Related papers: Fractional Euler-Bernoulli beams: theory, numerica…
Euler equations are the basic system in fluid dynamics describing the motion of incompressible and inviscid ideal fluids. For a bounded smooth domain $\Omega$ in $\mathbb{R}^n$. The well-posedness of Euler equations is well-known in Sobolev…
Energy-based models (EBMs) provide a powerful and flexible way of learning a joint probability distribution over data by constructing an energy surface. This energy surface enables insight extraction and conditional sampling. We apply EBMs…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
This paper concerns the reconstruction of properties of narrow laser beams propagating in turbulent atmospheres. We consider the setting of off-axis measurements, based on light detection away from the main path of the beam. We first model…
We discuss unique existence and microlocal regularity properties of Sobolev space solutions to the fractional Eringen wave equation, initially given in the form of a system of equations in which the classical non-local Eringen constitutive…
The parametric Nikiforov-Uvarov (N-U) method is employed in conjunction with a generalized fractional derivative (GFD) to investigate the energy eigenvalues and the total normalized wave function associated with the Coulomb plus screened…
Using the formalism of generalized fractional derivatives, a two-dimensional non-relativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum…
The fractional Planck distribution is calculated by applying the Caputo fractional derivative with order $p$ ($p > 0$) to the equation proposed by Planck in 1900. In addition, the integral representation of the Mittag--Leffler function is…
A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron…
The present article is devoting a numerical approach for solving a fractional partial differential equation (FPDE) arising from electromagnetic waves in dielectric media (EMWDM). The truncated Bernoulli and Hermite wavelets series with…
The most recent measurements of the observables $R_{D^{(*)}}$ are in tension with the Standard Model offering hints of New Physics in $b\rightarrow c \ell \bar{\nu}_{\ell}$ transitions. Motivated by these results, in this work we present an…
We show that the incompressible Euler equations in three spatial dimensions can be expressed in terms of an abelian gauge theory with a topological BF term. A crucial part of the theory is a 3-form field strength, which is dual to a…
In this work we investigate a very weak solution to the initial-boundary value problem of an Euler-Bernoulli beam model. We allow for bending stiffness, axial- and transversal forces as well as for initial conditions to be irregular…
In the present work we consider the electromagnetic wave equation in terms of the fractional derivative of the Caputo type. The order of the derivative being considered is 0 <\gamma<1. A new parameter \sigma, is introduced which…
By means of partial fraction method, we investigate the decomposition of rational functions. Several striking identities on harmonic numbers and generalized Apery numbers will be established, including the binomial-harmonic number identity…
In this work, we show that a recently proposed method for experimental nonlinear modal analysis based on the extended periodic motion concept is well suited to extract modal properties for strongly nonlinear systems (i.e. in the presence of…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…
Random effects are a flexible addition to statistical models to capture structural heterogeneity in the data, such as spatial dependencies, individual differences, temporal dependencies, or non-linear effects. Testing for the presence (or…
We propose and analyze a mixed finite element method for the spatial approximation of a time-fractional Fokker--Planck equation in a convex polyhedral domain, where the given driving force is a function of space. Taking into account the…
We consider theories with gauged chiral fermions in which there are abelian anomalies, and no nonabelian anomalies (but there may be nonabelian gauge fields present). We construct an associated theory that is gauge-invariant,…