High Quality Consistent Digital Curved Rays via Vector Field Rounding

We consider the consistent digital rays (CDR) of curved rays, which approximates a set of curved rays emanating from the origin by the set of rooted paths (called digital rays) of a spanning tree of a grid graph. Previously, a construction algorithm of CDR for diffused families of curved rays to attain an O(?{n log n}) bound for the distance between digital ray and the corresponding ray is known [Chun et al., 2019]. In this paper, we give a description of the problem as a rounding problem of the vector field generated from the ray family, and investigate the relation of the quality of CDR and the discrepancy of the range space generated from gradient curves of rays. Consequently, we show the existence of a CDR with an O(log ^{1.5} n) distance bound for any diffused family of curved rays

Application of tensor network method to two dimensional lattice N=1\mathcal{N}=1 Wess-Zumino model

We study a tensor network formulation of the two dimensional lattice $\mathcal{N}=1$ Wess-Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawa-type interaction of Majorana fermions and real scalar bosons. We present some numerical results.Comment: 8 pages, 4 figures, talk presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spai

Alloying Effect of Nickel–Cobalt Based Binary Metal Catalysts Supported on α-Alumina for Ammonia Decomposition

The development of a base metal catalyst which shows high performance for the ammonia (NH3) decomposition have been conducted. For the Ni and Co based catalysts using α-Al2O3 as a support, the performance of the single metal catalysts was lower than that of the γ-Al2O3 supported catalysts. However, its performance was greatly improved by using a binary metal catalyst system. Based on the XRD analysis, it was found that Ni and Co supported on α-Al2O3 were alloyed. TEM observation confirmed that the metal particle size in the α-Al2O3 supported Ni-Co catalyst is smaller than that of the single metal catalysts (Ni/α-Al2O3 or Co/α-Al2O3). Furthermore, in-situ XRD and H2-TPR measurements revealed that the Ni-Co alloy forms during the reduction process. The optimum mixing ratio of Ni and Co components was 1:1, and the optimum pre-reduction temperature before the performance test was 600 °C. Studies on the differences of support oxides proved that the improvement effect by alloying can be similarly obtained with the SiO2 supported catalyst, indicating that the catalyst using the support with less interaction between the active metal and the support is more likely to obtain the performance improvement effect by alloying

Tensor network formulation for two-dimensional lattice N=1\mathcal{N}=1 Wess-Zumino model

Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case.Comment: 31 pages, 10 figures, revised versio

Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group

We develop a calculational method for fermionic Green functions in the framework of Grassmann higher-order tensor renormalization group. The validity of the method is tested by applying it to the three-dimensional free Wilson fermion system. We compare the numerical results for the chiral condensate and two-point correlation functions with the exact ones obtained by analytical methods

Tensor network formulation for two-dimensional lattice N = 1 Wess-Zumino model

Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In this work, we present a tensor network formulation of the two-dimensional lattice N = 1 Wess-Zumino model while showing that numerical results agree with the exact solutions for the free case