Related papers: Memory Elements: A Paradigm Shift in Lagrangian Mo…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring…
The formulation of a generalized classical electromagnetism that includes both electric and magnetic charges, is explored in the framework of two potential approach. It is shown that it is possible to write an action integral from which one…
Students often have difficulty in understanding qualitatively the behaviour of simple electric circuits. In particular, as different studies have shown, they find multiple batteries connected in multiple loops difficult to analyse. In a…
A model calculation using the Darwin Lagrangian is carried out for a magnet consisting of two current-carrying charges constrained by centripetal forces to move in a circular path in the presence of the electric field from a distant…
Several devices exhibiting memory effects have shown up in nonlinear circuit theory in recent years. Among others, these circuit elements include Chua's memristors, as well as memcapacitors and meminductors. These and other related devices…
A circuit-field problem is considered. A resistor conducting a constant current is argued to be associated with electromagnetic energy accumulated in the surrounded space, though contrary to the case of an inductor or a capacitor, this…
Memristor, memory resistor, is an emerging technology for computational memory. Number of different memristor models are available based on the physical experiments. To use memristor as a computational memory element, one should know how…
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional scalar variable $z$. This provides a geometric framework for…
Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
If a Lagrangian of gauge theory of internal symmetries is not gauge-invariant, the energy-momentum fails to be conserved in general.
Once referred to as the missing circuit component, memristor has come long way across to be recognized and taken as important to future circuit designs. The memristor due to its ability to memorize the state, switch between different…
Minimizing the Action integral of a Lagrangian provides the Euler-Lagrange equation of motion in the elegant machinery of Lagrangian Mechanics. However two relations define the divergence of current and energy-momentum, and provide an…
Effective Lagrangians, including those that are spontaneously broken, contain redundant terms. It is shown that the classical equations of motion may be used to simplify the effective Lagrangian, even when quantum loops are to be…
In 2008, researchers at the Hewlett-Packard (HP) laboratories claimed to have found an analytical physical model for a genuine memristor device [1]. The model is considered for a thin TiO_2 film containing a region which is highly…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
The present paper is devoted to the group classification of magnetogasdynamics equations in which dependent variables in Euler coordinates depend on time and two spatial coordinates. It is assumed that the continuum is inviscid and…
We investigate quantum synchronization phenomena in electrical circuits that incorporate specifically designed nonconservative elements. A dissipative theory of classical and quantized electrical circuits is developed based on the Rayleigh…
We propose the interaction of two quantum memristors via capacitive and inductive coupling in feasible superconducting circuit architectures. In this composed system the input gets correlated in time, which changes the dynamic response of…