Description of the thermodynamic properties and fluid-phase behavior of aqueous solutions of linear,branched, and cyclic amines

The SAFT-γ Mie group-contribution equation of state is used to represent the fluid-phase behavior of aqueous solutions of a variety of linear, branched, and cyclic amines. New group interactions are developed in order to model the mixtures of interest, including the like and unlike interactions between alkyl primary, secondary, and tertiary amine groups (NH₂, NH, N), cyclic secondary and tertiary amine groups (cNH, cN), and cyclic methine-amine groups (cCHNH, cCHN) with water (H₂O). The group-interaction parameters are estimated from appropriate experimental thermodynamic data for pure amines and selected mixtures. By taking advantage of the group-contribution nature of the method, one can describe the fluid-phase behavior of mixtures of molecules comprising those groups over broad ranges of temperature, pressure, and composition. A number of aqueous solutions of amines are studied including linear, branched aliphatic, and cyclic amines. Liquid–liquid equilibria (LLE) bounded by lower critical solution temperatures (LCSTs) have been reported experimentally and are reproduced here with the SAFT-γ Mie approach. The main feature of the approach is the ability not only to represent accurately the experimental data employed in the parameter estimation, but also to predict the vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria, and LCSTs with the same set of parameters. Pure compound and binary phase diagrams of diverse types of amines and their aqueous solutions are assessed in order to demonstrate the main features of the thermodynamic and fluid-phase behavior.     

Systematic convergence of nonlinear stochastic estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group with the tracking error of the normalized Euclidean distance meeting predefined transient and steady‐state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low‐cost inertial measurement units. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form.     

Spiraling elliptic breathers in nonlocal nonlinear media with linear anisotropy

The dynamical properties of spiraling elliptic breathers in nonlocal nonlinear media with linear anisotropy are analytically discussed. Using a two-dimensional asynchronous fractional Fourier transform, the exact analytical solutions of spiraling elliptic breathers are obtained to the nonlocal nonlinear Schrödinger equation with unequal diffraction coefficients in the highly nonlocal limit. It is found that the spiraling elliptic breathers exhibit a kind of molecule-like libration due to the combined effects of the linear anisotropy and the orbital angular momentum. The angular velocity of the spiraling elliptic breathers is discussed, which can be controlled by the linear anisotropy parameter. In the media with linear anisotropy such as uniaxial crystals, the angular velocity of the spiraling elliptic breathers can be controlled by changing the propagation directions of optical beams. Furthermore, the nonlinearity of media is found to enhance the rotation effect of spiraling elliptic breathers.     

Experimental investigation and numerical simulation analysis of sintered micro-fluidic devices

ABSTRACT

This study investigates the use of numerical simulations to describe the solid-state diffusion of a sintering stage during a metal injection moulding process for micro-fluidic components with 316L stainless steel powders. Finite element (FE) analysis based on a thermo-elasto-viscoplastic model was conducted to describe the densification process of a stainless steel porous component during solid-state sintering. The numerical analyses, which were performed on a 3D micro-structured component with various powder volume loadings to take into account the thermal debinding effect to propose a full debinding sintering simulation, demonstrated that the FE simulation results are in agreement with the experimental ones.     

Global weak solutions to a spatio-temporal fractional Landau–Lifshitz–Bloch equation

The present paper deals with global existence of weak solutions of a time-space fractional Landau–Lifshitz–Bloch equation involving the weak Caputo derivative and a fractional Laplacian. We use Faedo–Galerkin method with some commutator estimates in order to prove global existence of weak solutions for the model. The uniqueness is also discussed in a special one dimensional case.     

An efficient NFEM for optimal control problems governed by a bilinear state equation

In this paper, a nonconforming finite element method (NFEM) is proposed for the constrained optimal control problems (OCPs) governed by a bilinear state equation. The state and adjoint state are approximated by the nonconforming $E{Q}_1^{rot}$ element, and the control is approximated by the orthogonal projection through the state and adjoint state. Some superclose and superconvergence properties are obtained by full use of the distinguish characters of this $E{Q}_1^{rot}$ element, such as the interpolation operator equals the Ritz projection, and the consistency error is one order higher than its interpolation error in the broken energy norm. Finally, some numerical results are provided to verify the theoretical analysis.     

Superconvergence analysis of nonconforming finite element method for time-fractional nonlinear parabolic equations on anisotropic meshes

In this paper, we prove a novel result of the consistency error estimate with order $O\left(h^2\right)$ for $E{Q}_1^{rot}$ element (see Lemma 2) on anisotropic meshes. Then, a linearized fully discrete Galerkin finite element method (FEM) is studied for the time-fractional nonlinear parabolic problems, and the superclose and superconvergent estimates of order $O(\tau +h^2)$ in broken $H^1$-norm on anisotropic meshes are derived by using the proved character of $E{Q}_1^{rot}$ element, which improve the results in the existing literature. Numerical results are provided to confirm the theoretical analysis.     

A discontinuous least-squares finite-element method for second-order elliptic equations

In this paper, a discontinuous least-squares (DLS) finite-element method is introduced. The novelty of this work is twofold, to develop a DLS formulation that works for general polytopal meshes and to provide rigorous error analysis for it. This new method provides accurate approximations for both the primal and the flux variables. We obtain optimal-order error estimates for both the primal and the flux variables. Numerical examples are tested for polynomials up to degree 4 on non-triangular meshes, i.e. on rectangular and hexagonal meshes.     

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations, are obtained using the exp_a function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.