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Understanding the atomistic mechanism of ion conduction in solid electrolytes is critical for the advancement of all-solid-state batteries. Glass-ceramics, which undergo crystallization from a glass state, frequently exhibit unique properties including enhanced ionic conductivities compared to both the original crystalline and glass forms. Despite these distinctive features, specific details regarding the behavior of ion conduction in glass-ceramics, particularly concerning conduction pathways, remain elusive. In this study, we demonstrate the crystallization process of glass-Li$_3$PS$_4$ through molecular dynamics simulations employing machine learning interatomic potentials constructed from first principles calculation data. Our analyses of Li conduction using the obtained partially crystallized structures reveal that the diffusion barriers of Li decrease as the crystallinity in Li$_3$PS$_4$ glass-ceramics increases. Furthermore, Li displacements predominantly occur in the precipitated crystalline portion, suggesting that percolation conduction plays a significant role in enhanced Li conduction. These findings provide valuable insights for the future utilization of glass-ceramic materials.

In this article, a numerical scheme is introduced for solving the fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM) by using an efficient class of finite difference methods. The numerical scheme is based on the Hermite formula. The Caputo's fractional derivatives in time are discretized by a finite difference scheme of order $\mathcal{O}(k^{(4-\alpha)})$ \& $\mathcal{O}(k^{(4-\beta)})$, $1<\beta <\alpha \leq 2$. The stability and the convergence analysis of the proposed methods are given by a procedure similar to the standard von Neumann stability analysis under mild conditions. Also for FPDE, accuracy of order $\mathcal{O}\left( k^{(4-\alpha)}+k^{(4-\beta)}+h^2\right) $ is investigated. Finally, several numerical experiments with different fractional-order derivatives are provided and compared with the exact solutions to illustrate the accuracy and efficiency of the scheme. A comparative numerical study is also done to demonstrate the efficiency of the proposed scheme., Comment: Some major revision needed

The present article is devoted to developing the Legendre wavelet operational matrix method (LWOMM) to find the numerical solution of two-dimensional hyperbolic telegraph equations (HTE) with appropriate initial time boundary space conditions. The Legendre wavelets series with unknown coefficients have been used for approximating the solution in both of the spatial and temporal variables. The basic idea for discretizing two-dimensional HTE is based on differentiation and integration of operational matrices. By implementing LWOMM on HTE, HTE is transformed into algebraic generalized Sylvester equation. Numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme. Comparisons of numerical results associated with the proposed method with some of the existing numerical methods confirm that the method is easy, accurate and fast experimentally. Moreover, we have investigated the convergence analysis of multidimensional Legendre wavelet approximation. Finally, we have compared our result with the research article of Mittal and Bhatia (see [1])., Comment: 31 pages, 12 figures

The recent decade has witnessed phenomenal growth in communication technology. Development of user-friendly software platforms, such as Facebook, WhatsApp etc. have facilitated ease of communication and thereby people have started freely sharing messages and multimedia over the Internet. Further, there is a shift in trends with services being accessed from smartphones over personal computers. To protect the security and privacy of the smartphone users, most of the applications use encryption that encapsulates communications over the Internet. However, research has shown that the statistical information present in a traffic can be used to identify the application, and further, the activity performed by the user inside that application. In this paper, we extend the scope of analysis by proposing a learning framework to leverage application and activity data to profile smartphone users in terms of their gender, profession age group etc. This will greatly help the authoritative agencies to conduct their investigations related to national security and other purposes.

In this paper we investigate fractional differential equations with Hilfer fractional derivative of order $1<\gamma<2$ and type $\delta \in [0,1]$ in a Banach space. We introduce a family of general fractional cosine operator functions of order $1<\gamma<2$ and type $\delta \in [0,1]$ and discuss their properties to give a suitable definition of mild solution of a semilinear evolution equation. In last section an example is presented.

Electron transfer processes at molecule-semiconductor interfaces involve a complex mixture of thermionic, tunneling and hopping events. Traditionally these processes have been modeled in a piece-meal fashion, relying on phenomenological treatments such as Simmons and Richardson equations that are not vetted in atomistic systems and do not flow seamlessly into each other. We present a unified modeling approach, based on the Non-equilibrium Greens function (NEGF) formalism that allows us to integrate diverse transport regimes and establish a comprehensive quantitative theory. By comparing our simulations with experiments on a metal-molecule-semiconductor junction (varying molecular lengths ~1-3nm), we identify the role of molecular monolayers in tuning the semiconductor band-bending, and thereby overall device conductivity. We find that the principal role of molecules is to act as a voltage divider, altering the Schottky barriers, thereby modulating current levels, voltage-asymmetries and crossover from Schottky to tunneling transport. While this provides an appealingly simple explanation for our observed experimental trends, the calculated shifts in crossover voltages are insufficient to explain the experiments quantitatively. Quantitative correspondence with experiments requires invocation of an additional voltage divider arising from molecular dipoles that further tunes semiconductor band-bending. The extracted dipole moments are rationalized using ab-initio calculations for each molecule, along-with a dilution of packing fraction for the shortest molecular lengths. The methodology described herein can be used to better understand and predict transport characteristics of such junctions.