The patterns of traveling wave on shallow water modeled by Green-Naghdi equation

The Green-Naghdi equations are a shallow water waves model which play important roles in nonlinear wave fields. By using the trial equation method and the Complete discrimination system for the polynomial we obtained the classification of travelling wave patterns. Among those patterns, new singular patterns and double periodic patterns are obtained in the first time. And we draw the graphs which help us to understand the dynamics behaviors of the Green-Naghdi model intuitionally.

On shock-induced light-fluid-layer evolution

Shock-induced light-fluid-layer evolution is firstly investigated experimentally and theoretically. Specifically, three quasi-one-dimensional helium gas layers with different layer thicknesses are generated to study the wave patterns and interface motions. Six quasi-two-dimensional helium gas layers with diverse layer thicknesses and amplitude combinations are created to explore the Richtmyer–Meshkov instability of a light-fluid layer. Due to the multiple reflected shocks reverberating inside a light-fluid layer, the speeds of the two interfaces gradually converge, and the layer thickness saturates eventually. A general one-dimensional theory is adopted to describe the two interfaces’ motions and the layer thickness variations. It is found that, for the first interface, the end time of its phase reversal determines the influence of the reflected shocks on it. However, the reverberated shocks indeed lead to the second interface being more unstable. When the two interfaces are initially in phase, and the initial fluid layer is very thin, the two interfaces’ spike heads collide and stabilise the two interfaces. Linear and nonlinear models are successfully adopted by considering the interface-coupling effect and the reverberated shocks to predict the two interfaces’ perturbation growths in all regimes. The interfacial instability of a light-fluid layer is quantitatively compared with that of a heavy-fluid layer. It is concluded that the kind of waves reverberating inside a fluid layer significantly affects the fluid-layer evolution.

A SIMPLE APPROACH TO THE STUDY OF WAVE PATTERNS

The paper revisits some pioneering work of Sir Thomas Havelock on wave patterns with particular attention focussed on his graphical method of analysis. Motivated by a desire to explore this method further using numerical methods, it is extended in a simple manner to give three-dimensional illustrations of the wave patterns of a point disturbance in deep and shallow water. All results are confined to the sub- and trans-critical regimes with some obtained very close to the critical Depth Froude Number. Some conclusions are drawn on the wave types produced when operating close to the critical speed and their decay with distance off.

Recurring Spatiotemporal Patterns of COVID-19 in the United States

We analyzed the waxing and waning patterns ('surges') of reported SARS-CoV-2 cases from January 1, 2020 through Oct 31, 2021 in all states and provinces (n = 93) in the USA, Mexico, and Canada, and across all counties (N = 3142) in the USA. A correlation matrix of the 576 x 576 daily case incidence rates in the 50 US states generates a distinctive 'checkerboard' pattern showing that the epidemic has consisted of seven distinct internally coherent spatiotemporal wave patterns, four in the first year of the epidemic, and three thus far in the second year. Geoclustering of state case rate trajectories reveals three dominant co-varying spatial clusters of similar case rate trajectories, in the northeastern, southeastern and central/western regions of the USA. The spatiotemporal patterns of epidemic year 1 have thus far been repeated (p<.001) in epidemic year 2. The 'checkerboard' pattern of the correlation matrix of case trajectories can be closely simulated as three sets of interacting sine waves with annual frequencies of 1:1:2 major cycles per year, corresponding to the northeastern, central/western, and southeastern state clusters. Case incidence patterns in Mexico and Canada have been similar to nearby regions in the southern US and the northern US, respectively. Time lapse videos allow visualization of the wave patterns. These highly structured geographical and temporal patterns, coupled with emerging evidence of annual repetition of these same patterns, show that SARS-CoV-2 case rates are driven at least in part by predictable seasonal factors.

Locally synchronized ciliary domains and tissue-scale cilia alignment underlie global metachronal wave patterns

Motile cilia are hair-like cell extensions present in multiple organs of the body. How cilia coordinate their regular beat in multiciliated epithelia to efficiently displace fluids remains elusive. Here, we propose the zebrafish nose as an accessible model system to study ciliary dynamics, due to its conserved properties with other ciliated tissues and its high availability for non-invasive imaging. We reveal that cilia are locally synchronized, and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Despite this merely local synchronization, we observe global patterns of traveling metachronal waves across the multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right nose, revealing a chiral asymmetry of metachronal coordination. In conclusion, we show that local synchronization together with tissue-scale cilia alignment shape global wave patterns in multiciliated epithelia.

Boosting Brain Waves Improves Memory

Have you ever wanted to improve your memory? Or have you struggled to remember what you studied? Memory uses special patterns of activity in the brain. This experiment tested a new way to create brain wave patterns that help with memory. We wanted to see if we could improve memory by using lights and sounds that teach the brain waves to be in sync. People wore special goggles that made flashes of light and headphones that made beeping noises. This trained the brain through a process called entrainment. The entrainment put the brain in sync at a specific brain wave pattern called theta. People whose brains were trained to be in theta had better memory compared to people whose brains did not get trained. We learned that entrainment is a cool new way to make memory better.

E-Cannula reveals anatomical diversity in sharp-wave ripples as a driver for the recruitment of distinct hippocampal assemblies

The hippocampus plays a critical role in spatial navigation and episodic memory. However, research on in vivo hippocampal activity dynamics has mostly relied on single modalities such as electrical recordings or optical imaging, with respectively limited spatial and temporal resolution. This technical difficulty greatly impedes multi-level investigations into network state-related changes in cellular activity. To overcome these limitations, we developed the E-Cannula integrating fully transparent graphene microelectrodes with imaging-cannula. The E-Cannula enables the simultaneous electrical recording and two-photon calcium imaging from the exact same population of neurons across an anatomically extended region of the mouse hippocampal CA1 stably across several days. These large-scale simultaneous optical and electrical recordings showed that local hippocampal sharp wave ripples (SWRs) are associated with synchronous calcium events involving large neural populations in CA1. We show that SWRs exhibit spatiotemporal wave patterns along multiple axes in 2D space with different spatial extents (local or global) and temporal propagation modes (stationary or travelling). Notably, distinct SWR wave patterns were associated with, and decoded from, the selective recruitment of orthogonal CA1 cell assemblies. These results suggest that the diversity in the anatomical progression of SWRs may serve as a mechanism for the selective activation of the unique hippocampal cell assemblies extensively implicated in the encoding of distinct memories. Through these results we demonstrate the utility of the E-Cannula as a versatile neurotechnology with the potential for future integration with other optical components such as green lenses, fibers or prisms enabling the multi-modal investigation of cross-time scale population-level neural dynamics across brain regions.

Designing a Financial Mechanism for a “Technological Breakthrough”. How to “Format” Own Ecosystems so That Other People's Digital Devices and Financiers Should Not “Format” Us

Acceleration of technological and institutional development results in reduced lags between innovations and their installation in the economy and society, which modifies long-wave patterns (but doesn't cancel them). In this regard, the question arises on the possibility of a "Russian economic miracle" on a new financial and digital basis. This is a question about ecosystems (digital platforms — a relatively recent complex financial and production innovation), the prototypes of which, however, have already been in history. Historical studies of protoecosystems and modern ecosystems, addressed by the author, allow us to answer the question: “ecosystem” (convergent) technologies are a factor undermining macroeconomic stability in the interests of a narrow circle of global and local players and (or) a mechanism for changing technological and institutional patterns (?!).