Impacts of slip and mass transpiration on Newtonian liquid flow over a porous stretching sheet

This article focuses on analytic solutions for Newtonian fluid flow with slip and mass transpiration on a porous stretching sheet using the differential transform method and Pade approximants of an exceptionally nonlinear differential equation. The impacts of different parameters including mass transpiration (suction/injection), Navier's slip, and Darcy number parameters on the velocity of the liquid and tangential stress are discussed. A comprehensive comparison of our results with the previous one in the literature is made, and the results showed good agreement. An investigation is conducted of a combination of magnetic liquids that are conceivably pertinent for wound medicines, skin repair, and astute coatings for natural gadgets. It is found that there is a decrease in the velocity profiles and the boundary layer thickness for the case of suction.     

Time and space dependence of large-scale synthesis of colloidal particle with special morphology and tuneable polymer film architecture

This paper describes a facile method to control the morphology of polymer colloids and the architecture of polymer film via miniemulsion polymerization. By taking advantage of cyclization between the symmetrical diacrylate cross-linker hexamethylene diacrylate (HDDA) and the pendent vinyl in colloidal particles, the morphology of polymer colloids and the architecture of the after-formed polymer film were able to be well controlled by tuning the loading of cross-linker HDDA and crosslinking time. Four kinds of polymer colloid morphologies and four kinds of film architecture (honeycomb, close-packed, loose-packed, and enhanced-honeycomb) were characterized by TEM. The film formation mechanisms behind them were proposed based on the special and interesting results including Z-average size of the colloidal particles, Mc (molecular weight between crosslinking points) and mechanical properties of polymer film. Our results highly suggested that the morphology of polymer colloids and the polymer film architecture together determine the adhesive properties of the colloidal polymer film. The best of 180°-peel resistance, T-peel resistance and shear resistance of the polymer films were 138.12 N/25 mm, 40.98 N/25 mm and 25.72 N/cm² at 2.0 phm, 2.0 phm and 0.4 phm with the same crosslinking time of 90 min, respectively. The proposed method is promising to be scaled up for industrial production due to its well adaptability.     

A new linearly constrained minimum variance beamformer for reconstructing EEG sparse sources

Brain source imaging based on EEG aims to reconstruct the neural activities producing the scalp potentials. This includes solving the forward and inverse problems. The aim of the inverse problem is to estimate the activity of the brain sources based on the measured data and leadfield matrix computed in the forward step. Spatial filtering, also known as beamforming, is an inverse method that reconstructs the time course of the source at a particular location by weighting and linearly combining the sensor data. In this paper, we considered a temporal assumption related to the time course of the source, namely sparsity, in the Linearly Constrained Minimum Variance (LCMV) beamformer. This assumption sounds reasonable since not all brain sources are active all the time such as epileptic spikes and also some experimental protocols such as electrical stimulations of a peripheral nerve can be sparse in time. Developing the sparse beamformer is done by incorporating L1-norm regularization of the beamformer output in the relevant cost function while obtaining the filter weights. We called this new beamformer SParse LCMV (SP-LCMV). We compared the performance of the SP-LCMV with that of LCMV for both superficial and deep sources with different amplitudes using synthetic EEG signals. Also, we compared them in localization and reconstruction of sources underlying electric median nerve stimulation. Results show that the proposed sparse beamformer can enhance reconstruction of sparse sources especially in the case of sources with high amplitude spikes.     

Classic and inverse compositional Gauss-Newton in global DIC

Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss-Newton implementation of finite element DIC is proposed as a cost-effective and mathematically sound alternative to this approximation.     

Continuum model of two-dimensional crystal lattice of metamaterials

The continuum models of two-dimensional crystal lattice of metamaterial are investigated in this paper. The equivalent classical continuum requires the introduction of frequency-dependent mass density that becomes negative or infinite near the resonance frequency. In order to avoid the frequency-dependent mass density and make the dispersive characteristic of the elastic waves propagating in the equivalent continuum approximating that of lattice wave in two-dimensional crystal lattice of metamaterial, three kinds of continuum models, namely, the multiple displacements continuum model, the strain gradient continuum model and the nonlocal strain gradient continuum model, are investigated. It is found that the nonlocal gradient continuum model may better represent the dispersive relation and the bandgap characteristics of the metamaterial by the appropriate selection of nonlocal parameters.     

An inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval

This paper is concerned with the inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval. Firstly, we give the definitions of generalized weight numbers for this operator which may have the multiple spectrum and then investigate the connections between the generalized weight numbers and other spectral characteristics. Secondly, we obtain the generalized spectral data, which consists of the generalized weight numbers and the spectrum. Then the operator is determined uniquely by the method of spectral mappings. Finally, we give an algorithm for reconstructing the potential function and the coefficients of the boundary conditions and the coefficients of the discontinuity conditions.     

New approach to identify the initial condition in degenerate hyperbolic equation

This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov’s regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach.     

Engineering the Structure of Mesoporous Bioactive Glass Microspheres by the Surface Effect of Inverse Opal Templates and Temperature

The interactions of ions and molecules with material surface are highly dependent on the surface properties of the material. Therefore, the distribution of ions or molecules near the material surface may be affected by the surface properties. This phenomenon can be significant enough for controlling the structure of a material synthesized in the sub‐micrometer scale confinement space of a template. This work confirms that inverse opals are perfect templates for offering confinement space, while their different surface properties can strongly affect ion and block copolymer distribution in the confinement space. This surface effect principle can be used for the controlled synthesis of colloids with complex composition. As an example, four kinds of mesoporous magnetic bioactive glass colloids with ordered mesopores, core–shell structure, open surface pores, or disordered mesopores are prepared by using polystyrene and carbon inverse opal templates. This work reveals that inverse opal templates possess great advantage in controlled synthesizing colloidal structures due to their surface effect on ions and molecules and confinement space.