Magnetotransport properties in \text{ Ni }_{81}\text{ Fe }_{19}\text{/Zr } multi-layers

In this work, we present a study of the magneto transport properties in magnetic multilayered structure $\text{ Ni }_{81}\text{ Fe }_{19}\text{/Zr }$ Ni 81 Fe 19 /Zr . The magnetic $(\text{ Ni }_{81}\text{ Fe }_{19})$ ( Ni 81 Fe 19 ) and non magnetic (Zr) layer thickness $(\mathbf{t}_\mathbf{NiFe}, \mathbf{t}_\mathbf{zr})$ ( t NiFe , t zr ) effects on the magneto resistance (MR) are discussed theoretically in the framework of the Johnson–Camley semi classical approach based on the Boltzmann transport equation. A comparison between calculated and measured MR is obtained. The observed MR ratio oscillates for Zr layer thickness with an average period of 7Å. A generally weak $\text{ MR }(\text{ t }_{\mathrm{NiFe}})$ MR ( t NiFe ) ratio for fixed $\mathbf{t}_\mathbf{zr}$ t zr is obtained and it shows a maxima peak of the MR with a value of 1.8 % located at $\mathbf{t}_\mathbf{NiFe}= 80$ t NiFe = 80 Å.     

Optical properties of ZnTe doped with transition metals (Ti, Cr and Mn)

The electronic and optical properties of $\text{ Zn }_{1-\mathrm{x}}\text{ M }_\mathrm{x}\text{ Te }$ with (M = Cr, Mn, Ti) have been investigated, within generalized gradient approximation (GGA) using the full potential linear augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. This work presents detailed information about optical properties like absorbance, refractive index and reflectivity. The result of this study shows that doped ZnTe material with Ti, Cr and Mn shift the absorption spectrum and reflection to the infrared spectral domain or to the ultra violet region, depending on the nature of the dopant. Dielectric functions for different compositional alloys are calculated for 16-atom cubic supercell structure. The calculated band gaps are fitted with a linear equation: ( $\upalpha \text{ h }\upnu )^{2} = \text{ A }(\text{ h }\upnu -\text{ Eg }$ ). For all types of doping the position of critical points (CP’s) $\text{ E }_{0}, \text{ E }_{1}$ and $\text{ E }_{2}$ show good agreement with the experimental data.     

Local structure of Fe-doped In 2 O 3 films investigated by X-ray absorption fine structure spectroscopy

$(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ $(x=0.07, 0.09, 0.16, 0.22, 0.31)$ films were deposited on Si (100) substrates by RF-magnetron sputtering technique. The influence of Fe doping on the local structure of films was investigated by X-ray absorption spectroscopy (XAS) at Fe K-edge and L-edge. For the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ films with $x=0.07, 0.09 \mbox{ and } 0.16$ , Fe ions dissolve into $\mathrm{In}_{2}\mathrm{O}_{3}$ and substitute for $\mathrm{In}^{3+}$ sites with a mixed-valence state ( $\mathrm{Fe}^{2+}/\mathrm{Fe}^{3+}$ ) of Fe ions. However, a secondary phase of Fe metal clusters is formed in the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ films with $x=0.22 \mbox{ and } 0.31$ . The qualitative analyses of Fe-K edge extended X-ray absorption fine structure (EXAFS) reveal that the Fe–O bond length shortens and the corresponding Debye–Waller factor ( $\sigma^{2}$ ) increases with the increase of Fe concentration, indicating the relaxation of oxygen environment of Fe ions upon substitution. The anomalously large structural disorder and very short Fe–O distance are also observed in the films with high Fe concentration. Linear combination fittings at Fe L-edge further confirm the coexistence of $\mathrm{Fe}^{2+}$ and $\mathrm{Fe}^{3+}$ with a ratio of ${\sim}3:2$ ( $\mathrm{Fe}^{2+}: \mathrm{Fe}^{3+}$ ) for the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ film with $x=0.16$ . However, a significant fraction ( ${\sim}40~\mbox{at\%}$ ) of the Fe metal clusters is found in the $(\mathrm{In}_{1-x}\mathrm{Fe}_{x})_{2}\mathrm{O}_{3}$ film with $x=0.31$ .     

Investigation on an ultra-compact 1\times 2 polymer electro-optic switch using cross-coupling 2N+1 vertical-turning serial-coupled microrings

Generic model and thorough investigation are proposed for a novel $1\times 2$ 1 × 2 polymer electro-optic (EO) switch based on one-group $2N+1$ 2 N + 1 vertical-turning serial-coupled microrings. For realizing boxlike flat spectrum as well as low crosstalk and insertion loss, resonance order and coupling gaps are optimized. The MRR switches with $N \ge 1$ N ≥ 1 reveal favorable boxlike spectrum as when compared with the simple device with only one microring ( $N = 0$ N = 0 ). For obtaining $<-30\,\text{ dB }$ < - 30 dB crosstalk under through-state, the dependency of switching voltage on $N$ N is determined as $7.19 \times \text{ exp }(-N/0.72) + 1.72\,(\text{ V })$ 7.19 × exp ( - N / 0.72 ) + 1.72 ( V ) . Under the operation voltages of 0 V (drop state) and the predicted switching voltages (through state), the device performances are analyzed, and $1 \le N \le 10$ 1 ≤ N ≤ 10 is required for dropping the insertion loss (drop state) below 10 dB. The crosstalk of the ten devices ( $N = 1-10$ N = 1 - 10 ) are $< -19.5\,\text{ dB }$ < - 19.5 dB under drop state and $< -28.7\,\text{ dB }$ < - 28.7 dB under through state, and the insertion losses of the devices ( $N = 1-10$ N = 1 - 10 ) are $< 9.715\,\text{ dB }$ < 9.715 dB under drop state and $< 1.573\,\text{ dB }$ < 1.573 dB under through state. The device also has ultra-compact footprint size of only 0.33–1.06 mm, which is only 1/10–1/3 of those of our previously reported polymer EO switches based on directional coupler or Mach–Zehnder interferometer structures. Therefore, the proposed device is capable of highly integration onto optical networks-on-chip.     

Long-time Asymptotic for the Derivative Nonlinear Schrödinger Equation with Step-like Initial Value

We study long-time asymptotics of the solution to the Cauchy problem for the Gerdjikov-Ivanov type derivative nonlinear Schrödinger equation i q t + q xx ? i q 2 q ? x + 1 2 | q | 4 q = 0 $$iq_{t}+q_{xx}-iq^{2}\bar{q}_{x}+\frac{1}{2}|q|^{4}{q}=0 $$ with step-like initial data q ( x , 0 ) = 0 $q(x,0)=0$ for x ≤ 0 $x \leqslant 0$ and q ( x , 0 ) = A e ? 2 iBx $q(x,0)=A\mathrm {e}^{-2iBx}$ for x > 0 $x>0$ , where A > 0 $A>0$ and B ∈ ? $B\in \mathbb R$ are constants. We show that there are three regions in the half-plane { ( x , t ) | ? ∞ < x < ∞ , t > 0 } $\{(x,t) | -\infty <x<\infty , t>0\}$ , on which the asymptotics has qualitatively different forms: a slowly decaying self-similar wave of Zakharov-Manakov type for x > ? 4 tB $x>-4tB$ , a plane wave region: x > ? 4 t B + 2 A 2 B + A 2 4 $x<-4t\left (B+\sqrt {2A^{2}\left (B+\frac {A^{2}}{4}\right )}\right )$ , an elliptic region: ? 4 t B + 2 A 2 B + A 2 4 > x > ? 4 tB $-4t\left (B+\sqrt {2A^{2}\left (B+\frac {A^{2}}{4}\right )}\right )<x<-4tB$ . Our main tools include asymptotic analysis, matrix Riemann-Hilbert problem and Deift-Zhou steepest descent method.     

Fougerite FeII − III oxyhydroxycarbonate in environmental chemistry and nitrate reduction

The identification of the fougerite mineral responsible for the bluish-green shade of gleysols in aquifers as being the Fe^II???III oxyhydroxycarbonate $\text{GR}(\text{CO}_{3}^{2-})^*$ of formula, $[\text{Fe}^{\rm II}_{6x}\text{Fe}^{\rm III}_{6(1 - x)}\text{O}_{12}\text{H}_{2(7-3x)}]^{2+}\bullet[\text{CO}_{3}^{2-}\bullet3\text{H}_{2}\text{O}]^{2-}$ where the ferric molar ratio x = [Fe^III/Fe_total] is restricted to the domain [1/3–2/3] induces to study the reactivity of the synthetic green rust for reducing some major pollutants. The oxidation within the solid compound $\text{GR}(\text{CO}_{3}^{2-})^*$ in the presence of nitrates is followed by miniaturized Mössbauer spectrometer (MIMOS). Ratio x = [Fe^III/Fe_total] increases up to 0.67 where $\text{GR}(\text{CO}_{3}^{2-})^*$ transforms gradually into magnetite. This could well explain the composition variability of fougerite occurrences.     

Preliminary studies of the Raman spectra of \hbox {Ag}_{2}\hbox {Te}\hbox { and }\hbox {Ag}_{5}\hbox {Te}_{3}

The theoretical calculations indicated that the monoclinic low-temperature phase of silver telluride $(\upbeta \hbox {-Ag}_{2}\hbox {Te})$ is a new binary topological insulator with highly anisotropic single Dirac cone surface. We obtained $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ crystal ingots containing few grains by the Bridgman method. We also deposited thin films of tellurium, $\hbox {Ag}_{5}\hbox {Te}_{3}\hbox { and }(\hbox {Te+Ag}_{5}\hbox {Te}_{3})$ by thermal evaporation method. The Raman spectra of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ were measured at three excitation wave lengths: 633, 515 and 488 nm. The Raman active modes of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ are situated at frequencies below 300  $\hbox {cm}^{-1}$ while vibrations of other phases appear at higher frequencies.     

Quasi solid state dye-sensitized solar cells based on polyvinyl alcohol (PVA) electrolytes containing \mathbf{I}^{\mathbf{-}}/\mathbf{I}_{\mathbf{3}}^{\mathbf{-}} redox couple

Quasi solid state dye-sensitized solar cells (DSSCs) have been fabricated with electrolytes containing $\text{ I }^{-}/\text{ I }_{3}^{-}$ redox couple using 80 % hydrolyzed polyvinyl alcohol (PVA) doped with potassium iodide (KI) and a mixture of potassium iodide and tetrapropyl ammonium iodide ( $\text{ Pr }_{4}\text{ NI }$ ) salts. The quasi solid state gel polymer electrolytes were prepared using 1:1 ethylene carbonate (EC):propylene carbonate (PC) mixture. The solar cells have the structure of ITO/ $\text{ TiO }_{2}$ /N3-Dye/electrolyte/Pt/ITO. The conductivity of the electrolytes has been calculated from the bulk resistance value determined using the electrochemical impedance spectroscopy. The performance of the DSSCs has been studied by varying the concentration of the doping salts in the electrolyte and incident light intensity. The DSSC fabricated with the KI salt electrolyte containing 9.9 wt% PVA, 39.6 wt% EC, 39.6 wt% PC, 10.9 wt% KI $(+\text{ I }_{2})$ exhibited the best power conversion efficiency of 1.97 %. However, the DSSC with a double-salt electrolyte containing 9.9 wt% PVA: 39.6 wt% EC: 39.6 wt% PC: (6.5 wt% KI: 4.4 wt% $\text{ Pr }_{4}\text{ NI }$ ) ( $+\text{ I }_{2}$ ) exhibited a higher efficiency of 3.27% under $100 \text{ mW/cm }^{2}$ light intensity. The efficiency of this cell increased to 4.59 % under dimmer light of intensity of $54 \text{ mW/cm }^{2}$ .     

Theoretical study of collision and collision-free radiative lifetimes of {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right)

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the $ {B^3}\Sigma_u^{-} $ and $ {X^3}\Sigma_g^{-} $ states of the collision-free S₂ molecule and the T-shape collision complex S₂?CHe using cc-pVQZ basis sets. We obtain the transition dipole moments of the $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) $ and the Franck?CCondon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S₂ laser pumped by a transverse fast discharge.     

An interacting dark energy model in a non-flat universe

In this paper, an interacting dark energy model in a non-flat universe is studied, with taking interaction form $C=\alpha H\rho _{de}$ C = α H ρ d e . And in this study a property for the mysterious dark energy is aforehand assumed, i.e. its equation of state $w_{\Lambda }=-1$ w Λ = - 1 . After several derivations, a power-law form of dark energy density is obtained $\rho _{\Lambda } \propto a^{-\alpha }$ ρ Λ ∝ a - α , here $a$ a is the cosmic scale factor, $\alpha $ α is a constant parameter introducing to describe the interaction strength and the evolution of dark energy. By comparing with the current cosmic observations, the combined constraints on the parameter $\alpha $ α is investigated in a non-flat universe. For the used data they include: the Union2 data of type Ia supernova, the Hubble data at different redshifts including several new published datapoints, the baryon acoustic oscillation data, the cosmic microwave background data, and the observational data from cluster X-ray gas mass fraction. The constraint results on model parameters are $\Omega _{K}=0.0024\,(\pm 0.0053)^{+0.0052+0.0105}_{-0.0052-0.0103}, \alpha =-0.030\,(\pm 0.042)^{+0.041+0.079}_{-0.042-0.085}$ Ω K = 0.0024 ( ± 0.0053 ) - 0.0052 - 0.0103 + 0.0052 + 0.0105 , α = - 0.030 ( ± 0.042 ) - 0.042 - 0.085 + 0.041 + 0.079 and $\Omega _{0m}=0.282\,(\pm 0.011)^{+0.011+0.023}_{-0.011-0.022}$ Ω 0 m = 0.282 ( ± 0.011 ) - 0.011 - 0.022 + 0.011 + 0.023 . According to the constraint results, it is shown that small constraint values of $\alpha $ α indicate that the strength of interaction is weak, and at $1\sigma $ 1 σ confidence level the non-interacting cosmological constant model can not be excluded.     

Mössbauer spectroscopy in the investigation of new mineral–related materials

New materials based on the composition of the mineral schafarzikite, FeSb $_{2}\textit {O}_{4}$ , have been synthesised. $^{57}$ Fe- and $^{121}$ Sb- Mössbauer spectroscopy shows that iron is present as Fe $^{2+}$ and that antimony is present as Sb $^{3+}$ . The presence of Pb $^{2+}$ on the antimony sites in materials of composition FeSb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ induces partial oxidation of Fe $^{2+}_{}$ to Fe $^{3+}$ . The quasi-one-dimensional magnetic structure of schafarzikite is retained in FeSb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ and gives rise to weakly coupled non-magnetic Fe $^{2+}$ ions coexisting with Fe $^{3+}$ ions in a magnetically ordered state. A similar model can be applied to account for the spectra recorded from the compound Co $_{0.5}$ Fe $_{0.5}$ Sb $_{1.5}$ Pb $_{0.5}\textit {O}_{4}$ .     

Spectroscopic properties of Ho 3 + -doped K–Sr–Al phosphate glasses

Trivalent holmium-doped K–Sr–Al phosphate glasses ( $\mathrm{P}_{2}\mathrm{O}_{5}$ – $\mathrm{K}_{2}\mathrm{O}$ –SrO– $\mathrm{Al}_{2}\mathrm{O}_{3}$ – $\mathrm{Ho}_{2}\mathrm{O}_{3}$ ) were prepared, and their spectroscopic properties have been evaluated using absorption, emission, and excitation measurements. The Judd–Ofelt theory has been used to derive spectral intensities of various absorption bands from measured absorption spectrum of 1.0 mol% $\mathrm{Ho}_{2}\mathrm{O}_{3}$ -doped K–Sr–Al phosphate glass. The Judd–Ofelt intensity parameters ( $\varOmega_{\lambda}$ , $\times10^{-20}~\mathrm{cm}^{2}$ ) have been determined of the order of $\varOmega_{2} = 11.39$ , $\varOmega_{4} = 3.59$ , and $\varOmega_{6} = 2.92$ , which in turn used to derive radiative properties such as radiative transition probability, radiative lifetime, branching ratios, etc. for excited states of $\mathrm{Ho}^{3+}$ ions. The radiative lifetimes for the ${}^{5}F_{4}$ , ${}^{5}S_{2}$ , and ${}^{5}F_{5}$ levels of $\mathrm{Ho}^{3+}$ ions are found to be 169, 296, and 317 μs, respectively. The stimulated emission cross-section for 2.05-μm emission was calculated by the McCumber theory and found to be $9.3\times10^{-2 1}~\mathrm{cm}^{2}$ . The wavelength-dependent gain coefficient with population inversion rate has been evaluated. The results obtained in the titled glasses are discussed systematically and compared with other $\mathrm{Ho}^{3+}$ -doped systems to assess the possibility for visible and infrared device applications.     

One-step hydrothermal synthesis of nitrogen and tungsten codoped TiO2 nanorods with high visible light photocatalytic activity

N,W codoped TiO 2 $\mathrm{TiO}_{2}$ nanorods were synthesized via a one-step hydrothermal method using ammonium metatungstate as the nitrogen and tungstate sources. The prepared samples were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), UV–visible diffuse reflectance spectroscopy (DRS), and X-ray photoelectron spectroscopy (XPS). The results indicated that the N,W codoped TiO 2 $\mathrm{TiO}_{2}$ nanorods exhibited a higher photocatalytic activity under visible light irradiation compared with P25 and undoped TiO 2 $\mathrm{TiO}_{2}$ , because the codoping of N and W ions not only extended the visible light absorption but also promoted the separation of the photogenerated electrons and holes.     

Global Existence for the Critical Dissipative Surface Quasi-Geostrophic Equation

In this article, we study the critical dissipative surface quasi-geostrophic equation (SQG) in ${\mathbb{R}^2}$ R 2 . Motivated by the study of the homogeneous statistical solutions of this equation, we show that for any large initial data θ ₀ liying in the space ${\Lambda^{s} (\dot{H}^{s}_{uloc}(\mathbb{R}^2)) \cap L^\infty(\mathbb{R}^2)}$ Λ s ( H ˙ u l o c s ( R 2 ) ) ∩ L ∞ ( R 2 ) the critical (SQG) has a global weak solution in time for 1/2 <  s <  1. Our proof is based on an energy inequality verified by the equation ${(SQG)_{R,\epsilon}}$ ( S Q G ) R , ? which is nothing but the (SQG) equation with truncated and regularized initial data. By classical compactness arguments, we show that we are able to pass to the limit ( ${R \rightarrow \infty}$ R → ∞ , ${\epsilon \rightarrow 0}$ ? → 0 ) in ${(SQG)_{R,\epsilon}}$ ( S Q G ) R , ? and that the limit solution has the desired regularity.     

Quinazoline-2,4(1H,3H)-diones inhibit the growth of multiple human tumor cell lines

Quinazoline-2,4( $1H,3H$ )-diones exhibit a wealth of biological activities including antitumor proliferation. We established an improved method for the synthesis of quinazoline-2,4( $1H,3H$ )-dione derivatives with three points of molecular diversity. Data indicate that compounds 60 (average $\text{ logGI}_{50} \!=\! -6.1$ ), 65 (average $\text{ logGI}_{50} \!=\! -6.13$ ), 69 (average $\text{ logGI}_{50} \!=\! -6.44$ ), 72 (average $\text{ logGI}_{50} \!=\! -6.39$ ), and 86 (average $\text{ logGI}_{50} = -6.45$ ) significantly inhibited the in vitro growth of 60 human tumor cell lines tested. Structure–activity relationship analyses indicate that chlorophenethylureido is the necessary substituent at the $\text{ D}_{3}$ diversity point (7-position of quinazoline-2,4( $1H,3H$ )-dione), in particular, $o$ -chlorophenethylurea (69) achieved optimal activity. $o$ - or $m$ -Chlorophenethyl substitutions (69 and 72) at the $\text{ D}_{2}$ diversity point (3-position of quinazo line-2,4( $1H,3H$ )-dione) gave the most potent compounds. Methoxyl and 4-methylpiperazin-1-yl substitution at the $\text{ D}_{1}$ diversity point (6-position of quinazoline-2,4( $1H,3H$ )-dione skeleton) may yield better activity than other groups. The quinazoline-2,4( $1H,3H$ )-dione scaffold can be effectively replaced by 2 $H$ -benzo[b][1,4]thiazin-3(4 $H$ )-one.     

Quantum Marginal Inequalities and the Conjectured Entropic Inequalities

A conjecture – the modified super-additivity inequality of relative entropy – was proposed in Zhang et al. (Phys. Lett. A 377:1794–1796, 2013): There exist three unitary operators \(U_{A}\in \mathrm {U}(\mathcal {H}_{A}), U_{B}\in \mathrm {U}(\mathcal {H}_{B})\) , and \(U_{AB}\in \mathrm {U}(\mathcal {H}_{A}\otimes \mathcal {H}_{B})\) such that $$\mathrm{S}\left(U_{AB}\rho_{AB}U^{\dagger}_{AB}||\sigma_{AB}\right)\geqslant \mathrm{S}\left(U_{A}\rho_{A}U^{\dagger}_{A}||\sigma_{A}\right) + \mathrm{S}\left(U_{B}\rho_{B}U^{\dagger}_{B}||\sigma_{B}\right), $$ where the reference state σ is required to be full-ranked. A numerical study on the conjectured inequality is conducted in this note. The results obtained indicate that the modified super-additivity inequality of relative entropy seems to hold for all qubit pairs.     

Effect of Y3+ substitution on the structural,dielectric, and electrical properties of nanosized ZnAl 2 O 4 spinel

In the present work, we have studied the structural, dielectric, and electrical properties of a series of nanosized $\mathrm{ZnAl}_{2-2x}\mathrm{Y}_{2x}\mathrm{O}_{4}$ ( $x = 0.00$ , 0.01, 0.02, 0.03, 0.04, 0.05, 0.07, and 0.10) system prepared by chemical coprecipitation method. Powder X-ray diffraction (XRD) was carried out to study the influence of $\mathrm{Y}^{3+}$ substitution on the crystal structure of these samples. High Resolution Transmission Electron Microscopy (HRTEM) images reveal the nanocrystalline nature of the samples. The Fourier Transform Infrared (FTIR) spectra confirmed the preference of $\mathrm{Y}^{3+}$ ions at the octahedral B site. The variation of dielectric constant and loss tangent (1 kHz to 1 MHz) at room temperature for all the samples show the normal behavior of spinel compounds. AC conductivity study reveals that the conduction is due to small polaron hopping. The electrical modulus analysis shows that nanocrystalline $\mathrm{ZnAl}_{2-2x}\mathrm{Y}_{2x}\mathrm{O}_{4}$ system exhibits non-Debye-type relaxation. The DC electrical resistivity measured in the temperature range 303–373 K was found to increase with temperature and yttrium content.     

Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law

In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the following steady problem: $$v \cdot \nabla _{x}F =\frac{1}{{\rm K}_{\rm n}}Q(F,F),\qquad (x,v)\in \Omega \times \mathbf{R}^{3}, \quad \quad (0.1) $$ v · ? x F = 1 K n Q ( F , F ) , ( x , v ) ∈ Ω × R 3 , ( 0.1 ) $$F(x,v)|_{n(x)\cdot v<0} = \mu _{\theta}\int_{n(x) \cdot v^{\prime}>0}F(x,v^{\prime})(n(x)\cdot v^{\prime})dv^{\prime},\quad x \in\partial \Omega,\quad \quad (0.2) $$ F ( x , v ) | n ( x ) · v < 0 = μ θ ∫ n ( x ) · v ′ > 0 F ( x , v ′ ) ( n ( x ) · v ′ ) d v ′ , x ∈ ? Ω , ( 0.2 ) where Ω is a bounded domain in ${\mathbf{R}^{d}, 1 \leq d \leq 3}$ R d , 1 ≤ d ≤ 3 , K_n is the Knudsen number and ${\mu _{\theta}=\frac{1}{2\pi \theta ^{2}(x)} {\rm exp} [-\frac{|v|^{2}}{2\theta (x)}]}$ μ θ = 1 2 π θ 2 ( x ) exp [ - | v | 2 2 θ ( x ) ] is a Maxwellian with non-constant(non-isothermal) wall temperature θ(x). Based on new constructive coercivity estimates for both steady and dynamic cases, for ${|\theta -\theta_{0}|\leq \delta \ll 1}$ | θ - θ 0 | ≤ δ ? 1 and any fixed value of K_n, we construct a unique non-negative solution F _s to (0.1) and (0.2), continuous away from the grazing set and exponentially asymptotically stable. This solution is a genuine non-equilibrium stationary solution differing from a local equilibrium Maxwellian. As an application of our results we establish the expansion ${F_s=\mu_{\theta_0}+\delta F_{1}+O(\delta ^{2})}$ F s = μ θ 0 + δ F 1 + O ( δ 2 ) and we prove that, if the Fourier law holds, the temperature contribution associated to F ₁ must be linear, in the slab geometry.     

Structural, morphological and optical properties of \hbox {In}_{2}\hbox {S}_{3} thin films obtained by SILAR method

$\hbox {In}_{2}\hbox {S}_{3}$ thin films have been elaborated onto glass substrate by SILAR method at room temperature using different immersion time in the solution of cation and anion and fixing the rinsing time. The film composition, morphology and structure were investigated using energy dispersive X-ray analysis (EDAX), scanning electron microscopy (SEM) and X-ray diffraction techniques. Optical properties, such transmission and band gap have been also analyzed. The effects of annealing on the morphological structure thin films are also described. The x-rays diffraction spectra indicated that the formed compounds are $\upbeta $ - $\hbox {In}_{2}\hbox {S}_{3}$ polycrystalline thin films with $\hbox {In}_{6}\hbox {S}_{7 }$ as second phase in sample S1 and sample S2 and no another phase in sample 3. SEM revealed homogeneous and relatively uniform films and EDAX shows sample 3 with S/In=1.44. For sample 1 and sample 2, we noted an increase of band gap when rinsing time increases.