Q evolution equations are important not only for describing hadron reactions in accelerator experiments but also for investigating ultrahigh-energy cosmic rays. The standard ones are called DGLAP evolution equations, which are integrodifferential equations. There are methods for solving the Q evolution equations for parton-distribution and fragmentation functions. Because the equations cannot b...

In this paper the energy absorption capacity of stiffened circular composite tube is considered. The governing equations and dynamic equilibrium are first derived and then solved. Additionally, a finite element model of reinforced circular composite tube structure is modeled. At the following, the effects of various parameters such as structural geometry, number of rings and stingers on mechani...

background: understanding of the incident electron energy and angular distributions from clinical electron accelerators (linacs) is important for dosimetry and treatment planning. the most important goals of this study were to evaluate the energy fluence and angular distributions of electron beams from a neptun 10pc linac using the monte carlo (mc) code. materials and methods: the linac electro...

Abstract. A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic band approximation are treated in detail. In these cases, the set of equations is equivalent to those obtained in the spherical-harmonics expansion....

Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponentia...

It is shown that partial differential equations of Hamiltonian type admit global solutions in time if (a) the initial data is near equilibrium (or the coupling constant is small) (b) the linear terms have positive energy and (c) the non-linear terms are smooth functions in the topology of the linearized energy norm. The non-linear terms need not have positive energy. The result is applied to no...

Fundamental conservation equations for mass, momentum and energy of chemical species can be combined with thermodynamic relations to obtain secondary forms, such as conservation equations for phases, an internal energy balance and a mechanical energy balance. In fact, the forms of secondary equations are infinite and depend on the criteria used in determining which species-based equations to em...

In this paper, we study Landau-Lifshitz equations of ferromagnetism with a total energy that does not include a so-called exchange energy. Many problems, including existence, stability, regularity and asymptotic behaviors, have been extensively studied for such equations of models with the exchange energy. Problems turn out quite different and challenging for Landau-Lifshitz equations of no-exc...

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Here we investigate the energy and momentum in a closed system composed of a propagating electromagnetic field an...