An application of weighted Hardy spaces to the Navier–Stokes equations

In this article, we consider the mapping properties of convolution operators with smooth functions on weighted Hardy spaces H^p(w)$H^p(w)$ with w   belonging to Muckenhoupt class _A∞$A_{\infty }$. As a corollary, one obtains decay estimates of heat semigroup on weighted Hardy spaces. After a weighted version of the div–curl lemma is established, these estimates on weighted Hardy spaces are applied to the investigation of the decay property of global mild solutions to Navier–Stokes equations with the initial data belonging to weighted Hardy spaces.     

Infinitely many solutions for a nonlinear Schrödinger equation with general nonlinearity

We prove the existence of infinitely many solutions for

$$\begin{aligned} - \Delta u + V(x) u = f(u) \quad \text { in } \mathbb {R}^N, \quad u \in H^1(\mathbb {R}^N), \end{aligned}$$

where V(x) satisfies \(\lim _{|x| \rightarrow \infty } V(x) = V_\infty >0\) and some conditions. We require conditions on f(u) only around 0 and at \(\infty \).

     

On the multiple existence of semi-positive solutions for a nonlinear Schrödinger system

The paper concerns multiplicity of vector solutions for nonlinear Schrödinger systems, in particular of semi-positive solutions. New variational techniques are developed to study the existence of this type of solutions. Asymptotic behaviors are examined in various parameter regimes including both attractive and repulsive cases.     

Evolution of long-period stacking order (LPSO) in Mg97Zn1Gd2 cast alloys viewed by HAADF-STEM multi-scale electron tomography

We have studied three-dimensional (3D) structures and growth processes of 14H-type long-period stacking order (LPSO) formed in Mg₉₇Zn₁Gd₂ cast alloys by single tilt-axis electron tomography (ET) using high-angle annular dark-field scanning transmission electron microscopy. Evolution of the solute-enriched stacking faults (SFs) and the 14H LPSO by ageing were visualised in 3D with a high spatial resolution in multi-scale fields of views from a few nanometres to ~10 μm. Lateral growth of the solute-enriched SFs and the LPSO in the (0?0?0?1)_Mg plane is notable compared to the out-of-plane growth in the [0?0?0?1]_Mg direction. The 14H LPSO grows at the cost of decomposition of the (Mg, Zn)₃Gd-type precipitates, and accompany a change of in-plane edge angles from 30 to 60°. We have updated the Time–Temperature–Transformation diagram for precipitation in Mg₉₇Zn₁Gd₂ alloys: starting temperatures of both solute-enriched SFs and LPSO formation shifted to a shorter time side than those in the previous diagram.     

Dispersion and Confinement Loss Control in Modified Hexagonal Photonic Crystal Fibers

This paper presents a novel technique for the control of chromatic dispersion and confinement loss in hexagonal photonic crystal fibers (H-PCFs). It is demonstrated that it is possible to obtain very low chromatic dispersion of 0 ± 0:38 ps/(nm·km) in the wavelength range of 1.41 to 1.66 μm and confinement loss of less than 0.0001 dB/km from a six ring modified H-PCF (MH-PCF). The higher order dispersion at 1.55 μm is about −0.001 ps/(nm²-km).     

Efficient decoherence-free entanglement distribution over lossy quantum channels

We propose and demonstrate a scheme for boosting the efficiency of entanglement distribution based on a decoherence-free subspace over lossy quantum channels. By using backward propagation of a coherent light, our scheme achieves an entanglement-sharing rate that is proportional to the transmittance T of the quantum channel in spite of encoding qubits in multipartite systems for the decoherence-free subspace. We experimentally show that highly entangled states, which can violate the Clauser-Horne-Shimony-Holt inequality, are distributed at a rate proportional to T.     

Optical constants of polymer coatings in the infrared

The refractive indices and absorption coefficients of fluorocarbon, polymethyl methacrylate, and polyimide were measured in the wavelength range of 2–12 μm. The reflection losses of KRS-5 and CsI windows were reduced successfully by coating fluorocarbon polymers on the surfaces.     

New and simple method for fabricating polymer-coated silver hollow fibers with large mechanical strength

A new method is proposed for fabricating polymer-coated silver hollow glass fibers to avoid the flexibility deterioration after the curing process. Transmission properties of fibers made by the two procedures with and without curing process are compared. Little difference was observed in the transmission properties at the wavelength 2.94 μm of Er:YAG laser light and 10.6 μm of CO₂ laser light. The polymer layer is shown to be stable after 2-h, 5-W, continuous wave CO₂ laser light transmission.     

Flattened chromatic dispersion in square photonic crystal fibers with low confinement losses

This research presents a simple index-guiding square photonic crystal fibers (SPCFs) that has a silica core surrounded by air hole with two different diameters. It is demonstrated that the designed two-different-size hole-arrayed index-guiding SPCFs has a ultra-flattened chromatic dispersion of 0 ± 0.9 ps/(nm·km) in a wavelength range of 1.34 to 1.61 μm and low confinement loss of less than 10⁻⁷ dB/m in a wavelength range of 1.2 to 1.7 μm. It has also been shown that the proposed SPCFs show reasonable dispersion tolerance.     

Quantum phase transitions to charge-ordered and Wigner-crystal states under the interplay of lattice commensurability and long-range Coulomb interactions

The relationship among the Wigner crystal, charge ordering, and the Mott insulator is studied by the path-integral renormalization group method in two-dimensional systems with long-range Coulomb interaction. In contrast to the insensitivity of the Hartree-Fock results, the stability of the solid drastically decreases with the decrease in the lattice commensurability. The transition to liquid occurs at the electron gas parameter r(s) approximately 2 for the filling n=1/2, showing a large reduction from r(s) approximately 35 in the continuum limit. A correct account of quantum fluctuations is crucial to understanding the charge-order stability generally observed only at simple fractional fillings and the nature of quantum liquids away from them.