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A polymer network fractures by breaking covalent bonds, but the experimentally measured strength of the polymer network is orders of magnitude lower than the strength of covalent bonds. We investigate the effect of statistical variation of the number of links in polymer chains on strength using a parallel chain model. Each polymer chain is represented by a freely-jointed chain, with a characteristic J-shaped force–extension curve. The chain carries entropic forces for most of the extension and carries covalent forces only for a narrow range of extension. The entropic forces are orders of magnitude lower than the covalent forces. Chains with a statistical distribution of the number of links per chain are pulled between two rigid parallel plates. Chains with fewer links attain covalent forces and rupture at smaller extensions, while chains with more links still carry entropic forces. We compute the applied force on the rigid plates as a function of extension and define the strength of the parallel chain model by the maximum force divided by the total number of chains. With the J-shaped force–extension curve of each chain, even a small scatter in the number of links per chain greatly reduces the strength of the parallel chain model. We further show that the strength of the parallel chain model relates to the scatter in the number of links per chain according to a power law.

The Hispanic Chamber of Commerce of Wisconsin acknowledges that low voter turnout continues to plague Milwaukee's predominately Hispanic 12th Aldermanic District. However, the statements attributed to state Rep. Pedro Colon [...]

This 1998 report focuses on consumer trends information together with the initiatives of key influencer groups relating to the nutrition and health environment. These data lay the groundwork for our predictions for the top 10 consumer nutrition trends for 1998.

Responds to criticisms made by the Madison, Wisconsin-based Citizens Utility Board and Madison Gas & Electric against the Milwaukee, Wisconsin-based Wisconsin Electric Power Co. (WEPCO). Amount invested by WEPCO in Wisconsin in the ten years prior to 1999; Contributions made by WEPCO to local civic projects.

Presents pro and con arguments concerning the proposed building of a stadium for the Milwaukee Brewers baseball team in Wisconsin. Features of the financing package for the proposal; Importance of the Brewers to the city; Benefits of the plan.

Many processes in nature such as conformal changes in biomolecules and clusters of interacting particles, genetic switches, mechanical or electromechanical oscillators with added noise, and many others are modeled using stochastic differential equations with small white noise. The study of rare transitions between metastable states in such systems is of great interest and importance. The direct simulation of rare transitions is difficult due to long waiting times. Transition path theory is a mathematical framework for the quantitative description of rare events. Its crucial component is the committor function, the solution to a boundary value problem for the backward Kolmogorov equation. The key fact exploited in this work is that the optimal controller constructed from the committor leads to the generation of transition trajectories exclusively. We prove this fact for a broad class of stochastic differential equations. Moreover, we demonstrate that the committor computed for a dimensionally reduced system and then lifted to the original phase space still allows us to construct an effective controller and estimate the transition rate with reasonable accuracy. Furthermore, we propose an all-the-way-through scheme for computing the committor via neural networks, sampling the transition trajectories, and estimating the transition rate without meshing the space. We apply the proposed methodology to four test problems: the overdamped Langevin dynamics with Mueller's potential and the rugged Mueller potential in 10D, the noisy bistable Duffing oscillator, and Lennard-Jones-7 in 2D. • Methodology for sampling transition path processes using optimal stochastic control. • Theorems on the connection between the optimal control and the committor function. • A method for estimating transition rates using the controlled dynamics. • Inexact committors still give very good controllers. • Test cases include 10D and 14D benchmark problems. [ABSTRACT FROM AUTHOR]