Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Invariants of binary differential equations

In this paper, we study binary differential equations a(x, y)dy (2) + 2b(x, y) dx dy + c(x, y)dx (2) = 0, where a, b, and c are real analytic functions. Following the geometric approach of Bruce and Tari in their work on multiplicity of implicit differential equations, we introduce a definition of the index for this class of equations that coincides with the classical Hopf`s definition for positive binary differential equations. Our results also apply to implicit differential equations F(x, y, p) = 0, where F is an analytic function, p = dy/dx, F (p) = 0, and F (pp) not equal aEuro parts per thousand 0 at the singular point. For these equations, we relate the index of the equation at the singular point with the index of the gradient of F and index of the 1-form omega = dy -aEuro parts per thousand pdx defined on the singular surface F = 0.

Evaluation Of The Effect Of Different Methods Of Microabrasion And Polishing On Surface Roughness Of Dental Enamel.

The microabrasion technique of enamel consists of selectively abrading the discolored areas or causing superficial structural changes in a selective way. In microabrasion technique, abrasive products associated with acids are used, and the evaluation of enamel roughness after this treatment, as well as surface polishing, is necessary. This in-vitro study evaluated the enamel roughness after microabrasion, followed by different polishing techniques. Roughness analyses were performed before microabrasion (L1), after microabrasion (L2), and after polishing (L3).Thus, 60 bovine incisive teeth divided into two groups were selected (n=30): G1- 37% phosphoric acid (37%) (Dentsply) and pumice; G2- hydrochloric acid (6.6%) associated with silicon carbide (Opalustre - Ultradent). Thereafter, the groups were divided into three sub-groups (n=10), according to the system of polishing: A - Fine and superfine granulation aluminum oxide discs (SofLex 3M); B - Diamond Paste (FGM) associated with felt discs (FGM); C - Silicone tips (Enhance - Dentsply). A PROC MIXED procedure was applied after data exploratory analysis, as well as the Tukey-Kramer test (5%). No statistical differences were found between G1 and G2 groups. L2 differed statistically from L1 and showed superior amounts of roughness. Differences in the amounts of post-polishing roughness for specific groups (1A, 2B, and 1C) arose, which demonstrated less roughness in L3 and differed statistically from L2 in the polishing system. All products increased enamel roughness, and the effectiveness of the polishing systems was dependent upon the abrasive used.

Tuning The Surface Anisotropy In Fe-doped Nio Nanoparticles.

Ni(1-x)FexO nanoparticles have been obtained by the co-precipitation chemical route. X-ray diffraction analyses using Rietveld refinement have shown a slight decrease in the microstrain and mean particle size as a function of the Fe content. The zero-field-cooling (ZFC) and field-cooling (FC) magnetization curves show superparamagnetic behavior at high temperatures and a low temperature peak (at T = 11 K), which is enhanced with increasing Fe concentration. Unusual behavior of the coercive field in the low temperature region and an exchange bias behavior were also observed. A decrease in the Fe concentration induces an increase in the exchange bias field. We argue that these behaviors can be linked with the strengthening of surface anisotropy caused by the incorporation of Fe ions.

The Effect Of Poly(methyl Methacrylate) Surface Treatments On The Adhesion Of Silicone-based Resilient Denture Liners.

Different surface treatment protocols of poly(methyl methacrylate) have been proposed to improve the adhesion of silicone-based resilient denture liners to poly(methyl methacrylate) surfaces. The purpose of this study was to evaluate the effect of different poly(methyl methacrylate) surface treatments on the adhesion of silicone-based resilient denture liners. Poly(methyl methacrylate) specimens were prepared and divided into 4 treatment groups: no treatment (control), methyl methacrylate for 180 seconds, acetone for 30 seconds, and ethyl acetate for 60 seconds. Poly(methyl methacrylate) disks (30.0 × 5.0 mm; n = 10) were evaluated regarding surface roughness and surface free energy. To evaluate tensile bond strength, the resilient material was applied between 2 treated poly(methyl methacrylate) bars (60.0 × 5.0 × 5.0 mm; n = 20 for each group) to form a 2-mm-thick layer. Data were analyzed by 1-way ANOVA and the Tukey honestly significant difference tests (α = .05). A Pearson correlation test verified the influence of surface properties on tensile bond strength. Failure type was assessed, and the poly(methyl methacrylate) surface treatment modifications were visualized with scanning electron microscopy. The surface roughness was increased (P < .05) by methyl methacrylate treatment. For the acetone and ethyl acetate groups, the surface free energy decreased (P < .05). The tensile bond strength was higher for the methyl methacrylate and ethyl acetate groups (P < .05). No correlation was found regarding surface properties and tensile bond strength. Specimens treated with acetone and methyl methacrylate presented a cleaner surface, whereas the ethyl acetate treatment produced a porous topography. The methyl methacrylate and ethyl acetate surface treatment protocols improved the adhesion of a silicone-based resilient denture liner to poly(methyl methacrylate).

Electrochemical Oxidation Of Landfill Leachate In A Flow Reactor: Optimization Using Response Surface Methodology.

Response surface methodology based on Box-Behnken (BBD) design was successfully applied to the optimization in the operating conditions of the electrochemical oxidation of sanitary landfill leachate aimed for making this method feasible for scale up. Landfill leachate was treated in continuous batch-recirculation system, where a dimensional stable anode (DSA(©)) coated with Ti/TiO2 and RuO2 film oxide were used. The effects of three variables, current density (milliampere per square centimeter), time of treatment (minutes), and supporting electrolyte dosage (moles per liter) upon the total organic carbon removal were evaluated. Optimized conditions were obtained for the highest desirability at 244.11 mA/cm(2), 41.78 min, and 0.07 mol/L of NaCl and 242.84 mA/cm(2), 37.07 min, and 0.07 mol/L of Na2SO4. Under the optimal conditions, 54.99 % of chemical oxygen demand (COD) and 71.07 ammonia nitrogen (NH3-N) removal was achieved with NaCl and 45.50 of COD and 62.13 NH3-N with Na2SO4. A new kinetic model predicted obtained from the relation between BBD and the kinetic model was suggested.

Effect Of Sodium Hypochlorite And Peracetic Acid On The Surface Roughness Of Acrylic Resin Polymerized By Heated Water For Short And Long Cycles.

To evaluate the surface roughness of acrylic resin submitted to chemical disinfection via 1% sodium hypochlorite (NaClO) or 1% peracetic acid (C2H4O3). The disc-shaped resin specimens (30 mm diameter ×4 mm height) were polymerized by heated water using two cycles (short cycle: 1 h at 74°C and 30 min at 100°C; conventional long cycle: 9 h at 74°C). The release of substances by these specimens in water solution was also quantified. Specimens were fabricated, divided into four groups (n = 10) depending on the polymerization time and disinfectant. After polishing, the specimens were stored in distilled deionized water. Specimens were immersed in 1% NaClO or 1% C2H4O3 for 30 min, and then were immersed in distilled deionized water for 20 min. The release of C2H4O3 and NaClO was measured via visual colorimetric analysis. Roughness was measured before and after disinfection. Roughness data were subjected to two-way ANOVA and Tukey's test. There was no interaction between polymerization time and disinfectant in influencing the average surface roughness (Ra, P = 0.957). Considering these factors independently, there were significant differences between short and conventional long cycles (P = 0.012), but no significant difference between the disinfectants hypochlorite and C2H4O3 (P = 0.366). Visual colorimetric analysis did not detect release of substances. It was concluded that there was the difference in surface roughness between short and conventional long cycles, and disinfection at acrylic resins polymerized by heated water using a short cycle modified the properties of roughness.

Detection Of Explosives On The Surface Of Banknotes By Raman Hyperspectral Imaging And Independent Component Analysis.

The aim of this study was to develop a methodology using Raman hyperspectral imaging and chemometric methods for identification of pre- and post-blast explosive residues on banknote surfaces. The explosives studied were of military, commercial and propellant uses. After the acquisition of the hyperspectral imaging, independent component analysis (ICA) was applied to extract the pure spectra and the distribution of the corresponding image constituents. The performance of the methodology was evaluated by the explained variance and the lack of fit of the models, by comparing the ICA recovered spectra with the reference spectra using correlation coefficients and by the presence of rotational ambiguity in the ICA solutions. The methodology was applied to forensic samples to solve an automated teller machine explosion case. Independent component analysis proved to be a suitable method of resolving curves, achieving equivalent performance with the multivariate curve resolution with alternating least squares (MCR-ALS) method. At low concentrations, MCR-ALS presents some limitations, as it did not provide the correct solution. The detection limit of the methodology presented in this study was 50μgcm(-2).

Didanosine-loaded Chitosan Microspheres Optimized By Surface-response Methodology: A Modified Maximum Likelihood Classification" Approach Formulation For Reverse Transcriptase Inhibitors."

Didanosine-loaded chitosan microspheres were developed applying a surface-response methodology and using a modified Maximum Likelihood Classification. The operational conditions were optimized with the aim of maintaining the active form of didanosine (ddI), which is sensitive to acid pH, and to develop a modified and mucoadhesive formulation. The loading of the drug within the chitosan microspheres was carried out by ionotropic gelation technique with sodium tripolyphosphate (TPP) as cross-linking agent and magnesium hydroxide (Mg(OH)2) to assure the stability of ddI. The optimization conditions were set using a surface-response methodology and applying the Maximum Likelihood Classification, where the initial chitosan concentration, TPP and ddI concentration were set as the independent variables. The maximum ddI-loaded in microspheres (i.e. 1433mg of ddI/g chitosan), was obtained with 2% (w/v) chitosan and 10% TPP. The microspheres depicted an average diameter of 11.42μm and ddI was gradually released during 2h in simulated enteric fluid.

Assessment of ocular surface toxicity after topical instillation of nitric oxide donors

PURPOSE: To evaluate the ocular surface toxicity of two nitric oxide donors in ex vivo and in vivo animal models: S-nitrosoglutathione (GSNO) and S-nitroso-N-acetylcysteine (SNAC) in a hydroxypropyl methylcellulose (HPMC) matrix at final concentrations 1.0 and 10.0 mM. METHODS: Ex vivo GSNO and SNAC toxicities were clinically and histologically analyzed using freshly excised pig eyeballs. In vivo experiments were performed with 20 albino rabbits which were randomized into 4 groups (5 animals each): Groups 1 and 2 received instillations of 150 µL of aqueous HPMC solution containing GSNO 1.0 and 10.0 mM, respectively, in one of the eyes; Groups 3 and 4 received instillations of 150 µL of aqueous HPMC solution-containing SNAC 1.0 and 10.0 mM, respectively, in one of the eyes. The contralateral eyes in each group received aqueous HPMC as a control. All animals underwent clinical evaluation on a slit lamp and the eyes were scored according to a modified Draize eye test and were histologically analyzed. RESULTS: Pig eyeballs showed no signs of perforation, erosion, corneal opacity or other gross damage. These findings were confirmed by histological analysis. There was no difference between control and treated rabbit eyes according to the Draize eye test score in all groups (p>0.05). All formulations showed a mean score under 1 and were classified as non-irritating. There was no evidence of tissue toxicity in the histological analysis in all animals. CONCLUSION: Aqueous HPMC solutions containing GSNO and SNAC at concentrations up to 10.0 mM do not induce ocular irritation.

Effect of biofunctionalized implant surface on osseointegration: a histomorphometric study in dogs

Among the different properties that influence bone apposition around implants, the chemical or biochemical composition of implant surface may interfere on its acceptance by the surrounding bone. The aim of this study was to investigate if a biofunctionalization of implant surface influences the bone apposition in a dog model and to compare it with other surfaces, such as a microstructured created by the grit-blasting/acid-etching process. Eight young adult male mongrel dogs had the bilateral mandibular premolars extracted and each one received 6 implants after 12 weeks, totaling 48 implants in the experiment. Four groups of implants were formed with the same microrough topography with or without some kind of biofunctionalization treatment. After histomorphometric analysis, it was observed that the modified microstructured surface with a "low concentration of the bioactive peptide" provided a higher adjacent bone density (54.6%) when compared to the other groups (microstructured + HA coating = 46.0%, microstructured only = 45.3% and microstructured + "high concentration of the bioactive peptide" = 40.7%), but this difference was not statistically significant. In conclusion, biofunctionalization of the implant surface might interfere in the bone apposition around implants, especially in terms of bone density. Different concentrations of bioactive peptide lead to different results.

Assessment in vitro of brushing on dental surface roughness alteration by laser interferometry

Noncarious cervical lesions (NCCLs) are considered to be of multifactorial origin, normally associated with inadequate brushing. This study assessed the influence in vitro of simulated brushing on NCCL formation. Fifteen human premolars were submitted to brushing in the cementoenamel junction region, using hard-, medium- and soft-bristled brushes associated with a toothpaste of medium abrasiveness under a 200 g load, at a speed of 356 rpm for 100 minutes. The surface topography of the region was analyzed before and after brushing, by means of a laser interferometer, using "cut-off" values of 0.25 and considering roughness values in mm. The initial roughness (mm) results for dentin (D / bristle consistency: 1 - soft, 2 - medium and 3 - hard) were as follows: (D1) 1.25 ± 0.45; (D2) 1.12 ± 0.44; (D3) 1.05 ± 0.41. For enamel (E / bristle consistency: 1 - soft, 2 - medium and 3 - hard), the initial results were: (E1) 1.18 ± 0.35; (E2) 1.32 ± 0.25; (E3) 1.50 ± 0.38. After brushing, the following were the values for dentin: (D1) 2.32 ± 1.99; (D2) 3.30 ± 0.96; (D3) Over 500. For enamel, the values after brushing were: (E1) 1.37 ± 0.31; (E2) 2.15 ± 0.90; (E3) 1.22 ± 0.47. Based on the results of the ANOVA and Tukey statistical analyses (a = .05) it was concluded that soft, medium and hard brushes are not capable of abrading enamel, whereas dentin showed changes in surface roughness by the action of medium- and hard-bristled brushes.

Effect of different cleansers on the surface of removable partial denture

Removable partial dentures (RPD) demand specific hygienic cleaning and the combination of brushing with immersion in chemical solutions has been the most recommended method for control of biofilm. However, the effect of the cleansers on metallic components has not been widely investigated. This study evaluated the effect of different cleansers on the surface of RPD. Five disc specimens (12 mm x 3 mm metallic disc centered in a 38 x 18 x 4 mm mould filled with resin) were obtained for each experimental situation: 6 solutions [Periogard (PE), Cepacol (CE), Corega Tabs (CT), Medical Interporous (MI), Polident (PO), 0.05% sodium hypochlorite (NaOCl), and distilled water (DW) control] and 2 Co-Cr alloys [DeguDent (DD) and VeraPDI (VPDI)] were used for each experimental situation. A 180-day immersion was simulated and the measurements of roughness (Ra, µm) of metal and resin were analyzed using 2-way ANOVA and Tukey’s test. The surface changes and tarnishes were examined with a scanning electronic microscopy (SEM). In addition, energy dispersive x-ray spectrometry (EDS) analysis was carried out at representative areas. Visually, NaOCl and MI specimens presented surface tarnishes. The roughness of materials was not affected by the solutions (p>0.05). SEM images showed that NaOCl and MI provided surface changes. EDS analysis revealed the presence of oxygen for specimens in contact with both MI and NaOCl solutions, which might suggest that the two solutions promoted the oxidation of the surfaces, thus leading to spot corrosion. Within the limitations of this study, it may be concluded that the NaOCl and MI may not be suitable for cleaning of RPD.

Effect of fluoride-containing solutions on the surface of cast commercially pure titanium

This study evaluated the effects of fluoride-containing solutions on the surface of commercially pure titanium (CP Ti) obtained by casting. CP Ti specimens were fabricated and randomly assigned to 5 groups (n=10): group 1: stored in distilled water at 37 ± 1ºC; group 2: stored in distilled water at 37 ± 1ºC and daily immersed in 0.05% NaF for 3 min; group 3: stored in distilled water at 37 ± 1ºC and daily immersed in 0.2% NaF for 3 min; group 4: stored in distilled water at 37 ± 1ºC; and immersed in 0.05% NaF every 15 days for 3 min; and group 5: stored in distilled water at 37 ± 1ºC and immersed in 0.2% NaF every 15 days for 3 min. Surface roughness was measured with a profilometer immediately after metallographic polishing of the specimens (T0) and at 15-day intervals until completing 60 days of experiment (T15, T30, T45, T60). Data were analyzed statistically by ANOVA and Tukey's test (α=0.05). There was no statistically significant difference (p>0.05) in surface roughness among the solutions. In conclusion, fluoride-containing solutions (pH 7.0) used as mouthwashes do not damage the surface of cast CP Ti and can be used by patients with titanium-based restorations.