Mode selection mechanism in traveling and standing waves revealed by Min wave reconstituted in artificial cells

Reaction-diffusion coupling (RDc) generates spatiotemporal patterns, including two dynamic wave modes: traveling and standing waves. Although mode selection plays a significant role in the spatiotemporal organization of living cell molecules, the mechanism for selecting each wave mode remains elusive. Here, we investigated a wave mode selection mechanism using Min waves reconstituted in artificial cells, emerged by the RDc of MinD and MinE. Our experiments and theoretical analysis revealed that the balance of membrane binding and dissociation from the membrane of MinD determines the mode selection of the Min wave. We successfully demonstrated that the transition of the wave modes can be regulated by controlling this balance and found hysteresis characteristics in the wave mode transition. These findings highlight a novel role of the balance between activators and inhibitors as a determinant of the mode selection of waves by RDc and depict a novel mechanism in intracellular spatiotemporal pattern formations.

The physics remote laboratory: Implementation of an experiment on Standing Waves

There always have been some hurdles when it comes to the adequate use of didactical experimental activities in science education, such as the lack of proper training, insufficient time, and inadequate infrastructure. At this very moment, the pandemic has taught us that there may be also circumstances in which the traditional laboratory and the traditional activities are just not possible, thus online operable experiments might constitute a viable alternative for the practical lessons in higher education. In this paper, we discuss the development and the implementation of a remote-controlled didactical experiment on Standing Waves largely used in the physics basic program offered to the engineering courses. The development has combined applied knowledge from different areas, i.e. electric and electronics engineering, and computer science. In order to ascertain the experiment consistency, we have gathered data from the wave propagation speed and from the corresponding tension applied to the string and performed a χ-square linear fit in order to determine the correlation between the logarithm of both parameters. The experiment was successfully implemented and has been accessed by hundreds of different users from more than 30 different countries ever since. It has also been largely employed in practical activities at the university and has shown no significant signs of instability. It exhibited a total latency time inferior to 0.8 seconds on average and the results drawn from data it provides have shown to be accurate, within less than 0.8% of deviation with respect to the theoretical results.

Resonant waves drive long-range correlations in fMRI signals

The fundamental principles driving spontaneous long-range correlations between distant brain areas - known as intrinsic functional connectivity - remain unclear. To investigate this, we develop an ultrafast functional Magnetic Resonance Imaging (fMRI) approach with unprecedented temporal resolution (38 milliseconds) in the rat brain. We detect a repertoire of principal components exhibiting standing wave properties, i.e., with phase relationships varying gradually across space and oscillating in time, driving in- and anti-phase synchronization across distinct cortical and subcortical structures. The spatial configuration, stability and peak frequency of these standing waves is found to depend on the sedation/anaesthesia state, with medetomidine sedation revealing the most stable (i.e., less damped) standing waves, resonating at frequencies extending up to 0.25 Hz. Our findings show that the complex activity patterns observed in resting-state fMRI signals result from the superposition of standing waves, supporting the hypothesis that intrinsic functional connectivity is inherently associated to resonance phenomena.

Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ( $\eta =2A/\lambda _{a}$ ); the product of the fluid relaxation time times the angular frequency known as the Deborah number ( $De=\lambda _{1}\omega$ ); the aspect ratio between the microchannel height and the wavelength ( $\epsilon =2 H_{0}/\lambda _{a}$ ); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ( $\alpha =H_{0}/\delta _{\nu }$ ). In the limit when $\eta \ll 1$ , we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$ , and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$ . Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.

Existence of stable standing waves for the nonlinear Schrödinger equation with attractive inverse-power potentials

<abstract><p>In this paper, we consider the following nonlinear Schrödinger equation with attractive inverse-power potentials</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ i\partial_t\psi+\Delta\psi+\gamma|x|^{-\sigma}\psi+|\psi|^\alpha\psi = 0, \; \; \; (t, x)\in\mathbb{R}\times\mathbb{R}^N, $\end{document} </tex-math></disp-formula></p> <p>where $ N\geq3 $, $ 0 &lt; \gamma &lt; \infty $, $ 0 &lt; \sigma &lt; 2 $ and $ \frac{4}{N} &lt; \alpha &lt; \frac{4}{N-2} $. By using the concentration compactness principle and considering a local minimization problem, we prove that there exists a $ \gamma_0 &gt; 0 $ sufficiently small such that $ 0 &lt; \gamma &lt; \gamma_0 $ and for any $ a\in(0, a_0) $, there exist stable standing waves for the problem in the $ L^2 $-supercritical case. Our results are complement to the result of Li-Zhao in ^{[<xref ref-type="bibr" rid="b23">23</xref>]}.</p></abstract>

Upper tropospheric energetics of standing eddies In wave number domain during contrasting Monsoon activity over India

The upper tropospheric energetics of the standing eddies in wave number domain during contrasting monsoon' activity over India have been investigated. Two normal monsoon years (1970. 1971) and two drought monsoon years (1972, 1979) are considered for a comparative study, Energy equations of Saltzman (1957) are used to compute wave-wave Interaction and wave to zonal mean flow Interaction. Analysis of the results show that the standing eddies in the region of tropical easterlies (5°S-24 .2°N) have larger kinetic energy than those in the region of southern hemispheric, westerlies (24.2°S-5°S). Wave to zonal mean flow interaction of all waves (waves 1-15) Indicate that the standing eddies are a source of kinetic energy to zonal mean flow ID the region of easterlies and there sink of kinetic energy to zonal mean flow in the region of westerlies. In the region of easterlies planetary standing waves (waves 1-2) are the major kinetic energy source to other standing waves and wave-wave Interaction of all waves leads to positive Imbalance of kinetic energy during normal monsoon years (1970, 1971) and negative imbalance, of kinetic, energy during drought monsoon years (1972, 19~9). In the region of westerlies the imbalance of kinetic energy IS negative during normal monsoon years and positive during drought monsoon years.

Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction

In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.

Chladni Figures Simulation on a Rectangular Plate

An analytical model for creating flat Chladni figures is presented. The equation of a standing wave in the simplest boundary conditions and the Fourier transform are used. Top view images are shown at different frequencies. The practical significance of the results obtained for the further development of the field of creating Chladni figures based on standing waves of different physical nature has been determined.

Energetics of the lower tropospheric eddies in wave number domain during northern summer monsoon

Lower tropospheric energetics and energy processes of zonal waves for three consecutive northern summer monsoon seasons of 1994, 1995 and 1996 are presented. Fourier technique is used. The features of the tropical and extra-tropical regions are very well reflected by the data set used for this study. The results do not show marked year to year variations in the pattern of energy processes. The character of energy processes differs significantly from one latitudinal region to other. Wave to zonal mean flow interactions and wave to wave interactions are almost opposite in character over R1 (10° S -10° N) and R2 (10° N -30° N). L (n) interaction indicates that R1 acts as source of kinetic energy to the waves over R2. Particularly, standing waves I and 2 over RI are the major source of kinetic energy to the waves over R2. Extra-tropical region R3 (30° N -50° N) is dominated by transient waves while tropical regions R1 and R2 are dominated by standing waves. Medium and short waves have significant contributions over extra-tropical region whereas tropical regions are dominated by long waves. The pattern of energy processes over R3 is somewhat similar to the energy processes over R1. This is because both the regions have anti-cyclonic lateral shear.

Nodal Multi-peak Standing Waves of Fourth-Order Schrödinger Equations with Mixed Dispersion

We consider the existence and concentration properties of standing waves for a fourth-order Schrödinger equation with mixed dispersion, which was introduced to regularize and stabilize solutions to the classical time-dependent Schrödinger equation. This leads to study multi-peak solutions to the following singularly perturbed fourth-order nonlinear Schrödinger equation $$\begin{aligned} {\varepsilon ^{\text {4}}}{\Delta ^{\text {2}}}u - \beta {\varepsilon ^2}\Delta u + V(x)u = |u{|^{p - 2}}u{\text { in }}{\mathbb {R}^N},{\text { }}u \in {H^2}({\mathbb {R}^N}). \end{aligned}$$ ε 4 Δ 2 u - β ε 2 Δ u + V ( x ) u = | u | p - 2 u in R N , u ∈ H 2 ( R N ) . We first establish a local $${W^{4,p}}$$ W 4 , p -estimate for a class of fourth-order semilinear elliptic equations, which is a key to get the uniform and global $${L^\infty }$$ L ∞ -estimate of solutions to the considered singularly perturbed equation above. Next, under certain assumptions on $$\beta $$ β and the potential V(x), we construct a family of sign-changing multi-peak solutions with a unique maximum (or minimum) point on each component. We prove that these solutions concentrate around any prescribed finite set of local minima (possibly degenerate) of the potential V(x). Compared with the classical singularly perturbed Schrödinger equation, the presence of a fourth-order term in the problem above forces the development of new techniques to obtain qualitative properties of multi-peak solutions.