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R. Smirnov-Rueda

Publications and source records attributed to R. Smirnov-Rueda.

7 recordsLinked to original sources
arXiv2006

Experimental Evidence on Non-Applicability of the Standard Retardation Condition to Bound Magnetic Fields and on New Generalized Biot-Savart Law

In this work we made an analysis of the current status of velocity dependent (bound) field components in the framework of the standard electromagnetic theory. Preliminary discussions of the structure of the magnetic field due to an idealized oscillating magnetic dipole provided us with the quantitative insights on the relative contribution of velocity dependent (bound) and acceleration dependent (radiation) terms into the resultant magnetic field. According to this analysis we defined the methodological scheme based on a generalized (time-dependent) Biot-Savart law capable to test the applicability of the standard retardation condition on bound field components. In the second part of this work we made the theoretical analysis of the finite size multi-section antennas, confirming the validity of the methodological scheme conceived for an idealized magnetic dipole. The use of multi-section antennas is fully justified by a substantial rise of the ratio of bound-to-radiation field strength. Finally, we effected numerical calculations taking into account particular experimental settings and compared them with experimentally obtained data that unambiguously indicate on the non-applicability of the standard retardation condition to bound magnetic fields. In addition, experimental observations show a striking coincidence with the predictions of a new generalized Biot-Savart law which implies the spreading velocity of bound fields highly exceeding the velocity of light.

physics.class-ph↗
arXiv2005

On Mathematical Defect in Demonstration of Convection Theorem: Implications For Continuum Mechanics and Other Classical Field Theories

Serious mathematical defect in the important kinematics theorem known in continuum mechanics as Convection (or Transport) Theorem is reported. We claim that the traditional demonstration does not take into account a special constraint on integrand functions given in Lagrangian representation. Thus, we put in doubt that the traditional procedure for the transition from integral formulations of physical laws of some classical field theories to their differential form is mathematically rigorous. Reconsidered formulation shows the way how the system of fundamental differential equations of continuum mechanics and some other field theories could be modified without any change of the original integral formulation. The continuity equation and the differential form of the equation of motion for continuous media are discussed as examples of modification.

physics.class-ph↗
arXiv2005

On Essential Incompleteness of Hertz's Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertz's experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertz's experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertz's "\textit{crucial}" experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtz's electrodynamics did not contradict any of Hertz's experimental observations of transverse components as Maxwell's theory predicted. Moreover, as we now know from recently published Hertz's dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertz's experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtz's theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method.

physics.hist-ph↗
arXiv2005

On Two Complementary Types of Total Time Derivative in Classical Field Theories and Maxwell's Equations

Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very foundations of theoretical hydrodynamics. One of the defects concerns the traditional treatment of time derivatives in Eulerian hydrodynamic description. The other one resides in the conventional demonstration of the so-called Convection Theorem. Both approaches are thought to be necessary for cross-verification of the standard differential form of continuity equation. Any revision of these fundamental results might have important implications for all classical field theories. Rigorous reconsideration of time derivatives in Eulerian description shows that it evokes Minkowski metric for any flow field domain without any previous postulation. Mathematical approach is developed within the framework of congruences for general 4-dimensional differentiable manifold and the final result is formulated in form of a theorem. A modified version of the Convection Theorem provides a necessary cross-verification for a reconsidered differential form of continuity equation. Although the approach is developed for one-component (scalar) flow field, it can be easily generalized to any tensor field. Some possible implications for classical electrodynamics are also explored.

physics.class-ph↗
arXiv2004

On Two Complementary Types of Directional Derivative and Flow Field Specification in the Classical Field Theory

We discuss a general definition of directional derivative of any tensor flow field and its practical applications in physics. It is shown that both Lagrangian and Eulerian descriptions as complementary types of flow field specifications adopted in modern theoretical hydrodynamics, imply two complementary types of directional derivatives as corresponding mathematical constructions. One of them is the Euler substantive derivative useful only in the contexts of initial Cauchy problem and the other, called here as the local directional derivative, arises only in the context of so-called final Cauchy problem. The choice between Lagrangian and Eulerian specifications is demonstrated to be equivalent to the choice between space-time with Euclidean or Minkowski metric for any flow field domain, respectively. Mathematical consideration is developed within the framework of diffeomorfic transformations for general 4-dimensional differentiable manifold. The analytical expression for local directional derivative is formulated in form of a theorem. Although the consideration is developed for ideal one-component (scalar) flow field, it can be easily generalized to any tensor field. Some implications of the local directional derivative concept for the classical theory of fields are also explored.

physics.class-ph↗
arXiv2002

Brownian dynamics approach to interacting magnetic moments

The question how to introduce thermal fluctuations in the equation of motion of a magnetic system is addressed. Using the approach of the fluctuation-dissipation theorem we calculate the properties of the noise for both, the fluctuating field and fluctuating torque (force) representation. In contrast to earlier calculations we consider the general case of a system of interacting magnetic moments without the assumption of axial symmetry. We show that the interactions do not result in any correlations of thermal fluctuations in the field representation and that the same widely used formula can be used in the most general case. We further prove that close to the equilibrium where the fluctuation-dissipation theorem is valid, both, field and torque (force) representations coincide, being different far away from it.

cond-mat.stat-mech↗