Rains of solitons in a figure-of-eight passively mode-locked fiber laser

We report experimental observation of rains of solitons in figure-of-eight fiber laser passively mode-locked through nonlinear optical loop mirror. Soliton pulses are created from an extended noisy background and drift until they reach a condensed phase comprising several tens of aggregated solitons. The observation of this dynamics tends to strengthen the idea of the universality of the collective behavior of solitons.     

Effect of radial flow in the die entrance region on gross melt fracture of PDMS extrudate

The gross melt fracture defect is related to the flow instabilities developed in the contraction region. To mitigate these upstream instabilities, a convergent radial flow in the die entrance has been created. In fact, the ultimate objective of the present work is to examine the effect of the clearance width of radial flow on the appearance and development of gross melt fracture defect. So, capillary rheometer experiments were performed with linear polydimethylsiloxane (PDMS) oil.As for the influence of radial flow width on the morphology of gross melt fracture defect, extrudate photographs show that this imperfection can be mitigated since its frequency is higher and amplitude smaller when the gap of radial flow decreases. Such results may be related both to shear and elongational components of radial flow. Actually, when gap width is very small compared to the external diameter of radial flow, shear deformations become more enhanced with respect to the elongational deformations and thus the helical gross melt fracture becomes more like a surface defect than volume defect.     

Solutions of Super-Linear Elliptic Equations and Their Morse Indices

Mathematical Notes - We investigate the degenerate bi-harmonic equation $$\Delta_{m}^2 u=f(x,u)\quad \text{in} \ \ \Omega, \qquad u = \Delta u = 0\quad \text{on}\ \ \partial\Omega,$$ with $$m\ge...     

Universal soliton pattern formations in passively mode-locked fiber lasers

We investigate multiple-soliton pattern formations in a figure-of-eight passively mode-locked fiber laser. Operation in the anomalous dispersion regime with a double-clad fiber amplifier allows generation of up to several hundreds of solitons per round trip. We report the observation of remarkable soliton distributions: soliton gas, soliton liquid, soliton polycrystal, and soliton crystal, thus indicating the universality of such complexes.     

Theoretical Study of Electronic Structure and Stability of Mixed AlmBn−mH n 2− and CmBn−mH n 2−m (n = 6, 10, 12 and m = 1, 2) Clusters

Density functional theory (DFT) method with B3LYP functional and 6-311++G(d,p) basis set has been used to predict the geometries, relative stabilities, electronic structures and bonding analysis of Mixed Al_mB_n?mH _n ^2? and C_mB_n?mH _n ^2?m (n = 6, 10, 12 and m = 1, 2) clusters; being compared to the B_nH _n ^2? ones. Therefore, the DFT results suggest that the replacing of boron by aluminium or carbon is governed by Natural net charges following Gimar’s and Williams’s rules. The Al_mB_n?mH _n ^2? structures are relatively distorted compared to those of B_nH _n ^2? and C_mB_n?mH _n ^2?m . In Al_mB_n?mH _n ^2? structures Al atoms prefer the adjacent sites, however for the C₂B_n?2H_n cluster cages, the carbon atoms are positioned at diametrically opposed sites. The large HOMO–LUMO gaps show that the predicted clusters have chemical stabilities, principally, those of Al_mB_n?mH _n ^2? ones, which are not experimentally isolated. The optimized geometries obtained through boron substitution by Al and C lead to compactness and to contracted structures, respectively, where B–B bonds are the shortest in mono- and di-carbaboranes.     

Structure, magnetic properties and M?ssbauer spectra of La0.67Sr0.33FexMn1???xO3 manganites oxide prepared by mechanical ball milling method

La_0.67Sr_0.33Fe_xMn_1-xO₃, with x = 0.0, 0.1, 0.2 and 1 have been elaborated by mechanical system. X-ray diffraction, Scanning electron microscopy, Magnetic measurements and M?ssbauer spectroscopy for the systems have been investigated. Rietveld analysis of the X-ray powder diffraction show that the samples crystallise in the orthorhombic perovskite system with Pnma space group. The average particle size of about 60 nanometre was obtained from scanning electron microscopy and X-ray diffraction. The investigated samples exhibit a ferromagnetic to paramagnetic transition with increasing temperature. The presence of manganese in the structure leads to an increase of the Curie temperature as well as to spontaneous magnetization. The magnetization versus applied magnetic field shows a small coercive field and an unsaturated magnetization which indicates that the nanoparticles of all samples are superparamagnetic at around room temperature. Room temperature M?ssbauer spectra show that the samples with x = 0.1 and x = 1.0 contain minority α-Fe₂O₃ and other spinel ferrite species. Also, they indicate that Fe^3?+? ions are present in slightly distorted octahedral sites in the samples with x = 0.1 and 0.2, while mixed Fe valency was observed for the sample with x = 1.0.     

Characterization of soliton compounds in a passively mode-locked high power fiber laser

We characterize soliton complexes in a high power double-clad erbium-doped fiber laser passively mode-locked through nonlinear polarization evolution. Such complexes involve some hundreds of solitons and form self-organized or disorganized patterns analogous to the states of the matter. Experimentally these soliton compounds are characterized through the autocorrelation trace, the optical spectrum and the oscilloscope trace which is limited due to its finite bandwidth. We perform here a reconstruction of the experimental results thus allowing us to identify the temporal distribution of the solitons inside the cavity. The reconstruction allows us to clarify and either to confirm or to correct the former intuitive interpretation. Especially, a soliton ‘spray’ is identified.     

Homomorphisms with respect to a function

Let X be a realcompact space and ${H:C(X)\rightarrow\mathbb{R}}$ be an identity and order preserving group homomorphism. It is shown that H is an evaluation at some point of X if and only if there is ${\varphi\in C(\mathbb{R})}$ with ${\varphi(r)>\varphi(0)}$ for all ${r\in\mathbb{R}-\{0\}}$ for which ${H\circ\varphi=\varphi\circ H}$ . This extends (and unifies) classical results by Hewitt and Shirota.     

Homomorphisms with respect to a function

Let X be a realcompact space and H:C(X)?\mathbbR{H:C(X)\rightarrow\mathbb{R}} be an identity and order preserving group homomorphism. It is shown that H is an evaluation at some point of X if and only if there is j ? C(\mathbbR){\varphi\in C(\mathbb{R})} with ${\varphi(r)>\varphi(0)}${\varphi(r)>\varphi(0)} for all r ? \mathbbR-{0}{r\in\mathbb{R}-\{0\}} for which H°j = j°H{H\circ\varphi=\varphi\circ H} . This extends (and unifies) classical results by Hewitt and Shirota.     

A comparative study on the nanocrystalline ZnO thin films prepared by ultrasonic spray and sol⿿gel method

Nanocrystalline ZnO thin films are deposited through two different chemical methods: (i) the films prepared by ultrasonic spray with 0.1 M and (ii) dip-coating from zinc acetate complex solutions with 0.5 M, the films obtained at different temperatures. The XRD analyses indicated that ZnO films have nanocrystalline hexagonal structure with (0 0 2) preferential orientation and the maximum crystallite size value of 103 nm measured from the films prepared by dip-coating. UV?vis measurement indicated that all films are transparency in the visible region. The optical band gap increased with decreasing of the Urbach tail energy indicating that the increase in the transition tail width and decrease of the defects, respectively.