Multiple-frequency synchronization of the four exciters in a far super-resonant vibrating system with an isolation frame

Generally, the synchronization studies on two or multiple exciters are preconditioned by being a single frequency, while the multiple-frequency synchronization problems in a vibrating system, including double-frequency and triple-frequency, are less considered, which are also very significant in engineering. This paper attempts to solve this issue by considering a dynamical model with an isolation frame, driven by the four exciters. The synchronization for the four exciters and its stability under the double-frequency and triple-frequency conditions are studied in detail. Firstly, the mathematical modeling of the system is established, and the corresponding motion differential equations are derived. Using the asymptotic method and the average method, yields the theoretical condition of implementing multiple-frequency synchronization, and the theoretical condition for stability of the system complies with the Routh–Hurwitz criterion. The dynamic characteristics of the system, including stable phase differences, stability abilities, responses of the system, and relative motion relationship, are qualitatively discussed by numeric. Finally, simulations are performed by applying a Runge–Kutta program to validate the theoretical and numerical qualitative results. It is shown that, by reasonably matching the key parameters of the system, the stronger, stable, and valuable motion states of vibrating machines, including vibration amplitudes, frequencies, and motion trajectory, can be realized, which are exactly the desires in engineering.

Tensor Monopoles in superconducting systems

Topology in general but also topological objects such as monopoles are a central concept in physics. They are prime examples for the intriguing physics of gauge theories and topological states of matter. Vector monopoles are already frequently discussed such as the well-established Dirac monopole in three dimensions. Less known are tensor monopoles giving rise to tensor gauge fields. Here we report that tensor monopoles can potentially be realized in superconducting multi-terminal systems using the phase differences between superconductors as synthetic dimensions. In a first proposal we suggest a circuit of superconducting islands featuring charge states to realize a tensor monopole. As a second example we propose a triple dot system coupled to multiple superconductors that also gives rise to such a topological structure. All proposals can be implemented with current experimental means and the monopole readily be detected by measuring the quantum geometry.

Cellular inertia

It has been experimentally reported that chemotactic cells exhibit cellular memory, that is, a tendency to maintain the migration direction despite changes in the chemoattractant gradient. In this study, we analyzed a phenomenological model assuming the presence of cellular inertia, as well as a response time in motility, resulting in the reproduction of the cellular memory observed in the previous experiments. According to the analysis, the cellular motion is described by the superposition of multiple oscillative functions induced by the multiplication of the oscillative polarity and motility. The cellular intertia generates cellular memory by regulating phase differences between those oscillative functions. By applying the theory to the experimental data, the cellular inertia was estimated at $$m=3-6$$ m = 3 - 6 min. In addition, physiological parameters, such as response time in motility and intracellular processing speed, were also evaluated. The agreement between the experiemental data and theory suggests the possibility of the presence of the response time in motility, which has never been biologically verified and should be explored in the future.

L-Band SAR Co-Polarized Phase Difference Modeling for Corn Fields

This research aims at modeling the microwave backscatter of corn fields by coupling an incoherent, interaction-based scattering model with a semi-empirical bulk vegetation dielectric model. The scattering model is fitted to co-polarized phase difference measurements over several corn fields imaged with fully polarimetric synthetic aperture radar (SAR) images with incidence angles ranging from 20° to 60°. The dataset comprised two field campaigns, one over Canada with the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR, 1.258 GHz) and the other one over Argentina with Advanced Land Observing Satellite 2 (ALOS-2) Phased Array type L-band Synthetic Aperture Radar (PALSAR-2) (ALOS-2/PALSAR-2, 1.236 GHz), totaling 60 data measurements over 28 grown corn fields at peak biomass with stalk gravimetric moisture larger than 0.8 g/g. Co-polarized phase differences were computed using a maximum likelihood estimation technique from each field’s measured speckled sample histograms. After minimizing the difference between the model and data measurements for varying incidence angles by a nonlinear least-squares fitting, well agreement was found with a root mean squared error of 24.3° for co-polarized phase difference measurements in the range of −170.3° to −19.13°. Model parameterization by stalk gravimetric moisture instead of its complex dielectric constant is also addressed. Further validation was undertaken for the UAVSAR dataset on earlier corn stages, where overall sensitivity to stalk height, stalk gravimetric moisture, and stalk area density agreed with ground data, with the sensitivity to stalk diameter being the weakest. This study provides a new perspective on the use of co-polarized phase differences in retrieving corn stalk features through inverse modeling techniques from space.

Retrieval of Firn Thickness by Means of Polarisation Phase Differences in L-Band SAR Data

The knowledge of glacier zones’ extent and their temporal variations is fundamental for the retrieval of surface mass balance of glaciers and ice sheets. In this context, a key parameter is the firn line (FL), the lower boundary of the percolation zone, whose location is an indicator of time-integrated mass balance changes. Several approaches have been developed in the last decades to map the FL by means of Synthetic Aperture Radar (SAR) imagery, mainly exploiting backscatter intensities and their seasonal variation. In this paper, an alternative approach is proposed, based on co-polarisation phase differences (CPDs). In particular, CPDs are interpreted as the result of propagation through anisotropic firn layers and are, therefore, proposed as an indicator of the presence of firn. A model is employed to demonstrate the link between CPDs and firn depth, indicating the potential of polarimetric SAR to improve firn characterization beyond spatial extent and FL detection. The proposed approach is demonstrated on L-band airborne data, acquired on 21 May 2015 by the F-SAR sensor of DLR in West Greenland during the ARCTIC15 campaign, and validated with in-situ information available from other studies.

Roles of insolation forcing and CO2 forcing on Late Pleistocene seasonal sea surface temperatures

Late Pleistocene changes in insolation, greenhouse gas concentrations, and ice sheets have different spatially and seasonally modulated climatic fingerprints. By exploring the seasonality of paleoclimate proxy data, we gain deeper insight into the drivers of climate changes. Here, we investigate changes in alkenone-based annual mean and Globigerinoides ruber Mg/Ca-based summer sea surface temperatures in the East China Sea and their linkages to climate forcing over the past 400,000 years. During interglacial-glacial cycles, there are phase differences between annual mean and seasonal (summer and winter) temperatures, which relate to seasonal insolation changes. These phase differences are most evident during interglacials. During glacial terminations, temperature changes were strongly affected by CO2. Early temperature minima, ~20,000 years before glacial terminations, except the last glacial period, coincide with the largest temperature differences between summer and winter, and with the timing of the lowest atmospheric CO2 concentration. These findings imply the need to consider proxy seasonality and seasonal climate variability to estimate climate sensitivity.

Cluster solutions in networks of weakly coupled oscillators on a 2D square torus

We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.