Topological charge using cooling and the gradient flow

The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\tau$ and show that the results for the topological charge become equivalent when rescaling $\tau \simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\tau \simeq n_c/({3-15 c_1})$ leads to equivalent results.Comment: 21 pages, 10 figure

The electric dipole moment of the neutron from Nf=2+1+1N_f=2+1+1 twisted mass fermions

We extract the neutron electric dipole moment (nEDM) $\vert \vec{d}_n \vert$ on configurations produced with $N_f=2+1+1$ twisted mass fermions with lattice spacing of $a \simeq 0.082$ fm and a light quark mass that corresponds to $M_{\pi} \simeq 373$ MeV. We do so by evaluating the $CP$-odd form factor $F_3$ for small values of the $CP$-violation parameter $\theta$ in the limit of zero momentum transfer. This limit is extracted using the usual parametrization but in addition position space methods. The topological charge is computed via cooling and gradient flow using the Wilson, Symanzik tree-level improved and Iwasaki actions for smoothing. We obtain consistent results for all choices of smoothing procedures and methods to extract $F_3$ at zero momentum transfer. For the ensemble analyzed we find a value of nEDM of $\vert \vec{d}_n \vert / \theta = -0.045(6)(1) {\rm e} \cdot {\rm fm}$.Comment: 7 pages, 4 figures, talk presented at the 33rd International Symposium on Lattice Field Theory, 14 - 18 July 2015, Kobe, Japa

Advanced aeronatics design: Project based engineering education at WPI

One element of WPI\u27s project-based curriculum is its interdisciplinary Advanced Aeronautics Design Program. Students participating in the program are involved in the design, construction, and flight testing of non-traditional aircraft such as an ultralight solar-powered vehicle, microwave-powered long endurance aircraft, or a flying oblique wing. The WPI project philosophy and character are described and illustrated using examples from the AAD program

Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow

We compare lattice QCD determinations of topological susceptibility using a gluonic definition from the gradient flow and a fermionic definition from the spectral projector method. We use ensembles with dynamical light, strange and charm flavors of maximally twisted mass fermions. For both definitions of the susceptibility we employ ensembles at three values of the lattice spacing and several quark masses at each spacing. The data are fitted to chiral perturbation theory predictions with a discretization term to determine the continuum chiral condensate in the massless limit and estimate the overall discretization errors. We find that both approaches lead to compatible results in the continuum limit, but the gluonic ones are much more affected by cut-off effects. This finally yields a much smaller total error in the spectral projector results. We show that there exists, in principle, a value of the spectral cutoff which would completely eliminate discretization effects in the topological susceptibility.Comment: 18 pages, 19 figure

Modeling of Macroscopic/Microscopic Transport and Growth Phenomena in Zeolite Crystal Solutions Under Microgravity Conditions

Crystals grown from liquid solutions have important industrial applications. Zeolites, for instance, a class of crystalline aluminosilicate materials, form the backbone of the chemical process industry worldwide, as they are used as adsorbents and catalysts. Many of the phenomena associated with crystal growth processes are not well understood due to complex microscopic and macroscopic interactions. Microgravity could help elucidate these phenomena and allow the control of defect locations, concentration, as well as size of crystals. Microgravity in an orbiting spacecraft could help isolate the possible effects of natural convection (which affects defect formation) and minimize sedimentation. In addition, crystals will stay essentially suspended in the nutrient pool under a diffusion-limited growth condition. This is expected to promote larger crystals by allowing a longer residence time in a high-concentration nutrient field. Among other factors, the crystal size distribution depends on the nucleation rate and crystallization. These two are also related to the "gel" polymerization/depolymerization rate. Macroscopic bulk mass and flow transport and especially gravity, force the crystals down to the bottom of the reactor, thus forming a sedimentation layer. In this layer, the growth rate of the crystals slows down as crystals compete for a limited amount of nutrients. The macroscopic transport phenomena under certain conditions can, however, enhance the nutrient supply and therefore, accelerate crystal growth. Several zeolite experiments have been performed in space with mixed results. The results from our laboratory have indicated an enhancement in size of 30 to 70 percent compared to the best ground based controls, and a reduction of lattice defects in many of the space grown crystals. Such experiments are difficult to interpret, and cannot be easily used to derive empirical or other laws since many physical parameters are simultaneously involved in the process. At the same time, however, there is increased urgency to develop such an understanding in order to more accurately quantify the process. In order to better understand the results obtained from our prior space experiments, and design future experiments, a detailed fluid dynamic model simulating the crystal growth mechanism is required. This will not only add to the fundamental knowledge on the crystallization of zeolites, but also be useful in predicting the limits of size and growth of these important industrial materials. Our objective is to develop macro/microscopic theoretical and computational models to study the effect of transport phenomena in the growth of crystals grown in solutions. Our effort has concentrated so far in the development of separate macroscopic and microscopic models. The major highlights of our accomplishments are described

Start-up plane Poiseuille flow of a Bingham fluid

© 2018 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Supplementary Raw Research Data, is open data under the CC BY license http://creativecommons.org/licenses/by/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (October 2018) in accordance with the publisher’s archiving policyThe start-up flow of a Bingham plastic in a channel is considered and Safronchik’s solution [1] for the initial evolution of the yield surface and the core velocity is revisited. Stricter time bounds for the validity of the above solution are derived and the solution is extended to include the velocity profile in the evolving yielded zone. Comparisons are made with another approximate solution derived under the assumption that the velocity in the yielded zone is parabolic adjusting with the evolving yield surface. This approximation performs well for small values of the yield stress, or, equivalently, for large values of the imposed pressure gradient