Classical Physics
We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is…
An extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe power-law type of non-locality is discussed. Two phenomenological possibilities are explored. The first is based on the Caputo…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
In this paper we discuss about the validity of the Shannon entropy functional in connection with the correct Gibbs-Hertz probability distribution function. We show that there is no contradiction in using the Shannon-Gibbs functional and…
In this short note we derive an approximate expression for the mode density of modes carrying orbital angular momentum (OAM) in a cylindrical cavity which is large compared to the inverse wavevector in any direction. We argue that in the…
For nearly two centuries the dynamics of chains have offered examples of paradoxical theoretical predictions. Here we propose a theory for the dissipative dynamics of one-dimensional continua with singularities which provides a unified…
We study the problem of the definition of the energy-momentum tensor of light in general moving non-dispersive media with linear constitutive law. Using the basic principles of classical field theory, we show that for the correct…
How long does it take to fall down a tunnel through the center of the Earth to the other side? Assuming a uniformly dense Earth, it would take 42 minutes, but this assumption has not been validated. This paper examines the gravity tunnel…
Propagation delays are intensively used for Structural Health Monitoring or Sensor Network Localization. In this paper, we study the performances of acoustic propagation delay estimation between two sensors, using sources of opportunity…
Gradient index devices for the simultaneous control of the S 0 and A 0 Lamb modes are presented and numerically analysed. It is found a special relationship between the refractive indexes for these two modes which allows their simultaneous…
Self-propulsion of liquid marbles filled with aqueous alcohol solutions and placed on a water surface is reported. The characteristic of velocity of the marbles is about 0.1 m/s. The phenomenon of self-propulsion is related to the Marangoni…
The following inverse problem is discussed. A static electromagnetic field generated by a limited system of charges and currents is supposed to be known with its first derivatives at a point somewhere far from the system. This allows to…
This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to…
This paper deals with the mathematical modelling of large strain electro-viscoelastic deformations in electro-active polymers. Energy dissipation is assumed to occur due to mechanical viscoelasticity of the polymer as well as due to…
The definition of the induced $emf$ as the integral over a closed loop of the Lorentz force acting on a unit positive charge leads immediately to a general law for electromagnetic induction phenomena. The general law is applied to three…
Natural modes of helical structures are treated by using the periodic dyadic Green's functions in cylindrical coordinates. The formulation leads to an infinite system of one-dimensional integral equations in reciprocal (Fourier) space. Due…
A perturbation approach is used for analysis of a near-cloak in shielding a finite scatterer from an incident flexural wave. The effect of the boundary conditions on the interior surface of the cloaking layer is analysed in detail, based on…
In this paper we propose a new refined shear deformation plate theory which possesses a series of desirable features, the most salient of which are as follows: (i) The loads, which are generally considered to be applied on the middle…
We present a rigorous approach to compute the electromagnetic fields radiated by a thin circular loop with arbitrary current. We employ a polar transmission representation along with a Kontorovich-Lebedev transform to derive integral…
An analytical representation for the spatial and temporal dynamics of the simplest of the diffusions -- Bronwian diffusion in an homogeneous slab geometry, with radial symmetry -- is presented. This representation is useful since it…