Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

We derive an orthotropic model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data

Evaluating the Stormwater Treatment Performance of AbTech Industries Smart Sponge® Plus, Landry, N

The ability of AbTech’s Smart Sponge® Plus to remove fecal-borne bacteria from stormwater was evaluated in a storm drainage system located in Seabrook, New Hampshire. The Smart Sponge ® Plus was installed into a water quality inlet and samples were collected from influent (pre-treatment) and effluent (post-treatment) for analysis of bacterial concentrations and loadings during 15 storm events from September 3, 2003 to May 24, 2004, excluding winter months. The 15 storms included events with a range of rainfall intensities and amounts, as well as accompanying runoff volumes. Flow weighted composite samples were analyzed for fecal coliforms, Escherichia coli and enterococci to determine if concentrations were lowered as stormwater passed through the Smart Sponge® Plus material. In most cases, bacterial concentrations were reduced within the treatment system, but to varying degrees. The efficiency ratio based on reduction in event mean concentration for each bacterial indicator in the flow was calculated for each storm event. The values ranged most widely for fecal coliforms, whereas the range of ratios was narrower and the values were more consistent for enterococci. The overall load reductions for the bacterial indicators were 50.3% for fecal coliforms, 51.3% for Escherichia coli and 43.2% for enterococci. Relatively consistent pH values were observed in influent and effluent samples. The overall range of pH values was large, ranging from 5.21 units in influent from storm event #11 to 7.64 units in influent from storm event #1. Conductivity values were gr eater in the effluent in 14 of the 15 storm events, especially in storm events #12 and #13 when effluent conductivities were \u3e50% higher than influent values. Quality assurance/quality control procedures supported the methods and results of the study. Overall, the observed reductions in bacterial concentrations in post-treatment stormwater would still result in discharge of elevated bacterial levels that would continue to limit uses in receiving waters

On the complex singularities of the inverse Langevin function

We study the inverse Langevin function $\mathscr{L}^{-1}(x)$ because of its importance in modelling limited-stretch elasticity where the stress and strain energy become infinite as a certain maximum strain is approached, modelled here by $x\to1$. The only real singularities of the inverse Langevin function $\mathscr{L}^{-1}(x)$ are two simple poles at $x=\pm1$ and we see how to remove their effects either multiplicatively or additively. In addition, we find that $\mathscr{L}^{-1}(x)$ has an infinity of complex singularities. Examination of the Taylor series about the origin of $\mathscr{L}^{-1}(x)$ shows that the four complex singularities nearest the origin are equidistant from the origin and have the same strength; we develop a new algorithm for finding these four complex singularities. Graphical illustration seems to point to these complex singularities being of a square root nature. An exact analysis then proves these are square root branch points.Comment: 25 pages, 10 figures, 4 tables, 50 equations, 28 reference

The West: slowing, but still strong

Federal Reserve District, 12th

Transient deactivation of dorsal premotor cortex or parietal area 5 impairs feedback control of the limb in macaques

We can generate goal-directed motor corrections with surprising speed, but their neural basis is poorly understood. Here, we show that temporary cooling of dorsal premotor cortex (PMd) impaired both spatial accuracy and the speed of corrective responses, whereas cooling parietal area 5 (A5) impaired only spatial accuracy. Simulations based on optimal feedback control (OFC) models demonstrated that “deactivation” of the control policy (reduction in feedback gain) and state estimation (reduction in Kalman gain) caused impairments similar to that observed for PMd and A5 cooling, respectively. Furthermore, combined deactivation of both cortical regions led to additive impairments of individual deactivations, whereas reducing the amount of cooling to PMd led to impairments in response speed but not spatial accuracy, both also predicted by OFC models. These results provide causal support that frontoparietal circuits beyond primary somatosensory and motor cortices are involved in generating goal-directed motor corrections

Probability Distributions in the Glass Failure Prediction Model

Glass, a brittle material, fractures under tensile stress acting over a time duration. Lateral loads, such as wind, acting on a simply supported rectangular glass lite, put one surface of the lite primarily into tension. ASTM E 1300 defines load resistance of glass as the uniform lateral loading acting over a duration of 3 seconds that is associated with a probability of breakage of 8 lites per 1000 at the first occurrence of the loading. To determine load resistance, the underlying window glass failure prediction model facilitates determination of a probability distribution of 3 second equivalent failure loads, P3. The glass failure prediction model is based on a Weibull distribution, and most people believe the distribution of P3 is, in fact, a Weibull distribution. However, the authors contend that this is not the case. This paper provides an explanation of the glass failure prediction model, its basis, and a discussion of the method for determining surface flaw parameters with an example. The authors demonstrate the distribution of the equivalent failure loads does not follow a Weibull distribution, and they will elucidate the relationship between the distribution of P3 and the Weibull distribution

Loyalty Among Relationally Oriented Customers: Not Just an Issue of Managing Satisfaction: Working Paper Series--02-27

This paper explores empirically the relative impacts of satisfaction, brand community, and consumer experience on customer loyalty as expressed by future purchase intentions. Data drawn from qualitative research and a survey of relationally-oriented customers in a casino setting indicate that satisfaction yields to brand community as a key driver of loyalty. Important implications of this research for theory as well as marketing practice are discussed