Related papers: Memory Elements: A Paradigm Shift in Lagrangian Mo…
A fractional variational principle was derived in order to be used with lagrangians containing fractional derivatives of order 1/2. By forcing the action associated to this type of lagrangian to be stationary, a modified fractional…
We discuss the properties of the dynamics of purely memristive circuits using a recently derived consistent equation for the internal memory variables of the involved memristors. In particular, we show that the number of independent memory…
If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and…
Recently, Lobb and Nijhoff initiated the study of variational (Lagrangian) structure of discrete integrable systems from the perspective of multi-dimensional consistency. In the present work, we follow this line of research and develop a…
Memory effects in non-Markovian dynamics are often diagnosed either via quantum-correlation revivals or via non-monotonic classical information measures, yet a unified minimal framework comparing their ``backflow phases'' is still lacking.…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant…
Compact models of memristors are essential for simulating large-scale neuromorphic systems, yet they often do not include description of complex dynamics like volatile relaxation and synaptic plasticity. We introduce a modular,…
Fractional equations appear in the description of the dynamics of various physical systems. For Lagrangian systems, the embedding theory developped by Cresson ["Fractional embedding of differential operators and Lagrangian systems", J.…
We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor…
We suggest an approach to use memristors (resistors with memory) in programmable analog circuits. Our idea consists in a circuit design in which low voltages are applied to memristors during their operation as analog circuit elements and…
A general law for electromagnetic induction phenomena is derived from Lorentz force and Maxwell equation connecting electric field and time variation of magnetic field. The derivation provides with a unified mathematical treatment the…
The Faraday-Ampere laws of electro-magnetic induction are formulated in terms of plain and twisted differential forms, taking in due account the body motion in terms of Lie time-derivatives. Covariance of Lie derivatives with respect to…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincar\'{e} group is re-examined in the massless…
The dimensionful nature of the coupling in the Einstein-Hilbert action in four dimensions implies that the theory is non-renormalizable; explicit calculation shows that beginning at two loop order, divergences arise that cannot be removed…
This study provides new sets of experimental results supporting Westerlund's conjecture that Dead Matter Has Memory. Memory effects in the dynamic response of electric double-layer capacitors (EDLCs) that integrate its prior history of…
In this and companion papers, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the quantization of electromagnetism permits the…
Anyone who looks into the circuitry world will be familiar with the three fundamental circuit elements - capacitor, resistor, and inductor. These circuit elements are defined by the relation between two of the four fundamental circuit…
A modified lagrangian with causal and retrocausal momenta was used to derive a first causal wave equation and a second retrocausal wave equation using the principle of least action. The retrocausal wave function obtained through this method…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…