Classification of heterotic Pati–Salam models

We extend the classification of free fermionic heterotic-string models to vacua in which the SO(10)$\mathit{SO}(10)$ GUT symmetry is broken at the string level to the Pati–Salam subgroup. Using our classification method we recently presented the first example of a quasi-realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the Generalised GSO (GGSO) projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of models that we classify is ²⁵¹∼¹⁰¹⁵$2^{51}\sim {10}^{15}$. We perform a statistical sampling in this space of models and extract 10¹¹ GGSO configurations with Pati–Salam gauge group. Our results demonstrate that one in every 10⁶ vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.     

Some methods of training radial basis neural networks in solving the Navier‐Stokes equations

The purpose of this research is to analyze the application of neural networks and specific features of training radial basis functions for solving 2‐dimensional Navier‐Stokes equations. The authors developed an algorithm for solving hydrodynamic equations with representation of their solution by the method of weighted residuals upon the general neural network approximation throughout the entire computational domain. The article deals with testing of the developed algorithm through solving the 2‐dimensional Navier‐Stokes equations. Artificial neural networks are widely used for solving problems of mathematical physics; however, their use for modeling of hydrodynamic problems is very limited. At the same time, the problem of hydrodynamic modeling can be solved through neural network modeling, and our study demonstrates an example of its solution. The choice of neural networks based on radial basis functions is due to the ease of implementation and organization of the training process, the accuracy of the approximations, and smoothness of solutions. Radial basis neural networks in the solution of differential equations in partial derivatives allow obtaining a sufficiently accurate solution with a relatively small size of the neural network model. The authors propose to consider the neural network as an approximation of the unknown solution of the equation. The Gaussian distribution is used as the activation function.     

A Rapid Photopatterning Method for Selective Plating of 2D and 3D Microcircuitry on Polyetherimide

In this work, a method for the rapid synthesis of metallic microtracks on polyetherimide is presented. The method relies on the photosynthesis of silver nanoparticles on the surface of the polymer substrates from photosensitive silver chloride (AgCl), which is synthesized directly on the polyetherimide surface. The study reveals that the use of AgCl as a photosensitive intermediate accelerates the reactions leading to the formation of silver nanoparticles by up to two orders of magnitude faster than other photodecomposition schemes. The patterning can be conducted under blue light, with notable advantages over UV exposure. Polymers of significant interest to the microelectronics and 3D printing industries can be directly patterned by light using this photography‐inspired technique at throughputs high enough to be commercially advantageous. Light exposures as short as a few seconds are sufficient to allow the direct metallization of the illuminated polyetherimide surface. The results show that the silver required for the seed layer is minimal, and the later copper electroless plating results in the selective growth of conductive tracks for circuitry on the light‐patterned areas, both on flexible films and 3D printed surfaces.     

Dehydrogenation of Formic Acid in Liquid Phase over Pd Nanoparticles Supported on Reduced Graphene Oxide Sheets

Catalysis Surveys from Asia - Reduced graphene oxide sheets (rGO) were used in this study to support Pd nanoparticles through soil-immobilization and impregnation methods. The catalysts were...