Hydrophobic Texture Screening of Laser Ablated Silicon Carbide Surface and Its Influencing Factors Analysis and Optimization

Four types of micro textures (grid, strip, square, and circle) are engraved on SiC surface by nanosecond laser and the texture with the best hydrophobicity is screened. Influence of processing parameters on the hydrophobicity is obtained by orthogonal experiment, which led to the determination of the optimal parameter combination. Relationship between the contact angle and the structural parameters of the micro texture is further investigated. Results show that the strip texture has the best hydrophobic performance and the contact angle increases with time until it reaches a stabilization (≈124.4°) after 192 h. The optimal combination of processing parameters is determined as follows: line spacing C = 275 μm, scanning velocity V = 1100 mm s⁻¹, power W = 15%, frequency f = 35 kHz, and number N = 100. The contact angle is closely related to bulge width c₁, groove width c₂, and groove depth h_g of the micro texture, and a larger contact angle generally corresponds to a smaller c₂ and a lager h_g. The droplets on the strip-texture surface are in Wenzel–Cassie or Wenzel state, which presents hydrophobic and diversion characteristics under the action of micro-nano composite structure and the anisotropy of micro texture.     

Transport Properties of a Tl-2201 Film Close to the Critical Temperature: The Vortex Glass Transition

We have studied the I-V characteristics of a Tl-2201 film at zero field. In the regime in which flux creep is the dominant dissipation mechanism, the J _c -T curve is divided into two parts at a temperature T _g (about 82 K), close to the critical temperature (84 K). The I-V characteristics around T _g are well described using a flux creep model. For T>T _g , J _c /J _c (0) =0.445x(l-0.525t-0.5t ² ); for T _g , J _c /J _c (0) = 0.9x(1-0.595t-0.44t ² ). Differential resistance (dV/dI) as a function of the measuring current shows a change in curvature close to T _g . The I-V curves collapsed nicely into two branches by plotting (V/I)/|T–T _g | ^v(z-1) vs. (I/T)/|T _g –T| ^2v , indicating a current–reduced vortex glass transition.     

On the solution of an ill-posed design solidification problem using minimization techniques in finite- and infinite-dimensional function spaces

This paper provides a comparative study of two alternative methodologies for the solution of an inverse design solidification problem. It is the one-dimensional solidification problem of calculating the boundary heat flux history that achieves a desired freezing front velocity and desired heat fluxes at the freezing front. The front velocity h(t) and flux history q_mS(t) on the solid side of the front control the obtained cast structure. As such, the potential applications of the proposed methods to the control of casting processes are enormous. The first technique utilizes a finite-dimensional approximation of the unknown boundary heat flux function q₀(t). The second technique uses the adjoint method to calculate in L₂ the derivative of the cost functional, ‖T_m – T(h(t), t;q₀)‖, that expresses the square error between the calculated T(h(t), t; q₀) and the given freezing front temperature T_m. Both steepest descent (SDM) and conjugate gradient methods (CGM) are examined. A front tracking FEM technique is used for the discretization of the state space. A detailed numerical analysis of the space and time discretization of the ‘parameter’ and state spaces, of the effect of the end condition of the adjoint problem and of other parameters in the solution are examined.     

Tables of the Inverse Laplace Transform of the Function [... formula ...]

The inverse transform, g(t) = ?^?1(e^?sβ), 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g(t). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g(t) for a number of values of β between 0.25 and 0.999. In addition, since g(t), regarded as a function of β, is uni-modal with a peak occurring at t = t_max we both tabulate and graph t_max and 1/g(t_max) as a function of β, as well as giving polynomial approximations to 1/g(t_max).     

An algorithm for spectral factorization using random search techniques

An approximation method for the energy spectrum of a stationary stochastic dynamical system is presented, which allows approximate functional rational factorization.This paper is in three parts. The first deals with a theoretical problem of approximation in Hardy Spaces, whose main result is the following:Let S⁽ⁱⁿ⁾, S be positive functions belonging to L¹(R_gw), such that log S⁽ⁿ⁾ and log S belong to L¹(R_ω, dω/1 + ω²).Let h⁽ⁿ⁾, h be the outer functions of the Hardy Space H²(Π₊) such that S^(g) = |h⁽ⁿ⁾|² and S = |h|² on iR.If S⁽ⁿ⁾ n^→∝ S in L¹(R_ω), and log S⁽ⁿ⁾ n^→∝ log S in L¹(R_ω, dω/1 + ω²), then: h⁽ⁿ⁾ n^→∝ h in H²(Π₊).The second part describes an effective algorithm, using random search methods, and gives an almost sure convergence result for it.The third part treats numerically two examples, permitting comparison of this algorithm with others (whenever there are…): the first example is a problem of approximation for a nonrational process (turbulence) that was considered in Ref. 22: the second example is a problem of model reduction (automatic) considered in Ref. 4.     

Synthesis and photoluminescence properties of Yb doped Ba5(PO4)3Cl phosphor for white light-emitting diodes

Yb²⁺ ion doped Ba₅(PO₄)₃Cl phosphor was synthesized by solid state reaction. Four distinct absorption bands were observed in the Ultraviolet (UV) light region due to the electronic transitions of Yb²⁺ ion from ¹S₀ ground state to ²F_5/2(t_2g), ²F_5/2(e_g), ²F_7/2(t_2g), and ²F_7/2(e_g) excited states. The main emission wavelength of the phosphor was around 630 nm. The optimized Yb²⁺ ion concentration was 0.2 mol% (λ_exc. = 400 nm). The calculated critical distance was about 8.729 Å and the concentration quenching was observed above 0.2 mol% due to the electric dipole–dipole interaction.     

Multilayer Co/Pd films with nanocrystalline and amorphous Co layers: Coercive force, random anisotropy, and exchange coupling of grains

The values of saturation magnetization M _s, exchange coupling constant A, local magnetic anisotropy field H _a, random anisotropy correlation radius R _c, and coercive force H _c were independently measured for multilayer Co/Pd films with nanocrystalline and amorphous Co layers. It is shown that variation of the coercive force H _c(t _Co) as a function of the cobalt layer thickness t _Co is related to changes in characteristics of the magnetic microstructure. The main factor determining changes in the ferromagnetic correlation radius R _f and the average anisotropy 〈K〉 of a magnetic block in multilayer Co/Pd films is variation of exchange coupling constant A(t ^Co).     

Numerical Solution of Inverse Radiative–Conductive Transient Heat Transfer Problem in a Grey Participating Medium

The problem of simultaneous identification of the thermal conductivity Λ(T) and the asymmetry parameter g of the Henyey–Greenstein scattering phase function is under consideration. A one-dimensional configuration in a grey participating medium with respect to silica fibers for which the thermophysical and optical properties are known from the literature is accepted. To find the unknown parameters, it is assumed that the thermal conductivity Λ(T) may be represented in a base of functions {1, T, T ², . . .,T ^K } so the inverse problem can be applied to determine a set of coefficients {Λ₀, Λ₁, . . ., Λ _K ; g}. The solution of the inverse problem is based on minimization of the ordinary squared differences between the measured and model temperatures. The measured temperatures are considered known. Temperature responses measured or theoretically generated at several different distances from the heat source along an x axis of the specimen set are known as a result of the numerical solution of the transient coupled heat transfer in a grey participating medium. An implicit finite volume method (FVM) is used for handling the energy equation, while a finite difference method (FDM) is applied to find the sensitivity coefficients with respect to the unknown set of coefficients. There are free parameters in a model, so these parameters are changed during an iteration process used by the fitting procedure. The Levenberg– Marquardt fitting procedure is iteratively searching for best fit of these parameters. The source term in the governing conservation-of-energy equation taking into account absorption, emission, and scattering of radiation is calculated by means of a discrete ordinate method together with an FDM while the scattering phase function approximated by the Henyey–Greenstein function is expanded in a series of Legendre polynomials with coefficients {c _l } = (2l + 1)g ^l . The numerical procedure proposed here also allows consideration of some cases of coupled heat transfer in non-grey participating media. The inverse method may be treated, after performing a suitable validation, as an alternative method in relation to other classical measurement methods for investigation of thermophysical parameters of solid states.     

Magnetic Properties and Phase Transitions in a Diluted Ferromagnet: Ising,XY, and Heisenberg Models

The magnetic properties and phase transition of a ferromagnetic spin-S disordered diluted thin film with a face-centred cubic lattice are investigated using the high-temperature series expansion technique extrapolated with Padé approximant method for Heisenberg, XY and Ising models. The reduced critical temperature of the system t_c=\frack_BT_c2S(S+1)J_b\tau_{\mathrm{c}}=\frac{k_{\mathrm{B}}T_{\mathrm{c}}}{2S(S+1)J_{\mathrm{b}}} is studied as the function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J _b,J _s and J _⊥, respectively. It is found that τ _c increases with the exchange interactions of surface. The magnetic phase diagrams (τ _c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T _c(L) from the bulk value (\fracT_c(￥)T_c(L)-1)(\frac{T_{\mathrm{c}}(\infty )}{T_{\mathrm{c}}(L)}-1) can be described by a power law L ^−λ , where λ is the inverse of the correlation length exponent.     

Accelerated Life Testing for a Class of Linear Hazard Rate Type Distributions

Accelerated life testing for distributions with hazard rate functions of the form r(t) = Ag(t) + Bh(t) are considered. Let V ₁, …, V _k be stress levels larger than V ₀—the stress level under normal conditions [V ₀ > 0]—and let a(v) be a nondecreasing function on (0, ∞). We discuss a generalization of the common accelerated models (the power rule model and the Arrhenius model) by assuming that the hazard rate under the stress level V, is of the form (a(V _t )) ^P (Ag(t) + Bh(t)). The maximum likelihood estimators of A, B and P for complete and censored samples are studied. The estimation procedure reduces to a solution of one equation with one unknown parameter. The estimation procedure under the assumption of aging is also described. The asymptotic variance-covariance matrix is given.     

Sound Velocity Measurements in the Low and the High Field Phases of the Nuclear-Ordered bcc Solid 3He in Magnetic Fields

We have measured the temperature and magnetic-field dependences of the sound velocity for one longitudinal and two transverse waves in the low field phase (LFP) and the high field phase (HFP) of nuclear spin ordered bcc solid ³He crystals with a single magnetic domain along the melting curve. From sound velocity measurements for various crystal orientations as a function of the sound propagation direction, we determined the elastic stiffness constants, c _ij (T,B). In the LFP with tetragonal symmetry for the nuclear spin structure, we extracted six nuclear spin elastic stiffness constants Δc _ij ^ℓ (T,0.06 T) from the temperature dependence of the sound velocity at 0.06 T and Δc _ij ^ℓ (0.5 mK,B) from the magnetic-field dependence of sound velocity at 0.5 mK. In the HFP with cubic symmetry for the nuclear spin structure, we extracted three Δc _ij ^h (T,0.50 T) at 0.50 T and Δc _ij ^h (0.5 mK,B) at 0.5 mK. At the first-order magnetic phase transition from the LFP to the HFP at the lower critical field B _c1, large jumps in sound velocities were observed for various crystal directions and we extracted three . Using the thermodynamic relation between Δc _ij and the change in the internal energy for the exchange interaction in this system, ΔU _ex(T,B), Δc _ij are related to the generalized second-order Grüneisen constants Γ _ij ^X ≡∂ ²ln X/∂ ε _i ∂ ε _j as Δc _ij (T,B)=Γ _ij ^X ΔU _ex(T,B), where X represents some physical quantity which depends on the molar volume and ε _j is the j-th component of a strain tensor. In the LFP, the Δc _ij ^ℓ (T,0.06 T) were proportional to T ⁴, and Δc _ij ^ℓ (0.5 mK,B) were proportional to B ². We extracted for the spin wave velocity in the LFP, s ^ℓ , from Δc _ij ^ℓ (T,0.06 T) and for the inverse susceptibility, 1/χ ^ℓ from Δc _ij ^ℓ (0.5 mK,B). In the HFP, Δc _ij ^h (T,0.50 T) were proportional to T ⁴ and Δc _ij ^h (0.5 mK,ΔB) were proportional to ΔB(≡B−B _c1). We obtained for the spin wave velocity in the HFP, s ^h , from Δc _ij ^h (T,0.50 T) and for B _c1 from Δc _ij ^h (0.5 mK,ΔB). The values obtained for and were compared with the Multiple Spin Exchange model (MSE) with three parameters by using analytic expressions for s ^ℓ and χ ^ℓ . The three-parameter MSE does not agree with the observed Δc _ij in the LFP.      

Bayes estimation of the general hazard rate model

In reliability theory and life testing models, the life time distributions are often specified by choosing a relevant hazard rate function. Here a general hazard rate function h(t)=a+bt^c−1, where c, a, b are constants greater than zero, is considered. The parameter c is assumed to be known. The Bayes estimators of (a,b) based on the data of type II/item-censored testing without replacement are obtained. A large simulation study using Monte Carlo Method is done to compare the performance of Bayes with regression estimators of (a,b). The criterion for comparison is made based on the Bayes risk associated with the respective estimator. Also, the influence of the number of failed items on the accuracy of the estimators (Bayes and regression) is investigated. Estimations for the parameters (a,b) of the linearly increasing hazard rate model h(t)=a+bt, where a, b are greater than zero, can be obtained as the special case, letting c=2.     

Upper critical field of aD-wave superconductor stabilized by antiferromagnetic fluctuations

We have derived microscopic equations for the upper critical magnetic field of aD-wave superconductor stabilized by antiferromagnetic spin fluctuations. We present numerical results for the reduced fieldh _c2(t) as a function of reduced temperaturet when the magnetic field is along thez axis and also zero-order results when it is along thex ory axis. Two differentD-wave models are considered. The angular dependence ofH _c2 forT nearT _c is given as a function of polar angleϑ in thez−x orz−y plane.     

Hot hardness of (Fe,Cr)3C and (Fe,Cr)7C3 carbides

Hot hardness was measured on the primary carbides, (Fe, Cr)₃C and (Fe, Cr)₇C₃, in unidirectionally solidified iron-carbon-chromium hypereutectic alloys with chromium more than 4.8 wt %. The hardness-temperature relation was represented by two Ito-Shishokin formulae,H _v =A(— BT), and thus was drawn by two lines on a semilogarithmic graph. The inflection temperature where the two lines intersected was found at 730 to 860 K for (Fe, Cr)₃C carbide containing 0 to 14 wt % Cr, increasing with an increase in the chromium concentration in the carbide, and at about 910 K for (Fe, Cr)₇C₃ carbide containing 36 to 76 wt % Cr. With increasing chromium concentration in each carbide, the hardness of the carbide increased and the thermal softening coefficients decreased. The effect of chromium on the hardness, the inflection temperature and the thermal softening coefficients was more pronounced for (Fe, Cr)₃C carbide than for (Fe, Cr)₇C₃ carbide. Each of the thermal softening coefficients,B ₁(T<T _t),B ₂(T>T _t), the inflection temperature,T _t, room-temperature hardness,H _v(T _RT), and the hardness atT _t,H _v(T _t), related linearly to the chromium concentration in the carbides, and hence the hot hardness of the carbides could be expressed as functions of temperature and chromium concentration in the carbides. The relationships betweenH _v(T _RT) andH _v(T _t) and between the thermal softening coefficient,B ₂, and the activation energy for creep,Q _c(kJ mol^–1), were represented by the following equations:H _v(T _t)0.7H _v(T _RT),B ₂=1.26/Q _c.     

Global existence and blow-up analysis for a nonlinear diffusion equation with inner absorption and boundary flux

This article deals with a nonlinear diffusion equation with inner absorption u _t ?=?(log^σ(1?+?u)u _x ) _x ???λ(1?+?u)log ^p (1?+?u), in ?₊?×?(0,?+∞), subject to a logarithmic boundary flux ? log^σ(1?+?u)u _x (0,?t)?=?(1?+?u)log ^q (1?+?u)(0,?t), t?∈?(0,?+∞). We establish the critical global existence curve and give the asymptotic behaviour close to the blow-up time.     

Sorption of U(VI) from aqueous solutions on layered double hydroxides of Mg,Al, and Nd

Sorption of U(VI) from aqueous solutions of various compositions on layered double hydroxides (LDHs) of Mg, Al, and Nd, and also on layered double oxides (LDOs) of Mg and Al was studied. Experiments on sorption of UO₂²⁺ carbonate complexes from aqueous solution on LDO-Mg-Al showed that [UO₂(CO₃)₃]⁴⁻ ions are weakly captured by LDH-Mg-Al formed by contact of LDO-Mg-Al with water. With an increase in the uranium concentration in solution, K _d of U(VI) decreases. For 3.3 × 10⁻³ M [UO₂(CO₃)₃]⁴⁻ solutions, after 24-h contact of the solid and liquid phases, the distribution coefficients do not exceed 1.0 ml g⁻¹ at V/m = 50 ml g⁻¹. From aqueous nitrate solutions, U(VI) is sorbed on LDH-Mg-Al-NO₃ poorly: K _d of U(VI) does not exceed 1.0 ml g⁻¹ at 24-h contact of the solid and liquid phases and V/m = 50 ml g⁻¹. At the same time, U(VI) is efficiently sorbed from aqueous 10⁻³ M UO₂(NO₃)₂ solutions on LDH-Mg-Al and LDH-Mg-Nd with CO₃²⁻ and OH⁻ ions in the interlayer space. After 15-min contact of the solid and liquid phases, K _d of U(VI) exceeds 5 × 10³ ml g⁻¹. With an increase in the UO₂²⁺ concentration to 10⁻¹ M, K _d of U(VI) decreases considerably, becoming lower than 25 ml g⁻¹, but increases to ∼150 ml g⁻¹ with an increase in the contact time of the solid and liquid phases to 24 h. The effect of the Na⁺, Ca²⁺, Cl⁻, and SO₄²⁻ ions and of pH of the initial solution on the U(VI) sorption from aqueous UO₂(NO₃)₂ solutions on LDH-Mg-Al-CO₃ was examined.     

Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

Optical, electrical and magnetic properties of Co3O4 nanocrystallites obtained by thermal decomposition of sol–gel derived oxalates

Nanocrystallites of tricobalt tetraoxide (Co₃O₄) have been synthesized by sol–gel process using cobalt acetate tetrahydrate, oxalic acid as precursors and ethanol as a solvent. The process comprises of gel formation, drying at 80 °C for 24 h to obtain cobalt oxalate dihydrate (α-CoC₂O₄·2H₂O) followed by calcination at or above 400 °C for 2 h in air. These results combined with thermal analysis have been used to determine the scheme of oxide formation. The room temperature optical absorption spectra exhibits blue shift in both (i) ligand to metal (p(O²⁻) → e_g(Co³⁺), 3.12 eV), and (ii) metal to metal charge transfer transitions (a) t_2g(Co³⁺) → t₂(Co²⁺), 1.77 eV, (b) t₂(Co²⁺) → e_g(Co³⁺), 0.95 eV together with the d–d transitions (0.853 and 0.56 eV) within the Co²⁺ tetrahedra. The temperature dependent ac electrical and dielectric properties of these nanocrystals have been studied in the frequency range 100 Hz to 15 MHz. There are two regimes distinguishing different temperature dependences of the conductivity (70–100 K and 200–300 K). The ac conductivity in both the temperature regions is explained in terms of nearest neighbor hopping (NNH) mechanism of electrons. The carrier concentration measured from the capacitance (C)–voltage (V) measurements is found to be 1.05 × 10¹⁶ m⁻³. The temperature dependent dc magnetic susceptibility curves under zero field cooled (ZFC) and field cooled (FC) conditions exhibit irreversibilities whose blocking temperature (T_B) is centered at 35 K. The observed Néel temperature (T_N  25 K) is significantly lower than the bulk Co₃O₄ value (T_N = 40 K) possibly due to the associate finite size effects.     

Temperature dependence of third-sound velocity in the vicinity ofT c

We measure the temperature dependence of the velocity of third soundC ₃ in the vicinity of the critical temperatureT _c . It is found thatC ₃ ² is well fitted by the experimental formulaC ₃(T _c )²[1+1/2(–Ct)^1/2], wheret=(T–T _c )/T _c andC is a constant, equal to about 5.4. This (–t)^1/2 cusp is consistent with the theory of the Kosterlitz-Thouless (KT) transition in two dimensions. The chemical potential ₀ for the vortex pair excitation is estimated as ₀=3.03k _B T _c with the aid of the static theory of the KT transition. The consistency between the experimentally obtained value of ₀ and the KT transition theory is discussed.