相关论文: A new approach to single-phase systems under sinus…

We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…

Security assessment of large-scale, strongly nonlinear power grids containing thousands to millions of interacting components is a computationally expensive task. Targeting at reducing the computational cost, this paper introduces a…

In this paper, we first consider the Rosenau equation with the quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of the equation to ODEs, and find periodic analytical solutions in terms of elliptic…

A new effective field theory has been developed to describe shallow $P$-wave resonances using nonlocal, momentum-dependent two-body potentials. This approach is expected to facilitate many-body calculations and has been demonstrated to…

The power-grid frequency reflects the balance between electricity supply and demand. Measuring the frequency and its variations allows monitoring of the power balance in the system and, thus, the grid stability. In addition, gaining insight…

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the…

A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…

Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…

Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…

This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition…

We study nonadiabatic effects of geometric pumping. With arbitrary choices of periodic control parameters, we go beyond the adiabatic approximation to obtain the exact pumping current. We find that a geometrical interpretation for the…

We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…

This paper presents a perspective of functional analysis to analyze electric load and electricity pricing in the $L_2$ space and its isomorphic vector space, which also yields the general algebraic model of load and pricing associated with…

Networks with phase-valued nodal variables are central in modeling several important societal and physical systems, including power grids, biological systems, and coupled oscillator networks. One of the distinctive features of phase-valued…

Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the…

An important monitoring task for power systems is accurate estimation of the system operation state. Under the nonlinear AC power flow model, the state estimation (SE) problem is inherently nonconvex giving rise to many local optima. In…

Phase balancing is essential to safe power system operation. We consider a substation connected to multiple phases, each with single-phase loads, generation, and energy storage. A representative of the substation operates the system and…

The large penetration of distributed generations impacts both the secondary low-voltage (LV) and the primary medium-voltage (MV) segments of the distribution network. Optimizing power flow calculations for the integrated MV/LV networks is…

We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify…

Phase retrieval is a prevalent problem in digital signal processing and experimental physics that consists of estimating a complex signal from magnitude measurements. This paper expands the classical phase retrieval framework to electric…