945 resultados para Slit Pores


Relevância:

10.00% 10.00%

Publicador:

Resumo:

BACKGROUND: Suction-based wound healing devices with open-pore foam interfaces are widely used to treat complex tissue defects. The impact of changes in physicochemical parameters of the wound interfaces has not been investigated. METHODS: Full-thickness wounds in diabetic mice were treated with occlusive dressing or a suction device with a polyurethane foam interface varying in mean pore size diameter. Wound surface deformation on day 2 was measured on fixed tissues. Histologic cross-sections were analyzed for granulation tissue thickness (hematoxylin and eosin), myofibroblast density (α-smooth muscle actin), blood vessel density (platelet endothelial cell adhesion molecule-1), and cell proliferation (Ki67) on day 7. RESULTS: Polyurethane foam-induced wound surface deformation increased with polyurethane foam pore diameter: 15 percent (small pore size), 60 percent (medium pore size), and 150 percent (large pore size). The extent of wound strain correlated with granulation tissue thickness that increased 1.7-fold in small pore size foam-treated wounds, 2.5-fold in medium pore size foam-treated wounds, and 4.9-fold in large pore size foam-treated wounds (p < 0.05) compared with wounds treated with an occlusive dressing. All polyurethane foams increased the number of myofibroblasts over occlusive dressing, with maximal presence in large pore size foam-treated wounds compared with all other groups (p < 0.05). CONCLUSIONS: The pore size of the interface material of suction devices has a significant impact on the wound healing response. Larger pores increased wound surface strain, tissue growth, and transformation of contractile cells. Modification of the pore size is a powerful approach for meeting biological needs of specific wounds.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The objectives of the project were to develop methodologies for (i) prediction and measurement of the magnitude of pressure which develops within pores of saturated porous materials upon freezing, (ii) determination of pore structure (pore size distribution) of porous materials; (iii) prediction and measurement of the rate with which pore ice grows; and (iv) prediction of frost susceptibility of porous materials with varying pore structures. As with all research endeavors solution of one problem leads to another one and this project was no exception. Emergence of new problems and the measures taken as the work progressed were discussed in progress reports submitted to the board. This final report will discuss only the conclusive finds and suggest measures to be taken for future investigations. The theory discussed in the proposal is not repeated in this report for the sake of brevity. However, the paper published as part of this project containing the theory is attached as Appendix I for the reader interested in the theory. In conformity with the objectives, this report consists of four parts. In accordance with the project contract two ice porosimeters were built and one will be delivered to the Iowa DOT after training of a DOT technician under the supervision of Mr. Wendell Dubberke with assistance from ISU researchers. During the training period debugging and further improvements in software will continue.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

PURPOSE: To describe the use of anterior segment optical coherence tomography (AS-OCT) to clarify the position and patency of aqueous shunt devices in the anterior chamber of eyes where corneal edema or tube position does not permit a satisfactory view. DESIGN: Noncomparative observational case series. METHODS: Four cases are reported in which aqueous shunt malposition or obstruction was suspected but the shunt could not be seen on clinical examination. The patients underwent AS-OCT to identify the position and patency of the shunt tip. RESULTS: In each case, AS-OCT provided data regarding tube position and/or patency that could not be obtained by slit-lamp examination or by gonioscopy that influenced management. CONCLUSIONS: AS-OCT can be used to visualize anterior chamber tubes in the presence of corneal edema that precludes an adequate view or in cases where the tube is retracted into the cornea. In such cases, AS-OCT is useful in identifying shunt patency and position, which helps guide clinical decision making.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Needle fibre calcite is one of the most ubiquitous habits of calcite in vadose environments (caves deposits, soil pores, etc.). Its origin, either through inorganic, indirect or direct biological processes, has long been debated. In this study, investigations at 11 sites in Europe, Africa and Central America support arguments for its biogenic origin. The wide range of needle morphologies is the result of a gradual evolution of the simplest type, a rod. This rod is the elementary brick which, by aggregation and welding, builds more complex needles. The absence of cross-welded needles implies that they are welded in a mould, or under a longitudinal and unidirectional constraint, before being released inside the soil pores. The difference between the lengthening of the needles and the c axis can be explained by the existence of needles observed under a scanning electron microscope in organic sleeves, which can act as a mould during rod growth. Complex morphologies with epitaxial outgrowths on straight rods cannot have grown entirely inside organic microtubes; they must result from soil diagenesis after the release of straight rods in a soil-free medium. Whisker crystals are interpreted as the result of growth and coalescence of euhedral crystals on a rod. Rhomb chains are considered to be the consequence of successive epitaxial growth steps on a needle during variations in growth conditions. Isotopic signatures for needle fibre calcite vary from -16.63[per mille] to +1.10[per mille] and from -8.63[per mille] to -2.25[per mille] for Delta13C and Delta18O, respectively. The absence of high Delta18O values for needle fibre calcite precludes a purely physicochemical origin (evaporative) for this particular habit of calcite. As epitaxial growth cannot precipitate in the same conditions as initial needles, needle fibre calcite stable isotopic signatures should be used with caution as a proxy for palaeoenvironmental reconstructions. In addition, it is suggested that the term needle fibre calcite should be kept for the original biogenic form. The other habit should be referred to as epitaxial forms of needle fibre calcite.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Diabetic retinopathy is associated with ocular inflammation, leading to retinal barrier breakdown, macular edema, and visual cell loss. We investigated the molecular mechanisms involved in microglia/macrophages trafficking in the retina and the role of protein kinase Cζ (PKCζ) in this process. Goto Kakizaki (GK) rats, a model for spontaneous type 2 diabetes were studied until 12 months of hyperglycemia. Up to 5 months, sparse microglia/macrophages were detected in the subretinal space, together with numerous pores in retinal pigment epithelial (RPE) cells, allowing inflammatory cell traffic between the retina and choroid. Intercellular adhesion molecule-1 (ICAM-1), caveolin-1 (CAV-1), and PKCζ were identified at the pore border. At 12 months of hyperglycemia, the significant reduction of pores density in RPE cell layer was associated with microglia/macrophages accumulation in the subretinal space together with vacuolization of RPE cells and disorganization of photoreceptors outer segments. The intraocular injection of a PKCζ inhibitor at 12 months reduced iNOS expression in microglia/macrophages and inhibited their migration through the retina, preventing their subretinal accumulation. We show here that a physiological transcellular pathway takes place through RPE cells and contributes to microglia/macrophages retinal trafficking. Chronic hyperglycemia causes alteration of this pathway and subsequent subretinal accumulation of activated microglia/macrophages.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The purpose of breathing remained an enigma for a long time. The Hippocratic school described breathing patterns but did not associate breathing with the lungs. Empedocles and Plato postulated that breathing was linked to the passage of air through pores of the skin. This was refuted by Aristotle who believed that the role of breathing was to cool the heart. In Alexandria, breakthroughs were accomplished in the anatomy and physiology of the respiratory system. Later, Galen proposed an accurate description of the respiratory muscles and the mechanics of breathing. However, his heart-lung model was hampered by the traditional view of two non-communicating vascular systems - veins and arteries. After a period of stagnation in the Middle Ages, knowledge progressed with the discovery of pulmonary circulation. The comprehension of the purpose of breathing progressed by steps thanks to Boyle and Mayow among others, and culminated with the contribution of Priestley and the discovery of oxygen by Lavoisier. Only then was breathing recognized as fulfilling the purpose of respiration, or gas exchange. A century later, a controversy emerged concerning the active or passive transfer of oxygen from alveoli to the blood. August and Marie Krogh settled the dispute, showing that passive diffusion was sufficient to meet the oxygen needs. © 2014 S. Karger AG, Basel.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Two goals were pursued in this research: first, to evaluate statistically some effects of sample preparation and instrument geometry on reproducibility of X-ray diffraction intensity data; and second, to develop a procedure for finding minimum peak and background counting times for a desired level of accuracy. The ratio of calcite to dolomite in limestones was determined in trials. Ultra-fine wet grinding of the limestone in porcelain impact type ball mill gave most consistent X-ray results, but caused considerable line broadening, and peaks were best measured on an area count basis. Sample spinning reduced variance about one third, and a coarse beam-medium detector slit arrangement was found to be best. An equation is developed relating coefficient of variation of a count ratio to peak and background counts. By use of the equation or graphs the minimum coefficient of variation is predicted from one fast scan, and the number and optimum arrangement of additional counting periods to reduce variation to a desired limit may be obtained. The calculated coefficient is the maximum which may be attributed to the counting statistic but does not include experimental deviations.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

PURPOSE: To describe new affected individuals of Franceschetti's original pedigree of hereditary recurrent erosion and to classify a unique entity called Franceschetti corneal dystrophy. DESIGN: Observational case series. METHODS: Slit-lamp examination of 10 affected individuals was conducted. Biomicroscopic examinations were supplemented by peripheral corneal biopsy in 1 affected patient with corneal haze. Tissue was processed for light and electron microscopy and immunohistochemistry was performed. DNA analysis was carried out in 12 affected and 3 nonaffected family members. RESULTS: All affected individuals suffered from severe ocular pain in the first decade of life, attributable to recurrent corneal erosions. Six adult patients developed bilateral diffuse subepithelial opacifications in the central and paracentral cornea. The remaining 4 affected individuals had clear corneas in the pain-free stage of the disorder. Histologic and immunohistochemical examination of the peripheral cornea in a single patient showed a subepithelial, avascular pannus. There was negative staining with Congo red. DNA analysis excluded mutations in the transforming growth factor beta-induced (TGFBI) gene and in the tumor-associated calcium signal transducer 2 (TACSTD2) gene. CONCLUSION: We have extended the pedigree of Franceschetti corneal dystrophy and elaborated its natural history on the basis of clinical examinations. A distinctive feature is the appearance of subepithelial opacities in adult life, accompanied by a decreased frequency of recurrent erosion attacks. Its clinical features appear to distinguish it from most other forms of dominantly inherited recurrent corneal erosion reported in the literature.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Este trabalho teve por objetivo avaliar o efeito de três rações experimentais com diferentes níveis protéicos (33,6%, 26,6% e 22,5%), comparadas a uma ração comercial (46,5%), no desempenho e crescimento heterogêneo de girinos de rã-touro (Rana catesbeiana). Os girinos foram mantidos, durante três meses, em caixas de amianto abastecidas com 1.000 L de água corrente, na densidade de 1 girino L-1. Os girinos foram alimentados, diariamente, com duas porções iguais ad libitum e foram submetidos, quinzenalmente, à pesagem. Os grupos alimentados com a ração com 46,5% de proteína bruta mostraram maior ganho médio de peso, porém apresentaram crescimento heterogêneo mais elevado, e alguns indivíduos apresentaram deformações nos membros (27% no início da metamorfose e 5% no final). Os girinos que utilizaram as rações com 33,6% e 26,6% de proteína bruta tiveram desenvolvimento similar entre si, menor crescimento heterogêneo e não apresentaram deformações, o que demonstra que essas rações são mais adequadas do que a primeira. A ração com 22,5% de proteína bruta mostrou-se inadequada às necessidades dos girinos, o que provocou a exclusão dessa condição, antes do término do experimento, a fim de preservar o bem estar dos animais.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Concrete durability may be considered as the ability to maintain serviceability over the design life without significant deterioration, and is generally a direct function of the mixture permeability. Therefore, reducing permeability will improve the potential durability of a given mixture and, in turn, improve the serviceability and longevity of the structure. Given the importance of this property, engineers often look for methods that can decrease permeability. One approach is to add chemical compounds known as integral waterproofing admixtures or permeability-reducing admixtures, which help fill and block capillary pores in the paste. Currently, there are no standard approaches to evaluate the effectiveness of permeability-reducing admixtures or to compare different products in the US. A review of manufacturers’ data sheets shows that a wide range of test methods have been used, and rarely are the same tests used on more than one product. This study investigated the fresh and hardened properties of mixtures containing commercially available hydrophilic and hydrophobic types of permeability-reducing admixtures. The aim was to develop a standard test protocol that would help owners, engineers, and specifiers compare different products and to evaluate their effects on concrete mixtures that may be exposed to hydrostatic or non-hydrostatic pressure. In this experimental program, 11 concrete mixtures were prepared with a fixed water-to-cement ratio and cement content. One plain mixture was prepared as a reference, 5 mixtures were prepared using the recommended dosage of the different permeability-reducing admixtures, and 5 mixtures were prepared using double the recommended dosage. Slump, air content, setting time, compressive and flexural strength, shrinkage, and durability indicating tests including electrical resistivity, rapid chloride penetration, air permeability, permeable voids, and sorptivity tests were conducted at various ages. The data are presented and recommendations for a testing protocol are provided.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

BACKGROUND: Eotaxin-1 (CCL11) is a potent eosinophil chemotactic and activating peptide that may be implicated in the pathogenesis of chronic allergic eye disease and has been associated with the wearing of contact lenses (CL) in patients with contact lens papillary conjunctivitis (CLPC). The purpose of this study was to study eotaxin-1 expression in the tears of long-term CL wearers. PATIENTS AND METHODS: Tears were collected with glass capillaries from 15 patients (2 male, 13 female) with various degree of CLPC at 2-year intervals. CLPC severity was graded from 0 to 4 with reference to standard slit-lamp photographs of the superior tarsal conjunctiva. The eotaxin-1 level in the tears was measured by an ELISA, using mouse anti-human eotaxin monoclonal antibodies. RESULTS: The mean age was 32.5 ± 13.3 years (range: 17 - 69 years). The mean interval between the tear collections was 30 ± 4.8 months. The mean concentration of eotaxin was 2150 ± 477 pg/mL and 2486 ± 810 pg/mL for the first and second series, respectively. The difference was not statistically significant (paired Wilcoxon/Kruskal-Wallis, p = 0.803). The mean score of papilla grade was 1.26 ± 0.18 for the first sample and 1.40 ± 0.19 two years later. There was no significant difference of grading between the two time periods (paired Wilcoxon/Kruskal-Wallis, p = 0.751). CONCLUSIONS: the eotaxin-1 level remains up-regulated over a long time period in patients wearing CL, most of them with chronic CLPC. Eotaxin may play a role in the pathogenesis of contact lens intolerance.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The effects of diethylenetriaminpenta(methylenephosphonic acid) (DTPMP), a phosphonate inhibitor, on the growth of delayed ettringite have been evaluated using concrete in highway US 20 near Williams, Iowa, and the cores of six highways subject to moderate (built in 1992) or minor (built in 1997) deterioration. Application of 0.01 and 0.1 vol. % DTPMP to cores was made on a weekly or monthly basis for one year under controlled laboratory-based freeze-thaw and wet-dry conditions over a temperature range of -15 degrees to 58 degrees C to mimic extremes in Iowa roadway conditions. The same concentrations of phosphonate were also applied to cores left outside (roof of Science I at Iowa State University) over the same period of time. Nineteen applications of 0.1 vol. % DTPMP with added deicing salt solution (about 23 weight % NACL) were made to US 20 during the winters of 2003 and 2004. In untreated samples, air voids, pores, and occasional cracks are lined with acicular ettringite crystals (up to 50 micrometers in length) whereas air voids, pores, and cracks in concrete from the westbound lane of US 20 are devoid of ettringite up to a depth of about 0.5 mm from the surface of the concrete. Ettringite is also absent in zones up to 6 mm from the surface of concrete slabs placed on the roof of Science I and cores subject to laboratory-based freeze-thaw experiments. In these zones, the relatively high concentration of DTPMP caused it to behave as a chelator. Stunted ettringite crystals 5 to 25 micrometers in length, occasionally coated with porlandite, form on the margins of these zones indicating that in these areas DTPMP behaved as an inhibitor due to a reduction in the concentration of phosphonate. Analyses of mixes of ettringite and DTPMP using electrospray mass spectrometry suggests that the stunting of ettringite growth is caused by the adsorption of a Ca2+ ion and a water molecule to deprotonated DTPMP on the surface of the {0001} face of ettringite. It is anticipated that by using a DTPMP concentration of between 0.001 and 0.01 vol. % for the extended life of a highway (i.e. >20 years), deterioration caused by the expansive growth of ettringite will be markedly reduced.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Antimicrobial films were prepared by including enterocins to alginate, polyvinyl alcohol (PVOH), and zein films. The physical performance of the films was assessed by measuring color, microstructure (SEM), water vapor permeability (WVP), and tensile properties. All studied biopolymers showed poor WVP and limited tensile properties. PVOH showed the best performance exhibiting the lowest WVP values, higher tensile properties, and flexibility among studied biopolymers. SEM of antimicrobial films showed increased presence of voids and pores as a consequence of enterocin addition. However, changes in microstructure did not disturb WVP of films. Moreover, enterocin-containing films showed slight improvement compared to control films. Addition of enterocins to PVOH films had a plasticizing effect, by reducing its tensile strength and increasing the strain at break. The presence of enterocins had an important effect on tensile properties of zein films by significantly reducing its brittleness. Addition of enterocins, thus, proved not to disturb the physical performance of studied biopolymers. Development of new antimicrobial biodegradable packaging materials may contribute to improving food safety while reducing environmental impact derived from packaging waste.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

The Iowa Pore Index (IPI) measures the pore system of carbonate (limestone and dolomite) rocks using pressurized water to infiltrate the pore system. This technique provides quantitative results for the primary and capillary (secondary) pores in carbonate rocks. These results are used in conjunction with chemical and mineralogical test results to calculate a quality number, which is used as a predictor of aggregate performance in Portland cement concrete (PCC) leading to the durability classification of the aggregate. This study had two main objectives: to determine the effect different aggregate size has on IPI test results and to establish the precision of IPI test and test apparatus. It was found that smaller aggregate size fractions could be correlated to the standard 1/2”-3/4” size sample. Generally, a particle size decrease was accompanied by a slight decrease in IPI values. The IPI testing also showed fairly good agreement of the secondary pore index number between the 1/2”-3/4”and the 3/8”-1/2” fraction. The #4-3/8” showed a greater difference of the secondary number from the 1/2”-3/4” fraction. The precision of the IPI test was established as a standard deviation (Sr) of 2.85 (Primary) and 0.87 (Secondary) with a repeatability limit (%r) of 8.5% and 14.9% for the primary and secondary values, respectively.

Relevância:

10.00% 10.00%

Publicador:

Resumo:

Les problèmes d'écoulements multiphasiques en média poreux sont d'un grand intérêt pour de nombreuses applications scientifiques et techniques ; comme la séquestration de C02, l'extraction de pétrole et la dépollution des aquifères. La complexité intrinsèque des systèmes multiphasiques et l'hétérogénéité des formations géologiques sur des échelles multiples représentent un challenge majeur pour comprendre et modéliser les déplacements immiscibles dans les milieux poreux. Les descriptions à l'échelle supérieure basées sur la généralisation de l'équation de Darcy sont largement utilisées, mais ces méthodes sont sujettes à limitations pour les écoulements présentant de l'hystérèse. Les avancées récentes en terme de performances computationnelles et le développement de méthodes précises pour caractériser l'espace interstitiel ainsi que la distribution des phases ont favorisé l'utilisation de modèles qui permettent une résolution fine à l'échelle du pore. Ces modèles offrent un aperçu des caractéristiques de l'écoulement qui ne peuvent pas être facilement observées en laboratoire et peuvent être utilisé pour expliquer la différence entre les processus physiques et les modèles à l'échelle macroscopique existants. L'objet premier de la thèse se porte sur la simulation numérique directe : les équations de Navier-Stokes sont résolues dans l'espace interstitiel et la méthode du volume de fluide (VOF) est employée pour suivre l'évolution de l'interface. Dans VOF, la distribution des phases est décrite par une fonction fluide pour l'ensemble du domaine et des conditions aux bords particulières permettent la prise en compte des propriétés de mouillage du milieu poreux. Dans la première partie de la thèse, nous simulons le drainage dans une cellule Hele-Shaw 2D avec des obstacles cylindriques. Nous montrons que l'approche proposée est applicable même pour des ratios de densité et de viscosité très importants et permet de modéliser la transition entre déplacement stable et digitation visqueuse. Nous intéressons ensuite à l'interprétation de la pression capillaire à l'échelle macroscopique. Nous montrons que les techniques basées sur la moyenne spatiale de la pression présentent plusieurs limitations et sont imprécises en présence d'effets visqueux et de piégeage. Au contraire, une définition basée sur l'énergie permet de séparer les contributions capillaires des effets visqueux. La seconde partie de la thèse est consacrée à l'investigation des effets d'inertie associés aux reconfigurations irréversibles du ménisque causé par l'interface des instabilités. Comme prototype pour ces phénomènes, nous étudions d'abord la dynamique d'un ménisque dans un pore angulaire. Nous montrons que, dans un réseau de pores cubiques, les sauts et reconfigurations sont si fréquents que les effets d'inertie mènent à différentes configurations des fluides. A cause de la non-linéarité du problème, la distribution des fluides influence le travail des forces de pression, qui, à son tour, provoque une chute de pression dans la loi de Darcy. Cela suggère que ces phénomènes devraient être pris en compte lorsque que l'on décrit l'écoulement multiphasique en média poreux à l'échelle macroscopique. La dernière partie de la thèse s'attache à démontrer la validité de notre approche par une comparaison avec des expériences en laboratoire : un drainage instable dans un milieu poreux quasi 2D (une cellule Hele-Shaw avec des obstacles cylindriques). Plusieurs simulations sont tournées sous différentes conditions aux bords et en utilisant différents modèles (modèle intégré 2D et modèle 3D) afin de comparer certaines quantités macroscopiques avec les observations au laboratoire correspondantes. Malgré le challenge de modéliser des déplacements instables, où, par définition, de petites perturbations peuvent grandir sans fin, notre approche numérique apporte de résultats satisfaisants pour tous les cas étudiés. - Problems involving multiphase flow in porous media are of great interest in many scientific and engineering applications including Carbon Capture and Storage, oil recovery and groundwater remediation. The intrinsic complexity of multiphase systems and the multi scale heterogeneity of geological formations represent the major challenges to understand and model immiscible displacement in porous media. Upscaled descriptions based on generalization of Darcy's law are widely used, but they are subject to several limitations for flow that exhibit hysteric and history- dependent behaviors. Recent advances in high performance computing and the development of accurate methods to characterize pore space and phase distribution have fostered the use of models that allow sub-pore resolution. These models provide an insight on flow characteristics that cannot be easily achieved by laboratory experiments and can be used to explain the gap between physical processes and existing macro-scale models. We focus on direct numerical simulations: we solve the Navier-Stokes equations for mass and momentum conservation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. In the VOF the distribution of the phases is described by a fluid function (whole-domain formulation) and special boundary conditions account for the wetting properties of the porous medium. In the first part of this thesis we simulate drainage in a 2-D Hele-Shaw cell filled with cylindrical obstacles. We show that the proposed approach can handle very large density and viscosity ratios and it is able to model the transition from stable displacement to viscous fingering. We then focus on the interpretation of the macroscopic capillary pressure showing that pressure average techniques are subject to several limitations and they are not accurate in presence of viscous effects and trapping. On the contrary an energy-based definition allows separating viscous and capillary contributions. In the second part of the thesis we investigate inertia effects associated with abrupt and irreversible reconfigurations of the menisci caused by interface instabilities. As a prototype of these phenomena we first consider the dynamics of a meniscus in an angular pore. We show that in a network of cubic pores, jumps and reconfigurations are so frequent that inertia effects lead to different fluid configurations. Due to the non-linearity of the problem, the distribution of the fluids influences the work done by pressure forces, which is in turn related to the pressure drop in Darcy's law. This suggests that these phenomena should be taken into account when upscaling multiphase flow in porous media. The last part of the thesis is devoted to proving the accuracy of the numerical approach by validation with experiments of unstable primary drainage in a quasi-2D porous medium (i.e., Hele-Shaw cell filled with cylindrical obstacles). We perform simulations under different boundary conditions and using different models (2-D integrated and full 3-D) and we compare several macroscopic quantities with the corresponding experiment. Despite the intrinsic challenges of modeling unstable displacement, where by definition small perturbations can grow without bounds, the numerical method gives satisfactory results for all the cases studied.