Provo City Corp. v. Donna I. Knudsen : Brief of Respondent

Appeal from the Judgment of the Fourth District Court. The Honorable J. Robert Bullock

A size-dependent functionally graded sinusoidal plate model based on a modified couple stress theory

A size-dependent model for bending and free vibration of functionally graded plate is developed based on the modified couple stress theory and sinusoidal shear deformation theory. In the former theory, the small scale effect is taken into consideration, while the effect of shear deformation is accounted for in the latter theory. The equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions for the bending and vibration problems of simply supported plates are obtained. Numerical examples are presented to illustrate the influences of small scale on the responses of functionally graded microplates. The results indicate that the inclusion of small scale effects results in an increase in plate stiffness, and consequently, leads to a reduction of deflection and an increase in frequency. Such small scale effects are significant when the plate thickness is small, but become negligible with increasing plate thickness

On the thermodynamics of the Swift–Hohenberg theory

We present the microbalance including the microforces, the first- and second-order microstresses for the Swift–Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift–Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift–Hohenberg equation

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.Comment: 13 pages. Phys. Rev. D, to appea

Multiscale analysis of materials with anisotropic microstructure as micropolar continua

Multiscale procedures are often adopted for the continuum modeling of materials composed of a specific micro-structure. Generally, in mechanics of materials only two-scales are linked. In this work the original (fine) micro-scale description, thought as a composite material made of matrix and fibers/particles/crystals which can interact among them, and a scale-dependent continuum (coarse) macro-scale are linked via an energy equivalence criterion. In particular the multiscale strategy is proposed for deriving the constitutive relations of anisotropic composites with periodic microstructure and allows us to reduce the typically high computational cost of fully microscopic numerical analyses. At the microscopic level the material is described as a lattice system while at the macroscopic level the continuum is a micropolar continuum, whose material particles are endowed with orientation besides position. The derived constitutive relations account for shape, texture and orientation of inclusions as well as internal scale parameters, which account for size effects even in the elastic regime in the presence of geometrical and/or load singularities. Applications of this procedure concern polycrystals, wherein an important descriptor of the underlying microstructure gives the orientation of the crystal lattice of each grain, fiber reinforced composites, as well as masonry-like materials. In order to investigate the effects of micropolar constants in the presence of material non central symmetries, some numerical finite element simulations, with elements specifically formulated for micropolar media, are presented. The performed simulations, which extend several parametric analyses earlier performed [1], involve two-dimensional media, in the linear framework, subjected to compression loads distributed in a small portion of the medium

Introduction to This Special Issue on Open Design at the Intersection of Making and Manufacturing

What is ‘open design’ and who gets to say what it is? In the emerging body of literature on open design, there is a clear alignment to the values and practices of free culture and open source software and hardware. Yet this same literature includes multiple, sometimes even contradictory strands of technology practice and research. These different perspectives can be traced back to free culture advocates from the 1970s to the 1990s who formulated the ideal of the internet as inherently empowering, democratizing, and countercultural. However, more recent approaches include feminist and critical interventions into hacking and making as well as corporate strategies of “open innovation” that bring end-users and consumers into the design process. What remains today seems to fall into two schools of thought. On one hand, we have the celebratory endorsements of ‘openness’ as applied to technology and design. On the other hand, we have a continuous and expanding critique of these very ideals and questions, where that critique identifies persisting forms of racial, gender, age, and class-based exclusions, and questions about the relationship between open design, labor and power remain largely unanswered

Rectification of the Water Permeability in COS-7 Cells at 22, 10 and 0°C

The osmotic and permeability parameters of a cell membrane are essential physico-chemical properties of a cell and particularly important with respect to cell volume changes and the regulation thereof. Here, we report the hydraulic conductivity, Lp, the non-osmotic volume, Vb, and the Arrhenius activation energy, Ea, of mammalian COS-7 cells. The ratio of Vb to the isotonic cell volume, Vc iso, was 0.29. Ea, the activation energy required for the permeation of water through the cell membrane, was 10,700, and 12,000 cal/mol under hyper- and hypotonic conditions, respectively. Average values for Lp were calculated from swell/shrink curves by using an integrated equation for Lp. The curves represented the volume changes of 358 individually measured cells, placed into solutions of nonpermeating solutes of 157 or 602 mOsm/kg (at 0, 10 or 22°C) and imaged over time. Lp estimates for all six combinations of osmolality and temperature were calculated, resulting in values of 0.11, 0.21, and 0.10 µm/min/atm for exosmotic flow and 0.79, 1.73 and 1.87 µm/min/atm for endosmotic flow (at 0, 10 and 22°C, respectively). The unexpected finding of several fold higher Lp values for endosmotic flow indicates highly asymmetric membrane permeability for water in COS-7. This phenomenon is known as rectification and has mainly been reported for plant cell, but only rarely for animal cells. Although the mechanism underlying the strong rectification found in COS-7 cells is yet unknown, it is a phenomenon of biological interest and has important practical consequences, for instance, in the development of optimal cryopreservation