Search Results (20)

Designing waveforms with a Constant Modulus Constraint (CMC) to achieve desirable Slow-Time Ambiguity Function (STAF) characteristics is significantly important in radar technology. The problem is NP-hard, due to its non-convex quartic objective function and CMC constraint. Existing methods typically involve model-based approaches with relaxation and data-driven Deep Neural Networks (DNNs) methods, which face the challenge of dataimitation. We observe that the Complex Circle Manifold (CCM) naturally satisfies the CMC. By projecting onto the CCM, the problem is transformed into an unconstrained minimization problem that can be tackled using the CCM gradient descent model. Furthermore, we observe that the gradient descent model over the CCM can be unfolded as a Deep Learning (DL) network. Therefore, byeveraging the powerfulearning ability of DL and the CCM gradient descent model, we propose a Model-Adaptive Learned Network (MAL-Net) method without relaxation. Initially, we reformulate the problem as an Unconstrained Quartic Problem (UQP) on the CCM. Then, the MAL-Net is developed toearn the step sizes of allayers adaptively. This is accomplished by unrolling the CCM gradient descent model as the networkayer. Our simulation results demonstrate that the proposed MAL-Net achieves superior STAF performance compared to existing methods. Full article

The design and calculation of nonlinear observers for parameter estimation in multi-time-scale nonlinear systems present significant challenges due to the inherent complexity and stiffness of such systems. This study proposes a framework for designing observers for two-time-scale nonlinear systems, with the objective of overcoming the aforementioned challenges. The design procedure involves reducing the original two-time-scale nonlinear system to a lower-dimensional model that captures only the slow dynamics while approximating the fast states through the use of an algebraic slow motion invariant manifold function. Subsequently, an exponential observer can be devised for this reduced system, which is valid for both state and parameter estimation. By employing the output from the original system, this observer can be adapted for online state and parameter estimation for the detailed two-time-scale system. The challenges associated with estimating parameters in two-time-scale nonlinear systems, the complexities of designing observers for such systems, and the computational burden associated with computing observers for ill-conditioned systems can be effectively addressed through the application of this design framework. A rigorous error analysis validates the convergence of the proposed observer towards the states and parameters of the original system. The viability and necessity of this observer design framework are demonstrated through a numerical example and an anaerobic digestion process. This study presents a practical approach for state and parameter estimation with observers for two-time-scale nonlinear systems. Full article

In this paper, we study the creep phenomena for self-similar models of viscoelastic materials and derive a generalization of the Kelvin–Voigt model in the framework of fractal continuum calculus. Creep compliance for the Kelvin–Voigt model is extended to fractal manifolds through local fractal-continuum differential operators. Generalized fractal creep compliance is obtained, taking into account the intrinsic time $\tau$ and the fractal dimension of time-scale $\beta$. The model obtained is validated with experimental data obtained for resin samples with the fractal structure of a Sierpinski carpet and experimental data on rock salt. Comparisons of the model predictions with the experimental data are presented as the curves of slow continuous deformations. Full article

The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which $-\dot{H}\ll H^2$, with $H\left(t\right)$ being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics, which takes into account non-equilibrium effects associated with bulk viscosity, which may have been present as the early universe underwent an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring introducing additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk viscosity pressure turns out to be time dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in the presence of bulk viscosity pressure. In addition, we construct a fluid description of inflation and demonstrate that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity-supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations, finding good agreement in most cases. Full article

The global quasi-linearization (GQL) is used as a method to study and to reduce the complexity of mathematical models of mechanisms of chemical kinetics. Similar to standard methodologies, such as the quasi-steady-state assumption (QSSA), the GQL method defines the fast and slow invariant subspaces and uses slow manifolds to gain a reduced representation. It does not require empirical inputs and is based on the eigenvalue and eigenvector decomposition of a linear map approximating the nonlinear vector field of the original system. In the present work, the GQL-based slow/fast decomposition is applied for different combustion systems. The results are compared with the standard QSSA approach. For this, an implicit implementation strategy described by differential algebraic equations (DAEs) systems is suggested and used, which allows for treating both approaches within the same computational framework. Hydrogen–air (with 9 species) and ethanol–air (with 57 species) combustion systems are considered representative examples to illustrate and verify the GQL. The results show that 4D GQL for hydrogen–air and 14D GQL ethanol–air slow manifolds outperform the standard QSSA approach based on a DAE-based reduced computation model. Full article

In light of the energy and environment issues, fuel cell vehicles have many advantages, including high efficiency, low-temperature operation, and zero greenhouse gas emissions, making them an excellent choice for urban environments where air pollution is a significant problem. The dynamics of fuel cells, on the other hand, are relatively slow, owing principally to the dynamics of the air compressor and the dynamics of manifold filling. Because these dynamics can limit the overall performance of fuel cell vehicles, two key technologies that have emerged as critical components of electric vehicle powertrains are batteries and supercapacitors. However, choosing the best hybrid energy storage system that combines a battery and a supercapacitor is a critical task nowadays. An electric vehicle simulated application by MATLAB Code is modeled in this article using the multi-objective particle swarm optimization technique (MOPSO) to determine the appropriate type of batteries and supercapacitors in the SFTP-SC03 drive cycle. This application optimized both component sizing and power management at the same time. Batteries of five distinct types (Lithium, Li-ion, Li-S, Ni-Nicl2, and Ni-MH) and supercapacitors of two different types (Maxwell BCAP0003 and ESHSR-3000CO) were used. Each storage component is distinguished by its weight, capacity, and cost. As a consequence, using a Li-ion battery with the Maxwell BCAP0003 represented the optimal form of hybrid storage in our driving conditions, reducing fuel consumption by approximately 0.43% when compared to the ESHSR-3000CO. Full article

The Koper model is a vector field in which the differential equations describe the electrochemical oscillations appearing in diffusion processes. This work focuses on the understanding of the slow dynamics of a stochastic Koper model perturbed by stable Lévy noise. We establish the slow manifold for a stochastic Koper model with stable Lévy noise and verify exponential tracking properties. We also present two practical examples to demonstrate the analytical results with numerical simulations. Full article

A detailed analysis of the electronic structure and decay dynamics in a symmetric system with three electrons in three linearly aligned binding sites representing quantum dots (QDs) is given. The two outer A QDs are two-level potentials and can act as (virtual) photon emitters, whereas the central B QD can be ionized from its one level into a continuum confined on the QD axis upon absorbing virtual photons in the inter-Coulombic decay (ICD) process. Two scenarios in such an $ABA$ array are explored. One ICD process is from a singly excited resonance state, whose decay releasing one virtual photon we find superimposed with resonance energy transfer among both A QDs. Moreover, the decay-process manifold for a doubly excited (DE) resonance is explored, in which collective ICD among all three sites and excited ICD among the outer QDs engage. Rates for all processes are found to be extremely low, although ICD rates with two neighbors are predicted to double compared to ICD among two sites only. The slowing is caused by Coulomb barriers imposed from ground or excited state electrons in the A sites. Outliers occur on the one hand at short distances, where the charge transfer among QDs mixes the possible decay pathways. On the other hand, we discovered a shape resonance-enhanced DE-ICD pathway, in which an excited and localized $B^{*}$ shape resonance state forms, which is able to decay quickly into the final ICD continuum. Full article

After SARS-CoV-2 infection, the molecular phenoreversion of the immunological response and its associated metabolic dysregulation are required for a full recovery of the patient. This process is patient-dependent due to the manifold possibilities induced by virus severity, its phylogenic evolution and the vaccination status of the population. We have here investigated the natural history of COVID-19 disease at the molecular level, characterizing the metabolic and immunological phenoreversion over time in large cohorts of hospitalized severe patients (n = 886) and non-hospitalized recovered patients that self-reported having passed the disease (n = 513). Non-hospitalized recovered patients do not show any metabolic fingerprint associated with the disease or immune alterations. Acute patients are characterized by the metabolic and lipidomic dysregulation that accompanies the exacerbated immunological response, resulting in a slow recovery time with a maximum probability of around 62 days. As a manifestation of the heterogeneity in the metabolic phenoreversion, age and severity become factors that modulate their normalization time which, in turn, correlates with changes in the atherogenesis-associated chemokine MCP-1. Our results are consistent with a model where the slow metabolic normalization in acute patients results in enhanced atherosclerotic risk, in line with the recent observation of an elevated number of cardiovascular episodes found in post-COVID-19 cohorts. Full article

Future wireless networks will require advance physical-layer techniques to meet the requirements of Internet of Everything (IoE) applications and massive communication systems. To this end, a massive MIMO (m-MIMO) system is to date considered one of the key technologies for future wireless networks. This is due to the capability of m-MIMO to bring a significant improvement in the spectral efficiency and energy efficiency. However, designing an efficient downlink (DL) training sequence for fast channel state information (CSI) estimation, i.e., with limited coherence time, in a frequency division duplex (FDD) m-MIMO system when users exhibit different correlation patterns, i.e., span distinct channel covariance matrices, is to date very challenging. Although advanced iterative algorithms have been developed to address this challenge, they exhibit slow convergence speed and thus deliver high latency and computational complexity. To overcome this challenge, we propose a computationally efficient conjugate gradient-descent (CGD) algorithm based on the Riemannian manifold in order to optimize the DL training sequence at base station (BS), while improving the convergence rate to provide a fast CSI estimation for an FDD m-MIMO system. To this end, the sum rate and the computational complexity performances of the proposed training solution are compared with the state-of-the-art iterative algorithms. The results show that the proposed training solution maximizes the achievable sum rate performance, while delivering a lower overall computational complexity owing to a faster convergence rate in comparison to the state-of-the-art iterative algorithms. Full article

Due to their substantial fluorescence quantum yields in the crystalline phase, propeller-shaped molecules have recently gained significant attention as potential emissive materials for optoelectronic applications. For the family of cyclopentadiene derivatives, light-emission is highly dependent on the nature of heteroatomic substitutions. In this paper, we investigate excited state relaxation pathways in the tetraphenyl-furan molecule (TPF), which in contrast with other molecules in the family, shows emission quenching in the solid-state. For the singlet manifold, our calculations show nonradiative pathways associated with C-O elongation are blocked in both vacuum and the solid state. A fraction of the population can be transferred to the triplet manifold and, subsequently, to the ground state in both phases. This process is expected to be relatively slow due to the small spin-orbit couplings between the relevant singlet-triplet states. Emission quenching in crystalline TPF seems to be in line with more efficient exciton hopping rates. Our simulations help clarify the role of conical intersections, population of the triplet states and crystalline structure in the emissive response of propeller-shaped molecules. Full article

Previous studies have demonstrated, experimentally and theoretically, the existence of slow–fast evolutions, i.e., slow chaotic spiking sequences in the dynamics of a semiconductor laser with AC-coupled optoelectronic feedback. In this work, the so-called Flow Curvature Method was used, which provides the slow invariant manifold analytical equation of such a laser model and also highlights its symmetries if any exist. This equation and its graphical representation in the phase space enable, on the one hand, discriminating the slow evolution of the trajectory curves from the fast one and, on the other hand, improving our understanding of this slow–fast regime. Full article

In this short review, we attempt to unfold various aspects of excited-state intramolecular proton transfer (ESIPT) from the studies that are available up to date. Since Weller’s discovery of ESIPT in salicylic acid (SA) and its derivative methyl salicylate (MS), numerous studies have emerged on the topic and it has become an attractive field of research because of its manifold applications. Here, we discuss some critical aspects of ESIPT and tautomerization from the mechanistic viewpoint. We address excitation wavelength dependence, anti-Kasha ESIPT, fast and slow ESIPT, reversibility and irreversibility of ESIPT, hydrogen bonding and geometrical factors, excited-state double proton transfer (ESDPT), concerted and stepwise ESDPT. Full article

Recent technical developments and increased affordability of high-speed eye tracking devices have brought microsaccades to the forefront of research in many areas of sensory, perceptual, and cognitive processes. The present thematic issue on “Microsaccades: Empirical Research and Methodological Advances” invited authors to submit original research and reviews encompassing measurements and data analyses in fundamental, translational, and applied studies. We present the first volume of this special issue, comprising 14 articles by research teams around the world. Contributions include the characterization of fixational eye movements and saccadic intrusions in neurological impairments and in visual disease, methodological developments in microsaccade detection, the measurement of fixational eye movements in applied and ecological scenarios, and advances in the current understanding of the relationship between microsaccades and cognition. When fundamental research on microsaccades experienced a renaissance at the turn of the millennium (c.f. Martinez-Conde, Macknik, & Hubel, 2004), one could hardly have been so bold as to predict the manifold applications of research on fixational eye movements in clinic and practice. Through this great variety of areas of focus, some main topics emerge. One such theme is the applicability of microsaccade measures to neurological and visual disease. Whereas microsaccade quantifications have been largely limited to participants with intact visual and oculomotor systems, recent research has extended this interest into the realm of neural and ophthalmic impairment (see Alexander, Macknik, & Martinez-Conde, 2018, for a review). In this volume, Becker et al. analyze “Saccadic intrusions in amyotrophic lateral sclerosis (ALS)” and Kang et al. study “Fixational eye movement waveforms in amblyopia”, delving into the characteristics of fast and slow eye movements. Two other articles focus on how the degradation of visual information, which is relevant to many ophthalmic pathologies, affects microsaccadic features. Tang et al. investigate the “Effects of visual blur on microsaccades on visual exploration” and conclude that the precision of an image on the fovea plays an important role in the calibration of microsaccade amplitudes during visual scanning. Otero-Millan et al. use different kinds of visual stimuli and viewing tasks in the presence or absence of simulated scotomas, to determine the contributions of foveal and peripheral visual information to microsaccade production. They conclude that “Microsaccade generation requires a foveal anchor”. The link between microsaccadic characteristics and cognitive processes has been a mainstay of microsaccade research for almost two decades, since studies in the early 2000s connected microsaccade directions to the spatial location of covert attentional cues (Engbert & Kliegl, 2003; Hafed & Clark, 2002). In the present volume, Dalmaso et al. report that “Anticipation of cognitive conflict is reflected in microsaccades”, providing new insights about the top-down modulation of microsaccade dynamics. Ryan et al. further examine the relationship between “Microsaccades and covert attention” during the performance of a continuous, divided-attention task, and find preliminary evidence that microsaccades track the ongoing allocation of spatial attention. Krueger et al. discover that microsaccade rates modulate with visual attention demands and report that “Microsaccades distinguish looking from seeing”. Taking the ecological validity of microsaccade investigations one step further, Barnhart et al. evaluate microsaccades during the observation of magic tricks and conclude that “Microsaccades reflect the dynamics of misdirected attention in magic”. Two articles examine the role of individual differences and intraindividual variability over time on microsaccadic features. In “Reliability and correlates of intra-individual variability in the oculomotor system” Perquin and Bompas find evidence for intra-individual reliability over different time points, while cautioning that its use to classify self-reported individual differences remains unclear. Stafford et al. provide a counterpoint in “Can microsaccade rate predict drug response?” by supporting the use of microsaccade occurrence as both a trait measure of individual differences and as a state measure of response to caffeine administration. Methodological and technical advances are the subjects of three papers in this volume. In “Motion tracking of iris features to detect small eye movements” Chaudhary and Pelz describe a new video-based eye tracking methodology that relies on higher-order iris texture features, rather than on lower-order pupil center and corneal reflection features, to detect microsaccades with high confidence. Munz et al. present an open source visual analytics system called “VisME: Visual microsaccades explorer” that allows users to interactively vary microsaccade filter parameters and evaluate the resulting effects on microsaccade behavior, with the goal of promoting reproducibility in data analyses. In “What makes a microsaccade? A review of 70 years research prompts a new detection method” Hauperich et al. review the microsaccade properties reported between the 1940s and today, and use the stated range of parameters to develop a novel method of microsaccade detection. Lastly, Alexander et al. switch the focus from the past of microsaccade research to its future, by discussing the recent and upcoming applications of fixational eye movements to ecologically-valid and real-world scenarios. Their review “Microsaccades in applied environments: real-world applications of fixational eye movement measurements” covers the possibilities and challenges of taking microsaccade measurements out of the lab and into the field. Microsaccades have engaged the interest of scientists from different backgrounds and disciplines for many decades and will certainly continue to do so. One reason for this fascination might be microsaccades’ role as a link between basic sensory processes and high-level cognitive phenomena, making them an attractive focus of interdisciplinary research and transdisciplinary applications. Thus, research on microsaccades will not only endure, but keep evolving as the present knowledge base expands. Part 2 of the special issue on microsaccades is already in progress with articles currently under review and will be published in 2021. Full article

Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant ${\mathbf{k}}_{\perp }$ cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases. Full article