Subshifts and colorings on ascending HNN-extensions of finitely generated abelian groups

For an ascending HNN-extension $G*_{\psi }$ of a finitely generated abelian group G, we study how a synchronization between the geometry of the group and weak periodicity of a configuration in $\mathcal {A}^{G*_{\psi }}$ forces global constraints on it, as well as in subshifts containing it. A particular case are Baumslag–Solitar groups $\mathrm {BS}(1,N)$ , $N\ge 2$ , for which our results imply that a $\mathrm {BS}(1,N)$ -subshift of finite type which contains a configuration with period $a^{N^\ell }\!, \ell \ge 0$ , must contain a strongly periodic configuration with monochromatic $\mathbb {Z}$ -sections. Then we study proper n-colorings, $n\ge 3$ , of the (right) Cayley graph of $\mathrm {BS}(1,N)$ , estimating the entropy of the associated subshift together with its mixing properties. We prove that $\mathrm {BS}(1,N)$ admits a frozen n-coloring if and only if $n=3$ . We finally suggest generalizations of the latter results to n-colorings of ascending HNN-extensions of finitely generated abelian groups.

Complex shaped periodic corrugations for broadband Bull’s Eye antennas

Periodically corrugated metallic antennas have been developed in recent years from microwave to THz frequencies, due to their advantages of highly directive radiation patterns, low profile and ease of fabrication. However, the limited gain bandwidth of such antennas remains one of their inherent disadvantages. In terms of design, the majority of the existing implementations in literature utilize the standard rectangular shaped corrugated unit cell. In this paper, we propose novel complex shaped corrugated unit cells that produce a broadband performance when assembled in a periodic configuration. Two broadband prototypes are presented at the Ku frequency band that are formed of hybrid shaped corrugations. The first prototype of six periodic rings achieves, for the first time, a flat gain simulated response with a maximum value of 15.7 dBi, 1-dB gain bandwidth of 16.4%, and an extended 3-dB gain bandwidth of 19.64%. The second novel prototype of five rings achieves an enhanced 3-dB gain bandwidth of 15.2% and maximum gain of 18.1 dBi.

Periodic Schwarz–Christoffel mappings with multiple boundaries per period

We present an extension to the theory of Schwarz–Christoffel (S–C) mappings by permitting the target domain to be a single period window of a periodic configuration having multiple polygonal (straight-line) boundaries per period. Taking the arrangements to be periodic in the x -direction in an ( x , y )-plane, three cases are considered; these differ in whether the period window extends off to infinity as y → ± ∞, or extends off to infinity in only one direction ( y → + ∞ or y → − ∞), or is bounded. The preimage domain is taken to be a multiply connected circular domain. The new S–C mapping formulae are shown to be expressible in terms of the Schottky–Klein prime function associated with the circular preimage domains. As usual for an S–C map, the formulae are explicit but depend on a finite set of accessory parameters. The solution of this parameter problem is discussed in detail, and illustrative examples are presented to highlight the essentially constructive nature of the results.

A Numerical Study of Particle Migration and Sedimentation in Viscoelastic Couette Flow

In this work, a systematic investigation of the migration of sedimenting particles in a viscoelastic Couette flow is presented, using finite element 3D simulations. To this end, a novel computational approach is presented, which allows us to simulate a periodic configuration of rigid spherical particles accurately and efficiently. To study the different contributions to the particle migration, we first investigate the migration of particles sedimenting near the inner wall, without an externally-imposed Couette flow, followed by the migration of non-sedimenting particles in an externally-imposed Couette flow. Then, both flows are combined, i.e., sedimenting particles with an externally-imposed Couette flow, which was found to increase the migration velocity significantly, yielding migration velocities that are higher than the sum of the combined flows. It was also found that the trace of the conformation tensor becomes asymmetric with respect to the particle center when the particle is initially placed close to the inner cylinder. We conclude by investigating the sedimentation velocity with an imposed orthogonal shear flow. It is found that the sedimentation velocity can be both higher or lower then the Newtonian case, depending on the rheology of the suspending fluid. Specifically, a shear-thinning viscosity is shown to play an important role, which is in-line with previously-published results.

Preliminary Fluid Dynamic Analysis of Turbulent Flat and Ribbed Square Duct via CFD Approach

A preliminary numerical study of the fluid dynamic behavior of flat and ribbed square duct is presented. Fluid dynamics of two configurations is analyzed via Reynolds Averaged Navier Stokes (RANS) modeling in order to underline the main characteristics of each configuration and to give some information at global and local level. This kind of modeling is used as base for setting up a more detailed analysis such as Direct Numerical Simulation (DNS). Flat and ribbed square duct with a Reynolds number based on bulk velocity and hydraulic diameter of 10320 (Reτ=600 for the flat configuration) are analyzed and the results of the flat configuration are compared with available results obtained via DNS approach. The ribbed square duct is characterized by a two-pass configuration (aligned ribs in the top and bottom walls), with the duct height about six times the height of the obstacles for a blockage ratio of about 30%. Finally a pitch ratio (rib spacing to rib height) of 10 is used in order to obtain a k-type roughness permitting the flow to reattach before the next obstacle. Advanced U-RANS and RANS models such as Reynolds Stress Models (RSM), Explicit Algebraic Stress Models (EASM), v2f, and two-equation low Reynolds models have been used and compared. In this direction the validated results obtained for the smooth square duct are used to select the most appropriate RANS models and to evaluate their performance for a ribbed square duct at the same Reynolds number. A periodic configuration including one rib and considering the flow fully developed is used to reduce computational costs. The results of the ribbed square duct are hence analyzed in order to evaluate characteristics such as domain and mesh size.

Second-Order Two-Scale Finite Element Method for Piezoelectric Problem in Composite Plate

In this paper, we construct a second-order two-scale (SOTS) finite element method for piezoelectric problem in composite plate with 3-D periodic configuration by means of construction way. Based on theReissner-Mindlindeformation pattern and integral projection operator of electric field, the homogenization solution of piezoelectric problem is obtained based on finite element method. The SOTS's computational method is constructed by SOTS's asymptotic expansion. A set of numerical results are demonstrated for predicting the displacement and temperature of composite plate. It shows that SOTS's finite element method can capture the 3-D local behaviors caused by 3-D micro-structures well.