The one-dimensional φ 4 Model generalizes a harmonic chain with nearest-neighbor Hooke's-Law interactions by adding quartic potentials tethering each particle to its lattice site. In their studies of this model Kenichiro Aoki and Dimitri Kusnezov emphasized its most interesting feature: because the quartic tethers act to scatter long-wavelength phonons, φ 4 chains exhibit Fourier heat conduction. In his recent Snook-Prize work Aoki also showed that the model can exhibit chaos on the threedimensional energy surface describing a two-body two-spring chain. That surface can include at least two distinct chaotic seas. Aoki pointed out that the model typically exhibits different kinetic temperatures for the two bodies. Evidently few-body φ 4 problems merit more investigation. Accordingly, the 2019 Prizes honoring Ian Snook (1945-2013) [five hundred United States dollars cash from the Hoovers and an additional $500 cash from the Institute of Bioorganic Chemistry of the Polish Academy of Sciences and the Poznan Supercomputing and Networking Center] will be awarded to the author(s) of the most interesting work analyzing and discussing few-body φ 4 models from the standpoints of dynamical systems theory and macroscopic thermodynamics, taking into account the model's ability to maintain a steady-state kinetic temperature gradient as well as at least two coexisting chaotic seas in the presence of deterministic chaos.
PrefaceA decade after publishing Time Reversibility, Computer Simulation, and Chaos, World Scientific requested a Second Edition. We accepted. Carol took up my suggestion that we do this work together. In the decade since the original publication in 1999, and reprinting in 2001, questions from students, progress by researchers, plus the inevitable improvements in our understanding suggested this new book, "Time Reversibility, Computer Simulation, Algorithms, and Chaos". Time-Reversible Computer Simulation remains the fundamental basis of this work. Algorithms has been added to the title. They are the "sine qua non" of computer simulation. The recent literature has impressed us with the need for simple descriptions of the basics of computer simulation, the construction and implementation of algorithms. Our ability to formulate physical problems for computational solution and analysis has led us to an understanding of Chaos which has in turn enriched our understanding of irreversibility within the confines of a Time-Reversible description. We have found this understanding satisfying, rewarding, and continually challenging. We feel an obligation to pass it on to present and future readers.The plan of this book is reflected in our new title. In discussing Computer Simulation we emphasize the basics, Models describing selected aspects of the Real World and Algorithms suited to determining the models' properties and behavior. Models based on classical mechanics, both atomistic and continuous, support our work. These mechanical models can help us to formulate and generate both reversible and irreversible system trajectories. Irreversible behavior can be explicit. More often it emerges from formally reversible microscopic models. Traditional macroscopic treatments of processes follow Thermodynamics or Fluid Mechanics. The oneway increase of entropy found in these macroscopic treatments contrasts The purpose of this book is to make the unity of all these disparate descriptions of physical phenomena more transparent. It would not be possible without the algorithms for our computers, without the introduction of nonequilibrium constraints into mechanics, simulating irreversible processes, and without the graphical displays to bolster and stimulate our understanding. The powerful combination of all these computational tools provides us with a clearer understanding of the development of irreversibility from a time-reversible basis.One might expect that a soundly-based theoretical approach to nonequilibrium problems would provide a reliable path to "understanding". In fact, the judicious computer simulation of illustrative models is more productive and reliable than is theory. The fractal phase-space objects, the variety of computational thermostats, some of which "work" and some of which don't, the asymmetric Lyapunov spectra away from equilibrium, are all significant examples which are easily "understood" in retrospect but hard to predict.Throughout the book we illustrate the main points with worked-out computational exampl...
We sought to simulate auxetic behavior by carrying out dynamic analyses of mesoscopic model structures. We began by generating nearly periodic cellular structures. Four-node "Shell" elements and eightnode "Brick" elements are the basic building blocks for each cell. The shells and bricks obey standard elastic-plastic continuum mechanics. The dynamical response of the structures was next determined for a three-stage loading process: (1) homogeneous compression; (2) viscous relaxation; (3) uniaxial compression. The simulations were carried out with both serial and parallel computer codes -DYNA3D and ParaDyn -which describe the deformation of the shells and bricks with a robust contact algorithm. We summarize the results found here.
Purified bovine brain calmodulin was biotinylated with biotinyl-e-aminocaproic acid N-hydroxysuccinimide. Biotinylated calmodulin was used to detect and quantify calmodulin-binding proteins following both protein blotting and slot-blot procedures by using alkaline phosphatase or peroxidase coupled to avidin. When purified bovine brain calcineurin, a calmodulin-dependent protein phosphatase, was immobilized on nitrocellulose slot blots, biotinylated calmodulin bound in a calcium-dependent saturable manner; these blots were then quantified by densitometry. Biotinylated calmodulin was able to detect as little as 10 ng of calcineurin, and the binding was competitively inhibited by addition of either native calmodulin or trifluoperazine. When biotinylated calmodulin was used to probe protein blots of crude brain cytosol and membrane preparations after gel electrophoresis, only protein bands characteristic of known calmodulin-binding proteins (i.e., calmodulin-dependent protein kinase, calcineurin, spectrin) were detected with avidin-peroxidase or avidinalkaline phosphatase procedures. Purified calcineurin was subjected to one-and two-dimensional gel electrophoresis and protein blotting; as expected, only the 61-kDa calmodulinbinding subunit was detected. When the two-dimensional protein blot was incubated with biotinylated calmodulin and detected with avidin-alkaline phosphatase, several apparent forms of the 61-kDa catalytic subunit were detected, consistent with isozymic species of the enzyme. The results of these studies suggest that biotinylated calmodulin can be used as a simple, sensitive, and quantifiable probe for the study of calmodulinbinding proteins.Much of our current understanding of calmodulin-dependent control of cellular functions has stemmed from identification of the calmodulin-binding proteins, which are activated by Ca2+-calmodulin (1). Calmodulin has been shown to mediate activation of a number of calcium-dependent enzymes such as phosphodiesterase (2-4), adenylate cyclase (5), calmodulin-dependent protein kinases (6)(7)(8) (14) to immobilize proteins on nitrocellulose paper followed by incubation of the Tween-20 blocked paper with 1251I-labeled calmodulin (15).Avidin-biotin probes have been used to visualize biotinlabeled DNA in nitrocellulose blot hybridization studies (16). We have exploited the high-affinity avidin-biotin interaction (17) to afford detection of biotinylated calmodulin and calmodulin-binding proteins. We now report that biotinylated calmodulin can effectively bind both purified and crude preparations of calmodulin-binding proteins with sensitivity of detection in the nanogram range. Biotinylated calmodulin has also been used to develop a quantitative slot-blot procedure for the quantification of individual calmodulin-binding proteins. We have also used this approach to probe twodimensional gels of purified calcineurin and have found several apparent (isozymic) forms of the 61-kDa catalytic subunit (18). The use of biotinylated binding proteins as probes and detection ...
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