Two inverse problems in elasticity are addressed with motivation from cellular biomechanics. The first application is computation of holding forces on a cell during its manipulation and the second application is estimation of a cell’s interior elastic mapping (i.e., estimation of inhomogeneous distribution of stiffness) using only boundary forces and displacements. It is clear from recent works that mechanical forces can play an important role in developmental biology. In this regard, we have developed a vision-based force-sensing technique to estimate forces that are acting on a cell while it is manipulated. This problem is connected to one inverse problem in elasticity known as Cauchy’s problem in elasticity. Geometric nonlinearity under noisy displacement data is accounted while developing the solution procedures for Cauchy’s problem. We have presented solution procedures to the Cauchy’s problem under noisy displacement data. Geometric nonlinearity is also considered in order to account large deformations that the mechanisms (grippers) undergo during the manipulation. The second inverse problem is connected to elastic mapping of the cell. We note that recent works in biomechanics have shown that the disease state can alter the gross stiffness of a cell. Therefore, the pertinent question that one can ask is that which portion (for example Nucleus, cortex, ER) of the elastic property of the cell is majorly altered by the disease state. Mathematically, this question (estimation of inhomogeneous properties of cell) can be answered by solving an inverse elastic boundary value problem using sets of force-displacements boundary measurements. We address the theoretical question of number of boundary data sets required to solve the inverse boundary value problem.

In my dissertation, I developed mixed hp-finite element methods for linear elasticity with weakly imposed symmetry, which is based on Arnold-Falk-Winther's stable mixed finite elements. I have proved the h-stability of my method for meshes with arbitrary variable orders. In order to show the h-stability, I need an upper limit of the highest order of meshes, which can be an arbitrary nonnegative integer. / text

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This study determined whether variation in clone, weed control treatment, or stem dimensions, could have an impact upon outerwood stiffness in 17 year old Pinus radiata stems. An experiment located south west of the Dunsandel township in Canterbury, New Zealand, was used to collect measures of acoustic velocity (windward and downward sides) from each of the 278 trees. Diameter at breast height, tree height, and height to live crown were also recorded for each tree. Findings from this research were compared with previous research carried out when the trees were ages eight and eleven. Assuming a green density of 1,000 kg/m3, Young’s Modulus equation was used to convert acoustic velocity to wood stiffness, or, Modulus of Elasticity (MOE). The effect of wind direction upon mean wood stiffness was not significant (α = 0.05). Consequently, one measure of wood stiffness was calculated per tree. Mean stem slenderness and mean wood stiffness values were calculated by block, weed control treatment, and clone. Weed control treatments had a significant impact upon mean wood stiffness in comparison to the control treatment (0.03 m2 area of weed control). Significant differences did not exist between different levels of weed control, ie., 0.75 m2, 3.14 m2 and 9 m2 chemical spot spray area. Clonal variation and stem slenderness significantly affected mean wood stiffness measures. Stem slenderness appeared to be correlated with clonal variation (interaction between clone and slenderness was not significant), however, according to Dr. Euan Mason, this finding is not corroborated by findings from other research on the wood quality of clones in Canterbury (personal communication, September 16, 2013). An analysis of covariance (ANCOVA) determined that mean height to the live crown was not a significant predictor of wood stiffness. Comparison with earlier research showed no change in the ranking of wood stiffness values by clone or treatment.

This work examines problems in the statics and traveling wave propagation on uniform elastic rods with constant curvature and torsion, i.e. a straight rod and a helical rod. The first set of problems concerns planar traveling loop-like waves on intrinsically straight rods. It is shown that loops with compact support can exist on homogeneous rods with a nonlinear constitutive relation, where the strain-energy density contains a quartic term. Next, the effect of heterogeneity in the material properties on the shape of the loop is examined using a homogenization method. The second set of problems deals with a system consisting of a helical spring with a force and a torque applied along the helix axis. First, an overview is presented of problems of finding the stresses given the strains, or vice-versa, assuming that the elastic parameters of the spring are known. Then, the inverse problem is examined, where both stresses and strains are measured, and optimal elastic parameters within the linear consitutive model are sought. Various forms of measured strains are considered. Finally, the special problem with zero axial torque is considered, and criteria when the spring overwinds with a tensile axial force applied are established.

Despite increasing fuel cost volatility, regulatory uncertainty, and imminent shifts to industry dynamics, utility managers are forced to make tough decisions in regards to installing long-life generation assets. This study seeks to identify and quantify determinants of fuel choice in new electric power plants given vast uncertainties in the electricity generation sector. Using a probit functional form to estimate marginal effects on the likelihood of choosing wind versus natural gas powered generation, I find positive effects of natural gas prices in the period three years prior to initial operation of the new facility, positive effects of static-level standard score of mix, and positive effects of wind-power density. Additional feedstock choice sets and parameters are considered. All models suggest that (a) feedstock costs are significant predictors of fuel choice, (b) state-level regulatory learning enhances likelihood of choosing relatively young technologies, (c) Renewable Portfolio Standards result in artificial substitution between wind and solar technologies, and (d) population density, more so than political influence, predicts choices to install wind-powered capacity. Public policy and managerial implications are discussed.

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This thesis investigates the mechanical properties of the elastic proteins isolated by cyanogen bromide digestion from lamprey cartilages and compares them with the mammalian protein, elastin. Thermomechanical testing and measurements of the effects of hydrophobic solvents on mechanics are used to determine the energetic and entropic contributions to the mechanical properties and the role of solvent interactions. Raman microspectrometry is shown to be a valuable tool in determining the secondary structure of the proteins, their interactions with water and molecular-level effects of mechanical strain. The supramolecular structure of the proteins matrices are investigated using nonlinear microscopy and X-ray diffraction. The mechanical properties of fibrous elastin agreed with those previously reported with elastic moduli in the region of 0.2-0.4 MPa. Elastic moduli decrease by approximately 25% with increased temperature, which was accompanied by a small decrease in hysteresis loss. In agreement with earlier findings, an entropic mechanism of elasticity became dominant only at high temperatures with a major contribution from interactions with solvent water. The lamprey proteins can be divided into two broad groups, the 'soft' branchial and pericardial cartilages resembling elastin, with linear stress-strain behaviour over a range of strains, elastic moduli in the range 0.13 MPa to 0.35 MPa, breaking strains of up to 50% and low hysteresis. Annular and piston proteins showed a very different response having much higher elastic moduli (0.27 MPa to 0.75 MPa), higher breaking strains and large hysteresis. Similarities between elastin and the lamprey matrix proteins extended to their thermomechanical behaviour with a decrease in elastic moduli and a drive towards entropic elasticity at high temperatures, although the annulus and piston were less thermally stable. Raman spectroscopy was able to detect differences between the various proteins and between elastin fibres and fragmentation products. Although no vibrational modes associated with cross-linking of the fibres could be identified, the secondary structure of dehydrated fibrous elastin was significantly different from \alpha -elastin. The former differed from previous experimental measurements, but was close to the theoretical predictions with 36% \beta -structures, 46% unordered and 18% \alpha -helix. \alpha -Elastin contained 29% \beta -structures, 53% unordered and 18% \alpha -helix. Strains of up to 60% in ligament fibre bundles resulted in no significant shifts in peak positions or in secondary structure. Polarization measurements revealed that the peptide bonds and several of the bulky side-chains re-orientated closer to the fibre axis with strain. Heating nuchal elastin fibres to 60^{\circ} C to increase the energetic component of the elasticity was associated with a 30% increase in the proportion of \beta -structures in the amide I band, a 50% increase in the amide III band, and a 50% reduction in the signal from bound water. The Raman spectra of the lamprey matrix proteins are similar both to each other and when compared to fibrous elastin. Only small differences could be detected in side-chain modes consistent with reported biochemical differences. Decomposition of the amide I band indicated that the secondary structures were also very similar to that of elastin, with a preponderance of unordered structures which probably confer the high degree of conformational flexibility necessary for entropy elasticity. Piston and annular proteins, like elastin, showed a strong interaction with water, suggesting a greater role of hydrophobic interactions in their mechanics compared to the branchial and pericardial proteins. Elastin is well known to exhibit autofluorescence. However, only the branchial protein has been reported to autofluoresce. This study shows that all four lamprey matrix proteins investigated exhibit strong autofluorescence which was subsequently exploited to image these tissues using multiphoton microscopy. Microscopic investigations revealed that the architecture of lamprey proteins differ from that of elastin. Nuchal elastin forms bundles of fibres running predominantly parallel to the direction of applied force. The arrangement in lamprey cartilage is very different forming honeycomb structures, which in the case of annular and piston cartilages, is surrounded by a dense sheath of matrix material. Dye injections revealed that the branchial and pericardial form open systems whereas in piston and annular cartilages a closed system exists. These variations in architecture are reflected in their different mechanical properties and in vivo functions.

We consider two one-dimensional harmonic chains coupled along their length via linear springs. Casting the elastic wave equation for this system in a Dirac-like form reveals a directional representation. The elastic band structure, in a spectral representation, is constituted of two branches corresponding to symmetric and antisymmetric modes. In the directional representation, the antisymmetric states of the elastic waves possess a plane wave orbital part and a 4x1 spinor part. Two of the components of the spinor part of the wave function relate to the amplitude of the forward component of waves propagating in both chains. The other two components relate to the amplitude of the backward component of waves. The 4x1 spinorial state of the two coupled chains is supported by the tensor product Hilbert space of two identical subsystems composed of a non-interacting chain with linear springs coupled to a rigid substrate. The 4x1 spinor of the coupled system is shown to be in general not separable into the tensor product of the two 2x1 spinors of the uncoupled subsystems in the directional representation. (C) 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Master of Agribusiness / Department of Agricultural Economics / John Crespi / Hybrid seed corn pricing has increased significantly over the past six or seven years and continues to be a topic of conversation amongst farmers. This issue is also an area of concern for Monsanto. The hybrid corn pricing team at Monsanto is concerned that they price current products at a point to maximize profits while continuing to grow market share. The key is to price at a point that captures all the value of the differentiated products Monsanto offers. The objective for this study is to estimate a demand model for the hybrid seed corn industry. The demand model will allow us to look at many different aspects of the hybrid seed corn industry and also evaluate the own-price and cross-price elasticities. The own-price elasticity is especially important because it will be used to determine if current pricing is revenue or profit-maximizing. A hedonic pricing model was also estimated in this study to complement the demand model. It is important for Monsanto to understand what attributes or traits are significant in pricing and demand.