Patch Antenna Based on MUC for Wi-Fi and 5G

This communication reported the patch antenna working at Wi-Fi and 5G bands. To acquire compactness the side lengths of the patch are taken based on upper-frequency band (3.3 GHz). Dual-band operation (lower resonating band) is realized by loading the Mushroom Unit Cell (MUC) along the bottom right corner of the patch. To obtain Circular Polarization (CP) at the 5G band the conventional patch is modified with fractal boundary. This blend of the Double Negative Transmission Lines metamaterials (DNG TL), as well as fractal concepts yielded good compactness suitable for ultra-thin portable gadgets. Measured results have good correlation with simulated data from HFSS. The obtained bandwidths at the lower and upper bands are 2.51 % and 6.23 % when the Poly fractal curves are introduced. CP bandwidth of the proposed antenna at 5G band obtained from the measured data is 2.35 % which is the highest to the best of authors' knowledge for this type of thin antennas.

Planar random-cluster model: fractal properties of the critical phase

This paper is studying the critical regime of the planar random-cluster model on $${\mathbb {Z}}^2$$ Z 2 with cluster-weight $$q\in [1,4)$$ q ∈ [ 1 , 4 ) . More precisely, we prove crossing estimates in quads which are uniform in their boundary conditions and depend only on their extremal lengths. They imply in particular that any fractal boundary is touched by macroscopic clusters, uniformly in its roughness or the configuration on the boundary. Additionally, they imply that any sub-sequential scaling limit of the collection of interfaces between primal and dual clusters is made of loops that are non-simple. We also obtain a number of properties of so-called arm-events: three universal critical exponents (two arms in the half-plane, three arms in the half-plane and five arms in the bulk), quasi-multiplicativity and well-separation properties (even when arms are not alternating between primal and dual), and the fact that the four-arm exponent is strictly smaller than 2. These results were previously known only for Bernoulli percolation ($$q = 1$$ q = 1 ) and the FK-Ising model ($$q = 2$$ q = 2 ). Finally, we prove new bounds on the one, two and four-arm exponents for $$q\in [1,2]$$ q ∈ [ 1 , 2 ] , as well as the one-arm exponent in the half-plane. These improve the previously known bounds, even for Bernoulli percolation.

Boundary element methods for acoustic scattering by fractal screens

We study boundary element methods for time-harmonic scattering in $${\mathbb {R}}^n$$ R n ($$n=2,3$$ n = 2 , 3 ) by a fractal planar screen, assumed to be a non-empty bounded subset $$\Gamma $$ Γ of the hyperplane $$\Gamma _\infty ={\mathbb {R}}^{n-1}\times \{0\}$$ Γ ∞ = R n - 1 × { 0 } . We consider two distinct cases: (i) $$\Gamma $$ Γ is a relatively open subset of $$\Gamma _\infty $$ Γ ∞ with fractal boundary (e.g. the interior of the Koch snowflake in the case $$n=3$$ n = 3 ); (ii) $$\Gamma $$ Γ is a compact fractal subset of $$\Gamma _\infty $$ Γ ∞ with empty interior (e.g. the Sierpinski triangle in the case $$n=3$$ n = 3 ). In both cases our numerical simulation strategy involves approximating the fractal screen $$\Gamma $$ Γ by a sequence of smoother “prefractal” screens, for which we compute the scattered field using boundary element methods that discretise the associated first kind boundary integral equations. We prove sufficient conditions on the mesh sizes guaranteeing convergence to the limiting fractal solution, using the framework of Mosco convergence. We also provide numerical examples illustrating our theoretical results.

Fractional Cauchy problem on random snowflakes

We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the pre-fractal boundary obtaining asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain.

Quantum entanglement purification assisted by classical phase noise

Entanglement purification is a vital protocol to produce a high-quality entangled state from an ensemble of identical states. Based on the particular scheme of entanglement purification [Phys. Rev. A 87, 052316 (2013)], the effect of phase fluctuation is investigated. The convergence pattern of the initial states can be divided into two kinds of regions, corresponding to the purified outcomes being a maximally entangled state (MES) or a separable state. And there is the fractal-like structure near the boundary between these two regions. It is found that the phase noise plays a positive role in generating an MES for an initial states near some fractal boundary, which can only become the separable one if the noise is absent. It is also found that the minimal iteration steps to achieve the maximally entangled state with the phase noise can be decreased, which can save the resource in the protocol.