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Volume 19 (2) 2013
Get PDFPoznańStrong shockwaves generate entropy quickly and locally. The Newton-Hamilton equations of motion, which underly the dynamics, are perfectly time-reversible. How do they generate the irreversible shock entropy? What are the symptoms of this irreversibility? We investigate these questions using Levesque and Verlet’s bit-reversible algorithm. In this way we can generate an entirely imaginary past consistent with the irreversibility observed in the present. We use Runge-Kutta integration to analyze the local Lyapunov instability of nearby “satellite” trajectories. From the forward and backward processes we identify those particles most intimately connected with the irreversibility described by the Second Law of Thermodynamics. Despite the perfect time symmetry of the particle trajectories, the fully-converged vectors associated with the largest Lyapunov exponents, forward and backward in time, are qualitatively different. The vectors display a time-symmetry breaking equivalent to Time’s Arrow. That is, in autonomous Hamiltonian shockwaves the largest local Lyapunov exponents, forward and backward in time, are quite different
One-Sided Cumulative Sum (CUSUM) Control Charts for the Erlang-Truncated Exponential Distribution
No full textIn this article, we construct one-sided cumulative sum (CUSUM) control charts for controlling the parameters of a random variable with erlang-truncated exponential distribution. The rejection of the Wald’s sequential probability ratio test (SPRT) is viewed as the decision lines of a CUSUM control chart for which the variate is a quality characteristic. Parameters of the CUSUM chart, e.g. lead distance and mask angle, are presented. The results show that the Average Run Length (ARL) of the resulting control charts changes substantially for a slight shift in the parameters of the distribution
Negative Stiffness Demonstrated by NiAl Nanofilms
No full textThis paper studies the uniaxial strain control tension of NiAl nanofilms via molecular dynamics simulations. The nanofilm deforms elastically until fracture at tensile strain is as large as 37%. The stress-strain curve has a range where tensile deformation develops at decreasing tensile stress, thus indicating negative stiffness. Such deformation is thermodynamicallyunstable and the nanofilm splits into domains with two different values of elastic strain. Deformation within the unstable range is controlled by motion of the domain walls, resulting in the domains with larger strain grow at the expense of the domains with smaller strain
Erratum: Time’s Arrow for Shockwaves; Bit-Reversible Lyapunov and “Covariant” Vectors; Symmetry Breaking
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Monte Carlo Study of Patchy Nanostructures Self-Assembled from a Single Multiblock Chain
No full textWe present a lattice Monte Carlo simulation for a multiblock copolymer chain of length N=240 and microarchitecture (10 − 10)12. The simulation was performed using the Monte Carlo method with the Metropolis algorithm. We measured average energy, heat capacity, the mean squared radius of gyration, and the histogram of cluster count distribution. Those quantities were investigated as a function of temperature and incompatibility between segments, quantified by parameter ω. We determined the temperature of the coil-globule transition and constructed the phase diagram exhibiting a variety of patchy nanostructures. The presented results yield a qualitative agreement with those of the off-lattice Monte Carlo method reported earlier, with a significant exception for small incompatibilities, ω, and low temperatures, where 3-cluster patchy nanostructures are observed in contrast to the 2-cluster structures observed for the off-lattice (10 − 10)12 chain. We attribute this difference to a considerable stiffness of lattice chains in comparison to that of the off-lattice chains