Effect of anisotropy on elastic moduli measured by nanoindentation in human tibial cortical bone

Many biological materials are known to be anisotropic. In particular, microstructural components of biological materials may grow in a preferred direction, giving rise to anisotropy in the microstructure. Nanoindentation has been shown to be an effective technique for determining the mechanical properties of microstructures as small as a few microns. However, the effects of anisotropy on the properties measured by nanoindentation have not been fully addressed. This study presents a method to account for the effects of anisotropy on elastic properties measured by nanoindentation. This method is used to correlate elastic properties determined from earlier nanoindentation experiments and from earlier ultrasonic velocity measurements in human tibial cortical bone. Also presented is a procedure to determine anisotropic elastic moduli from indentation measurements in multiple directions. © 2001 John Wiley & Sons, Inc. J Biomed Mater Res.

Nonparametric Estimation in the Class of Bisexual Processes with Population-Size Dependent Mating

2000 Mathematics Subject Classification: 60J80, 62M05

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10

The influence of simulated exploitation onPatella vulgatapopulations: protandric sex change is size-dependent

Grazing mollusks are used as a food resource worldwide, and limpets are harvested commercially for both local consumption and export in several countries. This study describes a field experiment to assess the effects of simulated human exploitation of limpets Patella vulgata on their population ecology in terms of protandry (age-related sex change from male to female), growth, recruitment, migration, and density regulation. Limpet populations at two locations in southwest England were artificially exploited by systematic removal of the largest individuals for 18 months in plots assigned to three treatments at each site: no (control), low, and high exploitation. The shell size at sex change (L50: the size at which there is a 50:50 sex ratio) decreased in response to the exploitation treatments, as did the mean shell size of sexual stages. Size-dependent sex change was indicated by L50 occurring at smaller sizes in treatments than controls, suggesting an earlier switch to females. Mean shell size of P. vulgata neuters changed little under different levels of exploitation, while males and females both decreased markedly in size with exploitation. No differences were detected in the relative abundances of sexual stages, indicating some compensation for the removal of the bigger individuals via recruitment and sex change as no migratory patterns were detected between treatments. At the end of the experiment, 0–15 mm recruits were more abundant at one of the locations but no differences were detected between treatments. We conclude that sex change in P. vulgata can be induced at smaller sizes by reductions in density of the largest individuals reducing interage class competition. Knowledge of sex-change adaptation in exploited limpet populations should underpin strategies to counteract population decline and improve rocky shore conservation and resource management.

The influence of simulated exploitation onPatella vulgatapopulations: protandric sex change is size-dependent

Grazing mollusks are used as a food resource worldwide, and limpets are harvested commercially for both local consumption and export in several countries. This study describes a field experiment to assess the effects of simulated human exploitation of limpets Patella vulgata on their population ecology in terms of protandry (age-related sex change from male to female), growth, recruitment, migration, and density regulation. Limpet populations at two locations in southwest England were artificially exploited by systematic removal of the largest individuals for 18 months in plots assigned to three treatments at each site: no (control), low, and high exploitation. The shell size at sex change (L50: the size at which there is a 50:50 sex ratio) decreased in response to the exploitation treatments, as did the mean shell size of sexual stages. Size-dependent sex change was indicated by L50 occurring at smaller sizes in treatments than controls, suggesting an earlier switch to females. Mean shell size of P. vulgata neuters changed little under different levels of exploitation, while males and females both decreased markedly in size with exploitation. No differences were detected in the relative abundances of sexual stages, indicating some compensation for the removal of the bigger individuals via recruitment and sex change as no migratory patterns were detected between treatments. At the end of the experiment, 0–15 mm recruits were more abundant at one of the locations but no differences were detected between treatments. We conclude that sex change in P. vulgata can be induced at smaller sizes by reductions in density of the largest individuals reducing interage class competition. Knowledge of sex-change adaptation in exploited limpet populations should underpin strategies to counteract population decline and improve rocky shore conservation and resource management.

Size-dependent electronic properties of metal nanoparticles.

105 p.

The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Fingerprints of a size-dependent crossover in the dimensionality of electronic conduction in Au-seeded Ge nanowires

We studied the electrical transport properties of Au-seeded germanium nanowires with radii ranging from 11 to 80 nm at ambient conditions. We found a non-trivial dependence of the electrical conductivity, mobility and carrier density on the radius size. In particular, two regimes were identified for large (lightly doped) and small (stronger doped) nanowires in which the charge-carrier drift is dominated by electron-phonon and ionized-impurity scattering, respectively. This goes in hand with the finding that the electrostatic properties for radii below ca. 37 nm have quasi one-dimensional character as reflected by the extracted screening lengths.

Variation in dynamic elastic shear modulus of sandstone upon fluid saturation and substitution

Experimental acoustic measurements on sandstone rocks at both sonic and ultrasonic frequencies show that fluid saturation can cause a noticeable change in both the dynamic bulk and shear elastic moduli of sandstones. We observed that the change in dynamic shear modulus upon fluid saturation is highly dependent on the type of saturant, its viscosity, rock microstructure, and applied pressures. Frequency dispersion has some influence on dynamic elastic moduli too, but its effect is limited to the ultrasonic frequency ranges and above. We propose that viscous coupling, reduction in free surface energy, and, to a limited extent, frequency dispersion due to both local and global flow are the main mechanisms responsible for the change in dynamic shear elastic modulus upon fluid saturation and substitution, and we quantify influences.

Designing Temperature-Responsive Biocompatible Copolymers and Hydrogels Based on 2-Hydroxyethyl(meth)acrylates

Free-radical copolymerization of 2-hydroxyethyl methacrylate with 2-hydroxyethyl acrylate can be successively utilized for the synthesis of water-soluble polymers and hydrogels with excellent physicochemical properties, thus showing promise for pharmaceutical and biomedical applications. In the work presented it has been demonstrated that water-soluble copolymers based on 2-hydroxyethyl methacrylate and 2-hydroxyethyl acrylate exhibit lower critical solution temperature in aqueous solutions, whereas the corresponding high molecular weight homopolymers do not have this unique property. The temperature-induced transitions observed upon heating the aqueous solutions of these copolymers proceed via liquid−liquid phase separation. The hydrogels were also synthesized by copolymerizing 2-hydroxyethyl methacrylate and 2-hydroxyethyl acrylate in the absence of a bifunctional cross-linker. The cross-linking of these copolymers during copolymerization is believed to be due to the presence of bifunctional admixtures or transesterification reactions. Transparency, swelling behavior, mechanical properties, and porosity of the hydrogels are dependent upon the monomer ratio in the copolymers. Hydrogel samples containing more 2-hydroxyethyl methacrylate are less transparent, have lower swelling capacity, higher elastic moduli, and pores of smaller size. The assessment of the biocompatibility of the copolymers using the slug mucosal irritation test revealed that they are also less irritant than poly(acrylic acid).

What limits insect fecundity? Body size- and temperature-dependent egg maturation and oviposition in a butterfly

1. Large female insects usually have high potential fecundity. Therefore selection should favour an increase in body size given that these females get opportunities to realize their potential advantage by maturing and laying more eggs. However, ectotherm physiology is strongly temperature-dependent, and activities are carried out sufficiently only within certain temperature ranges. Thus it remains unclear if the fecundity advantage of a large size is fully realized in natural environments, where thermal conditions are limiting. 2. Insect fecundity might be limited by temperature at two levels; first eggs need to mature, and then the female needs time for strategic ovipositing of the egg. Since a female cannot foresee the number of oviposition opportunities that she will encounter on a given day, the optimal rate of egg maturation will be governed by trade-offs associated with egg- and time-limited oviposition. As females of different sizes will have different amounts of body reserves, size-dependent allocation trade-offs between the mother’s condition and her egg production might be expected. 3. In the temperate butterfly Pararge aegeria , the time and temperature dependence of oviposition and egg maturation, and the interrelatedness of these two processes were investigated in a series of laboratory experiments, allowing a decoupling of the time budgets for the respective processes. 4. The results show that realized fecundity of this species can be limited by both the temperature dependence of egg maturation and oviposition under certain thermal regimes. Furthermore, rates of oviposition and egg maturation seemed to have regulatory effects upon each other. Early reproductive output was correlated with short life span, indicating a cost of reproduction. Finally, large females matured more eggs than small females when deprived of oviposition opportunities. Thus, the optimal allocation of resources to egg production seems dependent on female size. 5. This study highlights the complexity of processes underlying rates of egg maturation and oviposition in ectotherms under natural conditions. We further discuss the importance of temperature variation for egg- vs. time-limited fecundity and the consequences for the evolution of female body size in insects.

Hypersonic elastic excitations in soft mesoscopic structures

This dissertation is devoted to the experimental exploration of the propagation of elastic waves in soft mesoscopic structures with submicrometer dimensions. A strong motivation of this work is the large technological relevance and the fundamental importance of the subject. Elastic waves are accompanied by time-dependent fluctuations of local stress and strain fields in the medium. As such, the propagation phase velocities are intimately related to the elastic moduli. Knowledge of the elastic wave propagation directly provides information about the mechanical properties of the probed mesoscopic structures, which are not readily accessible experimentally. On the other hand, elastic waves, when propagating in an inhomogeneous medium with spatial inhomogeneities comparable to their wavelength, exhibit rather rich behavior, including the appearance of novel physical phenomena, such as phononic bandgap formation. So far, the experimental work has been restricted to macroscopic structures, which limit wave propagation below the KHz range. It was anticipated that an experimental approach capable of probing the interplay of the wave propagation with the controlled mesoscopic structures would contribute to deeper insights into the fundamental problem of elastic wave propagation in inhomogeneous systems. The mesoscopic nature of the structures to be studied precludes the use of traditional methods, such as sound transmission, for the study of elastic wave propagation. In this work, an optical method utilizing the inelastic scattering of photons by GHz frequency thermally excited elastic waves, known as Brillouin light scattering spectroscopy (BLS), was employed. Two important classes of soft structures were investigated: thin films and colloidal crystals. For the former, the main interest was the effect of the one-dimensional (1D) confinement on the wave propagation due to the presence of the free-surface or interface of the layer and the utilization of these waves to extract relevant material parameters. For the second system, the primary interest was the interaction of the elastic wave and the strong scattering medium with local resonance units in a three-dimensional (3D) periodic arrangement.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.