A Numerical Study of Improved Quark Actions on Anisotropic Lattices

Tadpole improved Wilson quark actions with clover terms on anisotropic lattices are studied numerically. Using asymmetric lattice volumes, the pseudo-scalar meson dispersion relations are measured for 8 lowest lattice momentum modes with quark mass values ranging from the strange to the charm quark with various values of the gauge coupling $\beta$ and 3 different values of the bare speed of light parameter $\nu$. These results can be utilized to extrapolate or interpolate to obtain the optimal value for the bare speed of light parameter $\nu_{opt}(m)$ at a given gauge coupling for all bare quark mass values $m$. In particular, the optimal values of $\nu$ at the physical strange and charm quark mass are given for various gauge couplings. The lattice action with these optimized parameters can then be used to study physical properties of hadrons involving either light or heavy quarks.Comment: 22 pages, 7 figures, 2 tables. Analysis greatly modified compared with previous versio

Massive Overlap Fermions on Anisotropic Lattices

We formulate the massive overlap fermions on anisotropic lattices. We find that the dispersion relation for the overlap fermion resembles the continuum form in the low-momentum region once the bare parameters are properly tuned. The quark self-energy and the quark field renormalization constants are calculated to one-loop in bare lattice perturbation theory. We argue that massive domain wall quarks might be helpful in lattice QCD studies on heavy-light hadron spectroscopy.Comment: 21 pages, 5 figures, one reference added compared with v.

Static Quark Potential and the Renormalized Anisotropy on Tadpole Improved Anisotropic Lattices

Static quark potential is studied using a tadpole improved gauge lattice action. The scale is set using the potential for a wide range of bare parameters. The renormalized anisotropy of the lattice is also measured.Comment: 11 pages, 5 figures, accepted for publication in Int. J. Mod. Phys.

Massive Domain Wall Fermions on Four-dimensional Anisotropic Lattices

We formulate the massive domain wall fermions on anisotropic lattices. For the massive domain wall fermion, we find that the dispersion relation assumes the usual form in the low momentum region when the bare parameters are properly tuned. The quark self-energy and the quark field renormalization constants are calculated to one-loop in bare lattice perturbation theory. For light domain wall fermions, we verified that the chiral mode is stable against quantum fluctuations on anisotropic lattices. This calculation serves as a guidance for the tuning of the parameters in the quark action in future numerical simulations.Comment: 36 pages, 14 figures, references adde

Two Particle States in an Asymmetric Box

The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are obtained. These results can be viewed as a generalization of the corresponding formulae in a cubic box obtained by L\"uscher before. In particular, the s-wave scattering length is related to the energy shift in the finite box. Possible applications of these formulae are also discussed.Comment: 9 pages, typos corrected from version

CDOpt: A Python Package for a Class of Riemannian Optimization

Optimization over the embedded submanifold defined by constraints $c(x) = 0$ has attracted much interest over the past few decades due to its wide applications in various areas. Plenty of related optimization packages have been developed based on Riemannian optimization approaches, which rely on some basic geometrical materials of Riemannian manifolds, including retractions, vector transports, etc. These geometrical materials can be challenging to determine in general. Existing packages only accommodate a few well-known manifolds whose geometrical materials are easily accessible. For other manifolds which are not contained in these packages, the users have to develop the geometric materials by themselves. In addition, it is not always tractable to adopt advanced features from various state-of-the-art unconstrained optimization solvers to Riemannian optimization approaches. We introduce CDOpt (available at https://cdopt.github.io/), a user-friendly Python package for a class Riemannian optimization. Based on constraint dissolving approaches, Riemannian optimization problems are transformed into their equivalent unconstrained counterparts in CDOpt. Therefore, solving Riemannian optimization problems through CDOpt directly benefits from various existing solvers and the rich expertise gained over decades for unconstrained optimization. Moreover, all the computations in CDOpt related to any manifold in question are conducted on its constraints expression, hence users can easily define new manifolds in CDOpt without any background on differential geometry. Furthermore, CDOpt extends the neural layers from PyTorch and Flax, thus allows users to train manifold constrained neural networks directly by the solvers for unconstrained optimization. Extensive numerical experiments demonstrate that CDOpt is highly efficient and robust in solving various classes of Riemannian optimization problems.Comment: 31 page

Microfluidic spinning of topographical hollow fibers for the development of a 3D functional glomerulus in vitro

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A conceptual design specification based on user aesthetic information analysis and product functional reasoning

User satisfaction with a product plays a direct role in the purchasing decisions. With the enrichment of material life and the growth of individual requirements, this satisfaction is derived from the requirement for functionality to aesthetics. Conventional product design methods normally focus on achieving the required functions where its design specifications are mainly related to certain functional or usability requirements. In recent years, researchers have made efforts to develop methods for supporting aesthetic design activities during the product conceptual design phase. However, most of these methods hardly consider product aesthetics or the consumers’ emotional needs. Therefore, this study proposed a user-driven conceptual design specification integrating functional reasoning with aesthetic information analysis. The method consisted of two tasks, the construction of a mapping model and the implementation of the mapping model. Firstly, the mapping model was constructed for capturing the relationships between initial design specifications and user experience (UX). Secondly, the proposed design specifications were selected, refined, and optimized based on the mapping model. A case study on digital camera design was carried out to demonstrate the feasibility and effectiveness of the proposed method. The results showed that, compared with the initial design specification candidates, the UX was enhanced by applying the improved design specifications