Interior Layers Research Articles

A Synthesis, Properties and Application as a Possible Drug Delivery Systems Dendrimers – A Review

Dendrimer is derived from the Greek word “dendron” which is used for tree and from the Greek suffix “mer” (segment) which describes the synthetic, three-dimensional molecules having branching parts.“A dendrimer is generally described as a macromolecule, which is characterized by its dendritic and hyper branched 3D structure that offers a high degree of surface functionality and versatility.” Dendrimers possess three distinguishable architectural components i.e. an interior core, interior layer(generations) composed of repeating units radially attached to the interior core, and exterior (terminal functionality) attached to outermost interior generation (Fig. 1). The higher generation dendrimers, due to their globular structure, occupy a smaller hydrodynamic volume compared to the corresponding linear polymers. The dendritic structure is characterized by layer between each generation.Dendrimers are generally prepared using either a divergent method or a convergent one. There is a fundamental difference between these two construction concepts. Dendrimers shows the various properties such as structure, shape, aqueous solubility, non-polar solubility, &architecture. Dendrimer can be classification on the basis of their shape, structure, branching, solubility, chirality and attachment. Dendrimer can be differentiated on the basis of their shape, end functional groups and internal cavities.

Uniformly Convergent New Hybrid Numerical Method for Singularly Perturbed Parabolic Problems with Interior Layers

In this article, we deal with a class of singularly perturbed parabolic convection–diffusion initial-boundary-value problems having discontinuous convection coefficient. Aiming to get better numerical approximation to the solutions of this class of problems, we devise a new hybrid finite difference scheme on a layer-resolving piecewise-uniform Shishkin mesh in the spatial direction, and the time derivative is discretized by the backward-Euler method in the temporal direction. We discuss the stability of the proposed method and establish the parameter-uniform error estimate. Numerical results are also displayed to support the theoretical findings and compared with the existing hybrid scheme to show the improvement in terms of spatial order of convergence. Further, we carry out numerical experiment for the semi-linear parabolic initial-boundary-value problems.

A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition

Based on the basis of B-spline functions an efficient numerical scheme on a piecewise-uniform mesh is suggested to approximate the solution of singularly perturbed problems with an integral boundary condition and having a delay of unit magnitude. For the small diffusion parameter $$\varepsilon $$, an interior layer and a boundary layer occur in the solution. Unlike most numerical schemes our scheme does not require the differentiation of the problem data (integral boundary condition). The parameter-uniform convergence (the second-order convergence except for a logarithmic factor) is confirmed by numerical computations of two test problems. As a variant double mesh principle is used to measure the accuracy of the method in terms of the maximum absolute error.

Parameter-uniform numerical treatment of singularly perturbed initial-boundary value problems with large delay

In this article, a parameter-uniform implicit scheme is constructed for a class of parabolic singularly perturbed reaction-diffusion initial-boundary value problems with large delay in the spatial direction. In general, the solution of these problems exhibits twin boundary layers and an interior layer (due to the presence of the delay in the reaction term). Crank-Nicolson difference formula (on a uniform mesh) is used in time to semi-discretize the given PDE, and then the standard finite difference scheme (on a piecewise-uniform mesh) is used for the system of ordinary differential equations obtained in the semi-discretization. The convergence analysis shows that the method is ε-uniformly convergent of order two in the temporal direction and almost first-order in the spatial direction. Two test examples are encountered to show the efficiency of the method, validate the computational results, and to confirm the predicted theory.

A conservative method of lines for advection-reaction-diffusion equations

Purpose The purpose of this study is to develop a new method of lines for one-dimensional (1D) advection-reaction-diffusion (ADR) equations that is conservative and provides piecewise analytical solutions in space, compare it with other finite-difference discretizations and assess the effects of advection and reaction on both 1D and two-dimensional (2D) problems. Design/methodology/approach A conservative method of lines based on the piecewise analytical integration of the two-point boundary value problems that result from the local solution of the advection-diffusion operator subject to the continuity of the dependent variables and their fluxes at the control volume boundaries is presented. The method results in nonlinear first-order, ordinary differential equations in time for the nodal values of the dependent variables at three adjacent grid points and triangular mass and source matrices, reduces to the well-known exponentially fitted techniques for constant coefficients and equally spaced grids and provides continuous solutions in space. Findings The conservative method of lines presented here results in three-point finite difference equations for the nodal values, implicitly treats the advection and diffusion terms and is unconditionally stable if the reaction terms are implicitly treated. The method is shown to be more accurate than other three-point, exponentially fitted methods for nonlinear problems with interior and/or boundary layers and/or source/reaction terms. The effects of linear advection in 1D reacting flow problems indicates that the wave front steepens as it approaches the downstream boundary, whereas its back corresponds to a translation of the initial conditions; for nonlinear advection, the wave front exhibits steepening but the wave back shows a linear dependence on space. For a system of two nonlinearly coupled, 2D ADR equations, it is shown that a counter-clockwise rotating vortical field stretches the spiral whose tip drifts about the center of the domain, whereas a clock-wise rotating one compresses the wave and thickens its arms. Originality/value A new, conservative method of lines that implicitly treats the advection and diffusion terms and provides piecewise-exponential solutions in space is presented and applied to some 1D and 2D advection reactions.

A Stabilized Dual Mixed Hybrid Finite Element Method with Lagrange Multipliers for Three-Dimensional Elliptic Problems with Internal Interfaces

This work studies an elliptic boundary value problem with diffusive, advective and reactive terms, in a three-dimensional domain composed of two media separated by a selective interface. For the numerical approximation of the problem we propose a novel approach that combines, for the first time: (1) a dual mixed hybrid (DMH) finite element method (FEM) based on the lowest order Raviart–Thomas space (RT0); (2) a Three-Field formulation; and (3) a Streamline Upwind/Petrov–Galerkin (SUPG) stabilization method. After proving that the weak formulation of the proposed method and its numerical counterpart are both uniquely solvable and that the finite element scheme enjoys optimal convergence properties with respect to the discretization parameter, we present an efficient implementation based on static condensation, which reduces the method to a nonconforming finite element approach on a grid made by three-dimensional simplices. Extensive computational tests indicate that: (1) the theoretical convergence properties are verified; (2) the DMH-RT0 FEM is accurate and stable even in the presence of marked interface jump discontinuities in the solution and its associated normal flux; and (3) in the case of strongly dominating advective terms, the SUPG stabilization resolves accurately steep boundary and/or interior layers without introducing spurious unphysical oscillations or excessive smearing of the solution front.

An adaptive moving finite element method for steady low Mach number compressible combustion problems

SummaryThis work surveys an r‐adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the computation of such a problem is often extremely time‐consuming. Importantly, to capture the significant characteristics of the flame structure when using detailed chemistry, a much more stringent requirement on the spatial resolution of the interior layers of some intermediate species is necessary. Here, we propose a moving mesh method in which the mesh is obtained from the solution of so‐called moving mesh partial differential equations. Such equations result from the variational formulation of a minimization problem for a given target functional that characterizes the inherent difficulty in the numerical approximation of the underlying physical equations. Adaptive mesh movement has emerged as an area of intense research in mesh adaptation in the last decade. With this approach, points are only allowed to be shifted in space leaving the topology of the grid unchanged. In contrast to methods with local refinement, data structure hence is unchanged and load balancing is not an issue as grid points remain on the processor where they are. We will demonstrate the high potential of moving mesh methods for effectively optimizing the distribution of grid points to reach the required resolution for chemically reacting flows with extremely thin boundary layers.

Mineralogical evidence of unfavorable geochemical interactions between urban runoff pollutants and filter materials in low-impact systems

We report on the geochemical interactions between a synthetic urban runoff (SUR) and the minerals of materials used in a multi-layered column filter (soil, sand, gravel, and tezontle) at the laboratory scale, which mimicked an unvegetated low-impact development (LID) system. After five 8 h infiltration cycles using the SUR, the average concentrations of Pb and Mn decreased slightly at the column outlet, as did HCO3−, SO42-, and Na+, whereas Mg increased and Cl−, Ca2+, and K+ were only detected at the outlet. The filter materials were comprised of silicates, Mn-bearing oxides (hausmannite and manganite), carbonates (calcite), chlorides (sylvite), and sulfates (anglesite, lanarkite, barite, and epsomite). PHREEQC modeling allowed the identification of the geochemical processes that occurred in the filter. The results showed the removal capacity of the filter materials through the formation of secondary minerals such as rhodochrosite (MnCO3) and the over-saturation of anglesite (PbSO4), and also showed that they may mobilize ions from the upper to the interior layers (as Mg2+ from epsomite, MgSO4·7H2O, and Ba2+ from barite, BaSO4). We highlight the importance of knowing the geological nature of filter materials used in LID systems because they may lead to the geogenic mobilization of toxic contaminants to the environment.

Study on the synthesis and formation mechanism of Al2OC-AlN solid solution in Al–Al2O3 composite material in air at 1500 °C

The Al2OC-AlN solid solution reinforced Al–Al2O3 composite material was successfully synthesized by sintering Al–Al2O3 composites with the phenolic resin as binding reagent in air at 1500 °C. The reaction mechanism was investigated by XRD, SEM and thermodynamic analysis. Results showed that the surface layer of the sintered sample was fully oxidized. But Al2OC-AlN solid solution whiskers and particles were observed in the interior layer. In the surface layer, Al and C from resin were oxidized to Al2O3(s) and CO2(g). With the consumption of oxygen, p (O2) gradually decreased from the surface layer to the interior layer. And the oxidation product of Al and C transformed into Al2O(g) and CO(g). When the p (O2) further decreased, the metastable phase AlN was generated in the interior layer. Under the induction of the highly active AlN nucleus, the isostructural Al2OC-AlN solid solution whisker was generated from the gas phase reaction among Al2O(g), CO(g), Al(g) and N2(g). In the region with even lower oxygen partial pressure, particle-like Al2OC-AlN solid solution was generated from the reaction among Al(l), Al2O3(s), C(s) and N2(g).

Aspergillus spp. burden on filtering respiratory protective devices. Is there an occupational health concern?

There is scientific evidence that associates occupational exposure to fungi in the waste industry to health outcomes, being Aspergillus genera reported as the most prevalent. During Filtering Respiratory Protective Devices (FFR) use, humidity and temperature conditions provide favorable conditions for Aspergillus growth. The aim of this study was to characterize Aspergillus burden retained by FFR interior layer and exhalation valve. The sample consisted of 120 FFR and the correspondent interior layer and exhalation valves collected from different workstations from one waste sorting industry. The fungal content of exhalation valve and from the interior layer of the each FFR was extracted and inoculated on malt extract agar (MEA) supplemented with chloramphenicol (0.05%) and dichloran-glycerol agar (DG18). FFR extracts were also used for the molecular detection of Aspergillus sections Flavi and Fumigati. Valves presented Aspergillus spp. as the most prevalent genera on MEA media (44.4%), unlike what was observed in the FFR interior layer, where Aspergillus spp. was not the most prevalent genera (6.84% MEA; 5.2% DG18). Among the Aspergillus genera, section Fumigati was the one with highest prevalence, both in exhalation valves (76.57% MEA; 87.24% DG18) and interior layer (75.81% MEA; 51.22% DG18). qPCR analysis successfully amplified DNA from the Aspergillus sections Flavi and Fumigati. Interior layers presented statistically significant differences showing higher number of FFR contaminated with higher levels of Aspergillus in the workstations where workers contact directly with waste. This work, revealing strong fungal contamination of FFR used by workers at waste industry, clearly indicates that future trials to test FFR protective efficacy and establishment of times for FFR replacement should be performed.

Brezzi--Douglas--Marini Interpolation of Any Order on Anisotropic Triangles and Tetrahedra

Recently, the $\vec{H}(\operatorname{div})$-conforming finite element families for second order elliptic problems have come more into focus, since due to hybridization and subsequent advances in computational efficiency their use is no longer mainly theoretical. Their property of yielding exactly divergence-free solutions for mixed problems makes them interesting for a variety of applications, including incompressible fluids. In this area, boundary and interior layers are present, which demand the use of anisotropic elements. While for the Raviart-Thomas interpolation of any order on anisotropic tetrahedra optimal error estimates are known, this contribution extends these results to the Brezzi-Douglas-Marini finite elements. Optimal interpolation error estimates are proved under two different regularity conditions on the elements, which both relax the standard minimal angle condition. Additionally a numerical application on the Stokes equations is presented to illustrate the findings.

A higher-order hybrid numerical scheme for singularly perturbed convection-diffusion problem with boundary and weak interior layers

In this paper, we study the numerical solutions of singularly perturbed convection-diffusion two-point BVP as well as one-dimensional parabolic convection-diffusion IBVP with discontinuous convection coefficient (positive throughout the domain) and source term. The analytical solutions of these kind of problems exhibit a boundary layer near x = 0 and a weak interior layer near x = ξ. We discretise the spatial domain by the piecewise-uniform Shishkin mesh and the temporal domain by a uniform mesh. To approximate the spatial derivatives, we apply the hybrid finite difference scheme. The implicit-Euler scheme is used for discretising the temporal derivative. For the time independent problem, we derive that the proposed hybrid scheme is e-uniformly convergent of almost second-order and for the time dependent problem, we also prove that the proposed scheme is e-uniformly convergent of almost second-order in space and first-order in time. To validate the theoretical estimates, some numerical results are presented.

A higher-order hybrid numerical scheme for singularly perturbed convection-diffusion problem with boundary and weak interior layers

In this paper, we study the numerical solutions of singularly perturbed convection-diffusion two-point BVP as well as one-dimensional parabolic convection-diffusion IBVP with discontinuous convection coefficient (positive throughout the domain) and source term. The analytical solutions of these kind of problems exhibit a boundary layer near x = 0 and a weak interior layer near x = ξ. We discretise the spatial domain by the piecewise-uniform Shishkin mesh and the temporal domain by a uniform mesh. To approximate the spatial derivatives, we apply the hybrid finite difference scheme. The implicit-Euler scheme is used for discretising the temporal derivative. For the time independent problem, we derive that the proposed hybrid scheme is ε-uniformly convergent of almost second-order and for the time dependent problem, we also prove that the proposed scheme is ε-uniformly convergent of almost second-order in space and first-order in time. To validate the theoretical estimates, some numerical results are presented.

New Plasmonic Biosensors for Determination of Human Hemoglobin Concentration in Blood

Two new types of plasmonic biosensors are applied for detection of hemoglobin concentration in human blood by using the angular interrogation method. The first type of the fiber with five layers is made by a SiO2 core surrounded by GaP, gold, Al2O3 and hemoglobin layers. The second type of the fiber with six layers is made by a ZBLAN core surrounded by NaF, silicon, silver, Al2O3 and hemoglobin layers. For some thicknesses of the interior layers and for a hemoglobin concentration close to the mean value of a male human at a laser wavelength (1.53 μm), a large figure of merit and maximum value of the amplitude sensitivity are obtained at an angle very close to the resonance angle. For the second type of the sensor, 0.0036 g/dl resolution is obtained, which is 10% finer than the estimated detection limit (0.004 g/dl) reported very recently by using an electrochemical method. Also, our resolution is better than the previously reported value (0.006 g/dl if the angular resolution is 0.001°) by using a gold–aluminum-based surface plasmon resonance sensor.

Are workers from waste sorting industry really protected by wearing Filtering Respiratory Protective Devices? The gap between the myth and reality

One of the solutions for decreasing the workers' exposure to bioburden is the use of Filtering Respiratory Protective Devices (FRPD). As such it is important to determine whether these devices are fulfilling their protective role. This is the basis of the current study, aimed at characterizing bioburden retained by 120 FRPD (both in interior layers and in exhalation valves) through culture based-methods and molecular tools and also via analysis of antifungal resistance and mycotoxins profile. Our results show that Gram – Bacteria are present at a higher prevalence than total bacteria in both matrixes. Regarding fungal identification, Chrysonilia sitophila presented the highest prevalence on interior layers (55.1% on malt extract agar (MEA) supplemented with chloramphenicol (0.05%); 59.6% on dichloran-glycerol agar (DG18)), whereas on exhalation valves Aspergillus sp. presented the highest prevalence on MEA (6.8%) and C. sitophila on DG18 (36.3%). Among Aspergillus genera, section Fumigati was the one with the highest prevalence in both matrices. Aspergillus sp. was the most prevalent on exhalation valves (75.0% ITRA) in the screening of azole resistance. Fumigati section was the most abundant Aspergillus sp. detected on the interior layers (33.33%, 40 samples out of 120) and on the exhalation valves (1.66%, 2 samples out of 120). The interior layers and exhalation valves from workers with more waste contact showed an increased exposure to bioburden. This study showed that FRPD can have high levels of bioburden, toxigenic fungal strains and Aspergillus sections with reduced susceptibility to the tested azoles and can be used as a passive sampling method since it mimics the results obtained by active methods in previous studies. The gathered information will be useful to prioritize multiple interventions on workers’ education or even on FRPD replacement frequency.

A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction–convection–diffusion systems with two small parameters and discontinuous source terms

This paper aims at solving numerically the 1-D weakly coupled system of singularly perturbed reaction–convection–diffusion partial differential equations with two small parameters and discontinuous source terms. Boundary and interior layers appear in the solutions of the problem for sufficiently small values of the perturbation parameters. A numerical algorithm based on finite difference operators and an appropriate piecewise uniform mesh is constructed and its characteristics are analyzed. The method is confirmed to reach almost first order convergence, independently of the values of the perturbation parameters. Some numerical experiments are presented, which serve to illustrate the theoretical results.

Studies on the optimum double-skin curtain wall design for high-rise buildings in the Mediterranean climate

The fast growing numbers of high-rise buildings around the world, a product of expanding urbanization and population growth, dictate the implementation of design strategies towards the reduction of their high energy loads. This study focuses on an office high-rise building in the Mediterranean climate of Tel Aviv and the reduction of high cooling loads relevant to this climate. In this process, the design of the building envelope becomes the most important constituent between indoor and outdoor environment, by dictating the required use of energy for achieving thermal comfort. A double skin façade (DSF) layer is proposed as a more advanced envelope design compared to the single skin curtain walls (controlled ventilation, acoustic insulation etc.). A previous study based on thermal simulations in Tel Aviv, revealed that a ventilated DSF design with the LowE glazing as the exterior layer of the DSF reduced cooling loads by 15% on average, in comparison with a typical DSF design in temperate climates where the LowE glazing is on the interior layer of the DSF, and by an average of 50% from the option of single skin envelope with LowE glazing. This study draws from the conclusions of previous data, and tests the energy efficiency of different DSF cavities in the Mediterranean climate. Results revealed that by increasing the cavity width from 0.2 m to 0.5 m, cooling loads decrease significantly, while there are also substantial reductions, from 0.5 m to 1.0 m, and from 1.0 m to 2.0 m DSF cavity width.

Improved flexural strength of diamond/Cu–Fe composites with Cu–B–B4C coating

ABSTRACTThe interface between diamond and copper (Cu) alloy matrix in the composites significantly affects their mechanical properties. The functionalization of the diamond surface is of great potential for exploiting different advanced mechanical tools. In the present case, copper–boron–boron carbide (Cu–B–B4C) composite coating was grown simultaneously on the whole surface of diamonds. Subsequently, the diamond particles were reinforced with copper–iron (Cu–Fe) matrix composites through powder metallurgy. The microstructural analysis demonstrated that the composite coatings were composed of two layers: the interior layers of B4C and B as well as the exterior layer of Cu–B alloy. The bending strength of Cu–B–B4C composite-coated diamond was determined to be 701 MPa at a sintering temperature of 800°C, which was nearly 27% higher compared to that (553 MPa) of uncoated diamond/Cu–Fe composites.

Numerical approximation for a class of singularly perturbed delay differential equations with boundary and interior layer(s)

This paper is devoted to the study of singularly perturbed delay differential equations with or without a turning point. The solution of the considered class of problems may exhibit boundary or interior layer(s) due to the presence of the perturbation parameter, the turning point, and the delay term. Some a priori estimates are derived on the solution and its derivatives. To solve the problem numerically, a finite difference scheme on piecewise uniform Shishkin mesh along with interpolation to tackle the delay term is proposed. The solution is decomposed into regular and singular components to establish parameter uniform error estimate. It is shown that the proposed scheme converges to the solution of the continuous problem uniformly with respect to the singular perturbation parameter. The numerical experiments corroborate the theoretical findings.

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

The paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions.