Classical Physics
The generalized Taylor's Formula is used to derive a fractional radial-cylindrical diffusivity model via a fractional conservation of mass in radial geometry in a petroleum reservoir. The result is a space-fractional generalization of the…
A fractional generalization of the second author's higher-order diffusion theory is given and fundamental solutions are obtained. The extension from the integer to the fractional case involves a proper treatment of the fractional Laplacian…
In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the exact result, is used to describe a scattering process. The…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
We demonstrate a new method of achieving topologically protected states in a discrete hexagonal lattice by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail…
In this work, we introduce an elastic analog of the Purcell effect and show theoretically that spherical nanoparticles can serve as tunable and robust antennas for modifying the emission from localized elastic sources. This effect can be…
The accuracy of two equivalent antenna representations, near-field sources and far-field sources, are evaluated for an antenna installed on a simplified platform in a series of case studies using different configurations of equivalent…
Propagation of monochromatic elastic waves across cracks is investigated in 1D, both theoretically and numerically. Cracks are modeled by nonlinear jump conditions. The mean dilatation of a single crack and the generation of harmonics are…
The paraxial model of propagation is an approximation to the model described by the d'Alembert equation. It is widely used to describe beam propagation and near-field diffraction patterns. Therefore, its use in optics and acoustics…
Inverse problems associated with designing cylindrical thermal cloaking shells are studied. Using the optimization method these inverse problems are reduced to corresponding control problems in which the diagonal components of diagonal in…
We present the Eisenhart-lift formalism in which the dynamics of a system that evolves under the influence of a conservative force is equivalent to that of a free system embedded in a curved manifold with one additional generalised…
In this article, we first derive the wavevector- and frequency-dependent, microscopic current response tensor which corresponds to the "macroscopic" ansatz $\vec D = \varepsilon_0 \varepsilon_{\mathrm{eff}} \vec E$ and $\vec B = \mu_0…
In seeking a minimal variational formulation of Maxwell's equations, one is led naturally to the scalar and vector potentials as "adjoint" functions in a well-defined sense and to the crucial minus sign that defines the Lagrangian.
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
The extension of the wave zone of synchrotron radiation is studied.
Misinterpretations of Newton's second law for variable mass systems found in the literature are addressed. In particular, it is shown that Newton's second law in the form $\vec{F} = \dot{\vec{p}}$ is valid for variable mass systems in…
In-plane wave propagation in a periodic rectangular grid beam structure, which includes rotational inertia (so-called 'Rayleigh beams'), is analyzed both with a Floquet-Bloch exact formulation for free oscillations and with a numerical…
Topological defects with symmetry-breaking phase transitions have captured much attention. Vortex generated by topological defects exhibits exotic properties and its flow direction can be switched by altering the spin configurations.…
We revisit the electromagnetic problem of wave incidence upon a uniform, dissipative dielectric slab of finite thickness. While this problem is easily solved via interface field continuity, we treat it under the viewpoint of radiative…
We show that any continuously differentiable force is decomposed into the sum of a Rayleigh force and a gyroscopic force. We also extend this result to piecewise continuously differentiable forces. Our result improves the result on the…