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Polyvinylcarbazole Composite Membranes
Published in Narendra Pal Singh Chauhan, Functionalized Polymers, 2021
Gaurav Sharma, Balasubramanian Kandasubramanian
The continuous-time random walk model of Scher and Montroll is the most frequently used theoretical approach for defining charge carriers in PVK (Scher and Montroll 1975). This model was introduced as a generalization of physical diffusion process to efficiently describe the anomalous diffusion in polymers and thus PVK. The model assumes that charge transport in PVK is governed by a hopping rate w with a functional form: w∝er/r0e−ΔE/KT where w represents the hopping rate with hopping distance r, r0 characterizes the interaction range responsible for hopping, and ΔE is the activation energy for hopping. K is Boltzmann constant with T as temperature.
Comb Models for Transport along Spiny Dendrites
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
Méndez Vicenç, Iomin Alexander
In this way, systems with discrete time and space can be analyzed in terms of the continuous-time random walk (CTRW). Next, we add to every site of the backbone a secondary branch of length l, to produce a one-sided comb-like structure (see Figure 31.3). On such a structure, a walker that is at a given site of the backbone, can spend a certain amount of time in the secondary branch before jumping to one of the nearest-neighbor sites on the backbone. If we are only interested in the behavior of the system in the direction of the backbone, then, the secondary branches introduce a delay time for jumps between the neighboring sites on the backbone. The random walk on the comb structure can be modeled as a CTRW with Equation 31.1 and a renormalized waiting time pdf ϕ(t) that includes the effect of the delay due to the motion along the teeth.
A continuous-time Markov Stackelberg security game approach for reasoning about real patrol strategies
Published in International Journal of Control, 2018
This paper presented a solution model for non-cooperative SSGs using an expected average cost criterion in continuous-time Markov games employing the most important results in control theory and Markov chains developed by Dr Alexander S. Poznyak. More specifically, this paper presented several contributions. We suggested the joint format proposed by Tanaka and Yokoyama to characterise the equilibrium point and for representing the Stackelberg game, we used a two-level programming approach. We employed the extraproximal method for computing the Stackelberg/Nash equilibrium for continuous-time SSGs. We suggested a mathematical optimisation approach that, taking into account the average cost functions, extends the c-variable method for continuous-time. We proposed a continuous-time random walk model. Different classes of random walk models have been investigated in detail and in different contexts along the literature, suggesting a deep understanding of their properties. The continuous-time random walk model is probably the most advanced and flexible one. It is becoming a powerful and useful tool in CTMSG, in particular for reasoning about real patrol strategies. The main result is that by modelling the realisation as a continuous-time random walk, we were able to generate a dynamics that overcame the failures of classical SSG models which do not take such continuous-time property into account. Finally, we ran a numerical example, supported by CTMC, able to generate schedules that became close to reality.