Nonlinear Control Strategies (United States)

M-ary Aggregate Spread Pulse Modulation (M-ASPM) is a physical layer (PHY) modulation technique that is well suited for use in low-power wide-area networks (LPWANs). It combines high energy-per-bit efficiency, robustness, resistance to interference, a

A flower-like NiO@ASPNTs/C nanocomposite was successfully synthesized via a solvothermal process followed by annealing, and its electrochemical performance as a lithium-ion battery anode was systematically investigated. Morphological and structural characterizations reveal that the composite consisted of uniformly dispersed NiO nanoparticles anchored onto aminated polymer nanotubes (ASPNTs/C), forming a unique flower-like porous architecture. This architecture not only increased the specific surface area and interfacial active sites but also effectively buffered the volume variation of NiO during lithiation/delithiation. Electrochemical measurements demonstrated that NiO@ASPNTs/C delivered initial charge/discharge capacities of 2397.4/1676.3 mAh g–1 at 0.1 A g–1 with a Coulombic efficiency of 69.9%, and retained a stable capacity of 1200.7 mAh g–1 after 150 cycles. Moreover, the composite exhibited outstanding rate capability and long-term cycling stability, maintaining a reversible capacity of 351.7 mAh g–1 even after 2000 cycles at 5.0 A g–1. Mechanistic analysis revealed that amination facilitated Ni2+ adsorption and uniform NiO nucleation, while the flower-like structure provided abundant electrolyte penetration channels and continuous electron/ion transport networks. The synergistic effect of these features endows NiO@ASPNTs/C with superior lithium-storage properties. This work offers a new strategy for the rational design and application of transition metal oxide/carbon-based anode materials.

In the development of quantum mechanics in the 1920s, both matrix mechanics (developed by Born, Heisenberg and Jordon) and wave mechanics (developed by Schrödinger) prevailed. These early attempts corresponded to the quantum mechanics of particles. Matrix mechanics was found to lead directly to the Schrödinger equation, and the Schrödinger equation could be used to derive the alternative problem for matrix mechanics. Later emphasis lay on the development of the dynamics of fields, where the classical field equations were quantized (see, for example, Weinberg). Today, quantum field theory is one of the most successful physical theories ever developed. The symmetry between particle and wave mechanics is exploited herein. One of the important properties of quantum mechanics is that it is linear, leading to some confusion about how to treat the problem of nonlinear classical field equations. In the present paper we address the case of classical nonlinear soliton equations which are exactly integrable in terms of the periodic/quasiperiodic inverse scattering transform. This means that all physical spectral solutions of the soliton equations can be computed exactly for these specific boundary conditions. Unfortunately, such solutions are highly nonlinear, leading to difficulties in solving the associated quantum mechanical problems. Here we find a strategy for developing the quantum mechanical solutions for soliton dynamics. To address this difficulty, we apply a recently derived result for soliton equations, i.e., that all solutions can be written as quasiperiodic Fourier series. This means that soliton equations, in spite of their nonlinear solutions, are perfectly linearizable with quasiperiodic boundary conditions, the topic of finite gap theory, i.e., the inverse scattering transform with periodic/quasiperiodic boundary conditions. We then invoke the result that soliton equations are Hamiltonian, and we are able to show that the generalized coordinates and momenta also have quasiperiodic Fourier series, a generalized linear superposition law, which is valid in the case of nonlinear, integrable classical dynamics and is here extended to quantum mechanics. Hamiltonian dynamics with the quasiperiodicity of inverse scattering theory thus leads to matrix mechanics. This completes the main theme of our paper, i.e., that classical, nonlinear soliton field equations, linearizable with quasiperiodic Fourier series, can always be quantized in terms of matrix mechanics. Thus, the solitons and their nonlinear interactions are given an explicit description in quantum mechanics. Future work will be formulated in terms of the associated Schrödinger equation.

The Coherent Backscattering (CBS) peak is a well-known interferential signature of weak localization in disordered or chaotic systems. More recently, a second interference feature -- the Coherent Forward Scattering (CFS) peak -- was predicted to emerge in the regime of strong localization. However, it has never been directly observed. Here we report the first direct observation of the CFS peak and demonstrate its dual role as a signature of non-ergodicity and as a probe of symmetries in quantum chaotic systems. Using a shaken rotor model realized with a Bose-Einstein condensate (BEC) of ultracold atoms in a modulated optical lattice, we investigate dynamical localization in momentum space. The CFS peak emerges in the position distribution as a consequence of non-ergodic dynamics, while its growth timescale reveals the underlying localization length. By finely tuning the modulation, we control time-reversal and parity symmetries and measure their distinct effects on both CBS and CFS peaks. Our results highlight the strong link of both the temporal growth and contrast of the CFS with symmetry and localization, making it a robust probe of these properties. This work opens new directions for characterizing non-ergodicity and symmetries in quantum chaotic or disordered systems, with possible applications in many-body localization and chaos.

Stochastic resonance is a phenomenon possessed by some nonlinear oscillators, in which a weak signal is boosted by noise. Both the monostable and bistable Duffing oscillators can exhibit this property. However, stochastic resonance has a strong frequency-dependence, as only a band of frequencies may be boosted by noise. Adaptive oscillators are a subset of nonlinear oscillators that can learn the features of an external force. Here, an adaptive state is added to a Duffing oscillator. This adaptive state enables the Duffing adaptive oscillator to outperform stochastic resonance over a wide range of frequencies by learning a resonance condition.

In this study, we explain the impacts of nonlinearity and wave dispersion parameters on the soliton pulses of the (2+1)-dimensional Kundu–Mukherjee–Naskar equation (KMNE). In this regard, some new optical solitons are received via the unified method to the aforesaid equation to explain such impacts of the soliton pulses. The presenting optical solitons are expressed by the dark, periodic, bell, bright, kink, and singular soliton solutions. Taking into account the two impacts help stabilize the soliton pulses during their propagation by generating new dynamics depending upon the nonlinearity and the wave dispersion parameters of the studied equation. All the characteristics of the soliton pulses are exhibited graphically. It is found from the graphical outputs that the soliton profiles are decreasing and increasing with the increase of nonlinearity and dispersion parameters, respectively. The outcomes reveal that the soliton pulses are balanced due to the influences of nonlinearity and wave dispersion parameters of the aforementioned equation. It is mentioned that the impact of wave dispersion and nonlinearity parameters on the soliton pulses has not been discussed in the past. Therefore, the applied method permits the explanation of the various wave dynamics by analyzing the attained soliton solutions in nonlinear optical fibers systems, which can be used for further studies.

Phosphorescence is commonly utilized for applications including light-emitting diodes and photovoltaics. Machine learning (ML) approaches trained on ab-initio datasets of singlet-triplet energy gaps may expedite the discovery of phosphorescent compounds with the desired emission energies. However, we show that standard ML approaches for modeling potential energy surfaces inaccurately predict singlet-triplet energy gaps due to the failure to account for spatial localities of spin transitions. To solve this, we introduce localization layers in a neural network model that weight atomic contributions to the energy gap, thereby allowing the model to isolate the most determinative chemical environments. Trained on the singlet-triplet energy gaps of organic molecules, we apply our method to an out-of-sample test set of large phosphorescent compounds and demonstrate the substantial improvement that localization layers have on predicting their phosphorescence energies. Remarkably, the inferred localization weights have a strong relationship with the ab-initio spin density of the singlet-triplet transition, and thus infer localities of the molecule that determine the spin transition, despite the fact that no direct electronic information was provided during training. The use of localization layers is expected to improve the modeling of many localized, non-extensive phenomena and could be implemented in any atom-centered neural network model.

A system of micro-spheres immersed in a water-in-oil microemulsion (ME) is studied both theoretically and experimentally. A catalyst for the Belousov-Zhabotinsky (BZ) reaction is immobilized in the micro-spheres, which are called BZ micro-oscillators (BZ MOs). The ME is loaded with all the reagents of the BZ reaction, except the catalyst. Fresh BZ reagents in the ME constantly feed BZ MOs. Diffusively coupled BZ MOs in this system demonstrate excitatory coupling at short gaps and inhibitory coupling at long gaps between BZ MOs. The critical gap, at which the transition between excitatory and inhibitory types of coupling occurs, depends on both the BZ concentration and the size of the ME nanodroplets and can range from a few to tens of micrometers. Different oscillatory patterns of BZ MOs with in-phase and anti-phase oscillations of neighboring BZ MOs have been found. Turing patterns are found as well. A network of such BZ MOs can be used for the creation of a chemical computer.

The goal of this paper is to investigate the importance of the four-wave nonlinear interactions (SNL4) on the shape of the power spectrum of ocean waves. To this end, the following results are discussed: a number of authors have conducted modern experimental measurements of ocean waves over the past decades and found that the measured power spectrum has (a) a very high central peak (characterized by the parameter γ, developed in the 1970s in the JONSWAP program) and (b) enhanced high-frequency channels which lead to the phenomenon of “bimodality”, also a well-known phenomenon. We discuss how a numerical hindcast of the Draupner storm (1995) with the standard code WAVEWATCH-III with full Boltzmann interactions also reflects these previously experimentally determined spectral shapes. Our results suggest that the use of the full Boltzmann interactions (as opposed to the discrete interaction approximation often employed for forecasting/hindcasting) is important for obtaining this characteristic physical spectral shape of the power spectrum.