Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

GABAergic modification of myopic and hyperopic ocular tissue effects on scleral fibroblast growth

Purpose: Myopia is a common eye disorder affecting up to 90% of children in South East Asia and 30% of the population worldwide. Myopia of high severity is a leading cause of blindness around the world (4th to 5th most common). Changes and remodelling of the sclera i.e. increase cellular proliferation & increase protein synthesis within scleral cells (↑ scleral DNA) and thinning and lose of extracellular matrix of sclera (↓ scleral GAG synthesis) have been linked to myopic eye growth in animal models. Signals acting on the sclera are thought to originate in the retina, and are modulated by the retinal pigment epithelium (RPE) with limited evidence suggesting that the RPE can modify scleral cell growth in culture. However, the mechanism of retinal signal transmission and the role of posterior eye cup tissue, including the RPE, in mediating changes in scleral fibroblast growth during myopia development are unclear. Retinal transmitter systems are critically involved in pathways regulating eye growth, which ultimately lead to alterations in the sclera if eye size is to change. A dopaminergic agonist and muscarinic antagonists decrease the proliferation of scleral chondrocytes when co-cultured with chick’s retinal pigment epithelium (RPE). GABA receptors have recently been localised to chick sclera. We therefore hypothesised that posterior eye cup tissue from myopic eyes would stimulate and from hyperopic eyes would inhibit growth of scleral fibroblasts in vitro and that GABAergic agents could directly interact with scleral cells or indirectly modify the effects of myopic and hyperopic posterior eye cup tissue on scleral fibroblast growth. Method: Fibroblastic cells obtained from 8-day-old chick sclera were used to establish cell banks. Two major experiments were performed. Experiment 1: To determine if posterior eye cup tissues from myopic eye stimulates and hyperopic eye inhibits scleral cell proliferation, when co-cultured with scleral cells in vitro. This study comprised two linked experiments, i) monocular visual treatments of FDM (form-deprivation myopia), LIM (lens-induced myopia) and LIH (lens-induced hyperopia) with assessment of the effect of full punch eye cup tissue on DNA and GAG synthesis by cultured chick scleral fibroblasts, and ii) binocular visual treatments comprising LIM and LIH with assessment of the effect of individual layers of eye cup tissues (neural retina, RPE and choroid) on cultured chick scleral fibroblasts. Visual treatment was applied for 3 days. Experiment 2: To determine the direct interaction of GABA agents on scleral cell growth and to establish whether GABA agents modify the stimulatory/inhibitory effect of myopic and hyperopic posterior eye cup tissues on cultured scleral cell growth in vitro. Two linked experiments were performed. i) GABA agonists (muscimol and baclofen) and GABA antagonists (bicuculine (-), CGP46381 and TPMPA) were added to scleral cell culture medium to determine their direct effect on scleral cells. ii) GABAergic agents (agonists and antagonists) were administered to scleral fibroblasts co-cultured with posterior eye cup tissue (retina, RPE, retina/RPE, RPE/choroid). Ocular tissues were obtained from chick eyes wearing +15D (LIH) or -15D lenses (LIM) for 3 days. In both experiments, tissues were added to hanging cell culture insert (pore size 1.0ìm) placed over each well of 24 well plates while scleral cells were cultured in DMEM/F12, Glutamax (Gibco) plus 10% FBS and penicillin/streptomycin (50U/ml)) and fungizone (1.25ug/ml) (Gibco), at seeding density of 30,000 cells/well at the bottom of the well and allowed to grow for 3 days. Scleral cells proliferation rate throughout the study was evaluated by determining GAG and DNA content of scleral cells using Dimethylmethylene blue (DMMB) dye and Quant-iTTm Pico Green® dsDNA reagent respectively. Results and analysis: Based on DNA and GAG content, there was no significant difference in tissue effect of LIM and LIH eyes on scleral fibroblast growth (DNA: 8.4 ± 1.1μg versus 9.3 ± 2.3 μg, p=0.23; GAG: 10.13 ± 1.4 μg versus 12.67 ± 1.2 μg, F2,23=6.16, p=0.0005) when tissues were obtained from monocularly treated chick eyes (FDM or +15D lens or -15D lens over right eyes with left eyes untreated) and co-cultured as full punch. When chick eyes were treated binocularly with -15D lens (LIM) right eye and +15D lens (LIH) left eyes and tissue layers were separated, the retina from LIM eyes did not stimulate scleral cell proliferation compared to LIH eyes (DNA: 27.2 ± 6.7 μg versus 23.2 ± 1.5 μg, p=0.23; GAG: 28.1 ±3.7 μg versus 28.7 ± 4.2 μg, p=0.21). Similarly, the LIH and LIM choroid did not produce a differential effect based on DNA (LIM 46.9 ± 6.4 μg versus LIH 53.5 ± 4.7 μg, p=0.18), however the choroid from LIH eyes induced higher scleral GAG content than from LIM eyes (32.5 ± 6.7 μg versus 18.9 ± 1.2 μg, p=0.023). In contrast, the RPE from LIM eyes caused a significant increase in fibroblast proliferation whereas the RPE from LIH eyes was relatively inhibitory (72.4 ± 6.3 μg versus 27.9 ± 2.3 μg, F1, 6=69.99, p=0.0005). GAG data were opposite to DNA data e.g. the RPE from LIH eyes increased (33.7 ± 7.9 μg) while the RPE from LIM eyes decreased (28.2 ± 3.0 μg) scleral cell growth (F1, 6=13.99, p=0.010). Based on DNA content, GABA agents had a small direct effect on scleral cell growth; GABA agonists increased (21.4 ± 1.0% and 18.3 ± 1.0% with muscimol and baclofen, p=0.0021), whereas GABA antagonists decreased fibroblast proliferation (-23.7 ± 0.9% with bicuculine & CGP46381 and -28.1 ± 0.5% with TPMPA, p=0.0004). GABA agents also modified the effect of LIM and LIH tissues (p=0.0005).The increase in proliferation rate of scleral fibroblasts co-cultured with tissues (RPE, retina, RPE/retina and RPE/choroid) from LIM treated eyes was enhanced by GABA agonists (muscimol: 27.4 ± 1.2%, 35.8 ± 1.6%, 8.4 ± 0.3% and 11.9 ± 0.6%; baclofen: 27.0 ± 1.0%, 15.8 ± 1.5%, 16.8 ± 1.2% and 15.4 ± 0.4%, p=0.014) whereas GABA antagonists further reduced scleral fibroblasts growth (bicuculine: -52.5 ± 2.5%, -36.9 ± 1.4%, -37.5 ± 0.6% and -53.7 ± 0.9%; TPMPA: 57.3 ± 1.3%, -15.7 ± 1.2%, -33.5 ± 0.4% and -45.9 ± 1.5%; CGP46381: -51.9 ± 1.6%, -28.5 ± 1.5%, -25.4 ± 2.0% and -45.5 ± 1.9% respectively, p=0.0034). GAG data were opposite to DNA data throughout the experiment e.g. GABA agonists further inhibited while antagonists relatively enhanced scleral fibroblasts growth for both LIM and LIH tissue co-culture. The effect of GABA agents was relatively lower (p=0.0004) for tissue from LIH versus LIM eyes but was in a similar direction. There was a significant drug effect on all four tissue types e.g. RPE, retina, RPE/retina and RPE/choroid for both LIM and LIH tissue co-culture (F20,92=3.928, p=0.0005). However, the effect of GABA agents was greatest in co-culture with RPE tissue (F18,36=4.865, p=0.0005). Summary and Conclusion: 1) Retinal defocus signals are transferred to RPE and choroid which then exert their modifying effect on scleral GAG and DNA synthesis either through growth stimulating factors or directly interacting with scleral cells in process of scleral remodeling during LIM and LIH visual conditions. 2) GABAergic agents affect the proliferation of scleral fibroblasts both directly and when co-cultured with ocular tissues in vitro.

Comparative effects of posterior eye cup tissues from Myopic and Hyperopic chick eyes on cultured scleral fibroblasts

The role of individual ocular tissues in mediating changes to the sclera during myopia development is unclear. The aim of this study was to examine the effects of retina, RPE and choroidal tissues from myopic and hyperopic chick eyes on the DNA and glycosaminoglycan (GAG) content in cultures of chick scleral fibroblasts. Primary cultures of fibroblastic cells expressing vimentin and -smooth muscle actin were established in serum-supplemented growth medium from 8-day-old normal chick sclera. The fibroblasts were subsequently co-cultured with posterior eye cup tissue (full thickness containing retina, RPE and choroid) obtained from untreated eyes and eyes wearing translucent diffusers (form-deprivation myopia, FDM) or -15D lenses (lens-induced myopia, LIM) for 3 days (post hatch day 5 to 8) (n=6 per treatment group). The effect of tissues (full thickness and individual retina, RPE, and choroid layers) from -15D (LIM) versus +15D (lens-induced hyperopia, LIH) treated eyes was also determined. Refraction changes in the direction predicted by the visual treatments were confirmed by retinoscopy prior to tissue collection. Glycosaminoglycan (GAG) and DNA content of the scleral fibroblast cultures were measured using GAG and PicoGreen assays. There was no significant difference in the effect of full thickness tissue from either FDM or LIM treated eyes on DNA and GAG content of scleral fibroblasts (DNA 8.9±2.6 µg and 8.4±1.1 µg, p=0.12; GAG 11.2±0.6 µg and 10.1±1.0 µg, p=0.34). Retina from LIM eyes did not alter fibroblast DNA or GAG content compared to retina from LIH eyes (DNA 27.2±1.7 µg versus 23.2±1.5 µg, p=0.21; GAG 28.1±1.7 µg versus. 28.7±1.2 µg, p=0.46). Similarly, the choroid from LIH and LIM eyes did not produce a differential effect on DNA content (DNA, LIM 46.9±6.4 versus LIH 51.5±4.7 µg, p=0.31), whereas GAG content was higher for cells in co-culture with choroid from LIH eyes (GAG 32.5±0.7 µg versus 18.9±1.2 µg, F1,6=9.210, p=0.0002). In contrast, fibroblast DNA was greater in co-culture with RPE from LIM eyes than the empty basket and DNA content less for co-culture with RPE from LIH eyes (LIM: 72.4±6.3 µg versus Empty basket: 46.03±1.0 µg; F1,6=69.99, p=0.0005 and LIH: 27.9±2.3 µg versus empty basket: 46.03±1.0 µg; p=0.0004). GAG content was higher with RPE from LIH eyes (LIH: 33.7±1.9 µg versus empty basket: 29.5±0.8 µg, F1,6=13.99, p=0.010) and lower with RPE from LIM eyes (LIM: 27.7±0.9 µg versus empty basket: 29.5±0.8 µg, p=0.021). GAG content of cells in co-culture with choroid from LIH eyes was higher compared to co-culture with choroid from LIM eyes (32.5±0.7 µg versus 18.9±1.2 µg respectively, F1,6=9.210, p=0.0002). In conclusion, these experiments provide evidence for a directional growth signal that is present (and remains) in the ex-vivo RPE, but that does not remain in the ex-vivo retina. The identity of this factor(s) that can modify scleral cell DNA and GAG content requires further research.

The effects and interactions of GABAergic and dopaminergic agents in the prevention of form deprivation myopia by brief periods of normal vision

Intravitreal injections of GABA antagonists, dopamine agonists and brief periods of normal vision have been shown separately to inhibit form-deprivation myopia (FDM). Our study had three aims: (i) establish whether GABAergic agents modify the myopia protective effect of normal vision, (ii) investigate the receptor sub-type specificity of any observed effect, and (iii) consider an interaction with the dopamine (DA) system. Prior to the period of normal vision GABAergic agents were applied either (i) individually, (ii) in combination with other GABAergic agents (an agonist with an antagonist), or (iii) in combination with DA agonists and antagonists. Water injections were given to groups not receiving drug treatments so that all experimental eyes received intravitreal injections. As shown previously, constant form-deprivation resulted in high myopia and when diffusers were removed for 2 h per day the period of normal vision greatly reduced the FDM that developed. GABA agonists inhibited the protective effect of normal vision whereas antagonists had the opposite effect. GABAA/C agonists and D2 DA antagonists when used in combination were additive in suppressing the protective effect of normal vision. A D2 DA agonist restored some of the protective effect of normal vision that was inhibited by a GABA agonist (muscimol). The protective effect of normal vision against form-deprivation is modifiable by both the GABAergic and DAergic pathways.

A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

A meshfree model for plant tissue deformations during drying

Plant tissue has a complex cellular structure which is an aggregate of individual cells bonded by middle lamella. During drying processes, plant tissue undergoes extreme deformations which are mainly driven by moisture removal and turgor loss. Numerical modelling of this problem becomes challenging when conventional grid-based modelling techniques such as Finite Element Methods (FEM) and Finite Difference Methods (FDM) have grid-based limitations. This work presents a meshfree approach to model and simulate the deformations of plant tissues during drying. This method demonstrates the fundamental capabilities of meshfree methods in handling extreme deformations of multiphase systems. A simplified 2D tissue model is developed by aggregating individual cells while accounting for the stiffness of the middle lamella. Each individual cell is simply treated as consisting of two main components: cell fluid and cell wall. The cell fluid is modelled using Smoothed Particle Hydrodynamics (SPH) and the cell wall is modelled using a Discrete Element Method (DEM). During drying, moisture removal is accounted for by reduction of cell fluid and wall mass, which causes local shrinkage of cells eventually leading to tissue scale shrinkage. The cellular deformations are quantified using several cellular geometrical parameters and a favourably good agreement is observed when compared to experiments on apple tissue. The model is also capable of visually replicating dry tissue structures. The proposed model can be used as a step in developing complex tissue models to simulate extreme deformations during drying.

Inhibition of form-deprivation myopia by a GABAAOr receptor antagonist, (1,2,5,6-tetrahydropyridin-4-yl) methylphosphinic acid (TPMPA), in guinea pigs

Purpose To investigate the effects of the relatively selective GABAAOr receptor antagonist (1,2,5,6-tetrahydropyridin-4-yl) methylphosphinic acid (TPMPA) on form-deprivation myopia (FDM) in guinea pigs. Methods A diffuser was applied monocularly to 30 guinea pigs from day 10 to 21. The animals were randomized to one of five treatment groups. The deprived eye received daily sub-conjunctival injections of 100 μl TPMPA at a concentration of (i) 0.03 %, ( ii) 0.3 %, or (iii) 1 %, a fourth group (iv) received saline injections, and another (v) no injections. The fellow eye was left untreated. An additional group received no treatment to either eye. Prior to and at the end of the treatment period, refraction and ocular biometry were performed. Results Visual deprivation produced relative myopia in all groups (treated versus untreated eyes, P < 0.05). The amount of myopia was significantly affected by the drug treatment (one-way ANOVA, P < 0.0001); myopia was less in deprived eyes receiving either 0.3 % or 1 % TPMPA (saline = −4.38 ± 0.57D, 0.3 % TPMPA = −3.00 ± 0.48D, P < 0.01; 1 % TPMPA = −0.88 ± 0.51D, P < 0.001). The degree of axial elongation was correspondingly less (saline = 0.13 ± 0.02 mm, 0.3 % TPMPA = 0.09 ± 0.01 mm, P < 0.01, 1 % TPMPA = 0.02 ± 0.01 mm, P < 0.001) as was the VC elongation (saline = 0.08 ± 0.01 mm, 0.3 % TPMPA = 0.05 ± 0.01 mm, P < 0.01, 1 % TPMPA = 0.01 ± 0.01 mm; P < 0.001). ACD and LT were not affected (one-way ANOVA, P > 0.05). One percent TPMPA was more effective at inhibiting myopia than 0.3 % (P < 0.01), and 0.03 % did not appreciably inhibit the myopia (0.03 % TPMPA versus saline, P > 0.05). Conclusions Sub-conjunctival injections of TPMPA inhibit FDM in guinea pig models in a dose-dependent manner.

Numerical investigation of case hardening of plant tissue during dying and its influence on the cellular level shrinkage

Dried plant food materials are one of the major contributors to the global food industry. Widening the fundamental understanding on different mechanisms of food material alterations during drying assists the development of novel dried food products and processing techniques. In this regard, case hardening is an important phenomenon, commonly observed during the drying processes of plant food materials, which significantly influences the product quality and process performance. In this work, a recent meshfree-based numerical model of the authors is further improved and used to simulate the influence of case hardening on shrinkage characteristics of plant tissues during drying. In order to model fluid and wall mechanisms in each cell, Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) are used. The model is fundamentally more capable of simulating large deformation of multiphase materials, when compared with conventional grid-based modelling techniques such as Finite Element Methods (FEM) or Finite Difference Methods (FDM). Case hardening is implemented by maintaining distinct moisture levels in the different cell layers of a given tissue. In order to compare and investigate different factors influencing tissue deformations under case hardening, four different plant tissue varieties (apple, potato, carrot and grape) are studied. The simulation results indicate that the inner cells of any given tissue undergo limited shrinkage and cell wall wrinkling compared to the case hardened outer cell layers of the tissues. When comparing unique deformation characteristics of the different tissues, irrespective of the normalised moisture content, the cell size, cell fluid turgor pressure and cell wall characteristics influence the tissue response to case hardening.

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

Finite Element Solution Of Surface-Tension Driven Flows In Laser Surface-Melting

Lasers are very efficient in heating localized regions and hence they find a wide application in surface treatment processes. The surface of a material can be selectively modified to give superior wear and corrosion resistance. In laser surface-melting and welding problems, the high temperature gradient prevailing in the free surface induces a surface-tension gradient which is the dominant driving force for convection (known as thermo-capillary or Marangoni convection). It has been reported that the surface-tension driven convection plays a dominant role in determining the melt pool shape. In most of the earlier works on laser-melting and related problems, the finite difference method (FDM) has been used to solve the Navier Stokes equations [1]. Since the Reynolds number is quite high in these cases, upwinding has been used. Though upwinding gives physically realistic solutions even on a coarse grid, the results are inaccurate. McLay and Carey have solved the thermo-capillary flow in welding problems by an implicit finite element method [2]. They used the conventional Galerkin finite element method (FEM) which requires that the pressure be interpolated by one order lower than velocity (mixed interpolation). This restricts the choice of elements to certain higher order elements which need numerical integration for evaluation of element matrices. The implicit algorithm yields a system of nonlinear, unsymmetric equations which are not positive definite. Computations would be possible only with large mainframe computers.Sluzalec [3] has modeled the pulsed laser-melting problem by an explicit method (FEM). He has used the six-node triangular element with mixed interpolation. Since he has considered the buoyancy induced flow only, the velocity values are small. In the present work, an equal order explicit FEM is used to compute the thermo-capillary flow in the laser surface-melting problem. As this method permits equal order interpolation, there is no restriction in the choice of elements. Even linear elements such as the three-node triangular elements can be used. As the governing equations are solved in a sequential manner, the computer memory requirement is less. The finite element formulation is discussed in this paper along with typical numerical results.

GABAB Receptor antagonist CGP46381 inhibits form-deprivation myopia development in guinea pigs

The aim was to investigate the effects of the GABAB receptor antagonist, CGP46381, on form-deprivation myopia (FDM) in guinea pigs. Twenty-four guinea pigs had monocular visual deprivation induced using a diffuser for 11 days (day 14 to 25). The deprived eyes were treated with daily subconjunctival injections (100 μl) of either 2% CGP46381, 0.2% CGP46381, or saline or received no injection. The fellow eyes were left untreated. Another six animals received no treatment. At the start and end of the treatment period, ocular refractions were measured using retinoscopy and vitreous chamber depth (VCD) and axial length (AL) using A-scan ultrasound. All of the deprived eyes developed relative myopia (treated versus untreated eyes, P < 0.05). The amount of myopia was significantly affected by the drug treatment (one-way ANOVA, P < 0.0001). The highest dose tested, 2% CGP46381, significantly inhibited myopia development compared to saline (2% CGP46381: -1.08 ± 0.40 D, saline: -4.33 ± 0.67 D, P < 0.01). The majority of these effects were due to less AL (2% CGP46381: 0.03 ± 0.01 mm, saline: 0.13 ± 0.02 mm, P < 0.01) and VCD (2% CGP46381: 0.02 ± 0.01 mm, saline: 0.08 ± 0.01 mm, P < 0.01) elongation. The lower dose tested, 0.2% CGP46381, did not significantly inhibit FDM (P > 0.05). Subconjunctival injections of CGP46381 inhibit FDM development in guinea pigs in a dose-dependent manner.

Appraisal of Bishop's method of slope stability analysis

The stability of slopes is a major problem in geotechnical engineering. Of the methods available for the analysis of soil slopes such as limit equilibrium methods, limit analysis and numerical methods such as FEM and FDM, limit equilibrium methods are popular and generally used, owing to their simplicity in formulation and in evaluating the overall factor of safety of slope. However limit equilibrium methods possess certain disadvantages. They do not consider whether the slope is an embankment or natural slope or an excavation and ignore the effect of incremental construction, initial stress, stress strain behavior etc. In the work reported in this paper, a comparative study of actual state of stress and actual factor of safety and Bishop's factor of safety is performed. The actual factor of safety is obtained by consideration of contours of mobilised shear strains. Using Bishop's method of slices, the critical slip surfaces of a number of soil slopes with different geometries are determined and both the factors of safety are obtained. The actual normal stresses and shear stresses are determined from finite difference formulation using FLAG (Fast Lagrangian Analysis of Continuaa) with Mohr-Coulomb model. The comparative study is performed in terms of parameter lambda(c phi) (= gamma H tan phi/c). I is shown that actual factor of safety is higher than Bishop's factor of safety depending on slope angle and lambda(c phi).

Otimização da co-pirólise de gasóleo pesado com embalagens de PEAD pós-uso utilizando planejamento fatorial

A co-pirólise é uma rota promissora, uma vez que minimiza o impacto ambiental causado pela disposição do plástico de maneira inadequada, evita seu acúmulo em lixões e permite um melhor aproveitamento de um recurso natural não-renovável, o petróleo, matéria prima importante para a geração de energia e obtenção de produtos químicos. O presente trabalho teve como objetivo a definição das condições experimentais mais propícias à obtenção de líquidos pirolíticos com alta fração de óleo diesel, resultantes da co-pirólise de polietileno de alta densidade (PEAD) pós-consumo com gasóleo pesado tilizando-se catalisador de FCC (Fluid Catalytic Cracking). Como instrumento de otimização das condições experimentais, optou-se pela Metodologia Planejamento Fatorial. Foi também estudado o efeito das condições experimentais, como: a temperatura de reação, a relação gasóleo/polietileno e a quantidade de catalisador no meio reacional. As amostras de polietileno, gasóleo e catalisador foram submetidas à co-pirólise em sistema de leito fixo, sob fluxo constante de nitrogênio, variando-se a temperatura entre 450 C a 550 C, a quantidade de PEAD no meio reacional foi de 0,2 a 0,6 g, e a quantidade de catalisador foi de zero a 0,06 g, mantendo-se fixa a quantidade de gasóleo em 2 g. Foram efetuadas as caracterizações física e química do gasóleo, polietileno pós-uso e do catalisador. Como resultado, obteve-se a produção de 87% de fração de óleo diesel em duas condições diferentes: (a) 550 0C de temperatura sem catalisador; (b) 500 0C de temperatura e 25% de catalisador FCC. Em ambos os casos, a quantidade de gasóleo pesado e PEAD foram constantes (2 g Gasóleo; 0,2 g PEAD), assim com o tempo de reação de 15 minutos. A fração de óleo diesel obtida neste estudo alcançou o poder calorífico de 44,0 MJ/Kg que é similar ao óleo diesel comercial. É importante ressaltar que em ambos os casos nenhum resíduo foi produzido, sendo uma rota ambientalmente importante para reciclagem de embalagens plásticas contaminadas com óleo lubrificante originárias de postos de serviço, visando à recuperação de ambos conteúdo energético e orgânico dos resíduos de embalagens plásticas pós-uso