The exponentially growing market of electrochemical energy storage devices requires substitution of flammable, volatile, and toxic electrolytes. The use of Water in salt solutions (WiSE) regarded as green electrolyte might be of interest thanks to an
association of key features such as high safety, low cost, wide electrochemical stability, and high ionic conductivity. Here, we report comprehensive chemical-physical study of circumneutral WiSE based on ammonium acetate so as to investigate application in electrochemical energy storage systems, with focus on the effect of pH, density, viscosity, conductivity, and the ESW with salt concentration ranging from 1 to 30 mol/kg . Data are reported and discussed with respect to the structure of the solutions investigated by complemental IR and molecular dynamic study. The study is addressed through the showcase of an asymmetric supercapacitor based on Argan shell-derived carbon electrodes tested at temperatures ranging from -10 to 80 {deg}C.
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed random var
iables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.
We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with b
iased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process `{it space-time Mittag-Leffler process}. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a `well-scaled diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the `state density kernel solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.
With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the dev
elopment of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It turns out
that this generalization can be put in relation to a specific subordination of a homogeneous Poisson process by means of a subordinator for which it is possible to express the characterizing Levy measure explicitly. Moreover, the law of this subordinator solves a one-sided first-order differential equation in which a particular convolution-type integral operator appears, called Prabhakar derivative. In the last section of the paper, a similar model is introduced in which the Prabhakar derivative also acts in time. In this case, too, the probability generating function of the corresponding process and the probability distribution are determined.
Real-world networks may exhibit detachment phenomenon determined by the cancelling of previously existing connections. We discuss a tractable extension of Yule model to account for this feature. Analytical results are derived and discussed both asymp
totically and for a finite number of links. Comparison with the original model is performed in the supercritical case. The first-order asymptotic tail behavior of the two models is similar but differences arise in the second-order term. We explicitly refer to World Wide Web modeling and we show the agreement of the proposed model on very recent data. However, other possible network applications are also mentioned.
