Dynamics of dipole in a stationary non-homogeneous electromagnetic field

The non-relativistic equations of motion for a dipole in a stationary non-homogeneous electromagnetic field are derived and analysed. It is shown that they are Hamiltonian with respect to a certain degenerated Poisson structure. Described by them dynamics is complex because the motion of the centre of mass of the dipole is coupled with its rotational motion. The problem of the existence of linear in momenta first integrals which can be useful for the separation of rotational motion is discussed. The presence of such first integral appears to be related with a linear symmetry of electric and magnetic fields. Also results of search of quadratic in momenta first integrals for uniform and stationary electromagnetic fields are reported. Deriving equations of motion of a dipole in arbitrary stationary electromagnetic fields and analysis of described by them dynamics is important for the construction of electromagnetic traps for polar particles.

Prospects and Challenges of Microwave-Combined Technology for Biodiesel and Biolubricant Production through a Transesterification: A Review

Biodiesels and biolubricants are synthetic esters produced mainly via a transesterification of other esters from bio-based resources, such as plant-based oils or animal fats. Microwave heating has been used to enhance transesterification reaction by converting an electrical energy into a radiation, becoming part of the internal energy acquired by reactant molecules. This method leads to major energy savings and reduces the reaction time by at least 60% compared to a conventional heating via conduction and convection. However, the application of microwave heating technology alone still suffers from non-homogeneous electromagnetic field distribution, thermally unstable rising temperatures, and insufficient depth of microwave penetration, which reduces the mass transfer efficiency. The strategy of integrating multiple technologies for biodiesel and biolubricant production has gained a great deal of interest in applied chemistry. This review presents an advanced transesterification process that combines microwave heating with other technologies, namely an acoustic cavitation, a vacuum, ionic solvent, and a supercritical/subcritical approach to solve the limitations of the stand-alone microwave-assisted transesterification. The combined technologies allow for the improvement in the overall product yield and energy efficiency. This review provides insights into the broader prospects of microwave heating in the production of bio-based products.

MASSIVE FIELDS WITH ARBITRARY HALF-INTEGER SPIN IN CONSTANT ELECTROMAGNETIC FIELD

We study the interaction of gauge fields of arbitrary half-integer spins with the homogeneous electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian and transformations of the half-integer spin fields in the external field to an algebraic problem of search for a set of operators with certain algebraic features using the representation of the higher-spin fields as vectors in a pseudo-Hilbert space. We consider such construction at linear order in the external electromagnetic field and also present an explicit form of interaction Lagrangians and gauge transformations for the massive particles of spins [Formula: see text] and [Formula: see text] in terms of symmetric spin-tensor fields. The obtained result is valid for space–time of arbitrary even dimension.

MASSIVE FIELDS WITH ARBITRARY INTEGER SPIN IN HOMOGENEOUS ELECTROMAGNETIC FIELD

We study the interaction of gauge fields of arbitrary integer spins with the constant electromagnetic field. We reduce the problem of obtaining the gauge-invariant Lagrangian of integer spin fields in the external field to purely algebraic problem of finding a set of operators with certain features using the representation of the high-spin fields in the form of vectors in a pseudo-Hilbert space. We consider such a construction up to the second order in the electromagnetic field strength and also present an explicit form of interaction Lagrangian for a massive particle of spin s in terms of symmetrical tensor fields in linear approximation. The result obtained does not depend on dimensionality of space–time.