Preparation of nano-sized Al2O3–2SiO2 powder by sol–gel plus azeotropic distillation method

Nano-sized amorphous Al₂O₃–2SiO₂ powder was prepared by a sol–gel method coupled with azeotropic distillation. The structure of the powder was investigated by DTS, BET, TEM, FT-IR, TG-DTA and XRD, showing that n-butanol azeotropic distillation could effectively remove water from the aluminosilicate gels and prevent the formation of hard agglomerates in the drying process. The average particle diameter of the powder was about 70 nm. The largest BET specific surface area of the powder was 669 m²/g. To examine the alkali-activation reactivity of the powder, alkali-activation tests were performed with the powder reacting with sodium silicate solution. The synthetic powder was found to be highly reactive.     

Preparation of ternary Cr2O3–SiC–TiO2 composites for the photocatalytic production of hydrogen

Novel ternary Cr₂O₃–SiC–TiO₂ composites were synthesized by implanting Cr³⁺ into SiC–TiO₂ via sol–gel and impregnation approaches. The results from X-ray diffraction, scanning electron microscopy and transmission electron microscopy show that the Cr³⁺ species were doped onto the surface of the SiC–TiO₂ carrier. The diffuse reflectance ultraviolet–visible absorption spectra revealed that the absorption edges of the ternary Cr₂O₃–SiC–TiO₂ composites were gradually shifted red with increasing chromium content. The luminescence intensities of the composites decreased with increasing doped Cr³⁺ content due to the reduction in the number of recombination sites of electron–hole pairs. The ternary Cr₂O₃–SiC–TiO₂ composites showed high hydrogen-producing activities, which probably results from the formation of donor levels of the Cr³⁺ species in the forbidden band of the SiC semiconductor.     

Group Properties of 2–Submodels for the Evolutionary Class of Gas–Dynamic Equations

Invariant 2–submodels (submodels with two independent variables) of the evolutionary class are considered for the equations of gas dynamics with an equation of state of general form. Group analysis of these submodels is performed. Allowable operators and transformations of equivalence are indicated, and group classification is performed.     

Validation of a 2-D semi-coupled numerical model for fluid–structure–seabed interaction

A 2-D semi-coupled model PORO-WSSI 2D (also be referred as FSSI-CAS 2D) for the Fluid-Structure-Seabed Interaction (FSSI) has been developed by employing RANS equations for wave motion in fluid domain, VARANS equations for porous flow in porous structures; and taking the dynamic Biot's equations (known as "u − p" approximation) for soil as the governing equations. The finite difference two-step projection method and the forward time difference method are adopted to solve the RANS, VARANS equations; and the finite element method is adopted to solve the "u − p" approximation. A data exchange port is developed to couple the RANS, VARANS equations and the dynamic Biot's equations together. The analytical solution proposed by Hsu and Jeng (1994) and some experiments conducted in wave flume or geotechnical centrifuge in which various waves involved are used to validate the developed semi-coupled numerical model. The sandy bed involved in these experiments is poro-elastic or poro-elastoplastic. The inclusion of the interaction between fluid, marine structures and poro-elastoplastic seabed foundation is a special point and highlight in this paper, which is essentially different with other previous coupled models The excellent agreement between the numerical results and the experiment data indicates that the developed coupled model is highly reliablefor the FSSI problem.     

Local Dissipativity in L2 for the Kuramoto–Sivashinsky Equation in Spatial Dimension 2

We show the local dissipativity of the Kuramoto–Sivashinsky equation with periodic boundary conditions in a rectangular thin enough domain. More precisely, we give a sufficient condition on the width L ₂ of the domain, depending on the length L ₁, so that there exists a bounded local attracting set in _per ² which will be estimated, as well as its basin of attraction. We thus improve, and make more transparent, a result due to Sell and Taboada [14]. Finally, in the second part, we test our approach to another model to which it also applies.     

Periodic Klein–Gordon Chains with Three Particles in 1:2:2 Resonance

Journal of Dynamics and Differential Equations - In this paper, we deal with the three degrees of freedom Hamiltonian systems describing the Klein–Gordon chains with three particles of equal...     

Preparation of calcium sulfate whiskers from FGD gypsum via hydrothermal crystallization in the H2SO4–NaCl–H2O system

Little attention has thus far been paid to the potential effect of solution composition on the hydrothermal crystallization of calcium sulfate whiskers prepared from flue-gas desulfurization (FGD) gypsum. When purified FGD gypsum was used as raw material, the morphology and phase structure of the hydrothermal products grown in pure water, H₂SO₄–H₂O, NaCl–H₂O, and H₂SO₄–NaCl–H₂O solutions as well as the solubility of purified FGD gypsum in these solutions were investigated. The results indicate that calcium sulfate whiskers grow favorably in the H₂SO₄–NaCl–H₂O system. When prepared using 10–70 g NaCl/kg gypsum −0.01 M H₂SO₄–H₂O at 130 °C for 60 min, the obtained calcium sulfate whiskers had diameters ranging from 3 to 5 μm and lengths from 200 to 600 μm, and their phase structure was calcium sulfate hemihydrate (HH). Opposing effects of sulfuric acid and sodium chloride on the solubility of the purified FGD gypsum were observed. With the co-presence of sulfuric acid and sodium chloride in the reaction solution, the concentrations of Ca²⁺ and SO₄²⁻ can be kept relatively stable, which implies that the crystallization of the hydrothermal products can be controlled by changing the concentrations of sulfuric acid and sodium chloride.     

Weierstrass elliptic function solutions and their degenerate solutions of (2+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Nonlinear Dynamics - Weierstrass elliptic function solutions are investigated by applying the traveling wave transformation and auxiliary equations to a (2+1)-dimensional potential...     

Characteristics of the solitary waves and lump waves with interaction phenomena in a (2 + 1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation

In this paper, we consider a (\(2+1\))-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada (gCDGKS) equation, which is a higher-order generalization of the celebrated Kadomtsev–Petviashvili (KP) equation. By considering the Hirota bilinear form of the CDGKS equation, we study a type of exact interaction waves by the way of vector notations. The interaction solutions, which possess extensive applications in the nonlinear system, are composed by lump wave parts and soliton wave parts, respectively. Under certain conditions, this kind of solutions can be transformed into the pure lump waves or the stripe solitons. Moreover, we provide the graphical analysis of such solutions in order to better understand their dynamical behavior.     

Measure Valued Solutions of the 2D Keller–Segel System

We develop a theory of global measure-valued solutions for the classical Keller–Segel model. These solutions are obtained considering the limit of solutions of a regularized problem. We also prove that different regularizations yield different limit measures in the case in which classical solutions of the Keller–Segel system are not globally defined in time.     

Abundant fission and fusion solutions in the ( $$2+1$$ 2 + 1 )-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation

Nonlinear Dynamics - Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the ( $$2+1$$...     

2:1 and 1:1 frequency-locking in fast excited van der Pol–Mathieu–Duffing oscillator

The frequency-locking area of 2:1 and 1:1 resonances in a fast harmonically excited van der Pol–Mathieu–Duffing oscillator is studied. An averaging technique over the fast excitation is used to derive an equation governing the slow dynamic of the oscillator. A perturbation technique is then performed on the slow dynamic near the 2:1 and 1:1 resonances, respectively, to obtain reduced autonomous slow flow equations governing the modulation of amplitude and phase of the corresponding slow dynamics. These equations are used to determine the steady state responses, bifurcations and frequency-response curves. Analysis of quasi-periodic vibrations is carried out by performing multiple scales expansion for each of the dependent variables of the slow flows. Results show that in the vicinity of both considered resonances, fast harmonic excitation can change the nonlinear characteristic spring behavior from softening to hardening and causes the entrainment regions to shift. It was also shown that entrained vibrations with moderate amplitude can be obtained in a small region near the 1:1 resonance. Numerical simulations are performed to confirm the analytical results.     

2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term

We study the long time behavior of the solution X(t, s, x) of a 2D-Navier–Stokes equation subjected to a periodic time dependent forcing term. We prove in particular that as , approaches a periodic orbit independently of s and x for any continuous and bounded real function .      

Experimental investigations on a 1–2 heat exchanger with wire-wound tubes

This paper deals with experimental investigations on a 1–2 shell and tube heat exchanger, to study the effect of spiral turbulators on its performance. The heat exchanger has its tubes wound with copper wire, so that the winding acts as an augmenting device. Experiments were conducted with various winding wire diameters and pitches and the heat transfer coefficients were evaluated for a wide range of temperature levels and flow rates of the shell side fluid. The experimental results are discussed in detail and correlations are proposed to predict the shell side Nusselt number of the exchanger with varying winding pitches and diameters. The existence of optimum winding is also discussed in this paper. The present results are based on over 250 experimental observations made in the laminar range of flow.

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Experimentelle Untersuchungen an einem 1–2-Wärmetauscher mit drahtumwickelten Rohren

Zusammenfassung Diese Arbeit befaßt sich mit experimentellen Untersuchungen an einem 1–2-Zylindermantel/Rohrwärmetauscher und hat die Klärung des Einflusses von spiralförmigen Turbulenzpromotoren auf das Übertragungsverhalten zum Ziel. Die Rohre des Wärmetauschers sind mit Kupferdraht umwickelt, dessen Windungslagen den Austausch befördern. Die Experimente wurden mit verschiedenen Drahtdurchmessern und Steigungen durchgefürht und hieraus Wärmeübergangskoeffizienten in einem weiten Bereich der Temperaturniveaus und der Mengenströme des die Rohre umströmenden Fluids bestimmt. Die experimentellen Befunde werden eingehend diskutiert und Korrelationen zur Bestimmung der Nusselt-Zahl auf der Rohraußenseite in Abhängigkeit von Steigung und Durchmesser der Drahtwindungen angegeben. Die Ergebnisse basieren auf mehr als 250 Messungen im Bereich der Laminarströmung und belegen die Existenz einer optimalen Windungskonfiguration.

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Nomenclature A _o heat transfer surface area outside the tube, m² - A _i heat transfer surface area inside the tube, m² - d _o outer diameter of the tube, m - D inner diameter of the shell, m - D _e equivalent diameter of shell for heat transfer, m - d _w diameter of the winding wire, m - F _T LMTD correction factor [8] - h _i inside heat transfer coefficient, W/m² K - h _o outside heat transfer coefficient, W/m² K - k _o thermal conductivity of water outside tube, W/mK - L length of the shell, m - l _t tube length, m - l _w length of the winding wire, m - LMTD logarithmic mean temperature difference, K - m mass flow rate of cold fluid, kg/h - N number of tube passes - Nu _i inside Nusselt number for the tube - Nu _o outside Nusselt number for the tube - Nu _o * outside Nusselt number, average over the temperature range - n _t number of tubes per pass - P pitch of the winding wire, m - Pr _t Prandtl number, tube side - Q heat transfer rate, W - Re _t tube side Reynolds number - Re _s shell side Reynolds number for heat transfer - T corrected mean temperature difference, K [8] - Th _i inlet temperature of hot water, °C - Th _o exit temperature of hot water, °C - Ti _i inlet temperature of cold water, °C - Tc _o exit temperature of cold water, °C - U _o overall heat transfer coefficient, W/m² K     

The Damped-Driven 2D Navier–Stokes System on Large Elongated Domains

The Navier–Stokes system with damping, which is motivated by Stommel–Charney model of ocean circulation, is considered in a large elongated periodic rectangular domain with area of the order α⁻¹, as α → 0. We obtain estimates for the dimension of the global attractor that are sharp as both α → 0 and ν → 0, where ν is the viscosity coefficient. This work was supported in part by the US Civilian Research and Development Foundation, grant no. RUM1-2654-MO-05 (A.A.I. and E.S.T.). The work of A.A.I. was supported in part by the Russian Foundation for Fundamental Research, grants no. 06-001-0096 and no. 05-01-429, and by the RAS Programme no. 1 ‘Modern problems of theoretical mathematics’. The work of E.S.T. was supported in part by the NSF, grant no. DMS-0204794, the MAOF Fellowship of the Israeli Council of Higher Education, and by the BSF, grant no. 200423.     

Vlasov–Maxwell–Boltzmann Diffusive Limit

Inspired by the work (Bastea et al. in J Stat Phys 1011087–1136, 2000) for binary fluids, we study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov–Maxwell–Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of dissipative new macroscopic PDEs, the incompressible Vlasov–Navier–Stokes–Fourier system and its higher order corrections for describing a charged fluid, where the self-consistent electromagnetic field is present. The uniform estimate on the remainders is established via a unified nonlinear energy method and it guarantees the global in time validity of such an expansion up to any order.     

Yielding and intrinsic plasticity of Ti–Zr–Ni–Cu–Be bulk metallic glass

Bulk metallic glass with composition Ti₄₀Zr₂₅Ni₈Cu₉Be₁₈ exhibits considerably high compressive yield stress, significant plasticity (with a concomitant vein-like fracture morphology) and relatively low density. Yielding and intrinsic plasticity of this alloy are discussed in terms of its thermal and elastic properties. An influence of normal stresses acting on the shear plane is evidenced by: (i) the fracture angle (<45°) and (ii) finite-element simulations of nanoindentation curves, which require the use of a specific yield criterion, sensitive to local normal stresses acting on the shear plane, to properly match the experimental data. The ratio between hardness and compressive yield strength (constraint factor) is analyzed in terms of several models and is best adjusted using a modified expanding cavity model incorporating a pressure-sensitivity index defined by the Drucker–Prager yield criterion. Furthermore, comparative results from compression tests and nanoindentation reveal that deformation also causes strain softening, a phenomenon which is accompanied with the occurrence of serrated plastic flow and results in a so-called indentation size effect (ISE). A new approach to model the ISE of this metallic glass using the free volume concept is presented.     

Double Obstacle Problems with Obstacles Given by Non-C 2 Hamilton–Jacobi Equations

We prove optimal regularity for double obstacle problems when obstacles are given by solutions to Hamilton–Jacobi equations that are not C ². When the Hamilton–Jacobi equation is not C ² then the standard Bernstein technique fails and we lose the usual semi-concavity estimates. Using a non-homogeneous scaling (different speeds in different directions) we develop a new pointwise regularity theory for Hamilton–Jacobi equations at points where the solution touches the obstacle. A consequence of our result is that C ¹-solutions to the Hamilton–Jacobi equation $$\pm |\nabla h-a(x)|^2=\pm 1\,{\rm in}\,B_1,\quad h=f \,{\rm on}\, \partial B_1$$ , are, in fact, C ^1,α/2, provided that ${a \in C^\alpha}$ . This result is optimal and, to the authors’ best knowledge, new.     

A Feature-Based Stochastic Permeability of Shale: Part 2–Predicting Field-Scale Permeability

Transport in Porous Media - In a recent numerical study, it was demonstrated that characterizing reservoir permeability in terms of rock’s quality, as observed in lab and field, is the most...     

Existence,Uniqueness and Lipschitz Dependence for Patlak–Keller–Segel and Navier–Stokes in {\mathbb{R}^2} with Measure-Valued Initial Data

We establish a new local well-posedness result in the space of finite Borel measures for mild solutions of the parabolic–elliptic Patlak–Keller–Segel (PKS) model of chemotactic aggregation in two dimensions. Our result only requires that the initial measure satisfy the necessary assumption \({\max_{x \in \mathbb{R}^2} \mu (\{x\}) < 8 \pi}\) . This work improves the small-data results of Biler (Stud Math 114(2):181–192, 1995) and the existence results of Senba and Suzuki (J Funct Anal 191:17–51, 2002). Our work is based on that of Gallagher and Gallay (Math Ann 332:287–327, 2005), who prove the uniqueness and log-Lipschitz continuity of the solution map for the 2D Navier–Stokes equations (NSE) with measure-valued initial vorticity. We refine their techniques and present an alternative version of their proof which yields existence, uniqueness and Lipschitz continuity of the solution maps of both PKS and NSE. Many steps are more difficult for PKS than for NSE, particularly on the level of the linear estimates related to the self-similar spreading solutions.