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Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…
Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics. This provides a sense in which electromagnetism alone cannot be used to…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane.…
We demonstrate a method to determine energy level degeneracies using non-equilibrium electronic transport through voltage-biased quantum dots. We establish the general validity of this approach using single and double quantum dots in…
Many inverse problems in nuclear fusion and high-energy astrophysics research, such as the optimization of tokamak reactor geometries or the inference of black hole parameters from interferometric images, necessitate high-dimensional…
Modeling power electronic converters at frequencies close to or above half the switching frequency has been difficult due to the time-variant and discontinuous switching actions. This paper uses the properties of moving Fourier coefficients…
This paper proposes efficient policy iteration and value iteration algorithms for the continuous-time linear quadratic regulator problem with unmeasurable states and unknown system dynamics, from the perspective of direct data-driven…
Correlation is a common technique for the detection of shifts. Its generalization to the multidimensional geometric correlation in Clifford algebras additionally contains information with respect to rotational misalignment. It has been…
The effective way of energy transmission plays a key factor in improving the overall transmission systems efficiency. Many methods are proposed to control the reactive power flow, voltage fluctuations and power factor improvement, The…
This work presents a geometric formulation for transforming nonconservative mechanical Hamiltonian systems and introduces a new method for regularizing and linearizing central force dynamics -- in particular, Kepler and Manev dynamics --…
Grid-connected power converters are ubiquitous in modern power systems, acting as grid interfaces of renewable energy sources, energy storage systems, electric vehicles, high-voltage DC systems, etc. Conventionally, power converters use…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
The non-linearity and non-convexity of power flow models and the phase coupling challenge the analysis and optimization of unbalanced distribution networks. To tackle the challenges, this paper proposes an online feedback-based linearized…
We introduce here the concept of establishing Parity-time symmetry through a gauge transformation involving a shift of the mirror plane for the Parity operation. The corresponding unitary transformation on the system's constitutive matrix…
The integration of power electronic converters (PECs) and distributed energy resources (DERs) in modern power systems has introduced dynamism and complexity. Accurate simulation becomes essential to comprehend the influence of converter…