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Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…
Axisymmetric simulations of a liquid rocket engine are performed using a delayed detached-eddy-simulation (DDES) turbulence model with the Compressible Flamelet Progress Variable (CFPV) combustion model. Three different pressure instability…
The article presents a proposal to contextualize the study of movement in first courses of university physics, as a contribution to decision-making in situations of a social nature. For this, the case of the use of kinetic impact…
The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming…
The number of periodic solutions to Painlev\'e VI along a Pochhammer loop is counted exactly. It is shown that the number grows exponentially with period, where the growth rate is determined explicitly. Principal ingredients of the…
Simulation is a powerful tool to better understand physical systems, but generally requires computationally expensive numerical methods. Downstream applications of such simulations can become computationally infeasible if they require many…
The transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
Surface elasticity is central to understanding the mechanics and stability of surfaces and interfaces. It is characterized by quantities such as surface tension, residual surface stress, and surface stiffness, however their analytical…
Real-time prediction of the dynamics of energetic electrons in Earth's radiation belts incorporating incomplete observation data is important to protect valuable artificial satellites and to understand their physical processes.…
This article investigates the well-posedness of weak solutions to non-linear parabolic PDEs driven by rough coefficients with rough initial data in critical homogeneous Besov spaces. Well-posedness is understood in the sense of existence…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of $N$ dielectric spherical particles undergoing mutual polarisation.…
The seminal concept of characteristic polygon of an embedded algebroid surface, first developed by Hironaka, seems well suited for combinatorially (perhaps even effectively) tracking of a resolution process. However, the way this object…
The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical…
Contour integration is a crucial technique in many numeric methods of interest in physics ranging from differentiation to evaluating functions of matrices. It is often important to determine whether a given contour contains any poles or…
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
The smoothed-particle hydrodynamics (SPH) technique is a numerical method for solving gas-dynamical problems. It has been applied to simulate the evolution of a wide variety of astrophysical systems. The method has a second-order accuracy,…
We show how the recently proposed XCone jet algorithm smoothly interpolates between resolved and boosted kinematics. When using standard jet algorithms to reconstruct the decays of hadronic resonances like top quarks and Higgs bosons, one…