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A recently developed stochastic control formalism (Stochastic Thermodynamics) has opened for the first time the possibility to quantify energy exchange and entropy production in finite-time thermodynamic transitions, based on Langevin models for mesoscopic thermodynamic systems. Within this framework we quantify power output and efficiency of overdamped stochastic thermodynamic engines that are powered by a heat bath with temperature that varies periodically with time. Our setting is in contrast to most of the existing literature that considers the Carnot paradigm, alternating contact with heat baths having different fixed temperatures, hot and cold. Specifically, we consider a periodic and bounded but otherwise arbitrary temperature profile and derive explicit bounds on the power and efficiency achievable by a suitably controlling potential that couples the thermodynamic engine to the external world – the time-varying potential represents the control input to the system. A standing assumption in our analysis is that the norm of the gradient of the potentials is bounded – in the absence of any such constraint on the control input, the physically questionable conclusion of arbitrarily large power can be drawn. [ABSTRACT FROM AUTHOR]

Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3--60-day periods) in both GPH and SST and El Niño--Southern Oscillation (ENSO) at low frequencies (2--7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the gain and phase robustness of PID control in stabilizing linear time-invariant (LTI) systems subject to gain and phase variations. We consider specifically filtered PID controllers, out of the necessity in practical implementation of PID controllers. We examine first-order unstable systems and seek to find analytical expressions of the maximal gain and phase margins achievable by filtered PID control, where the maximal gain and phase margins are referred to as the largest ranges of gain and phase variations within which the system is guaranteed to be stabilizable. Our results show that the maximal gain margin can be determined explicitly, while the maximal phase margin can be computed by solving a third-order polynomial, which in turn can be solved explicitly. We also investigate the gain and phase maximization problems subject to a performance constraint, which has direct linkages to the steady-state and transient performances of a system. Our results show how in a practically implementable PID control scheme the gain and phase margins may be confined by the plant characteristics, and how in the limit it can perform equally well as other optimal controllers. The results also shed light into the tradeoff between performance and robustness of PID controllers. [ABSTRACT FROM AUTHOR]

We consider overdamped Brownian particles with two degrees of freedom (DoF) that are confined in a time-varying quadratic potential and are in simultaneous contact with heat baths of different temperatures along the respective DoF. The anisotropy in thermal fluctuations can be used to extract work by suitably manipulating the confining potential. The question of what the maximal amount of work that can be extracted is has been raised in recent work, and has been computed under the simplifying assumption that the entropy of the distribution of particles (thermodynamic states) remains constant throughout a thermodynamic cycle. Indeed, it was shown that the maximal amount of work that can be extracted amounts to solving an isoperimetric problem, where the 2-Wasserstein length traversed by thermodynamic states quantifies dissipation that can be traded off against an area integral that quantifies work drawn out of the thermal anisotropy. Here, we remove the simplifying assumption on constancy of entropy. We show that the work drawn can be computed similarly to the case where the entropy is kept constant while the dissipation can be reduced by suitably tilting the thermodynamic cycle in a thermodynamic space with one additional dimension. Optimal cycles can be locally approximated by solutions to an isoperimetric problem in a tilted lower-dimensional subspace.

We introduce an optimal mass transport framework on the space of Gaussian mixture models. These models are widely used in statistical inference. Specifically, we treat Gaussian mixture models as a submanifold of probability densities equipped with the Wasserstein metric. The topology induced by optimal transport is highly desirable and natural because, in contrast to total variation and other metrics, the Wasserstein metric is weakly continuous (i.e., convergence is equivalent to convergence of moments). Thus, our approach provides natural ways to compare, interpolate and average Gaussian mixture models. Moreover, the approach has low computational complexity. Different aspects of the framework are discussed and examples are presented for illustration purposes.

The form and function of river deltas is intricately linked to the evolving structure of their channel networks, which controls how effectively deltas are nourished with sediments and nutrients. Understanding the coevolution of deltaic channels and their flux organization is crucial for guiding maintenance strategies of these highly stressed systems from a range of anthropogenic activities. To date, however, a unified theory explaining how deltas self-organize to distribute water and sediment up to the shoreline remains elusive. Here, we provide evidence for an optimality principle underlying the self-organized partition of fluxes in delta channel networks. By introducing a suitable nonlocal entropy rate ([Formula: see text]) and by analyzing field and simulated deltas, we suggest that delta networks achieve configurations that maximize the diversity of water and sediment flux delivery to the shoreline. We thus suggest that prograding deltas attain dynamically accessible optima of flux distributions on their channel network topologies, thus effectively decoupling evolutionary time scales of geomorphology and hydrology. When interpreted in terms of delta resilience, high nER configurations reflect an increased ability to withstand perturbations. However, the distributive mechanism responsible for both diversifying flux delivery to the shoreline and dampening possible perturbations might lead to catastrophic events when those perturbations exceed certain intensity thresholds., Competing Interests: The authors declare no conflict of interest.