Rheology of the cytoskeleton as a fractal network

We model the cytoskeleton as a fractal network by identifying each segment with a simple Kelvin-Voigt element with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel, which may support stress, without relaxing. By considering a very simple regular self-similar structure of segments in series and in parallel, in one, two, or three dimensions, we are able to express the viscoelasticity of the network as an effective generalized Kelvin-Voigt model with a power law spectrum of retardation times L similar to tau(alpha). We relate the parameter alpha with the fractal dimension of the gel. In some regimes ( 0 < alpha < 1), we recover the weak power law behaviors of the elastic and viscous moduli with the angular frequencies G' similar to G" similar to w(alpha) that occur in a variety of soft materials, including living cells. In other regimes, we find different power laws for G' and G".

Caraterização das propriedades mecânicas de um adesivo estrutural de alta ductilidade

A tecnologia de ligação por adesivos estruturais tem vindo a ser utilizada ao longo de várias décadas, permitindo solucionar diversos problemas associados a técnicas chamadas "tradicionais" de ligação, como a soldadura, a rebitagem ou a ligação aparafusada. Esta é uma alternativa viável para substituir as ligações mecânicas, devido a diversos fatores como o menor peso estrutural, menor custo de fabricação e capacidade de união de diferentes materiais. O crescente recurso a materiais compósitos em diversas indústrias, nomeadamente a aeronáutica e naval, levaram ao consequente aumento da aplicação de ligações adesivas, por serem indicadas como forma de união destes materiais, onde é de enaltecer a sua elevada resistência à fadiga. Uma junta adesiva está maioritariamente sujeita a esforços de corte e arrancamento e portanto o conhecimento dos módulos de elasticidade à tração (E) ou corte (G) do adesivo, e ainda as resistências máximas à tração e ao corte, não é suficiente quando se pretende prever o comportamento da mesma. Na verdade, torna-se necessário abranger na análise a plastificação progressiva verificada nas juntas adesivas antes da rotura, sendo necessário o conhecimento de parâmetros tais como a taxa crítica de libertação de energia de deformação à tração (GIc) e corte (GIIc). Este trabalho pretende estudar um adesivo estrutural recentemente lançado no mercado, carecendo portanto da sua caracterização, para facilitar a previsão da resistência de estruturas adesivas ligadas com o mesmo. São 4 os ensaios a realizar: ensaios à tração de provetes em bruto, ensaios ao corte com a geometria Thick Adherend Shear Test (TAST), ensaios Double-Cantilever Beam (DCB) e ensaios End-Notched Flexure (ENF). Com a realização dos ensaios referidos, serão determinadas as propriedades mecânicas e de fratura à tração e ao corte, e serão fornecidos os parâmetros para a previsão da resistência de juntas adesivas com este adesivo por uma variedade de métodos, desde métodos analíticos mais expeditos até aos métodos numéricos mais avançados existentes atualmente. Os resultados foram de encontro aos disponibilizados pelo fabricante, sempre que estes se encontravam disponíveis, obtendo-se discrepâncias bastante reduzidas nos diversos parâmetros determinados.

Schottky principal G-bundles over compact Riemann surfaces

Fundação para a Ciência e a Tecnologia (FCT)- PhD grant SFRH/BD/37151/2007; projects PTDC/MAT/099275/2008; PTDC/MAT/119689/2010; PTDC/MAT/120411/2010; PTDC/MAT-GEO/0675/2012

Compact saloplastic membranes of natural polysaccharides for soft tissue engineering

The regeneration of soft biological tissues requires new substitutes that exhibit mechanical properties similar to the native tissue. Herein, thin saloplastic membranes with tunable physical properties are prepared by complexation of chitosan and alginate solutions containing different concentrations of sodium chloride. Polyelectrolyte complexes (PECs) are transferred to flat Petri dishes for compaction into membrane shapes by sedimentation and solvent evaporation. All membranes are resistant to degradation by lysozyme and are stable in solutions with pH values between 1 and 13. Immersing the different membranes in new doping solutions of increasing salt concentrations triggers the typical saloplastic behavior, with a high water absorption and decrease of the rigidity and ultimate tensile strength. The range of such variations is tuned by the sodium chloride amount used in the synthesis: high salt concentrations increase water uptake and tensile moduli, while decreasing the ultimate strength. Cellular assays demonstrate high proliferation rates and viability of L929 fibroblasts seeded onto the most rigid membranes. The results validate the use of saloplastic membranes as soft tissue substitutes for future biomedical applications.

Effect of binder on performance of intumescent coatings

This study investigates the role of the polymeric binder on the properties and performance of an intumescent coating. Waterborne resins of different types (vinylic, acrylic, and styrene-acrylic) were incorporated in an intumescent paint formulation, and characterized extensively in terms of thermal degradation behavior, intumescence thickness, and thermal insulation. Thermal microscopy images of charred foam development provided further information on the particular performance of each type of coating upon heating. The best foam expansion and heat protection results were obtained with the vinyl binders. Rheological measurements showed a complex evolution of the viscoelastic characteristics of the materials with temperature. As an example, the vinyl binders unexpectedly hardened significantly after thermal degradation. The values of storage moduli obtained at the onset of foam blowing (melamine decomposition) were used to explain different intumescence expansion behaviors.

Structure-property relationships in polymer nanocomposites

Tese de Doutoramento em Ciência e Engenharia de Polímeros e Compósitos

Poly(ester-urethane) scaffolds: effect of structure on properties and osteogenic activity of stem cells

The present study aimed to investigate the effect of structure (design and porosity) on the matrix stiffness and osteogenic activity of stem cells cultured on poly(ester-urethane) (PEU) scaffolds. Different three-dimensional (3D) forms of scaffold were prepared from lysine-based PEU using traditional salt-leaching and advanced bioplotting techniques. The resulting scaffolds were characterized by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), scanning electron microscopy (SEM), mercury porosimetry and mechanical testing. The scaffolds had various pore sizes with different designs, and all were thermally stable up to 300â °C. In vitrotests, carried out using rat bone marrow stem cells (BMSCs) for bone tissue engineering, demonstrated better viability and higher cell proliferation on bioplotted scaffolds compared to salt-leached ones, most probably due to their larger and interconnected pores and stiffer nature, as shown by higher compressive moduli, which were measured by compression testing. Similarly, SEM, von Kossa staining and EDX analyses indicated higher amounts of calcium deposition on bioplotted scaffolds during cell culture. It was concluded that the design with larger interconnected porosity and stiffness has an effect on the osteogenic activity of the stem cells.

Beeswax organogels: Influence of gelator concentration and oil type in the gelation process

This work focused on how different types of oil phase, MCT (medium chain triglycerides) and LCT (long chain triglycerides), exert influence on the gelation process of beeswax and thus properties of the organogel produced thereof. Organogels were produced at different temperatures and qualitative phase diagrams were constructed to identify and classify the type of structure formed at various compositions. The microstructure of gelator crystals was studied by polarized light microscopy. Melting and crystallization were characterized by differential scanning calorimetry and rheology (flow and small amplitude oscillatory measurements) to understand organogels' behaviour under different mechanical and thermal conditions. FTIR analysis was employed for a further understanding of oil-gelator chemical interactions. Results showed that the increase of beeswax concentration led to higher values of storage and loss moduli (G, G) and complex modulus (G*) of organogels, which is associated to the strong network formed between the crystalline gelator structure and the oil phase. Crystallization occurred in two steps (well evidenced for higher concentrations of gelator) during temperature decreasing. Thermal analysis showed the occurrence of hysteresis between melting and crystallization. Small angle X-ray scattering (SAXS) analysis allowed a better understanding in terms of how crystal conformations were disposed for each type of organogel. The structuring process supported by medium or long-chain triglycerides oils was an important exploit to apprehend the impact of different carbon chain-size on the gelation process and on gels' properties.

Embedding theorems of funcitional classes, III

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

What is the Jacobian of a Riemann surface with boundary?

We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of "open abelian varieties" which satisfies gluing axioms similar to those of Riemann surfaces, and therefore allows a notion of "conformal field theory" to be defined on this space. We further prove that chiral conformal field theories corresponding to even lattices factor through this moduli space of open abelian varieties.

Direct Determination of mechanical properties in shallow formations by (ultra) sonic methods

For several decades mechanical properties of shallow formations (soil) obtained by sonic to ultrasonic wave testing were reported to be greater than those based on mechanical tests. The present article relying on a statistical analysis of more than 300 tests shows that elastic moduli of the soil can indeed be obtained from (ultra)sonic tests and that they are identical to those resulting from mechanical tests.

Oscillation modes of microtubules.

Microtubules are long, filamentous protein complexes which play a central role in several cellular physiological processes, such as cell division transport and locomotion. Their mechanical properties are extremely important since they determine the biological function. In a recently published experiment [Phys. Rev. Lett. 89 (2002) 248101], microtubule's Young's and shear moduli were simultaneously measured, proving that they are highly anisotropic. Together with the known structure, this finding opens the way to better understand and predict their mechanical behavior under a particular set of conditions. In the present study, we modeled microtubules by using the finite elements method and analyzed their oscillation modes. The analysis revealed that oscillation modes involving a change in the diameter of the microtubules strongly depend on the shear modulus. In these modes, the correlation times of the movements are just slightly shorter than diffusion times of free molecules surrounding the microtubule. It could be therefore speculated that the matching of the two timescales could play a role in facilitating the interactions between microtubules and MT associated proteins, and between microtubules and tubulins themselves.

Estimation of inelastic seismic material properties of a surgical sea-bed from multi-component marine seismic data

To date, state-of-the-art seismic material parameter estimates from multi-component sea-bed seismic data are based on the assumption that the sea-bed consists of a fully elastic half-space. In reality, however, the shallow sea-bed generally consists of soft, unconsolidated sediments that are characterized by strong to very strong seismic attenuation. To explore the potential implications, we apply a state-of-the-art elastic decomposition algorithm to synthetic data for a range of canonical sea-bed models consisting of a viscoelastic half-space of varying attenuation. We find that in the presence of strong seismic attenuation, as quantified by Q-values of 10 or less, significant errors arise in the conventional elastic estimation of seismic properties. Tests on synthetic data indicate that these errors can be largely avoided by accounting for the inherent attenuation of the seafloor when estimating the seismic parameters. This can be achieved by replacing the real-valued expressions for the elastic moduli in the governing equations in the parameter estimation by their complex-valued viscoelastic equivalents. The practical application of our parameter procedure yields realistic estimates of the elastic seismic material properties of the shallow sea-bed, while the corresponding Q-estimates seem to be biased towards too low values, particularly for S-waves. Given that the estimation of inelastic material parameters is notoriously difficult, particularly in the immediate vicinity of the sea-bed, this is expected to be of interest and importance for civil and ocean engineering purposes.

Biomechanical characterization and in vitro mechanical injury of elderly human femoral head cartilage: comparison to adult bovine humeral head cartilage.

OBJECTIVES: In vitro mechanical injury of articular cartilage is useful to identify events associated with development of post-traumatic osteoarthritis (OA). To date, many in vitro injury models have used animal cartilage despite the greater clinical relevance of human cartilage. We aimed to characterize a new in vitro injury model using elderly human femoral head cartilage and compare its behavior to that of an existing model with adult bovine humeral head cartilage. DESIGN: Mechanical properties of human and bovine cartilage disks were characterized by elastic modulus and hydraulic permeability in radially confined axial compression, and by Young's modulus, Poisson's ratio, and direction-dependent radial strain in unconfined compression. Biochemical composition was assessed in terms of tissue water, solid, and glycosaminoglycan (GAG) contents. Responses to mechanical injury were assessed by observation of macroscopic superficial tissue cracks and histological measurements of cell viability following single injurious ramp loads at 7 or 70%/s strain rate to 3 or 14 MPa peak stress. RESULTS: Confined compression moduli and Young's moduli were greater in elderly human femoral cartilage vs adult bovine humeral cartilage whereas hydraulic permeability was less. Radial deformations of axially compressed explant disks were more anisotropic (direction-dependent) for the human cartilage. In both cartilage sources, tissue cracking and associated cell death during injurious loading was common for 14 MPa peak stress at both strain rates. CONCLUSION: Despite differences in mechanical properties, acute damage induced by injurious loading was similar in both elderly human femoral cartilage and adult bovine humeral cartilage, supporting the clinical relevance of animal-based cartilage injury models. However, inherent structural differences such as cell density may influence subsequent cell-mediated responses to injurious loading and affect the development of OA.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.