Distribution of first-reaction times with target regions on boundaries of shell-like domains

We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted "onion-shell" geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.

Electromagnetic Wave Equation Approximation using FDTD method on Conductivity Material

FDTD is a method that is applied in the simulation of electromagnetic waves. This study aims to simulate the propagation of electromagnetic waves on a material with conductivity and permittivity on the plate. The approximate form of Maxwell’s equations can be used to describe discrete electromagnetic waves. Signal analysis in the form of electromagnetic waves using position domains for magnetic field H and electric field E. By taking into consideration boundary conditions, stability, and boundary conditions, the proposed research employs the basic concept of differential equation method. The simulation results show that materials with high conductivity will cause the waves to decay. Under certain conditions, the relationship between the shape of the field to changes in conductivity and permittivity of the material is needed in the analysis process.

Design of linear surfaces that restrict the range of permissible positions of links of the manipulator mechanisms in implementation of instantaneous states

Linear surfaces are used in various spheres of human activity. One of the most common techniques of designing linear surfaces is based on the three directing curves. In some cases, one of these directing curves is not set, but rather replaced by some geometric condition imposed on the emerging surfaces, which can in form of a certain point correspondence established between the points of the rest two directing curves. The article reviews the example of designing such surfaces, which in an approximate form would restrict the zone that sets the permissible positions of links of the manipulator mechanism of certain given configuration in realization of permissible instantaneous states. The acquired linear surfaces underlie the algorithm for calculation of configurations, which do not intersect the restricted zone in case of a deadlock situation. The result of this research is the computer simulation of the motions of arm and torso mechanism of the Android robot using the obtained algorithm for calculation of configurations. The simulation of motion demonstrates that the use of linear surfaces in analysis of the relative position of the manipulator and restricted zones in the deadlock situations allows reducing the calculation time by 50-60 percent. Such reduction of calculation time is highly demanded in computer control of the arm and torso motions of the Android robot on a real time scale.

Gluon dynamics from an ordinary differential equation

We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the aforementioned kinetic term are related by a partial Slavnov–Taylor identity. The main ingredients entering in the solution are projection of the three-gluon vertex and a particular derivative of the ghost-gluon kernel, whose approximate form is derived from a Schwinger–Dyson equation. Crucially, the requirement of a pole-free answer determines the initial condition, whose value is calculated from an integral containing the same ingredients as the solution itself. This feature fixes uniquely, at least in principle, the form of the kinetic term, once the ingredients have been accurately evaluated. In practice, however, due to substantial uncertainties in the computation of the necessary inputs, certain crucial components need be adjusted by hand, in order to obtain self-consistent results. Furthermore, if the gluon propagator has been independently accessed from the lattice, the solution for the kinetic term facilitates the extraction of the momentum-dependent effective gluon mass. The practical implementation of this method is carried out in detail, and the required approximations and theoretical assumptions are duly highlighted.

Differential Dyson–Schwinger equations for quantum chromodynamics

Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

Dual solutions of the nonlinear problem of heat transfer in a straight fin with temperature-dependent heat transfer coefficient

Purpose In this paper, a numerical scheme is provided to predict and approximate the multiple solutions for the problem of heat transfer through a straight rectangular fin with temperature-dependent heat transfer coefficient. Design/methodology/approach The proposed method is based on the two-point Taylor formula as a special case of the Hermite interpolation technique. Findings An explicit approximate form of the temperature distribution is computed. The convergence analysis is also discussed. Some results are reported to demonstrate the capability of the method in predicting the multiplicity of the solutions for this problem. Originality/value The duality of the solution of the problem can be easily predicted by using the presented method. Furthermore, the computational results confirm the acceptable accuracy of the presented numerical scheme even for estimating the unstable lower solution of the problem.

Machine Learning Accurate Exchange and Correlation Functionals of the Electronic Density

<div>Density Functional Theory (DFT) is the standard formalism to study the electronic structure</div><div>of matter at the atomic scale. In Kohn-Sham DFT simulations, the balance between accuracy</div><div>and computational cost depends on the choice of exchange and correlation functional, which only</div><div>exists in approximate form. Here we propose a framework to create density functionals using</div><div>supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to</div><div>lift the accuracy of baseline functionals towards that are provided by more accurate methods while</div><div>maintaining their efficiency. We show that the functionals learn a meaningful representation of the</div><div>physical information contained in the training data, making them transferable across systems. A</div><div>NeuralXC functional optimized for water outperforms other methods characterizing bond breaking</div><div>and excels when comparing against experimental results. This work demonstrates that NeuralXC</div><div>is a first step towards the design of a universal, highly accurate functional valid for both molecules</div><div>and solids.</div>

Machine Learning Accurate Exchange and Correlation Functionals of the Electronic Density

<div>Density Functional Theory (DFT) is the standard formalism to study the electronic structure</div><div>of matter at the atomic scale. In Kohn-Sham DFT simulations, the balance between accuracy</div><div>and computational cost depends on the choice of exchange and correlation functional, which only</div><div>exists in approximate form. Here we propose a framework to create density functionals using</div><div>supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to</div><div>lift the accuracy of baseline functionals towards that are provided by more accurate methods while</div><div>maintaining their efficiency. We show that the functionals learn a meaningful representation of the</div><div>physical information contained in the training data, making them transferable across systems. A</div><div>NeuralXC functional optimized for water outperforms other methods characterizing bond breaking</div><div>and excels when comparing against experimental results. This work demonstrates that NeuralXC</div><div>is a first step towards the design of a universal, highly accurate functional valid for both molecules</div><div>and solids.</div>

Radiation hydrodynamics in simulations of the solar atmosphere

Nearly all energy generated by fusion in the solar core is ultimately radiated away into space in the solar atmosphere, while the remaining energy is carried away in the form of neutrinos. The exchange of energy between the solar gas and the radiation field is thus an essential ingredient of atmospheric modeling. The equations describing these interactions are known, but their solution is so computationally expensive that they can only be solved in approximate form in multi-dimensional radiation-MHD modeling. In this review, I discuss the most commonly used approximations for energy exchange between gas and radiation in the photosphere, chromosphere, and corona.