We systematically investigated the plasmon-polariton oscillations generated by a fast radiating charge (Cherenkov radiation) in a three-dimensional (3D) strongly disordered nanostructure. We studied the dynamic properties of an optical field in a random composition of empty single-wall nanotubes by using a 3D numerical finite-difference time domain technique. In our approach, only parameters of nanotube structures are fixed. The dynamic spectrum of internal field excitations was left to be defined as a result of numerical simulation. The patterns of total field (charge + carbon nanotubes) are determined by the interference of a moving charge field and the spectrum of surface plasmon-polaritons in disordered nanotubes. We found that the field energy losses, as a function of the charge velocity, has a clearly pronounced maximum when the characteristic frequency scale (defined by a charge velocity) is close to the frequency of the surface plasmon-polariton resonances generated in coupled nanotubes, even at a significant level of disorder. Our studies show that the shape of the resonance peak, depending on the charge velocity, is similar for carbon and TiO2 nanostructures, but, only for frequencies from the range of the surface plasmon polaritons of respective materials. The TiO2 nanostructure films for a classic cylindrical polytetrafluoroethylene cell was synthesized in our experiments too.

We systematically study the percolation phase transition at the change of concentration of the chaotic defects (pores) in an extended system where the disordered defects additionally have a variable random radius, using the methods of a neural network (NN). Two important parameters appear in such a material: the average value and the variance of the random pore radius, which leads to significant change in the properties of the phase transition compared with conventional percolation. To train a network, we use the spatial structure of a disordered environment (feature class), and the output (label class) indicates the state of the percolation transition. We found high accuracy of the transition prediction (except the narrow threshold area) by the trained network already in the two-dimensional case. We have also employed such a technique for the extended three-dimensional (3D) percolation system. Our simulations showed the high accuracy of prediction in the percolation transition in 3D case too. The considered approach opens up interesting perspectives for using NN to identify the phase transitions in real percolating nanomaterials with a complex cluster structure.

Abstract-We study the electrical conductivity of a three-dimensional (3D) nanocomposite with incorporated random carbon nanotubes (CNT). A large length of the remote nanotubes generates a lot of intersections that induce a rather small percolating threshold of the global conductivity in this medium. We simulate such a system by random cylinders placed in a percolating parallelepiped with the use of Monte Carlo method. The conductivity of such a structure is associated with the critical phenomena, where the main transition parameter is defined by the value of the percolation threshold. We calculate the minimal percolating threshold and determine the functional form of the conductivity by the global optimization technique. Such an approach allows studying the details of the electrical conductivity in nanocomposites even at significant level of the percolating fluctuations.

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Construimos una red neuronal (RN) que simula el efecto de percolación para el caso de sistemas 2D utilizando una red neuronal supervisada. Creamos una base de datos (DB) donde asignamos los valores de los poros con radio aleatorio que componen el sistema bidimensional para entrenar nuestra red, una vez entrenada, la RN fue capaz de detectar si había o no una transición de fase en sistemas 2D con las que se probó nuestra red. Realizamos varias pruebas introduciendo ruido en los radios de los poros en los sistemas de prueba y obtuvimos buenos resultados de predicción cuando el ruido era pequeño, mientras que para ruidos superiores a 0.3 la precisión de predicción tendía a disminuir.