Fluctuations for the Ginzburg-Landau $${\nabla \phi}$$ Interface Model on a Bounded Domain

We study the massless field on \({D_n = D \cap \tfrac{1}{n} \mathbf{Z}^2}\), where \({D \subseteq \mathbf{R}^2}\) is a bounded domain with smooth boundary, with Hamiltonian \({\mathcal {H}(h) = \sum_{x \sim y} \mathcal {V}(h(x) - h(y))}\). The interaction \({\mathcal {V}}\) is assumed to be symmetric and uniformly convex. This is a general model for a (2 + 1)-dimensional effective interface where h represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: h(x) = n x · u + f(x) for \({x \in \partial D_n,\,u \in \mathbf{R}^2}\), and f : R ² → R continuous. We prove that the fluctuations of linear functionals of h(x) about the tilt converge in the limit to a Gaussian free field on D, the standard Gaussian with respect to the weighted Dirichlet inner product \({(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i}\) for some explicit β = β(u). In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of h are asymptotically described by SLE(4), a conformally invariant random curve.     

One-pot synthesis of uniform hollow cuprous oxide spheres fabricated by single-crystalline particles via a simple solvothermal route

Uniform Cu₂O hollow spheres fabricated by single-crystalline particles (smaller than 20 nm) are facile synthesized in ethylene glycol (EG) solution by a simple solvothermal route without using pre-fabricated templates and reductive agents. EG in this protocol is not only used as a solvent, complexing agent, and reducing agent, but also served as a structure-directing agent for the formation of hollow structure. By control of reaction conditions, such as reaction time, temperature, and the anions, the morphology and structure of the hollow spheres can be tuned. A coordination adsorption and oriented attachment and Ostwald ripening mechanism is proposed for explaining the formation process of hollow Cu₂O spheres in EG solution; and importantly, the hollow Cu₂O spheres exhibit an excellent property for the electro-catalytic oxidization of ascorbic acid in acetic acid buffer solution. Moreover, the hollow spherical Cu₂O particles could be potentially applied in catalysis, sensor, and as model for fundamental research.     

A new form of symplectically invariant multimode uncertainty relations

We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson–Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail.     

Thermodynamic properties of gold–water nanolayer mixtures using molecular dynamics

The physical behavior of a fluid in contact with solid layers is still not fully understood. The present work focuses on the study and understanding of thermodynamic and structural properties of gold–water nanolayer mixtures using molecular dynamics simulations. Two different systems are considered, where approximately 1,700 water molecules are confined between gold nanolayers with separations of 7.4 and 6.2 nm, respectively. Novelties of the present work are in the use of accurate force fields for modeling the inter- and intra-molecular interactions of the components, and providing comprehensive thermodynamic properties of the mixtures. The results are validated by examination of the pure fluid and pure solid properties. Results indicate that the thermodynamics of the system does not behave as an ideal mixture. The structure of the pure fluid is also analyzed and compared against the structure of the confined fluid in the mixture. Anisotropicity is observed in the fluid structure close to the surface of the nanolayer. Higher ordering and higher flux are detected in the fluid molecules close to the fluid–solid interface. Unusual thermodynamic behavior, anisotropicity, liquid layering, and higher interfacial fluid flux could be just some of the factors leading to the enhanced energy transport observed in mixtures involving at least one nanoscale component, such as nanofluids.     

Intense Upconversion Luminescence of Yb<Superscript>3+</Superscript>-Er<Superscript>3+</Superscript> in Li<Subscript>2</Subscript>O Content Tungsten-tellurite Glasses

The Er³⁺ -Yb³⁺ codoped in Li₂O content tungsten -tellurite (TWL) transparent glasses are synthesized and measured the absorption, Raman and upconversion luminescence (UPL) spectra. At room temperature intense green emission peak at 560 nm ( ⁴S_3/2→⁴I_15/2) and red emission peak at 670 nm ( ⁴F_9/2→⁴I_15/2) of Er³⁺ observed even at minimum 86 mW pumping power of infrared 980 nm excitation. For structure of the TWL glass, Raman spectrum result revealed that an important role of WO₃ in the formation of glass network linkage with Li₂O. Under this influence estimated lifetime of the ⁴I_11/2 of Er³⁺ was 1.89 μs and due to lower phonon energy of the glass produce strong upconversion signal. The effect of Er₂O₃ concentration on emission intensity result indicated that green emission intensity initially increase in compare to red emission. Under the 980 nm pump power variation measured the relatively increases the red emission to the green emission intensity and analyze the possible upconversion mechanism and process.     

Synthesis of Ethynylated Phenothiazine Based Fluorescent Boronic Acid Probes

Ethynylated phenothiazine based fluorescent boronic acid probes were prepared. Sonogashira coupling reaction was used to introduce substituted phenylethynylene fragments to the phenothiazine fluorophore to extend the π-conjugation and to enhance the emission property. The photophysical properties and the binding properties of these probes with hydroxyl acids were investigated. We found that the probes with significant ICT effect show emissions which are sensitive to solvent polarity. The phenothiazine moiety is proved to be electron-donating. We found the substitution profile imparts significant effect on the photophysical properties of the probes. For example, one of the probes shows d-PeT effect, whereas the regioisomer probe with similar π-conjugation fragment but different substitution profile shows the a-PeT effect. The easy derivatization of phenothiazine fluorophore, the structure-photophysical property relation and the novel d-PeT fluorescence transduction profile of the phenothiazine based probes described herein may inspire more investigation into this fascinating research area.     

Preparation of functional spherical polysilsesquioxane/gold nanoparticle composites and their applications in DNA assay

Functional spherical solid and hollow particles of polysilsesquioxanes (PSQs) containing amine, thiol, and vinyl groups were prepared by polymerizing organotrialkoxysilanes (OTASs) containing corresponding chemical groups. Fluorescent PSQ particles were prepared by physically entrapping Rhodamine 6G, Coumarin 7, and Fluoresceine sodium salts. The intensity of fluorescent light increased initially with increasing amount of entrapped fluorophores and then leveled off or decreased slightly after reaching a maximum value. PSQ particles containing gold nanoparticles (GNPs), both inside and on the surface, were prepared by the in situ reduction of gold ions by the PSQ particles. When the reduction reaction was carried out for extended periods of time, the GNP that had formed inside the poly(3-mercaptopropyl)silsesquioxane (PMPSQ) and polyvinylsilsesequioxane (PVSQ) particles underwent interesting morphological changes. PSQ particles containing amine and thiol groups fixed the GNPs on the surface, which could be utilized further in binding amine-modified oligo-DNA strands. The aggregation of PSQ/GNP particles combined with complementary oligo-DNA strands was examined to demonstrate that these particles could be applied to DNA assays and isolation. The particles were characterized by scanning electron microscopy, transmission electron microscopy, solid state nuclear magnetic resonance spectroscopy, ultraviolet/visible spectroscopy, and fluorescence microscopy.     

AlF<Subscript>3</Subscript> coating of LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.5</Subscript>O<Subscript>4</Subscript> for high-performance Li-ion batteries

AlF₃-coating is attempted to improve the performance of LiNi_0.5Mn_1.5O₄ cathode materials for Li-ion batteries. The prepared powders are characterized by scanning electron microscope, powder X-ray diffraction, charge/discharge, and impedance. The coated LiNi_0.5Mn_1.5O₄ samples show higher discharge capacity, better rate capability, and higher capacity retention than the uncoated samples. Among the coated samples, 1.0 mol% AlF₃-coated sample shows highest capacity after charge–discharged at 30 mA/g for 3 cycles, but 4.0 mol% coated sample exhibits the highest capacity and cycling stability when cycled at high rate of 150 and 300 mA/g. The 40th cycle discharge capacity at 300 mA/g current still remains 114.8 mAh/g for 4.0 mol% AlF₃-coated LiNi_0.5Mn_1.5O₄, while only 84.3 mAh/g for the uncoated sample.