Gold Nanoparticles as Effective ion Traps in Poly(dimethylsiloxane) Cross-Linked by Metal-Ligand Coordination

At this time, the development of advanced elastic dielectric materials for use in organic devices, particularly in organic field-effect transistors, is of considerable interest to the scientific community. In the present work, flexible poly(dimethylsiloxane) (PDMS) specimens cross-linked by means of ZnCl₂-bipyridine coordination with an addition of 0.001 wt. %, 0.0025 wt. %, 0.005 wt. %, 0.04 wt. %, 0.2 wt. %, and 0.4 wt. % of gold nanoparticles (AuNPs) were prepared in order to understand the effect of AuNPs on the electrical properties of the composite materials formed. The broadband dielectric spectroscopy measurements revealed one order of magnitude decrease in loss tangent, compared to the coordinated system, upon an introduction of 0.001 wt. % of AuNPs into the polymeric matrix. An introduction of AuNPs causes damping of conductivity within the low-temperature range investigated. These effects can be explained as a result of trapping the Cl⁻ counter ions by the nanoparticles. The study has shown that even a very low concentration of AuNPs (0.001 wt. %) still brings about effective trapping of Cl⁻ counter anions, therefore improving the dielectric properties of the investigated systems. The modification proposed reveals new perspectives for using AuNPs in polymers cross-linked by metal-ligand coordination systems.     

Cauchy boundary andb-incompleteness of space-time

It is shown that if a space-time (M, g) is time-orientable and its Levi-Civita connection [in the bundle of orthonormal frames over (M, g)] is reducible to anO(3) structure, one can naturally select a nonvanishing timelike vector field and a Riemann metricg ⁺ onM. The Cauchy boundary of the Riemann space (M, g ⁺) consists of endpoints ofb-incomplete curves in (M, g); we call it theCauchy singular boundary. We use the space-time of a cosmic string with a conic singularity to test our method. The Cauchy singular boundary of this space-time is explicitly constructed. It turns out to consist of what should be expected.     

Preparation and semiconducting properties of Th3As4

The resistivity, thermoelectric power and Hall constant in the temperature range of 78–830 K were determined for polycrystalline Th₃As₄ samples obtained by annealing thin thorium slabs in arsenic vapour. The samples examined were n-type semiconductors with a carrier concentration ranging from 1.0 × 10¹⁸cm^?3 to 2.8 × 10¹⁸ cm^?3 for which the effective mass was found to be equal to 0.55–0.76m₀. The Hall mobility, about 450cm²V^?1s^?1 at room temperature, obeys a $\text{T}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ law at high temperatures. On the basis of the electrical measurements the forbidden gap of Th₃As₄ was found to be equal to 0.43 eV.     

How should one define a (weak) crystal?

We compare two proposals for the study of positional long-range order: one in terms of the spectrum of the translation operator, the other in terms of the Fourier spectrum. We point out that only the first one allows for the consideration of molecular, as opposed to atomic, (weakly) periodic structures. We illustrate this point on the Thue-Morse system.     

Critical circle maps near bifurcation

We estimate harmonic scalings in the parameter space of a one-parameter family of critical circle maps. These estimates lead to the conclusion that the Hausdorff dimension of the complement of the frequency-locking set is less than 1 but not less than 1/3. Moreover, the rotation number is a Hölder continuous function of the parameter.Partially supported by KBN grant Iteracje i Fraktale #210909101.Partially supported by NSF Grant #DMS-9206793 and the Sloan Research Fellowship.     

Phase retrieval from spectral interferograms including a stationary-phase point

We report on a simple processing procedure to retrieve the phase from spectral interferograms including a stationary-phase point. First, the numerical simulations are performed to demonstrate high precision of the phase retrieval from the spectral interferogram. Second, the feasibility of the procedure is confirmed in processing the experimental data from a dispersive Michelson interferometer comprising a cube beam splitter and a plate made of BK7 optical glass. From the retrieved spectral phase, the effective thickness of the BK7 optical glass is determined precisely.     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

The localization of energy in gauge field theories and in linear gravitation

It is shown how the energy-positivity criterion enables us to localize the energy in various field theories. For this purpose the role of surface integrals in a canonical formalism is investigated. The same techniques are applied to linearized gravity, where the mixed Cauchy-boundary value problem in a finite volume is analyzed. Unconstrained degrees of freedom and boundary data which have to be controlled are found. This paper is part of a program to analyze the possibility of localization of gravitational energy in complete General Relativity.     

Formation of pits during growth of Si/Ge nanostructures

Alternating deposition of Ge and Si in the step-flow growth regime using Bi acting as a surfactant can lead to a spontaneous formation of one atomic layer deep pits in the area of surface covered by Ge. During Si growth Ge atoms of the epitaxial 2D Ge layer move to Si step edges where stronger bonds with Si atoms are formed. Appropriate growth conditions can suppress or enhance the pit formation effect and consequently a new type of self-organized nanostructures can be formed.     

A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface

We report on an exact vector (polarized) radiative transfer (VRT) model for coupled atmosphere and ocean systems. This VRT model is based on the successive order of scattering (SOS) method, which virtually takes all the multiple scattering processes into account, including atmospheric scattering, oceanic scattering, reflection and transmission through the rough ocean surface. The isotropic Cox–Munk wave model is used to derive the ref and transmission matrices for the rough ocean surface. Shadowing effects are included by the shadowing function. We validated the SOS results by comparing them with those calculated by two independent codes based on the doubling/adding and Monte Carlo methods. Two error analyses related to the ocean color remote sensing are performed in the coupled atmosphere and ocean systems. One is the scalar error caused by ignoring the polarization in the whole system. The other is the error introduced by ignoring the polarization of the light transmitted through the ocean interface. Both errors are significant for the cases studied. This code fits for the next generation of ocean color study because it converges fast for absorbing medium as, for instance, ocean.