Target Waves Research Articles

Thermosensitive double-membrane neurons and their network dynamics

Abstract Cell membrane of biological neurons has distinct geometric structure, and involvement of diffusive term is suitable to estimate the spatial effect of cell membrane on neural activities. The gradient field diversity between two sides of the cell membrane can be approached by using a double-layer membrane model for the neuron. Therefore, two capacitive variables and diffusive terms are used to investigate the neural activities of cell membrane, and the local kinetics is described by a functional circuit composed of two capacitors. The voltages for the two parallel capacitors describe the inner and outer membrane potentials, and the diffusive effect of ions is considered on the membrane surface. The results reveal that neural activities are relative to the capacitance ratio between the inside and outside of the membrane and diffusive coefficient. High-energy periodic external stimulation induces the target waves to spread uniformly, while low-energy chaotic stimulation results in wave fragmentation. Furthermore, when the capacitance ratio exhibits exponential growth under an adaptive control law, the resulting energy gradient within the network induces stable target waves. That is, energy distribution affects the wave propagation and pattern formation in the neuron. The result indicates that the spatial diffusive effect and capacitance diversity between outer and inner cell membranes are important for selection of firing patterns and signal processing during neural activities. This model is more suitable to estimate neural activities than using generic oscillator-like or map neurons without considering the spatial diffusive effect.

An adaptive internal mass source wave-maker for short wave generation

The mass source wave-maker is commonly employed for generating water waves in numerical simulations, during which a correct amount of mass is introduced or subtracted from the internal flow region to produce target waves. The method has proven to be effective in producing waves in shallow and intermediate water depths, while its efficiency is declined for short wave generation. The main reason for this efficiency declination is that the internal mass source in deeper water region is not effective to generate short waves with their motions primarily on water surface. In order to overcome this shortcoming, many of the previous numerical treatments have introduced various enhancement factors into the source functions, which are empirically obtained and also violate the law of mass conservation. In this study, we develop a new adaptive internal wave-maker model that can be self-adjusted to suit different wave conditions. The line source starts from the bottom and extends to the computational cell right beneath free surface at each time step. The depth dependent weighting coefficient is introduced to the source function based on the linear wave theory for each wave component. No empirical coefficients are necessary, and the mass conservation is strictly and explicitly enforced. In principle, the method can be applied to all types of linear waves in the entire range of kh. The numerical experiments show that the present method can produce very good results for linear waves with kh up to 16.11, adequate for most of wave conditions in coastal engineering. For generation of fifth-order Stokes waves, the method can be extended straightforwardly for each of five wave components. For irregular waves composed of many linear wave components, different weighting coefficients can be readily calculated for each of them, respectively. As a result, the new model can generate irregular waves with overall better performance of reproducing wave spectrum, whose high-frequency part has been underestimated by previous methods. The numerical experiments also show that the new model can produce better results for focused waves where many linear waves of different frequencies start from the same point with specific phase angles, due to its capability of generating shorter wave components.

Study of the acoustic transmission characteristics of a pipe opening with a baffle considering structural elasticity

Noise can radiate to the external environment through pipe openings. The acoustic transmission characteristics of the pipe openings greatly affect the efficiency of sound radiation. In fluid-filled elastic pipelines, the sound radiation is significantly influenced by the coupling between the fluid and the elastic structure. The elastic structure studied in this paper includes the pipe wall, as well as the baffle attached to it. Waveguide analysis of fluid-filled elastic pipelines shows that the coupling results in the presence of several types of propagating waves within the pipeline, even bellow the cut-on frequency. To evaluate the acoustic transmission characteristics of the pipe opening, it is necessary to separate the components of the lowest-order fluid type wave from these waves. A multi-case approach is developed to separate the target waves successfully, thereby obtaining the characteristics of the pipe opening. The accuracy of the proposed method is verified, and the impact of structural elasticity is analyzed. Subsequently, the effects of the dimensions of the baffle are discussed.

Symmetry Breaking of Three Self-Organization Rules: A General Theory for the Origin of Complexity

Complex spatiotemporal patterns in nature significantly challenge reductionism-based modern science. The lack of a paradigm beyond reductionism hinders our understanding of the emergence of complexity. The diversity of countless patterns undermines any notion of universal mechanisms. Here, however, we show that breaking the symmetry of three simple and self-organization rules gives rise to nearly all patterns in nature, such as a wide variety of Turing patterns, fractals, spiral, target and plane waves, as well as chaotic patterns. The symmetry breaking is rooted in the basic physical quantities, such as positive and negative forces, space, time and bounds. Besides reproducing the hallmarks of complexity, we discover some novel phenomena, such as abrupt percolation of Turing patterns, phase transition between fractals and chaos, chaotic edge in traveling waves, etc. Our asymmetric self-organization theory established a simple and unified framework for the origin of complexity in all fields, and unveiled a deep relationship between the first principles of physics and the complex world.

Incident component extraction from disturbed waves around large fixed cylindrical structures

The parameters of incident waves are critical for real-time wave load estimation of structures in service. Nonetheless, it is challenging to characterize incident waves accurately using the measured wave surface elevation around large fixed cylindrical structures due to the interaction with the structure in the wave field. To provide a better understanding of incident waves, which are usually buried in directly measured waves, a new time-domain method for the extraction of first-order and second-order incident waves around large fixed cylindrical structures is proposed. In contrast to most existing separation methods that are suitable for structures with equal reflection coefficients, the amplitude and phase changes of near-field waves around cylindrical structures can be determined by considering the significant diffraction effect, and then the time-frequency characteristic of the wavelet transform is employed, which enables the extraction of incident waves in the time domain. The accuracy of the proposed method is studied using several examples with known incident waves which are generated with the OpenFOAM. The numerical results show that the deviations between the exact and extracted incident waves change from 6.16% to 16.77% for different wave conditions. To further investigate the performance of the proposed method, an experimental study on waves around a mono-pile offshore wind turbine (OWT) is conducted in the laboratory of the Ocean University of China. The predicted results basically agree well with the target waves in terms of amplitude and phase. The deviations between predicted waves using the proposed method and target waves are 110% smaller than those between directly experimental measured waves and target waves for all tested conditions. Finally, 48 h of measured wave data were obtained during calm and typhoon periods around a mono-pile OWT located near Rudong County, Jiangsu Province, in the Yellow Sea of China. There are almost 150% and 30% differences between the extraction results and measured data in the time series and statistical wave heights, respectively, which means that employing disturbed wave data as the input for calculating real-time wave loads leads to deviations that cannot be ignored.

A possible new cardiac heterogeneity as an arrhythmogenic driver

Atrial fibrillation (AF) is the commonest cardiac arrhythmia, affecting 3 million people in the USA and 8 million in the EU (according to the European Society of Cardiology). So, why is it that even with the best medical care, around a third of the patients are treatment resistant. Extensive research of its etiology showed that AF and its mechanisms are still debatable. Some of the AF origins are ascribed to functional and ionic heterogeneities of the heart tissue and possibly to additional triggering agents. But, have all AF origins been detected? Are all accepted origins, in fact, arrhythmogenic? In order to study these questions and specifically to check our new idea of intermittency as an arrhythmogenesis agent, we chose to employ a mathematical model which was as simple as possible, but which could still be used to observe the basic network processes of AF development. At this point we were not interested in the detailed ionic propagations nor in the actual shapes of the induced action potentials (APs) during the AF outbreaks. The model was checked by its ability to exactly recapture the basic AF developmental stages known from experimental cardiac observations and from more elaborate mathematical models. We use a simple cellular automata 2D mathematical model of N × N matrices to elucidate the field processes leading to AF in a tissue riddled with randomly distributed heterogeneities of different types, under sinus node operation, simulated by an initial line of briefly stimulated cells inducing a propagating wave, and with or without an additional active ectopic action potential pulse, in turn simulated by a transitory operation of a specific cell. Arrhythmogenic contributions, of three different types of local heterogeneities in myocytes and their collaborations, in inducing AF are examined. These are: a heterogeneity created by diffuse fibrosis, a heterogeneity created by myocytes having different refractory periods, and a new heterogeneity type, created by intermittent operation of some myocytes. The developmental stages (target waves and spirals) and the different probabilities of AF occurring under each condition, are shown. This model was established as being capable of reproducing the known AF origins and their basic development stages, and in addition has shown: (1) That diffuse fibrosis on its own is not arrhythmogenic but in combination with other arrhythmogenic agents it can either enhance or limit AF. (2) In general, combinations of heterogeneities can act synergistically, and, most importantly, (3) The new type of intermittency heterogeneity proves to be extremely arrhythmogenic. Both the intermittency risk and the fibrosis role in AF generation were established. Knowledge of the character of these arrhythmogenesis agents can be of real importance in AF treatment.

Patterns stability in cardiac tissue under spatial electromagnetic radiation

The electric activity in myocardial tissue is controlled by the target waves emitted from the sinoatrial node and then the Calcium flow is controlled to regulate the heartbeat. The occurrence of local defects can block the wave propagation in the cardiac tissue and then the heartbeat can be disturbed completely. During the electrophysiological activity including stochastic diffusion of intracellular ions and continuous exchange of extracellular ions along ion channel embedded in the cell membrane, electromagnetic induction occurs in the cardiac tissue and the involvement of external electromagnetic radiation can change the excitability and the neural activities. In this paper, based on a memristive cardiac tissue model by incorporating magnetic flux variable and induction current into the two-variable cardiac model for discerning cardiac excitation, spatial electromagnetic radiation is applied to investigate the stability and propagation of waves in the cardiac tissue. Wave propagation in the reaction-diffusion equations for cardiac tissue is approached by an equivalent diffusive neural network on square array after discretization. Local heterogeneity is produced by introducing diversity in initial value for inducing spiral seed, and stable spiral waves are developed as initial states, which represent tachycardia and arrhythmia in the cardiac tissue. It is found that symmetric spatial patterns can be controlled by the external electromagnetic radiation, in particular, nonlinear resonance is enhanced and specific spatial patterns are developed under noisy radiation.

Formation of local heterogeneity under energy collection in neural networks

Static distribution of intracellular and extracellular ions can induce the spatial distribution of electric field in the cell, while stochastic diffusion and propagation of ions can generate channel current accompanied by the magnetic field. In fact, the field energy (including magnetic and electric fields) in each cell or neuron can be changed under external stimuli or the deformation of shape. Furthermore, energy pumping occurs, and the synaptic connection is created adaptively to keep energy balance when more neurons are clustered in the same region because of electromagnetic field superposition. For a synchronous and homogeneous network, all neurons keep energy balance with the adjacent neurons, and the network becomes uniform and identical. For cardiac tissue and biological media, local heterogeneity such as sinoatrial node can emit continuous wave front, and target waves are propagated to regulate the neural activities and heartbeat rhythm. In this paper, the Hamilton energy in a simple neuron model is calculated according to the Helmholtz theorem, and more neurons are clustered to build a regular network (chain network and square array). The creation and growth of synapse connection are controlled to pump energy, and local heterogeneity is formed by taming one intrinsic parameter when more energy is accumulated in a few neurons in the network. These results indicate that asymmetrical energy transport will induce the occurrence of heterogeneity in the network, and adaptive synaptic regulation on neurons is activated to keep local energy balance before reaching perfect synchronization. When external stimuli with diversity in intensity are applied, neurons are excited with energy diversity, and possible shape deformation is induced to keep local energy balance. As a result, heterogeneity is developed in a local area.

Numerical investigation of wave amplitude spectra effects on focusing wave generation

Focusing waves are often considered as an effective simulation of freak waves observed in oceans, or extreme sea states for marine structures design. The understanding of factors in generating prescribed focusing wave is of great importance for its generation in both numerical and physical wave tank. Based on the fully nonlinear potential theory solved by the QALE-FEM, this paper numerically investigates the effect of wave amplitude distribution over the frequency band under a series of the crest elevation parameters and frequency ranges on focusing wave generation, including focusing wave crest elevations and focusing positions. The results suggest that focusing wave crest elevation is significantly affected by the wave amplitude distribution especially for target waves with large wave crests or those are assigned at low frequency domain. Moreover, generation positions of focusing wave are also strongly correlated to amplitude spectra through phase shift of the wave surface and wave nonlinearity denoted by wave steepness.

Frequency modes of unstable spiral waves in two-dimensional Rosenzweig–MacArthur ecological networks

The existence of two frequency regimes in a two-dimensional (2D) Rosenzweig–MacArthur ecological network is debated. The semi-discrete approximation differentiates the two regimes, each described by a 2D complex Ginzburg–Landau equation. Using the standard theory of the linear stability analysis, a generalized expression for the modulational instability growth rate is derived for each frequency mode. The parametric study of the growth rate of modulational instability reveals its sensitivity to the changes in the recruitment rate of the resources. Moreover, direct numerical simulations are carried out to confirm our analytical results. Over the prolonged evolution of the perturbed plane wave solution, the high-frequency mode entertains spiral wave patterns. In contrast, the appearance of target waves manifests the low-frequency regime. In that context, we further explore the impact of the recruitment rate of resources and give the qualitative meaning of the obtained dynamical behaviors and their ecological implications. This work may additionally provide more insight into the mechanism leading to spiral and target waves in environmental systems.

Non-Hermitian quantum-like cascaded nonlinear optical frequency conversion and splitting in dissipative media

It is shown that cascaded nonlinear optical frequency conversion over an intermediate wavelength, subjected to dissipation, behaves similarly to population transfer via a decaying state in a three-state non-Hermitian quantum system. The intermediate dissipation leads to a fixed phase relationship between the input signal wave and the wave at the target frequency, what finally stabilizes both waves preventing any spatial oscillation of their powers. The cascaded conversion acts as a stable wave splitter between the input and target waves, the latter being nearly immune to power fluctuations of the pumps. A case of a simultaneous cascade of the sum frequency generation and the difference frequency generation processes is discussed as an example. A possible implementation, based on aperiodically engineered quasi-phase-matching in lithium niobate, is proposed.

Heteroclinic units acting as pacemakers: entrained dynamics for cognitive processes

Heteroclinic dynamics is a suitable framework for describing transient and reproducible dynamics such as cognitive processes in the brain. We demonstrate how heteroclinic units can act as pacemakers to entrain larger sets of units from a resting state to hierarchical heteroclinic motion that is able to describe fast oscillations modulated by slow oscillations. Such features are observed in brain dynamics. The entrainment range depends on the type of coupling, the spatial location of the pacemaker and the individual bifurcation parameters of the pacemaker and the driven units. Noise as well as a small back-coupling to the pacemaker facilitate synchronization. Units can be synchronously entrained to different temporal patterns encoding transiently excited neural populations, depending on the selected path in the heteroclinic network. Via entrainment, these temporal patterns, locally generated by the pacemakers, can be communicated to the resting units in target waves over a spatial grid. For getting entrained there is no need of fine-tuning the parameters of the resting units. Thus, entrainment provides one way of processing information over the grid, when information is encoded in the generated spatiotemporal patterns.

Different Mechanisms of Pattern Formation in a Plankton Model with Cross-Diffusion and Fitness

Pattern formation is a ubiquitous phenomenon encountered in various nonequilibrium physical, chemical and biological systems. The resulting spatiotemporal patterns as well as their characteristics are often determined by the type of instability. However, when different instabilities occur simultaneously, the generated pattern formation cannot be expected to be a simple superposition of patterns. To address this issue, we study spatiotemporal dynamics driven by different mechanisms in a reaction–advection–diffusion plankton model. Linear stability analysis is performed upon the uniform steady state to identify conditions for the predator–prey interaction driven, taxis-diffusion driven and cross-diffusion-driven instabilities. For the cross-diffusion-driven instability, we employ weakly nonlinear analysis to derive amplitude equations, which helps to predict the type of patterns turning out to emerge with parameters that are varying. Theoretical results are verified by numerical simulations, and some interesting patterns including spiral and target waves are also numerically observed.

Spiral waves and their characterization through spatioperiod and spatioenergy under distinct excitable media

The external periodic stimulus is typically used to activate each cell in an excitable media which in turn triggers the stable pulse or target waves in the network. In this work, the spatiotemporal pattern in excitable media is investigated by applying a periodic stimulus to a specific cell site. To do so, three distinct arrays of single-layer networks, namely the modified Hindmarsh-Rose neuron, the hybrid neuron, and the Morris-Lecar neuron models are considered. The existence of spiral waves and their characteristics are studied with periodic excitation. We considered the modified Hindmarsh-Rose neuron model, hybrid neuron, and Morris-Lecar neuron model for the investigation. The results obtained are highlighting the existence of disordered broken spiral seeds at low coupling values and the formation of spiral waves as coupling strength increased to higher levels. Importantly, the characteristics of the nodes in the network are manifested using the spatioperiod and spatioenergy. Furthermore, we discover that the core of the spiral has low excitability and energy when compared to the other nodes in the spiral. Notably, the spatioenergy clearly shows the actual position of the spiral core. Finally, we confirmed the spatiotemporal patterns and their characteristics by extending the network to the two and three-layer Morris-Lecar neural systems.

An experiment on reconstruction and analyses of in-situ measured freak waves

Freak waves are destructive to marine and offshore structures, but their generation mechanisms are still unclear. To explore the possible generation mechanism of freak waves, some in-situ measured waves are reconstructed in a wave flume at model scale. To generate high-quality target waves, a modified time reversal (TR) method including a correction step is proposed. Five scaled in-situ measured waves, containing three freak waves and two non-freak waves, are reconstructed successfully.As reconstructed waves provide good agreement with the scaled in-situ measured waves, their formation mechanisms are analyzed by applying various dispersion relations. The results show the key contributions of the dispersive focusing in the freak wave formation. Then, to explore the nonlinear interactions of the quadratic order of these reconstructed waves, the wavelet-based bicoherence and its total bicoherence are presented, and large surface elevations are found to be related to high total bicoherences, indicating inescapable effects of wave-wave interactions in the wave formation. Furthermore, a phase coincidence level F is proposed to evaluate the phase coincidence level of these reconstructed waves. The results show that a low F (high phase focus level) means a high wave height, while a high wave height does not always exhibit a low F.

A graphene-based THz wave duplexer and filter: Switching via gate biasing

This work introduces a Graphene-based multi-layer reconfigurable device as a wave duplexer in the THz frequency range. Adjusting transmitting and reflecting parts of incident waves alongside controlling absorption provides the interesting capability to select target waves in different frequencies. The proposed device includes periodic graphene patterns on both sides of silicon dioxide as substrate. Additionally, the patterns are biased differently compared to conventional patterns which makes it possible to achieve two distinct behaviors versus frequency. Exploiting equivalent circuit models (ECM) for graphene and dielectric, the whole device is modeled by passive RLC circuits. According to simulation results, the proposed device can transmit and reflect incident THz waves at desired frequencies in 0.1–30 THz which makes it an ideal candidate for manipulating THz waves in terms of transmission and reflection.

Pattern selection in thermosensitive neuron network induced by noise

It is well known that the firing modes of biological neurons are sensitive to slight temperature changes in their environments. In this paper, a type of noise, which is dependent on temperature changes, is introduced to describe the effect of varying external environments. The effect of this type of noise on the mode transition of the collective dynamical behaviors of coupled thermosensitive neurons in a regular network is investigated. In the simulation, noise is imposed on the network in two ways: on the center area and on the boundary of the network. The results show that the target waves could be induced with noise being imposed on the center area of the network, and traveling waves could be generated with noise imposed on the boundary region of the network. All these results verify that noise could regulate the modes’ transitions of the collective electrical activities in the network, transforming them from synchronization to another ordered collective dynamics type (target wave or traveling wave). Furthermore, the synchronization factors for two cases are calculated, and the results confirm that noise could make network become from high order to low order, but it cannot transform it from low to high order.

Spatiotemporal characteristics in systems of diffusively coupled excitable slow-fast FitzHugh-Rinzel dynamical neurons.

In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the formation of spatiotemporal patterns. We focus on local, nonlinear excitations and diverse neural responses in an excitable one- and two-dimensional configuration of diffusively coupled FitzHugh-Rinzel neurons. The study of the emerging spatiotemporal patterns is essential in understanding the working mechanism in different brain areas. We derive analytically the coefficients of the amplitude equations in the vicinity of Hopf bifurcations and characterize various patterns, including spirals exhibiting complex geometric substructures. Furthermore, we derive analytically the condition for the development of antispirals in the neighborhood of the bifurcation point. The emergence of broken target waves can be observed to form spiral-like profiles. The spatial dynamics of the excitable system exhibits two- and multi-arm spirals for small diffusive couplings. Our results reveal a multitude of neural excitabilities and possible conditions for the emergence of spiral-wave formation. Finally, we show that the coupled excitable systems with different firing characteristics participate in a collective behavior that may contribute significantly to irregular neural dynamics.

Applying a global pulse disturbance to eliminate spiral waves in models of cardiac muscle* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11875042 and 11505114), and the Shanghai project for construction of top disciplines (Grant No. USST-SYS01).

Removal of spiral waves in cardiac muscle is necessary because of their threat to life. Common methods for this removal are to apply a local disturbance to the media, such as a periodic forcing. However, most of these methods accelerate the beating of the cardiac muscle, resulting in the aggravation of the ventricular tachycardia, which directly threatens life. In the present study, in order to clear off spiral waves, a global pulse-disturbance is applied to the media based on three models of cardiac muscle. It is found that the spiral waves are eliminated and the frequency of the cardiac muscle is decreased in a short time, and finally, the state of the medium reaches the normal oscillation, which supports a target waves. Our method sheds light on the removal of spiral waves in cardiac muscle and can prevent the ventricular tachycardia as well as the ventricular fibrillation.x

A generalized second-order 3D theory for coupling multidirectional wave propagation from a numerical model to a physical model. Part II: Experimental validation using an I-shaped segmented wavemaker

This paper provides the experimental validation of the generalized second-order three-dimensional (3D) coupling theory outlined by Yang et al. [Z. Yang, S. Liu, X. Ji, and H.B. Bingham, 2020. A generalized second-order 3D theory for coupling multidirectional nonlinear wave propagation from a numerical model to a physical model. Part I: Derivation, implementation and model verification, submitted for publication] using multidirectional nonlinear 3D irregular waves. Based on the second-order theory for two-dimensional (2D) irregular waves described by Yang et al. (2014a), this work provides a second-order dispersive correction for the physical wavemaker signal which improves the nonlinear 3D wave information transfer between the numerical and physical models compared to the first-order method of Zhang et al. (2007). The important coupling equation and its discretization schemes were presented in detail in Part I. For further validating the performance of the second-order 3D coupling model under complex waves and bathymetry conditions, in this Part II, a careful experimental validation has been carried out by establishing a flat coupling basin and a concave-convex coupling basin. In addition, a sequence of progressively more complex numerical target waves has been used and an I-shaped segmented piston-type wavemaker system has been considered for verification of the theory. The effectiveness, adaptability, and precision of the second-order 3D coupling model have been discussed in detail. The effects of the wave parameters and its nonlinearity on the coupling simulation have also been evaluated from the discrepancy error and a wave harmonic analysis. By defining a space synchronization error, the overall error of the spatial wave field has been analyzed. Coupling simulation experiments using oblique regular and irregular waves, unidirectional irregular waves, and multidirectional irregular waves show that the traditional first-order coupling model has limitations when coupling complex waves with strong nonlinearity. When controlling the waves using the second-order 3D coupling signal, the higher harmonics underlying the numerical waves are accurately captured and transferred into the physical model, and the unwanted second-order spurious free waves are substantially reduced. Results obtained from the experimental verification described in this paper demonstrate the strengths of the second-order 3D coupling theory, which are more evident with increased wave nonlinearity.