Massive field contributions to the QCD vacuum tunneling amplitude

For the one-loop contribution to the QCD vacuum tunneling amplitude by quarks of generic mass value, we make use of a calculational scheme exploiting a large mass expansion together with a small mass expansion. The large mass expansion for the effective action is given by a series involving higher-order Seeley-DeWitt coefficients, and we carry this expansion up to order $1/(m\rho)^8$, where $m$ denotes mass of the quark and $\rho$ the instanton size parameter. For the small mass expansion, we use the known exact expression for the particle propagation functions in an instanton background and evaluate explicitly the effective action to order $(m\rho)^2$. A smooth interpolation of the results from both expansions suggests that the quark contribution to the instanton tunneling amplitude have a relatively simple $m\rho$-dependent behavior.Comment: revtex, 4figures, 33page

Solutions of Schr\"odinger equations\\ with symmetry in orientation preserving tetrahedral group

We consider the nonlinear Schr\"odinger equation \begin{equation*} \Delta u = \big( 1 +\ve V_1(|y|)\big)u - |u|^{p-1}u \quad \text{in} \quad \mathbb{R}^N, \quad N\ge 3, \quad p \in \left(1, \frac{N+2}{N-2}\right).\end{equation*} The phenomenon of pattern formation has been a central theme in the study of nonlinear Schr\"odinger equations. However, the following nonexistence of $O(N)$ symmetry breaking solution is well-known: if the potential function is radial and radially nondecreasing, any positive solution must be radial. Therefore, solutions of interesting patterns, such as those with symmetry in a discrete subgroup of $O(N)$, can only exist after violating the assumptions. For a potential function that is radial but asymptotically decreasing, a solution with symmetry merely in a discrete subgroup of $O(2)$ has been presented. These observations pose the question of whether patterns of higher dimensions can appear. In this study, the existence of nonradial solutions whose symmetry group is a discrete subgroup of $O(3)$, more precisely, the orientation-preserving regular tetrahedral group is shown

Rarity and shifts in occurrence of endangered butterflies in South Korea

Endangered species are often the focus of public attention, partly because of their vulnerability to environmental changes, such as climate and land use change, and subsequently being at high risk of extinctions. Hence, red lists of endangered species play anessential in nature conservation. Although several endangered butterfly species have been previously listed as endangered species by government and/or individuals in South Korea, these red listsrarely include reliable quantitative population data. This has led to endless and unproductive debates on the selection of endangered species. Following Korean butterfly atlases, we assessed the population status of Korean endangered butterfly species whose distributions have been previously published. We hypothesized that these endangered species are rare and are decreasing in occurrence. We found that the decrease in occurrence is more important in determining endanger status than rarity. Using values of rarity and shifts in species occurrence, we selected endangered species from the previously published endangered species. Only eight species of 20 previous endangered species were defined as endangered by this semi-quantitative classification. This finding suggests that the subjective determination based on expert's perception would define more species as endangered compared to the quantitative determination based on population data.Article信州大学農学部紀要 50（1-2）: 37-42(2014)departmental bulletin pape

Evaluation of tensile properties using instrumented indentation technique for small scale testing

The Instrumented indentation technique (IIT) is a useful tool for estimating various mechanical properties such as tensile properties, fracture toughness, and residual stress by analyzing the load and depth curve. Unlike conventional test such as tensile test, CTOD, since IIT makes an indent with rigid indenter and measures load and depth continuously, it requires only a localized area and small area on the target material. IIT also has merits of simple specimen preparation and experimental procedure in terms of time and cost. Also, it can be applied to in-field structures nondestructively. In this study, we introduce a method for evaluating tensile properties, primary yield strength and tensile strength using representative stress-strain beneath the rigid spherical indenter through numerous investigations of instrumented indentation curves. Analytic models and procedures for estimating the mechanical characterization of materials using IIT are proposed. The representative stress-strain method directly correlates indentation stress and strain beneath indenter to true stress and strain of the tensile test by taking into account the plastic constraint effect. The experimental results from IIT were verified by comparing results from the uniaxial tensile test. In particular, the applications of IIT in small scale and localized area of materials are presented. Reference 1) D. Tabor: Hardness of metal, (first ed. Clarendon Press, New York, 1951) 2) W.C. Oliver and G.M. Pharr, J. Mater, Res, Vol. 7, (1992), p. 1564 3) S.-K. Kang, Y.-C. Kim, K.-H. Kim, J.-Y. Kim and D. Kwon, Int. J. Plast. 49, 1 (2013

Relative entropy technique in terms of position and momentum and its application to Euler-Poisson system

This paper presents a systematic study of the relative entropy technique for compressible motions of continuum bodies described as Hamiltonian flows. While the description for the classical mechanics of $N$ particles involves a Hamiltonian in terms of position and momentum vectors, that for the continuum fluid involves a Hamiltonian in terms of density and momentum. For space dimension $d\ge 2$, the Hamiltonian functional has a non-convex dependency on the deformation gradient or placement map due to material frame indifference. Because of this, the applicability of the relative entropy technique with respect to the deformation gradient or the placement map is inherently limited. Despite these limitations, we delineate the feasible applications and limitations of the technique by pushing it to its available extent. Specifically, we derive the relative Hamiltonian identity, where the Hamiltonian takes the position and momentum field as its primary and conjugate state variables, all within the context of the referential coordinate system that describes the motion. This approach, when applicable, turns out to yield rather strong stability statements. As instances, we consider Euler-Poisson systems in one space dimension. For a specific pressureless model, we verify non-increasing $L^2$ state differences before the formation of $\delta$-shock. In addition, weak-strong uniqueness, stability of rarefaction waves, and convergence to the gradient flow in the singular limit of large friction are shown. Depending on the presence or absence of pressure, assumptions are made to suitably accommodate phenomena such as $\delta$-shocks, vacuums, and shock discontinuities in the weak solutions.Comment: 35 page

Density functional calculations of the electronic structure and magnetic properties of the hydrocarbon K3picene superconductor near the metal-insulator transition

We have investigated the electronic structures and magnetic properties of of K3picene, which is a first hydrocarbon superconductor with high transition temperature T_c=18K. We have shown that the metal-insulator transition (MIT) is driven in K3picene by 5% volume enhancement with a formation of local magnetic moment. Active bands for superconductivity near the Fermi level E_F are found to have hybridized character of LUMO and LUMO+1 picene molecular orbitals. Fermi surfaces of K3picene manifest neither prominent nesting feature nor marked two-dimensional behavior. By estimating the ratio of the Coulomb interaction U and the band width W of the active bands near E_F, U/W, we have demonstrated that K3picene is located in the vicinity of the Mott transition.Comment: 5 pages, 5 figure