Fabrication high-purity Fe nanochains with near theoretical limit value of saturation magnetization of bulk Fe

High-yield purity chain-like one-dimensional nanostructures consisting of single crystal Fe nanoparticles have been produced by using solution dispersion approach. Room temperature magnetic measurement shows that the as-fabricated Fe nanochains are ferromagnetic with a high saturation magnetization (203 emu/g) whereas the nanoparticles are single magnetic domains, which indicate that the as-synthesized products have superparamagnetism behavior with the saturation magnetization of about 28 emu/g. Maybe this results from the directional alignment of the nanoparticles. The excellent characteristic may have led to the potential applications in spin filtering, high density magnetic recording, and nanosensors.     

Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene

The effect of Coulomb interaction between Dirac fermions on the formation of the Kohn-Luttinger superconducting state in bilayer doped graphene is studied disregarding of the effect of the van der Waals potential of the substrate and impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting phases with the f-, p + ip-, and d + id-wave symmetries of the order parameter. It is demonstrated that the account for the interlayer Coulomb interaction enhances the critical temperature of the transition to the superconducting phase.     

Higher-dimensional black holes with Dirac–Born–Infeld (DBI) global defects

It is well-known that the exact solution of non-linear \(\sigma \) model coupled to gravity can be perceived as an exterior gravitational field of a global monopole. Here we study Einstein’s equations coupled to a non-linear \(\sigma \) model with Dirac–Born–Infeld (DBI) kinetic term in D dimensions. The solution describes a metric around a DBI global defects. When the core is smaller than its Schwarzschild radius it can be interpreted as a black hole having DBI scalar hair with deficit conical angle. The solutions exist for all D, but they can be expressed as polynomial functions in r only when D is even. We give conditions for the mass M and the scalar charge \(\eta \) in the extremal case. We also investigate the thermodynamic properties of the black holes in canonical ensemble. The monopole alter the stability differently in each dimensions. As the charge increases the black hole radiates more, in contrast to its counterpart with ordinary global defects where the Hawking temperature is minimum for critical \(\eta \). This behavior can also be observed for variation of DBI coupling, \(\beta \). As it gets stronger (\(\beta \ll 1\)) the temperature increases. By studying the heat capacity we can infer that there is no phase transition in asymptotically-flat spacetime. The AdS black holes, on the other hand, undergo a first-ordered phase transition in the Hawking–Page type. The increase of the DBI coupling renders the phase transition happen for larger radius.     

Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming from the integration of the Friedmann equation is expressed in terms of elliptic integrals. For a negative cosmological constant, we identify the allowed ranges for the model’s parameters. Within the quantum analysis, the Wheeler–De Witt (WDW) equation turns into a modified Morse equation whose solutions are Mathieu and Heun functions.     

Quantum Corrections for Regular Black Holes with Charge and Coupling Constant

In this paper, we use semi-classical tunneling approach to calculate the quantum corrections to the Hawking temperature as well as entropy of the Kehagias-Sftesos asymptotically flat black hole solution and charged regular black hole with Fermi-Dirac distribution. For this purpose, we apply the first law of black hole thermodynamics to investigate the semi-classical entropy of both black holes having mass as well as charge or coupling constant. For both black holes, the entropy corrections contain the logarithmic term as a leading order correction term. For Kehagias-Sftesos asymptotically flat black hole, the semi-classical Hawking temperature and black hole entropy will behave asymptotically by considering the vanishing coupling constant b = 0. We have obtained the same analysis for the corrected thermodynamical quantities for this BH. For charged regular black hole with Fermi-Dirac distribution, if we neglect the charged effects in our analysis, i.e., q = 0, then these corrections approximately leads to the Schwarzschild black hole which is already given in the literature.     

Microwave-Assisted Combustion Synthesis of ZnO:Eu Nanoparticles: Effect of Fuel Types

Nanoparticles of Europium oxide doped with Zinc oxide were synthesized via microwave-assisted combustion method. Citric acid as a simultaneous fuel and chelating agent and glycine as a fuel and mixture of these fuels were sleeted. X-Ray diffraction patterns (XRD) indicated the formation of ZnO structure with a few amount of Eu₂O₃ phase. Fourier transformation infra red (FTIR) spectra reveal the increase of ZnO₄ bonds with glycine content of fuels mixture. Scanning electron microscope (SEM) images showed the conversion of nanosphere to spongy-like structure with respect to change of fuel mixtures from citric to glycine. From transmission electron microscopy (TEM) nanoparticles of a mean size 30 nm are observed Green fluorescence emission of different samples was due to activation of self activated center of ZnO structure through transition of electron from Eu³⁺ to V_zn sites.     

A Rhodamine Derivative Based Chemosensor with High Selectivity and Quick Respond to Cr<Superscript>3+</Superscript> in Aqueous Solution

In this paper, a new kind of colorimetric chemsensor aiming at detecting Cr³⁺ has been synthesized, and it is based on the “Off-On” effect of a rhodamine derivative. Comparing with other metal irons (Na⁺, K⁺, Ni²⁺, Hg²⁺, Fe³⁺, Mn²⁺, Co²⁺, Cd²⁺, Cu²⁺, Pb²⁺, Zn²⁺, Mg²⁺, Ba²⁺, Ag⁺, Fe²⁺, Ce³⁺), the chemsensor has a quick and accurate response to Cr³⁺ in H₂O-EtOH solution (4/1, v/v). There is an obvious change in color, from colorless to bright pink when Cr³⁺ is detected. According to the fitting curve based on Benesi-Hildebrand equation and working curve of absorption strength in UV-vis spectrum, the binding pattern of Cr³⁺ and the rhodamine derivative follows a 1:1 stoichiometry. The chemsensor shows great potential in monitoring Cr³⁺ in the aqueous medium with high efficiency, which is supposed to complete the recognition in the minimum as 5.2?×?10^?7 mol/L within 5 min.     

Summability of Connected Correlation Functions of Coupled Lattice Fields

We consider two nonindependent random fields \(\psi \) and \(\phi \) defined on a countable set Z. For instance, \(Z=\mathbb {Z}^d\) or \(Z=\mathbb {Z}^d\times I\), where I denotes a finite set of possible “internal degrees of freedom” such as spin. We prove that, if the cumulants of \(\psi \) and \(\phi \) enjoy a certain decay property, then all joint cumulants between \(\psi \) and \(\phi \) are \(\ell _2\)-summable in the precise sense described in the text. The decay assumption for the cumulants of \(\psi \) and \(\phi \) is a restricted \( \ell _1\) summability condition called \(\ell _1\)-clustering property. One immediate application of the results is given by a stochastic process \(\psi _t(x)\) whose state is \(\ell _1\)-clustering at any time t: then the above estimates can be applied with \(\psi =\psi _t\) and \(\phi =\psi _0\) and we obtain uniform in t estimates for the summability of time-correlations of the field. The above clustering assumption is obviously satisfied by any \(\ell _1\)-clustering stationary state of the process, and our original motivation for the control of the summability of time-correlations comes from a quest for a rigorous control of the Green–Kubo correlation function in such a system. A key role in the proof is played by the properties of non-Gaussian Wick polynomials and their connection to cumulants     

Uniqueness of Mass-Conserving Self-similar Solutions to Smoluchowski’s Coagulation Equation with Inverse Power Law Kernels

Uniqueness of mass-conserving self-similar solutions to Smoluchowski’s coagulation equation is shown when the coagulation kernel K is given by \(K(x,x_*)=2(x x_*)^{-\alpha }\), \((x,x_*)\in (0,\infty )^2\), for some \(\alpha >0\).