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We demonstrate second-order interferometric autocorrelation of a pulse in the vacuum-ultraviolet (VUV) spectral range using an optical arrangement equivalent to a Michelson interferometer. In an all-reflective design, wavefront splitting is realized with two moveable interdigitated reflective gratings forming a diffraction pattern with well separated orders and an intensity distribution depending on the precisely adjustable path-length difference. An imaging time-of-flight spectrometer is able to spatially select ions created by nonlinear two-photon absorption in the focus of the zeroth diffraction order. This arrangement is used to demonstrate interferometric autocorrelation in krypton with femtosecond VUV pulses at 160 nm wavelength. In addition to the pulse duration, which is already accessible with non-collinear intensity autocorrelation, the full interferometric contrast of the presented approach enables us to extract also information on temporal phases.

We theoretically study the nature of parametrically driven dissipative Kerr soliton (PD-DKS) in a doubly resonant degenerate micro-optical parametric oscillator (DR-DμOPO) with the cooperation of and nonlinearities. Lifting the assumption of close-to-zero group velocity mismatch (GVM) that requires extensive dispersion engineering, we show that there is a threshold GVM above which single PD-DKS in DR-DμOPO can be generated deterministically. We find that the exact PD-DKS generation dynamics can be divided into two distinctive regimes depending on the phase matching condition. In both regimes, the perturbative effective third-order nonlinearity resulting from the cascaded quadratic process is responsible for the soliton annihilation and the deterministic single PD-DKS generation. We also develop the experimental design guidelines for accessing such deterministic single PD-DKS state. The working principle can be applied to different material platforms as a competitive ultrashort pulse and broadband frequency comb source architecture at the mid-infrared spectral range.

Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland Ice Sheets (GIS) and West Antarctic Ice Sheets, the Atlantic meridional overturning circulation (AMOC), the El-Niño Southern Oscillation and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. By combining these two methodologies with a large-scale Monte Carlo approach, we are able to propagate the many uncertainties associated with the critical temperature thresholds and the interaction strengths of the tipping elements. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 °C above pre-industrial climate conditions, representing a highly undesired state where a majority of the tipping elements reside in the transitioned regime. For lower levels of warming, states including disintegrated ice sheets on west Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the GIS and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.

Safe and stable operation plays an important role in the chemical industry. Fault detection and diagnosis (FDD) make it possible to identify abnormal process deviations early and assist operators in taking proper action against fault propagation. After decades of development, data-driven process monitoring technologies have gradually attracted attention from process industries. Although many promising FDD methods have been proposed from both academia and industry, challenges remain due to the complex characteristics of industrial data. In this work, classical and recent research on data-driven process monitoring methods is reviewed from the perspective of characterizing and mining industrial data. The implementation framework of data-driven process monitoring methods is first introduced. State of art of process monitoring methods corresponding to common industrial data characteristics are then reviewed. Finally, the challenges and possible solutions for actual industrial applications are discussed.

Biased, incomplete numerical models are often used for forecasting states of complex dynamical systems by mapping an estimate of a “true” initial state into model phase space, making a forecast, and then mapping back to the “true” space. While advances have been made to reduce errors associated with model initialization and model forecasts, we lack a general framework for discovering optimal mappings between “true” dynamical systems and model phase spaces. Here, we propose using a data‐driven approach to infer these maps. Our approach consistently reduces errors in the Lorenz‐96 system with an imperfect model constructed to produce significant model errors compared to a reference configuration. Optimal pre‐ and post‐processing transforms leverage “shocks” and “drifts” in the imperfect model to make more skillful forecasts of the reference system. The implemented machine learning architecture using neural networks constructed with a custom analog‐adjoint layer makes the approach generalizable across applications. Plain Language Summary Modeling and forecasting natural systems, such as Earth's oceans and atmosphere, is difficult due to their inherent unpredictability, our incomplete understanding of their dynamics, and their vastness and complexity. One way to improve forecasts is by improving physical representations within numerical models. However, models will always have shortcomings. The alternative approach explored here is to maximize the utility of available imperfect or incomplete models by revising how the model is used and how its forecast is interpreted. Here, we employ machine learning to learn pre‐ and post‐processing operators, called cross‐attractor transforms (CATs), which reduce the overall forecast errors from imperfect models. We demonstrate the framework's efficacy by using a simplified dynamical model as an imperfect representation of a higher‐dimensional chaotic dynamical system, analogous to using a simple pendulum to forecast the behavior of a double pendulum. In addition to improving forecasts, CATs offer insights into how the two systems evolve in time. The approach is generalizable across dynamical systems and disciplines. Key Points Forecasts from imperfect models are improved using optimized pre‐ and post‐processing operators Neural networks trained on imperfect models and reference truth forecasts efficiently derive these operators Forecasts from this hybrid machine‐learning approach are more accurate than purely data‐driven methods when applied to an idealized system

High-order harmonic generation in solids, the nonlinear up-conversion of coherent radiation resulting from the interaction of a strong and short laser pulse with a solid sample, has come to age. Since the first experiments and theoretical developments, there has been a constant and steady interest in this topic. In this paper, we summarize the progress made so far and propose new possibilities for the generation of high-order harmonics with the aid of plasmonic fields. The driven fields could be adequately engineered both spatially and temporally with nanometric and attosecond resolution, offering to the conventional solid-HHG novel and exciting coherent sources. Just to cite an example, the generation of attosecond pulses using bulk matter is strongly linked to the appropriate manipulation of the driven field to avoid, for instance, reaching the damage threshold of the material. Plasmonics fields as an alternative to conventional laser beams could open new avenues in the development of table-top sources of ultrashort and strong coherent radiation.

Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) and demonstrates the application to two chemical process examples. First, the proposed methodology that integrates a neural network model and a first-principles model in the optimization problems of RTO and MPC is discussed. Then, two chemical process examples are presented. In the first example, a continuous stirred tank reactor (CSTR) with a reversible exothermic reaction is studied. A feed-forward neural network model is used to approximate the nonlinear reaction rate and is combined with a first-principles model in RTO and MPC. An RTO is designed to find the optimal reactor operating condition balancing energy cost and reactant conversion, and an MPC is designed to drive the process to the optimal operating condition. A variation in energy price is introduced to demonstrate that the developed RTO scheme is able to minimize operation cost and yields a closed-loop performance that is very close to the one attained by RTO/MPC using the first-principles model. In the second example, a distillation column is used to demonstrate an industrial application of the use of machine learning to model nonlinearities in RTO. A feed-forward neural network is first built to obtain the phase equilibrium properties and then combined with a first-principles model in RTO, which is designed to maximize the operation profit and calculate optimal set-points for the controllers. A variation in feed concentration is introduced to demonstrate that the developed RTO scheme can increase operation profit for all considered conditions.

In this paper, a novel data-driven approach for the development of soft sensors (SSs) for multi-step-ahead prediction of industrial process variables is proposed. This method is based on the recent developments in Koopman operator theory and dynamic mode decomposition (DMD). It is derived from Hankel DMD with control (HDMDc) to deal with highly nonlinear dynamics using augmented linear models, exploiting input and output regressors. The proposed multi-step-ahead HDMDc (MSA-HDMDc) is designed to perform multi-step prediction and capture complex dynamics with a linear approximation for a highly nonlinear system. This enables the construction of SSs capable of estimating the output of a process over a long period of time and/or using the developed SSs for model predictive control purposes. Hyperparameter tuning and model order reduction are specifically designed to perform multi-step-ahead predictions. Two real-world case studies consisting of a sulfur recovery unit and a debutanizer column, which are widely used as benchmarks in the SS field, are used to validate the proposed methodology. Data covering multiple system operating points are used for identification. The proposed MSA-HDMDc outperforms currently adopted methods in the SSs domain, such as autoregressive models with exogenous inputs and finite impulse response models, and proves to be robust to the variability of systems operating points.

Soil, being a natural body which, on the one hand, obeys the internal laws of self-development (in particular, the erasure of lithomemory and the development of pedomemory during one stage of evolution) and, on the other, is exposed to various (including anthropogenic) factors. The soil shows, theoretically, all types of nonlinear dynamic behavior. The most common are multistability and amplitude shrinkage. The realization that processes occurring in soils are nonlinear in time, whether in daily, annual (seasonal), or long-term cycles of development (self-development) of these soils, allows us to bring soil closer to other biotic, bio-abiotic, and inert natural and natural-anthropogenic “nonlinear” objects. The study of such a “class of nonlinear objects” is essential to be able to create sustainable management systems for territories.