Nonlinear dynamics of cilia and flagella

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

A sensitivity study of the human crystalline lens using finite element analysis

Finite element analysis is a useful tool in understanding how the accommodation system of the eye works. Further to simpler FEA models that have been used hitherto, this paper describes a sensitivity study which aims to understand which parameters of the crystalline lens are key to developing an accurate model of the accommodation system. A number of lens models were created, allowing the mechanical properties, internal structure and outer geometry to be varied. These models were then spun about their axes, and the deformations determined. The results showed the mechanical properties are the critical parameters, with the internal structure secondary. Further research is needed to fully understand how the internal structure and properties interact to affect lens deformation.

Structural behaviour of glass reinforced plastics

The aim of this research is to promote the use of G.R.P. as a structural material. In the past, the use of G.R.P. has been confined to non-load carrying applications. Such uses are still rapidly increasing but in addition significant changes have been made during the last decade in the development of semi-structural and now even fully structural applications. Glass-reinforced plastic is characterized by a high strength but a relatively low modulus of elasticity. For this reasona G.R.P. structure can expect to show large deformations as a result of which the individual structural members will fail under load due to a loss of stability rather than approaching the ultimate strength of the material. For this reason the selection of the geometrical shapes of G.R.P. structural elements is considered to be an important factor in designing G.R.P. structures. The first chapter of this thesis deals with a general review of the theoretical and experimental methods used to describe the structural properties of G.R.P. The research programme includes five stages dealing with the structural behaviour of G.R.P. The first stage (Chapter 2) begins with selecting and designing an optimum box beam cross-section which gives the maximum flexural and torsional rigidity. The second stage of investigation (Chapter 3) deals with beam to beam connections. A joint was designed and manufactured with different types of fasteners used to connect two beam units. A suitable fastener was selected and the research extended to cover the behaviour of long span beams using multiple joints. The third part of the investigation includes a study of the behaviour of box beams subjected to combined bending, shear and torsion. A special torque rig was developed to perform the tests. Creep deformation of 6 m span G.R.P. was investigated as the fourth stage under a range of loading conditions. As a result of the phenomenon of post buckling behaviour exhibited in the compression flange during testing of box beams during earlier stages of the investigation it was decided to consider this phenomenon in more detail in the final stage of the investigation. G.R.P. plates with different fibre orientation were subjected to uniaxial compression and tested up to failure. In all stages of the investigation theoretical predictions and experimental results were compared and generally good correlation between theory and experimental data was observed.

A study of fatigue failure in vulcanized rubber

Some aspects of fatigue failure in rubbers have been examined. Scanning electron micrographs of the surface exposed by the failure confirm the incremental, crack-propagation nature, of the fatigue process. Many other features of the failure surface have been identified and related to this process. The complicating effect of a reinforcing filler has also been investigated. The fatigue resistance of rubber test-pieces deformed in simple tension was measured as a function of frequency and temperature. This showed that an increase in frequency was equivalent to a decrease in temperature; for an amorphous unfilled rubber the time and temperature effects of crystallisation and fillers on the validity of this transformation is considered. This transformation indicates that hysteresis plays an important part in the fatigue process. Torsional pendulum measurements were used to demonstrate the dependence of the fatigue life on the mechanical damping. An apparatus was developed to measure the hysteresial energy loss directly at deformations, rates of deformation and temperatures consistent with a typical fatigue test. Measurements made with this apparatus are compared with fatigue values and a quantitative relationship is suggested describing fatigue, in terms of the energy lost per unit energy input in a cycle of a fatigue test.

Cerami (C) Condition and Mountain Pass Theorem for Multivalued Mappings

Partially supported by Sapientia Foundation.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

The Deformed Trigonometric Functions of two Variables

MSC 2010: 33B10, 33E20

Controlled growth of carbon nanotubes for high performance nanoelectronics

Unique electrical and mechanical properties of single-walled carbon nanotubes (SWNTs) have made them one of the most promising candidates for next-generation nanoelectronics. Efficient utilization of the exceptional properties of SWNTs requires controlling their growth direction (e.g., vertical, horizontal) and morphologies (e.g., straight, junction, coiled). ^ In this dissertation, the catalytic effect on the branching of SWNTs, Y-shaped SWNTs (Y-SWNTs), was investigated. The formation of Y-shaped branches was found to be dependent on the composition of the catalysts. Easier carbide formers have a strong tendency to attach to the sidewall of SWNTs and thus enhance the degree of branching. Y-SWNTs based field-effect transistors (FETs) were fabricated and modulated by the metallic branch of the Y-SWNTs, exhibiting ambipolar characteristics at room temperature. A subthreshold swing of 700 mV/decade and an on/off ratio of 105 with a low off-state current of 10-13 A were obtained. The transport phenomena associated with Y- and cross-junction configurations reveals that the conduction mechanism in the SWNT junctions is governed by thermionic emission at T > 100 K and by tunneling at T < 100 K. ^ Furthermore, horizontally aligned SWNTs were synthesized by the controlled modification of external fields and forces. High performance carbon nanotube FETs and logic circuit were demonstrated utilizing the aligned SWNTs. It is found that the hysteresis in CNTFETs can be eliminated by removing absorbed water molecules on the CNT/SiO2 interface by vacuum annealing, hydrophobic surface treatment, and surface passivation. SWNT “serpentines” were synthesized by utilization of the interaction between drag force from gas flow and Van der Waals force with substrates. The curvature of bent SWNTs could be tailored by adjusting the gas flow rate, and changing the gas flow direction with respect to the step-edges on a single-crystal quartz substrate. Resistivity of bent SWNTs was observed to increase with curvature, which can be attributed to local deformations and possible chirality shift at curved part. ^ Our results show the successful synthesis of SWNTs having controllable morphologies and directionality. The capability of tailoring the electrical properties of SWNTs makes it possible to build an all-nanotube device by integrating SWNTs, having different functionalities, into complex circuits. ^

Effect of water on olivine single crystals plasticity, deformed under high pressure and high temperature

The Earth's upper mantle, mainly composed of olivine, is seismically anisotropic. Seismic anisotropy attenuation has been observed at 220km depth. Karato et al. (1992) attributed this attenuation to a transition between two deformation mechanisms, from dislocation creep above 220km to diffusion creep below 220km, induced by a change in water content. Couvy (2005) and Mainprice et al. (2005) predicted a change in Lattice Preferred Orientation induced by pressure, which comes from a change of slip system, from [100] slip to [001] slip, and is responsible for the seismic anisotropy attenuation. Raterron et al. (2007) ran single crystal deformation experiments under anhydrous conditions and observed that the slip system transition occurs around 8GPa, which corresponds to a depth of 260Km. Experiments were done to quantify the effects of water on olivine single crystals deformed using D-DIA press and synchrotron beam. Deformations were carried out in uniaxial compression along [110]c, [011]c, and [101]c, crystallographic directions, at pressure ranging from 4 to 8GPa and temperature between 1373 and 1473K. Talc sleeves about the annulus of the single crystals were used as source of water in the assembly. Stress and specimen strain rates were calculated by in-situ X-ray diffraction and time resolved imaging, respectively. By direct comparison of single crystals strain rates, we observed that [110]c deforms faster than [011]c below 5GPa. However above 6GPa [011]c deforms faster than [110]c. This revealed that [100](010) is the dominant slip system below 5GPa, and above 6GPa [001](010) becomes dominant. According to our results, the slip system transition, which is induced by pressure, occurs at 6GPa. Water influences the pressure where the switch over occurs, by lowering the transition pressure. The pressure effect on the slip systems activity has been quantified and the hydrolytic weakening has also been estimated for both orientations. Data also shows that temperature affects the slip system activity. The regional variation of the depth for the seismic anisotropy attenuation, which would depend on local hydroxyl content and temperature variations and explains the seismic anisotropy attenuation occurring at about 220Km depth in the mantle, where the pressure is about 6GPa. Deformation of MgO single crystal oriented [100], [110] and [111] were also performed. The results predict a change in the slip system activity at 23GPa, again induced by pressure. This explains the seismic anisotropy observed in the lower mantle.

Relative basicities of free base porphyrins; understanding the role of macrocyclic distortion

Porphyrins have been the center of numerous investigations in different areas of chemistry, geochemistry, and the life sciences. In nature the conformation of the porphyrin macrocycle varies, depending on the function of its apoenzyme. It is believed that the conformation of the porphyrin ring is necessary for the enzyme to achieve its function and modify its reactivity. It is important to understand how the conformation of the porphyrin ring will influence its properties. ^ In synthetic porphyrins particular conformations and ring deformations can be achieved by peripheral substitution, metallation, core substitution, and core protonation among other alterations of the macrocycle. The macrocyclic distortions will affect the ring current, the ability of pyrroles to intramolecularly hydrogen bond and the relative basicity of each of the porphyrins. To understand these effects different theoretical models are used. The ground state structure of each of 19 free base porphyrins is determined using molecular mechanics (MM+) and semiempirical methods (PM3). The energetics of deformation of the macrocyclic core is calculated by carrying out single point energy calculations for the conformation achieved by each synthetic compound. Enthalpies of solution and enthalpies of protonation of 10 porphyrins with varying degrees of macrocyclic deformation and varying electron withdrawing groups in the periphery are determined using solution calorimetry. Using Hess's Law, the relative basicity of each of the different free base porphyrins is calculated. NMR results are described, including the determination of free energies of activation of ring tautomerization and hydrogen bonding for several compounds. It was found that in the absence of electronic effects, the greater macrocyclic deformation, the greater the basicity of the porphyrins. This basicity is attenuated by the presence of electron withdrawing groups and ability to of the macrocycle to intramolecularly hydrogen bond. ^

Relative basicities of free base porphyrins : understanding the role of macrocyclic distortion

Porphyrins have been the center of numerous investigations in different areas of chemistry, geochemistry, and the life sciences. In nature the conformation of the porphyrin macrocycle varies, depending on the function of its apoenzyme. It is believed that the conformation of the porphyrin ring is necessary for the enzyme to achieve its function and modify its reactivity. It is important to understand how the conformation of the porphyrin ring will influence its properties. In synthetic porphyrins particular conformations and ring deformations can be achieved by peripheral substitution, metallation, core substitution, and core protonation among other alterations of the macrocycle. The macrocyclic distortions will affect the ring current, the ability of pyrroles to intramolecularly hydrogen bond and the relative basicity of each of the porphyrins. To understand these effects different theoretical models are used. The ground state structure of each of 19 free base porphyrins is determined using molecular mechanics (MM+) and semiempirical methods (PM3). The energetics of deformation of the macrocyclic core is calculated by carrying out single point energy calculations for the conformation achieved by each synthetic compound. Enthalpies of solution and enthalpies of protonation of 10 porphyrins with varying degrees of macrocyclic deformation and varying electron withdrawing groups in the periphery are determined using solution calorimetry. Using Hess's Law, the relative basicity of each of the different free base porphyrins is calculated. NMR results are described, including the determination of free energies of activation of ring tautomerization and hydrogen bonding for several compounds. It was found that in the absence of electronic effects, the greater macrocyclic deformation, the greater the basicity of the porphyrins. This basicity is attenuated by the presence of electron withdrawing groups and ability to of the macrocycle to intramolecularly hydrogen bond.

Areia sob os pés da alma: uma leitura da vida e obra de Oswaldo Lamartine de Faria

This study followed the development of Oswaldo Lamartine de Faria as an intellectual, with the aim of establishing the emergence of that de Faria’s work under the umbrella of the sertão (hinterland) in Northeast Brazil. It accompanied the emergence of the researcher, his discovery of his mission to study the sertão in Seridó and the vital importance of his relationship with Luís da Câmara Cascudo, since despite being a natural born observer, Oswaldo Lamartine embarked on a career as a researcher after encouragement by Cascudo. The first chapter of this study, denominated The Gates of Time, portrays the country during the drought of 1919, the year Lamartine was born. It describes his childhood and first encounters with Câmara Cascudo; his urban exile in Rio de Janeiro; the books written by the young Oswaldo, those that came later, and his definitive return to the state of Rio Grande do Norte. The following two chapters, Sand beneath the Feet of the Soul and Images of a Nobleman from the Sertão, summarize Lamartine’s books and describe his entry into the canon of the state’s culture, with particular prominence given to his interview for the documentary “Oswaldo Lamartine: prince of the sertão”, highlighting his attempt (through his writing) to preserve his own existence. In the second section, Verses, Bold, Between the Lines features analyses of texts dedicated to Oswaldo Lamartine, such as those written by de Zila Mamede, Maria Lúcia Dal Farra and Paulo de Tarso Correia de Melo. The next chapter, entitled Warm and Vivid Ashes, highlights Lamartine’s correspondence with Luís da Câmara Cascudo and the incredible friendship between the two researchers. Cascudo’s letters are analyzed through the book De Cascudo para Oswaldo (From Cascudo to Oswaldo) and and are a powerful testimony of Oswaldo Lamartine’s permanent connection to Rio Grande do Norte. In conclusion, the final chapter entitled Combine, Tattoo, Imprint analyzes the writer’s five-book collection entitled Sertões do Seridó (Hinterlands of Seridó). In reading each of these, it becomes clear that observing reality was vital to the writer’s work. This is one of the first studies to be conducted about Oswaldo Lamartine at the Federal University of Rio Grande do Norte and its main theoretical references were the reflections of authors Jacques Le Goff (2003), Lejeune (1994; 2008), Maurice Blanchot (1987; 2005), Alfredo Bosi (1987) and Gaston Bachelard (n.d.).

Estudo da evolução das tensões residuais através da difratometria de raios x em aço rolamento submetido a esforços cíclicos

The micro-deformations caused by cyclic loading origins the variation of the distances between atoms of the crystal lattice producing the irreversible component. In order to study and understand the microstructural behavior of the material this paper investigated the influence suffered by residual stresses in thrust rolling bearing races fabricated in AISI 52100 steel, after tests by cyclic rolling contact in a tribometer at 1m/s under two contact pressures (500 MPa and 1400 MPa) in dry and boundary lubrication conditions. Procedures of tests thermo-acustically isolated were developed for monitoring the contact temperature and sound pressure level signals to establish a comparison between the residual stress measurements, micro-hardness Vickers and micrographic registers searching an indication of wear evolution. The sin²ψ method by X-ray diffraction technique was used to quantify the residual stresses. Three raceway zones were selected for the evaluation of wear and surface morphology after predetermined cycling, comparing with their new condition ("as received"). Micro-hardness and residual stress measurements showed significant changes after the tests and it was possible to observe the relationship between the increase of sound pressure level and the residual stress for dry and lubricated conditions.

Estudo da evolução das tensões residuais através da difratometria de raios x em aço rolamento submetido a esforços cíclicos

The micro-deformations caused by cyclic loading origins the variation of the distances between atoms of the crystal lattice producing the irreversible component. In order to study and understand the microstructural behavior of the material this paper investigated the influence suffered by residual stresses in thrust rolling bearing races fabricated in AISI 52100 steel, after tests by cyclic rolling contact in a tribometer at 1m/s under two contact pressures (500 MPa and 1400 MPa) in dry and boundary lubrication conditions. Procedures of tests thermo-acustically isolated were developed for monitoring the contact temperature and sound pressure level signals to establish a comparison between the residual stress measurements, micro-hardness Vickers and micrographic registers searching an indication of wear evolution. The sin²ψ method by X-ray diffraction technique was used to quantify the residual stresses. Three raceway zones were selected for the evaluation of wear and surface morphology after predetermined cycling, comparing with their new condition ("as received"). Micro-hardness and residual stress measurements showed significant changes after the tests and it was possible to observe the relationship between the increase of sound pressure level and the residual stress for dry and lubricated conditions.

Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.