as the $S$-wave isospin-3/2 scattering length.Comment: 17 pages, 18 figures, 9 table

Excited State Effects in Nucleon Matrix Element Calculations

We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge $g_A$ and for the first moment of the isovector unpolarized parton distribution $_{u-d}$. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using $N_f=2+1+1$ maximally twisted mass Wilson fermions.Comment: 7 pages, 4 figures. Talk given at the XXIX International Symposium on Lattice Field Theory - Lattice 2011, Lake Tahoe, California, US