Locomotive and reptation motion induced by internal force and friction

We propose a simple mechanical model of locomotion induced by internal force and friction. We first construct a system of two elements as an analog of the bipedal motion. The internal force does not induce a directional motion by itself because of the action-reaction law, but a directional motion becomes possible by the control of the frictional force. The efficiency of these model systems is studied using an analogy to the heat engine. As a modified version of the two-elements model, we construct a model which exhibits a bipedal motion similar to kinesin's motion of molecular motor. Next, we propose a linear chain model and a ladder model as an extension of the original two-element model,. We find a transition from a straight to a snake-like motion in a ladder model by changing the strength of the internal force.Comment: 10 pages, 7 figur

Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers

We present a semi-analytical solution for the transient streaming potential response of an unconfined aquifer to continuous constant rate pumping. We assume that flow occurs without leakage from the unit below a transverse anisotropic aquifer and neglect flow in the unsaturated zone by treating the water-table as a moving material boundary. In the development of the solution to the streaming potential problem, we impose insulating boundary conditions at land surface and the lower boundary of the lower confining unit. We solve the problem exactly in the double Laplace—Hankel transform space and obtain the inverse transforms numerically. The solution is used to analyse transient streaming potential data collected during dipole hydraulic tests conducted at the Boise Hydrogeophysical Research Site in 2007 June. This analysis yields estimates of aquifer hydraulic parameters. The estimated hydraulic parameters, namely, hydraulic conductivity, transverse hydraulic anisotropy, specific storage and specific yield, compare well to published estimates obtained by inverting drawdown data collected at the field site

General Sum Rules for WW Scattering in Higgsless Models: Equivalence Theorem and Deconstruction Identities

We analyze inelastic 2 to 2 scattering amplitudes for gauge bosons and Nambu-Goldstone bosons in deconstructed Higgsless models. Using the (KK) Equivalence Theorem in 4D (5D), we derive a set of general sum rules among the boson masses and multi-boson couplings that are valid for arbitrary deconstructed models. Taking the continuum limit, our results naturally include the 5D Higgsless model sum rules for arbitrary 5D geometry and boundary conditions; they also reduce to the elastic sum rules when applied to the special case of elastic scattering. For the case of linear deconstructed Higgsless models, we demonstrate that the sum rules can also be derived from a set of general deconstruction identities and completeness relations. We apply these sum rules to the deconstructed 3-site Higgsless model and its extensions; we show that in 5D ignoring all higher KK modes (n>1) is inconsistent once the inelastic channels become important. Finally, we discuss how our results generalize beyond the case of linear Higgsless models.Comment: 36 pages, 2 figure

Generalized Duffy transformation for integrating vertex singularities

For an integrand with a 1/r vertex singularity, the Duffy transformation from a triangle (pyramid) to a square (cube) provides an accurate and efficient technique to evaluate the integral. In this paper, we generalize the Duffy transformation to power singularities of the form p(x)/r α , where p is a trivariate polynomial and α > 0 is the strength of the singularity. We use the map (u, v, w) → (x, y, z) : x = u β , y = x v, z = x w, and judiciously choose β to accurately estimate the integral. For α = 1, the Duffy transformation (β = 1) is optimal, whereas if α ≠ 1, we show that there are other values of β that prove to be substantially better. Numerical tests in two and three dimensions are presented that reveal the improved accuracy of the new transformation. Higher-order partition of unity finite element solutions for the Laplace equation with a derivative singularity at a re-entrant corner are presented to demonstrate the benefits of using the generalized Duffy transformation

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature rule to surface elements containing the singularity and classical Gaussian quadrature to the remaining elements. Two of the four schemes additionally consider a special treatment for elements near to the singularity, where refined Gaussian quadrature and a new moment-fitting quadrature rule are used. The hybrid quadrature schemes are systematically studied on flat B-spline patches and on NURBS spheres considering two different sphere discretizations: An exact single-patch sphere with degenerate control points at the poles and an approximate discretization that consist of six patches with regular elements. The efficiency of the quadrature schemes is further demonstrated in boundary element analysis for Stokes flow, where steady problems with rotating and translating curved objects are investigated in convergence studies for both, mesh and quadrature refinement. Much higher convergence rates are observed for the proposed new schemes in comparison to classical schemes

Static and Dynamic Response of Silty Toyoura Sand with PVA Fibre and Cement Additives

After the Great East Japan Earthquake of 2011, nearly 24 million tons of disaster debris such as concrete products, natural and polymeric fibres, and tsunami deposits remained on the coast of Japan. Much of this debris was recycled and repurposed in engineering projects such as embankments, park restoration, and agricultural field restoration around Tokyo Bay, one of the hardest hit regions of the country. Such a major disaster developed a need for the stabilization of the liquefaction susceptible regions of the reclaimed Tokyo Bay coastline. This thesis specifically focuses on the stabilization against liquefaction of Toyoura sand with the typical silt contents found in the Tokyo Bay region using polyvinyl alcohol (PVA) fibres and Ordinary Portland Cement (OPC). A link between the large strain static and dynamic behavior of the silty sand and the microstructural elements controlling the mechanical response of the amended soil was developed. On a macro scale (Rowe cell, bender element, & cyclic triaxial tests), trends based on cement content, fibre content, silica flour content, and cyclic stress ratio were developed to aid the prediction of the mechanical response of the soil mixture. On a micro scale (SEM and CT scans, mercury intrusion porosimetry), the pore structure, soil structure and soil fabric were visualized to understand the mechanisms underlying these trends. Results from the many tests performed confirmed that the addition of polymer fibres and cement improve the liquefaction resistance, undrained shear strength, and stiffness of silty and clean Toyoura sand. In general, the results suggest that the addition of silica flour is beneficial until a threshold percentage of 28-35% is reached, after which the soil becomes mechanically unstable and more susceptible to static and cyclic liquefaction. The addition of 0-2% fibres provides minimal improvement in all tests. Cement, as expected, improves the soils stiffness and liquefaction resistance proportional to the addition percentage

Microstructure and mechanical behavior of carbides

Microstructure and mechanical properties of carbide

The biology behind the human intervertebral disc and its endplates

The intervertebral discs (IVDs) are roughly cylindrical, fibrocartilaginous, articulating structures connecting the vertebral bodies, and allowing movement in the otherwise rigid anterior portion of the vertebral column. They also transfer loads and dissipate energy. Macroscopically the intervertebral disc can be divided into an outer annulus fibrosus surrounding a centrally located nucleus pulposus. The endplates surround the IVD from both the cranial and caudal ends, and separate them from the vertebral bodies and prevent the highly hydrated nucleus pulposus from bulging into the adjacent vertebrae. The IVD develop from the mesodermal notochord and receive nutrients mostly through the cartilaginous endplates. Physiologically they are innervated only in the outer annulus fibrosus by sensory and sympathetic perivascular nerve fibres, branches from the sinuvertebral nerve, the ventral rami of spinal nerves or from the grey rami communicantes. The IVD undergo changes with ageing and degeneration, the latter having two types i.e. “endplate-driven” involving endplate defects and inward collapse of the annulus fibrosus and “annulus-driven” involving a radial fissure and/or an IVD prolapse. This review summarises and updates the current state of knowledge on the embryology, structure, and biomechanics of the IVD and its endplates. To further translate this into a more clinical context this review also demonstrates the impact of ageing and degeneration on the above properties of both the IVD and its endplates.