Equations of Electrodynamics

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

Equations of Electrodynamics

The equations of electrodynamics are presented, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward. Fields of uniformly moving charges are also solutions of equations. The question of finding a universal form of equations admitting a solution in the form of a field of an arbitrarily moving charge remains open. The question is raised about the existence of a two-parameter group of transformations of electromagnetic fields along with the well-known one-parameter group. The equation of motion of a charged particle in an electromagnetic field is considered without simplifying approximations. The principle of operation of an unconventional alternator in a constant electric field and a corresponding engine, as well as new types of generators of direct and impulse current, are described.

Covariant Homogeneous Nets of Standard Subspaces

Rindler wedges are fundamental localization regions in AQFT. They are determined by the one-parameter group of boost symmetries fixing the wedge. The algebraic canonical construction of the free field provided by Brunetti–Guido–Longo (BGL) arises from the wedge-boost identification, the BW property and the PCT Theorem. In this paper we generalize this picture in the following way. Firstly, given a $$\mathbb Z_2$$ Z 2 -graded Lie group we define a (twisted-)local poset of abstract wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges and study special wedge configurations. This allows us to exhibit an analog of the Haag–Kastler one-particle net axioms for such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL construction. The construction is possible for a large family of Lie groups and provides several new models. We further comment on orthogonal wedges and extension of symmetries.

KMS states on the crossed product -algebra of a homeomorphism

Let $\phi :X\to X$ be a homeomorphism of a compact metric space X. For any continuous function $F:X\to \mathbb {R}$ there is a one-parameter group $\alpha ^{F}$ of automorphisms (or a flow) on the crossed product $C^*$ -algebra $C(X)\rtimes _{\phi }\mathbb {Z}$ defined such that $\alpha ^{F}_{t}(fU)=fUe^{-itF}$ when $f \in C(X)$ and U is the canonical unitary in the construction of the crossed product. In this paper we study the Kubo--Martin--Schwinger (KMS) states for these flows by developing an intimate relation to the ergodic theory of non-singular transformations and show that the structure of KMS states can be very rich and complicated. Our results are complete concerning the set of possible inverse temperatures; in particular, we show that when $C(X) \rtimes _{\phi } \mathbb Z$ is simple this set is either $\{0\}$ or the whole line $\mathbb R$ .

Bayesian uncertainty quantification for guided-wave-based multidamage localization in plate-like structures using Gibbs sampling

In this article, a new Bayesian approach for guided-wave-based multidamage localization by employing Gibbs sampling is proposed. By using the information of time-of-flight (ToF) embedded in guided wave signals, the posterior probability distributions of three parameter groups, that is, the horizontal and vertical coordinates of the multidamage locations (x, y) and wave velocity v, are characterized using Gibbs sampling samples. To obtain the analytical form of the conditional posterior probability density function of each parameter group conditional on the other two and the available ToF data, a first-order Taylor expansion of the nonlinear ToF-based damage localization model with respect to each parameter group is performed. Two Gibbs sampling algorithms are proposed, which differ in their strategies to address the posterior uncertainty of the prediction error parameter; however, both algorithms iteratively sample from conditional posterior probability density functions of three parameter groups. Therefore, the effective number of dimensions for Gibbs sampling is always three, regardless of the number of defects. The final damage localization results are obtained by grouping all ToFs and then comparing the posterior uncertainty of localization results of each grouping scheme to obtain the most reliable sampling results among all candidates. The proposed method not only identifies the group velocity but also localizes multiple defects by sharing the same characteristics of damage localization. Furthermore, this method can quantify the uncertainty of multidamage localization to automatically find the most reliable damage locations. The effectiveness and robustness of the proposed algorithms are validated by both numerical and experimental examples.

Optimization of healing in patients with odontogenic phlegmon of the maxillofacial region

Aim. This study aims to increase the efficiency of the wound process in patients with odontogenic phlegmons of the maxillofacial region by using energotropic and antioxidant agents. Material and methods. The clinical study included 42 patients with odontogenic phlegmons of the maxillofacial region. The patients were divided into two groups: comparison group (patients received traditional treatment) and main group (patients received treatment with Cytoflavin in the treatment regimen). Results. In the main group, the appearance of the first granulations occurred 2.1 times faster (on average on the 3rd day) in comparison with the granulation tissue in patients of the comparison group. Signs of edge epithelialization of wounds appeared almost 3 days earlier (on average on the 6th day) in the main group than in the comparison group; on the 7th day, secondary sutures were already applied, which was 1.6 times faster than the same parameter group 2, clearly suggesting the acceleration of reparative processes. Conclusion. The dynamics of clinical manifestations indicates the comparative effectiveness of using Cytoflavin as part of complex therapy. This finding is confirmed by the accelerated terms of wound healing, the appearance of granulations, epithelialization of the wound edges, and the imposition of secondary sutures.

THE GENERALIZED SPHERICALLY-SYMMETRIC METRIC

Four parameter group of transformations containing rotations and time translations is consi[1]dered due to spherical symmetry and stationarity of the space-time metric. It is found that there exists such a quartet of Killing vector fields which constitute the Lie algebra of the transforma[1]tion group and in which space-like vectors are not orthogonal to the time-like one. The metric corresponding to the Lie algebra of Killing vectors is composed. It is shown that the metric is non-static.