Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $\Gamma$ and any field \K, the space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

Welfare loss with municipal amalgamations and the willingness-to-pay for the municipality name

Functional advantages and drawbacks are commonly mentioned to rationally justify or condemn municipality amalgamations. However, many consolidation projects are resisted by local governments or citizens on the grounds that amalgamation would dampen local identity. A municipality's name change is probably the most visible sign of the loss of community bond experienced by citizens at amalgamation time. This article aims to put a value on this loss by measuring citizen willingness to pay for their city name. This methodological approach innovates upon the literature on municipal amalgamation and place branding by exploiting the versatility of the so-called contingent valuation method (CVM). CVM confronts respondents, in a survey setting, with a hypothetical market in which a characteristic of interest is exchanged. Here the characteristic is the possibility to retain one's city name for an amalgamated jurisdiction. The article presents the estimates provided by a survey conducted in four Swiss cities

Ex-post survey on the consequences and perceptions about amalgamation : The case of two Swiss municipalities

In 2006, two municipalities located in the canton of Fribourg (Switzerland), La Tour-de-Trême and Bulle, amalgamated. In this study, we report on the evolution of citizen perceptions as well as try to better understand the reasons behind the respondents various positions concerning this new political and territorial entity. Five-hundred individuals were surveyed almost four years after the amalgamation came into effect. Our results show that if the amalgamation was voted again, it would be necessary to be particularly attentive to citizen access to municipal offices and to local service provisions, to citizen identification to their municipality as well as to the life of the local associations. Indeed, these are clearly important issues for small localities. Furthermore, citizens of the newly amalgamated municipality are mostly sensitive to access to municipal offices and to contact with local representatives. Improving the population's perceptions of these particular issues could lead to a 12 percentage point increase in support for the amalgamation

Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belaru

Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

Mechanics of Notched Izod impact testing of polycarbonate

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.Includes bibliographical references (leaf 62).Polycarbonate is widely used as a transparent protective material because of its low density and excellent mechanical properties. However, when defects such as cracks or notches are introduced, it is subject to catastrophic brittle failure at relatively low loads. Notched Izod testing is a common qualitative measure of toughness of a material, measuring energy absorbed prior to failure under high triaxiality and high rate loading conditions. Much research has been done using Izod testing to compare the fracture energies of blends of Polycarbonate and rubbery materials; however the specific yielding and fracture mechanisms associated with each blend are rarely analyzed. This study presents detailed images, fracture energies, and time durations of the deformation and failure processes actively occurring during the Notched Izod testing of 3.23mm and 6.35mm thick Polycarbonate specimens, as well as of a quasi-static version of Notched Izod bending. The thin specimens were found to yield in a ductile manner followed by tearing across most of the ligament width, resulting in a final failure including a small plastically-deformed ligament hinging the two failure surfaces in both the Notched Izod impact and Quasi-Static tests.(cont). The thick specimens exhibited slight yielding followed by catastrophic failure, where the crack initiated ahead of the notch and then propagating back towards the notch root as well as across the remaining ligament.. In the thick Izod tests local pre-failure yielding was evident at the notch root resulting in extensive blunting of the notch. The fracture energies per unit thickness for the thin specimens were almost a full order of magnitude larger than those for the thick specimens. A finite element simulation for the Notched Izod Impact test was developed using the Arruda and Boyce(1988) constitutive model of polymers as modified by Mulliken and Boyce(2004) for high rate deformation. The 3.23mm Notched Izod impact test was successfully modeled from initial contact of the pendulum through initiation of failure and early tearing. The yielding patterns and failure occurred along the same lines as in the experiment where diagonal shear bands and lobes initiate plastic deformation from the notch tip and tearing progresses in a horizontal manner across the specimen width. An extensive shear yielded region is observed ahead of the propagating tear. The 6.35mm thick model shows the beginning of the formation pressure concentration which causes brittle fracture, but further refinement of the mesh needs to be performed for more accurate modeling.by Meredith N. Silberstein.S.B

Mechanics of proton exchange membranes : time, temperature, and hydration dependence of the stress-strain behavior of persulfonated polytetrafluorethylene

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.Includes bibliographical references (leaves 169-170).Fuel cells are an important part of the future strategy for reducing dependence on fossil fuels as the world's supplies become more limited and greenhouse gasses become more of a concern. Proton Exchange Membrane Fuel Cells (PEMFC), in which protons from hydrogen gas are passed across a membrane to react with oxygen gas producing electricity, with water as the only waste product, are a cleaner and potentially more efficient chemical energy conversion method. However, the current usefulness of PEMFC is limited by the lifespan and high cost of the fuel cell unit, and more specifically the membrane electrode assembly (MEA). At the center of most contemporary MEA is a thin membrane (- 25 - 100pm thick) of persulfonated polytetrafluoroethylene manufactured by Dupont and known commercially as Nafion. Nafion has the unique quality of being microphase separated into hydrophobic and hydrophilic domains composed of backbone rich and sulfonic acid side chain rich regions respectively. This polymer electrolyte membrane is responsible for rapidly conducting the protons from the hydrogen side to the oxygen side while preventing electrons, hydrogen, and oxygen from passing through. Because of this selective permeability requirement it is important that the membrane possess good mechanical durability so that it does not form pinholes during operation (something which it has been shown to do experimentally). The goal of this thesis was to develop an understanding of the mechanical properties of Nafion as well as a comprehensive material model that captures all the features that are important to how a membrane deforms in an operational fuel cell, including the time, temperature, and hydration dependence of the elastic regime, yield, strain hardening, and stress relaxation at low to moderate strains.(cont) In order to accomplish this understanding a comprehensive experimental study was undertaken in which Nafion was characterized in uniaxial tension under monotonic, cyclic, and stress relaxation loading profiles at strain rates from 0.001/s to 0.1/s, temperatures from 250C to 1000C, and from dry to fully hydrated conditions. The evolution of the microstructure with applied deformation was then investigated with diffraction techniques. Wide and small angle x-ray scattering data was collected during uniaxial tensile monotonic extension, cyclic, and stress relaxation loading profiles. The SAXS peaks and two WAXS peaks were seen to be isotropic in the initial state. Their evolution with strain was interpreted to indicate that the ionic clusters deform to an elliptical shape with major axis parallel to the tensile direction with an applied strain, whereas the backbone segments align themselves parallel to the tensile direction with an applied strain. Combining these results with those in literature we revise an existing conceptual model for how each of the micromechanical features evolves with strain and how that contributes to the stress response. From mechanical and microstructural data, a constitutive model was developed which is able to capture the key features of the mechanical behavior of Nafion as functions of time, temperature, and hydration. The model is then applied to a simulated fuel cell. The results from the fuel cell simulations indicate that the hypothesis that cyclic stress states and permanent membrane deformation result from hygro-thermal cycling and can lead to pinhole formation.by Meredith Natania Silberstein.S.M

Mechanics and multi-physics deformation behavior of polymer electrolyte membranes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 176-184).Fuel cells are a developing technology within the energy sector that offer both efficiency and environmental advantages over traditional combustion processes. In particular, proton exchange membrane fuel cells (PEMFC) are promising for transportation and portable devices due to their low operating temperature, reduced C02 emissions, and scalability. A central component is the polymer electrolyte membrane (PEM) which conducts protons from the fuel source (typically either hydrogen or methanol) at the anode to the cathode where it reacts with oxygen while preventing the transport of either electrons or the fuel itself. Historically membranes have been designed primarily in terms of maximizing proton conductivity, but it is also important that they prevent fuel crossover and have minimal chemical and mechanical degradation over the target lifetime of the fuel cell. Membrane mechanical integrity is thus a critical concern for commercial distribution of PEMFC technology. This thesis has two primary focus areas: (1) characterization and modeling of Nafion, the benchmark PEM, in order to understand hygro-thermal loading in the existing technology and (2) mechanical characterization and modeling toward the development of an alternative polymer electrolyte membrane. These two areas are linked by the common technological application of low temperature fuel cells and can also be placed more broadly in the field of microstructurally and micromechanically informed constitutive modeling. The presulfonated polytetrafluoroethylene membrane Nafion is perhaps the most commercially prominent and widely studied polymer electrolyte membrane (PEM). Here Nafion is experimentally characterized first under monotonic and cyclic uniaxial tensile loading as a function of rate, temperature, and hydration. The data is used to develop a microstructurally motivated three-dimensional constitutive model. The Nafion model is validated under uniaxial tension for monotonic, cyclic, stress relaxation, and creep loading at various environmental conditions. Small and wide angle x-ray scattering characterization is then performed during uniaxial tensile testing in order to assign a microstructural interpretation to the mechanical behavior. The model is then validated for loading conditions which are expected to occur in the fuel cell, specifically, biaxial tension in the membrane plane and constrained swelling. Biaxial characterization is conducted via in-plane tensile testing of cruciform shaped specimens. The biaxial response is found to be qualitatively similar to the uniaxial response with the stiffness and strength in a given direction dependent on the degree of biaxiality. The constitutive model was shown to well predict this complex multiaxial deformation response when the model is implemented in the experimental geometry and reduced by the same methods as the experimental results. Biniaterial strip swelling of Nafion and typical gas diffusion layer material (GDL) is used to probe the partially constrained swelling behavior of Nafion. When the strip is hydrated the membrane swells causing the strip to curl with the membrane on the convex side until the force from the membrane is balanced by a moment in the GDL. Upon drying, plastic deformation that occurred during hydration induces a residual curvature of the opposite convexity. The hydrated and dried radii are found to agree with the finite element simulation predictions for two thicknesses of Nafion to within experimental error. Finally, the Nafion constitutive model is used to simulate a simplified fuel cell cycle. A negative hydrostatic pressure develops in the membrane upon drying, suggesting a driving force for cavitation or crazing. A study of the effect of ramp rate and hold time reveal a significant time dependence of the pressure, which is not surprising given the significant rate dependence observed for Nafion under uniaxial mechanical loading. Simulations of this nature are useful in guiding startup and shutdown procedures for fuel cells, for designing/validating potential procedures for accelerated lifetime testing, and for designing alternative fuel cell geometries. Focus is then shifted to the design of new polymer electrolyte membranes for direct methanol fuel cells (DMFC) which are a special case of PEMFC. DMFC operate under the same principal as PEMFC., however the fuel is liquid methanol rather than hydrogen. The high energy density of methanol makes DMFC particularly promising for portable applications where they could replace Li-ion batteries. In contrast to PEMFC, fuel crossover is a major design concern even when the membrane is fully intact. Given the multi-functionality of a DMFC PEM, it is natural to look to a composite solution. For the proton transport and fuel crossover resistance we use a chemistry and synthesis technique developed in the Hammond lab at MIT. This membrane is itself a composite of sulfonated Poly(2,6-dimethyl 1,4-phenylene oxide) (sPPO) and poly(diallyl dimethyl ammonium chloride) (PDAC) assembled via layer-by-layer (LBL) deposition. Unfortunately these films tear easily under dry conditions and are almost fluid like under hydrated conditions. The PDAC/sPPO membrane must therefore be combined with a mechanical support component. Here we use a highly porous and mechanically robust mat produced by electrospinning polyamide (EFM). In this thesis, focus is on the mechanical aspects of the design. A model for the mechanical behavior of the composite is developed based on experiments and models of the component materials. Uniaxial tensile tests are conducted on each of the materials (LBL, EFM, and LBL coated EFM) and the material morphology is examined via scanning electron microscopy where appropriate (EFM and LBL coated EFM). A micromechanically motivated constitutive model is then developed separately for the LBL and the EFM. The LBL model is a single mechanism elastic-plastic model that is highly hydration sensitive. The EFM structure is idealized as a layered triangulated network of elastic-plastic fibers. The behavior of the constituent fibers is taken to be elastic-plastic accounting for stretching and bending of the fibers when subjected to end tensile and compressive loads; the bending of the fibers when a fiber is locally under compression is found to be the key mechanism enabling the mat to consolidate during tensile loading. The layers of triangles impose mutual kinematic constraints emulating the layered structure of real mats, providing greater isotropy to the yield and post-yield behavior. A composite model is then developed as the superposition of the two materials. It is found that a composite model consisting of a weighted summation of the two component behaviors can capture the dry behavior. but not the hydrated behavior. In the hydrated state, the LBL, which is itself quite compliant under uniaxial loading, is found to inhibit fiber bending, thereby lending initial elastic stiffness and reducing post-yield hardening in a non-additive manner.by Meredith Natania Silberstein.Ph.D