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A modern notion of integrability is that of multidimensional consistency (MDC), which classically implies the coexistence of (commuting) dynamical flows in several independent variables for one and the same dependent variable. This property…
Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is…
The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient and widely applicable but not suited to transient phenomena and time dependent currents because it assumes that the charge carrier…
The mathematical logic of a true nature of mirror symmetry expresses, in the case of the Dirac Lagrangian, the ideas of the left- and right-handed photons referring to long- and short-lived particles, respectively. Such a difference in…
A new classical 2-spinor approach to $U(1)$ gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
The Maxwell vector potential and the Dirac spinor used to describe the classical theory of electrodynamics both have components which are considered to be ordinary smooth functions on space-time. We reformulate electrodynamics by adding an…
Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics…
Resistive switching devices emerged a huge amount of interest as promising candidates for non-volatile memories as well as artificial synapses due to their memristive behavior. The main physical and chemical phenomena which define their…
Using a Dirac-matrix substitution rule, applied to the electric charge, the anomalous magnetic moments of fermions are incorporated in local form in the two-body relativistic wave equations of constraint theory. The structure of the…
In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum and the unitarity…
Neuromorphic circuits mimic partial functionalities of brain in a bio-inspired information processing sense in order to achieve similar efficiencies as biological systems. While there are common mathematical models for neurons, which can be…
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…
The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin Lagrangian…
We reformulate classical electromagnetism within the matter-space framework of relativistic fluid dynamics. The central assumption is that the relevant degrees of freedom are encoded in differential forms on a three-dimensional matter space…
We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors…
In almost all of the currently working circuits, especially in analog circuits implementing signal processing applications, basic arithmetic operations such as multiplication, addition, subtraction and division are performed on values which…
It has been recently noted that for a class of dynamical systems with explicit conservation laws represented via projector operators the dynamics can be understood in terms of lower dimensional equations This is the case for instance of…
By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion…
We have obtained an electromagnetic PIC (EM-PIC) algorithm based on time-space-extended particle in cell model. In this model particles are shaped objects extended over time and space around Lagrangian markers. Sources carried by these…