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Coordinate transformations provide dimensional reduction benefits across power system analysis, electric machine modeling, and power electronic converter control. This paper introduces a novel transformation based on Geometric Algebra that…
In this work, a quaternion-valued model is proposed in lieu of the Clarke's \alpha, \beta transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion…
Affordable and reliable electric power is fundamental to modern society and economy, with the Smart Grid becoming an increasingly important factor in power generation and distribution. In order to fully exploit it advantages, the analysis…
This article introduces the Clarke transform and Clarke coordinates, which present a solution to the disengagement of an arbitrary number of coupled displacement actuation of continuum and soft robots. The Clarke transform utilizes the…
The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but…
Unbalanced three-phase systems still lack a compact phasor-domain representation of power that makes phase asymmetry explicit while remaining consistent with established apparent-power definitions. This paper addresses that point through a…
For almost all tendon-driven continuum robots, a segment is actuated by three or four tendons constrained by its mechanical design. For both cases, methods to account for the constraints are known. However, for an arbitrary number of…
The Darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states. Classical system corresponding to a transformed quantum system is…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
The dipolar universality class describes the phase transition in 3D ferromagnets with strong dipolar interactions, as first discussed by Aharony and Fisher in the 1970s. While this universality class has been studied theoretically using…
In this letter, we demonstrate that previously proposed improved state parameterizations for soft and continuum robots are specific cases of Clarke coordinates. By explicitly deriving these improved parameterizations from a generalized…
We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
A low-cost reconfiguration stage connected at the output of balanced three-phase, multi-terminal ac/dc/ac converters can increase the feasible set of power injections substantially, increasing converter utilization and therefore achieving a…
Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (eLOCC) are studied. We propose a new method to reveal the different convertibility by local…
This paper proposes a novel two-layer Volt/VAR control (VVC) framework to regulate the voltage profiles across an unbalanced active distribution system, which achieves both the efficient open-loop optimization and accurate closed-loop…
The characterization of transformations among entangled pure states via local operations assisted by classical communication (LOCC) is a crucial problem in quantum information theory for both theoretical and practical reasons. As LOCC has a…
We investigate the phase diagram of non-perturbative three-dimensional Lorentzian quantum gravity with the help of Monte Carlo simulations. The system has a first-order phase transition at a critical value $k_0^c$ of the bare inverse…
Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question: Can a transformation of the generalized coordinates under which the actuators…
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…