## What is/are Dynamics Beyond?

Dynamics Beyond - In order to study the dynamics beyond the Hopf bifurcation, a nonlinear equation for the amplitude of the growing oscillatory mode is derived.^{[1]}Correlations due to the Coulomb repulsion between electrons on the dot are treated with a Green's function decoupling scheme which, although similar to the Hubbard-I approximation, captures some of the dynamics beyond.

^{[2]}Objectives: Vasodilating antihypertensives prevent stroke and potentially cerebral small vessel disease but their effects on cerebrovascular haemodynamics beyond blood pressure lowering are unclear.

^{[3]}We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity.

^{[4]}While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal.

^{[5]}The combination of losartan and amlodipine was more favorable in 24-hour ambulatory central hemodynamics beyond BP-lowering efficacy than the combination of losartan and hydrochlorothiazide, regardless of office BP.

^{[6]}Consequently, a major portion of the solvation dynamics remained undetected and moreover we could not monitor the dynamics beyond 0.

^{[7]}The proposed representation encodes geographic knowledge of the environment, makes the interactions among environmental elements explicit, supports geographic process simulation, opens opportunities for deep knowledge mining, and grounds a foundation for GeoAI to discover geographic complexity and dynamics beyond the support of conventional theme-centric inquiries in GIS.

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## rotating wave approximation

This work has significant implications for engineering light-matter interaction and novel quantum many-body dynamics beyond the rotating-wave approximation.^{[1]}We combine quantum dynamics beyond the rotating-wave approximation with classical electromagnetic calculations in order to compute the time evolution of quantum discord and entanglement using entanglement of formation.

^{[2]}This lasing multistability regime provides an opportunity to explore the effects of coherent spin-oscillator dynamics beyond the usual rotating-wave approximation at relatively weak couplings.

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## Quantum Dynamics Beyond

The dependence of this OTOC on the initial state makes it function like a microscope, allowing us to investigate the fine structure of quantum dynamics beyond the thermal state.^{[1]}The results show that Holstein couplings may accelerate transfer through sub-optimal network configurations but cannot accelerate quantum dynamics beyond the limit of the transfer time in an optimal phonon-free configuration.

^{[2]}We combine quantum dynamics beyond the rotating-wave approximation with classical electromagnetic calculations in order to compute the time evolution of quantum discord and entanglement using entanglement of formation.

^{[3]}The framework enables us to investigate a variety of random quantum dynamics beyond Haar random circuits and Brownian circuits.

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## Evolutionary Dynamics Beyond

The advent of high-throughput sequencing technologies has enabled investigation of genome evolutionary dynamics beyond model plants to provide exciting new insights in species across the biodiversity of life.^{[1]}The parameterized mathematical models are then used to extrapolate the viral evolutionary dynamics beyond the experimental settings.

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## dynamics beyond conventional

An analysis of results and papers linked to 25 popular benchmarks shows that research dynamics beyond conventional co-authorship has developed in this area.^{[1]}An analysis of overlapping and contrary sociotechnical island imaginaries that attends to such key visions allows for delineating heterogeneous dynamics beyond conventional categories like biodiversity, science, or culture.

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