Transient analysis of power loss density with time-harmonic electromagnetic waves in Debye media

Due to the complex permittivity, it is difficult to directly clarify the transient mechanism between electromagnetic waves and Debye media. To overcome the above problem, the temporal relationship between the electromagnetic waves and permittivity is explicitly derived by applying the Fourier inversion and introducing the remnant displacement. With the help of the Poynting theorem and energy conservation equation, the transient power loss density is derived to describe the transient dissipation of electromagnetic field and the mechanism on phase displacement has been explicitly revealed. Besides, the unique solution can be obtained by applying the time-domain analysis method rather than involving the frequency-domain characteristics. The effectiveness of transient analysis is demonstrated by giving a comparison simulation on one-dimensional example.

A Poynting theorem formulation for the gravitational wave stress pseudo tensor

A very simple and physical derivation of the conservation equation for the propagation of gravitational radiation is presented. The formulation is exact. The result takes the readily recognisable and intuitive form of a Poynting-style equation, in which the outward propagation of stress energy is directly related to the volumetric equivalent of a radiation reaction force acting back upon the sources, including the purely gravitational contribution to the sources. Upon averaging, the emergent pseudo tensor for the gravitational radiation is in exact agreement with that found by much more labour-intensive methods.

Electromagnetic Energy Balance Equations and Poynting Theorem

<p>Poynting theorem plays a very important role in analyzing electromagnetic phenomena. The electromagnetic power flux density is usually expressed with the Poynting vector. However, since Poynting theorem basically focuses on the power balance in a system, it is not so convenient in some situations to use it for evaluating the electromagnetic energies. The energy balance issue for time varying fields is revisited in this paper, and a set of energy balance equations are introduced, and a modified method for evaluating power flux is proposed.</p>

Electromagnetic Energy Balance Equations and Poynting Theorem

<p>Poynting theorem plays a very important role in analyzing electromagnetic phenomena. The electromagnetic power flux density is usually expressed with the Poynting vector. However, since Poynting theorem basically focuses on the power balance in a system, it is not so convenient in some situations to use it for evaluating the electromagnetic energies. The energy balance issue for time varying fields is revisited in this paper, and a set of energy balance equations are introduced, and a modified method for evaluating power flux is proposed.</p>

Effects of Sample Shapes and Thickness on Distribution of Temperature inside the Mineral Ilmenite Due to Microwave Heating

The study of interaction between microwave radiation and minerals is gaining increasing interest in the field of minerals and material processing. Further studies are, however, still required to deepen the understanding of such microwave heating mechanisms in order to develop innovative techniques for mineral treatment using microwave heating. In this paper, effects of sample shapes and thickness on the distribution of temperature inside the mineral ilmenite (FeTiO3) due to microwave heating were numerically studied using the finite element (FE) method. The analysis was carried out in such a way that the flux of microwave energy was converted into an equivalent amount of heat generation in the mineral through the Poynting theorem of conservation of energy for the electromagnetic field. In this study, as a first attempt, the cylinder and slab of ilmenite were modeled to be irradiated from top and bottom surfaces with the variation of cylinder and slab thicknesses. Temperature-dependent material properties of ilmenite were taken into account in the FE simulation. Corresponding boundary conditions were then applied accordingly to the cylinder and slab of ilmenite with comparable characteristic length. Numerical results showed that, in terms of temperature differences between locations having maximum and minimum temperatures, slab geometries tended to produce higher values in comparison to those of cylinder geometries with the thickness variation, while the profiles of temperature inside the ilmenite samples were similar for both geometries. For the same duration of microwave heating, the slab geometry, hence, induced greater non-uniformity of temperature inside the ilmenite. It was also observed that, for the ilmenite samples with thickness value greater than 1.5 cm, the hotspot locations were not in the center of the sample, but on the surface of sample. Moreover, from several thickness values considered in this study, the ilmenite sample with thickness value of 3 cm gave a good trade-off between the maximum temperature value attained and temperature differences inside the sample, for both geometries. Thus, the shape and thickness of ilmenite samples affect the effectiveness of microwave heating of ilmenite, in terms of maximum temperature attained, temperature differences, and uniformity of temperature.

Equations of Motion in the Theory of Relativistic Vector Fields

Within the framework of the theory of relativistic vector fields, the covariant expressions are presented for the equations of motion of the matter and the field. These expressions can be written either in terms of the field tensors, that is, the fields’ strengths and solenoidal vectors, or in terms the four-potentials, that is, the fields’ scalar and vector potentials. This state of things is due to the fact that the Lagrange function initially implied the complementarity of description in terms of the strengths and the field potentials. It is shown that the equation for the fields, obtained by taking the covariant derivative in the equation for the metric, has a deeper meaning than the ordinary equation of motion of the matter, found with the help of the principle of least action. In particular, the above-mentioned equation for the fields leads to the generalized Poynting theorem, and after integration over the volume it allows us to introduce for consideration the integral vector as a measure of the energy and the fields’ energy fluxes, associated with a system of particles and fields.

Quaternionic representation of electromagnetism for material media

In this study, the electromagnetic fields are developed in the presence of both the electric and magnetic induction fields by quaternion algebra. In this sense, the polarization and magnetization effects, which are valid in the material media, gain much importance. Quaternions are one of the most convenient tools for representing electromagnetism with regard to having non-commutative but associative algebraic division ring. By defining the quaternion induction field, the quaternion source term has been obtained in basic and elegant notation for the first time. In addition, one type of Poynting theorem, named as the Minkowski form, has been presented including the permittivity and permeability constants by quaternions.