Experiments in the HMX-based condensed explosive PBX-9501 were carried out to validate a reduced, asymptotically derived description of detonation shock dynamics (DSD) where it is assumed that the normal detonation shock speed is determined by the total shock curvature. The passover experiment has a lead disk embedded in a right circular cylindrical charge of PBX-9501 and is initiated from the bottom. The subsequent detonation shock experiences a range of dynamic states with both diverging (convex) and converging (concave) configurations as the detonation shock passes over the disk. The time of arrival of the detonation shock at the top surface of the charge is recorded and compared against DSD simulation and direct multi-material simulation. A new wide-ranging equation of state (EOS) and rate law that is constrained by basic explosive characterization experiments is introduced as a constitutive description of the explosive. This EOS and rate law is used to compute the theoretical normal shock velocity, curvature relation of the explosive for the reduced description, and is also used in the multi-material simulation. The time of arrival records are compared against the passover experiment and the dynamic motion of the shock front and states within the explosive are analysed. The experiment and simulation data are in excellent agreement. The level of agreement, both qualitative and quantitative, of theory and simulation with experiment is encouraging because it indicates that descriptions such as the wide-ranging EOS/rate law and the corresponding reduced DSD description can be used effectively to model real explosives and predict complex dynamic behaviors.
We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the past 20 years two apparently different diagnostic techniques have been established: the first is based on the observation that the multifractal spectrum of healthy patients is broader than the multifractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with pathologic patients hosting uncorrelated Poisson-like events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of uncorrelated Poisson-like events hosted by heartbeats has the effect of making their multifractal spectrum narrower, thereby establishing that the two different diagnostic techniques are compatible with one another and, at the same time, establishing a dynamic interpretation of multifractal processes that had been previously overlooked.
In the wide literature on the brain and neural network dynamics the notion of criticality is being adopted by an increasing number of researchers, with no general agreement on its theoretical definition, but with consensus that criticality makes the brain very sensitive to external stimuli. We adopt the complexity matching principle that the maximal efficiency of communication between two complex networks is realized when both of them are at criticality. We use this principle to establish the value of the neuronal interaction strength at which criticality occurs, yielding a perfect agreement with the adoption of temporal complexity as criticality indicator. The emergence of a scale-free distribution of avalanche size is proved to occur in a supercritical regime. We use an integrate-and-fire model where the randomness of each neuron is only due to the random choice of a new initial condition after firing.The new model shares with that proposed by Izikevich the property of generating excessive periodicity, and with it the annihilation of temporal complexity at supercritical values of the interaction strength. We find that the concentration of inhibitory links can be used as a control parameter and that for a sufficiently large concentration of inhibitory links criticality is recovered again. Finally, we show that the response of a neural network at criticality to a harmonic stimulus is very weak, in accordance with the complexity matching principle.
Linear response theory, the backbone of nonequilibrium statistical physics, has recently been extended to explain how and why nonergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established that a permanent correlation results between an external stimulus and the response of a complex system generating nonergodic renewal processes, when the stimulus is a similar nonergodic process. This is the principle of complexity management, whose proof relies on ensemble distribution functions. Herein we extend the proof to the nonergodic case using time averages and a single time series, hence making it usable in real life situations where ensemble averages cannot be performed because of the very nature of the complex systems being studied.
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