Periodic and homoclinic solutions of the modified 2+1 Chiral model

We use algebraic Backlund transformations (BTs) to construct explicit solutions of the modified 2+1 chiral model from $T^2\times R$ to SU(n), where $T^2$ is a 2-torus. Algebraic BTs are parameterized by $z\in C$ (poles) and holomorphic maps $\pi$ from $T^2$ to Gr$(k,C^n)$. We apply B\"acklund transformations with carefully chosen poles and $\pi$'s to construct infinitely many solutions of the 2+1 chiral model that are (i) doubly periodic in space variables and periodic in time, i.e., triply periodic, (ii) homoclinic in the sense that the solution $u$ has the same stationary limit $u_0$ as $t\to \pm\infty$ and is tangent to a stable linear mode of $u_0$ as $t\to\infty$ and is tangent to an unstable mode of $u_0$ as $t\to -\infty$.Comment: 17 page

Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the onlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.Comment: 22 pages with 9 figure

Parallaxes for star forming regions in the inner Perseus spiral arm

We report trigonometric parallax and proper motion measurements of 6.7-GHz CH3OH and 22-GHz H2O masers in eight high-mass star-forming regions (HMSFRs) based on VLBA observations as part of the BeSSeL Survey. The distances of these HMSFRs combined with their Galactic coordinates, radial velocities, and proper motions, allow us to assign them to a segment of the Perseus arm with ~< 70 deg. These HMSFRs are clustered in Galactic longitude from ~30 deg to ~50, neighboring a dirth of such sources between longitudes ~50 deg to ~90 deg.Comment: 18 pages, 4 figures, accepted for publication in The Astronomical Journal. arXiv admin note: text overlap with arXiv:1312.385

Approximation properties of Stancu type Szász-Mirakjan operators

In this paper, a class of Stancu type Szász-Mirakjan operators are introduced. The approximation properties of the operators are discussed using tools of modulus of continuity, modulus of smoothness and K-functional. The estimation of the Lipschitz function class by the operators is also studied. Later, the Voronvskaya type asymptotic expansion of the operators is established. Finally, we compare the convergence of these newly defined operators for certain functions with certain graphs

Stress and vibration of a viscoelastic damping isolator under impact loading

There are different types of isolators which include rubber type, coil spring type, slide and rotating type and there are different types of dampers which include viscous type, oil type, and try friction type. Both isolators and dampers are common used to reduce vibration caused by forging or stamping process. However, a new way to reduce the vibration of the punch press is viscoelastic damping isolator (VDI) which can be widely used in manufacturing, electricity and gas supply, construction, transportation and warehousing, and other industries. This study analyzes a VDI composed by partitions, damping fluid, steel springs and level adjusters. Different numbers of the partitions are welded on upper and lower rectangular steel plates, respectively. Up to 150 tons of weight of the punching machines supported by steel springs which are placed at the edges between the square upper/lower plates. Screw types of level adjusters are placed between lower plate and thick steel base to tune the horizontal level of the isolator. High viscosity damping fluid is filled in the space between interlacing partitions around 60 % of the height of the VDI. Punching induced impact energy is dissipated by shear deformation between the damping fluid and partitions. This study uses 3D graphing software and finite element method (FEM) to investigate the dynamic characteristic of the damping isolator after impacted by the puncher. The normal mode analysis of the VDI is obtained. The isolator is settled within 0.3 seconds after 300.000 N of shock impact and satisfies industrial specification of large punchers with loading frequency of 100 cycles per min