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We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions to a generalized breaking soliton system by the Hirota bilinear form and a mixture of exponentials and trigonometric functions are presented. Periodic-soliton, breather wave and periodic are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of double-periodic soliton and breather wave solutions are explained all right. The findings demonstrate the investigated model's broad variety of explicit solutions. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering. [ABSTRACT FROM AUTHOR]

Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator–prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive analysis of a nonlinear telecommunications model, exploring bifurcation, stability, and wave solutions using Hamiltonian and Jacobian techniques. The investigation begins with a thorough examination of bifurcation behavior, identifying critical points and their stability characteristics, leading to the discovery of diverse bifurcation scenarios. The stability of critical points is further assessed through graphical and numerical methods, highlighting the sensitivity to parameter variations. The study delves into the derivation of both numerical and analytical wave solutions, aligning them with energy orbits depicted in phase portraits, revealing a spectrum of wave behaviors. Additionally, the analysis extends to traveling wave solutions, providing insights into wave propagation dynamics. Notably, the study underscores the efficacy of the planar dynamical approach in capturing system behavior in harmony with phase portrait orbits. The findings have significant implications for telecommunications engineers and researchers, offering insights into system behavior, stability, and signal propagation, ultimately advancing our understanding of complex nonlinear dynamics in telecommunications networks. [ABSTRACT FROM AUTHOR]

Understanding the propagation of invasive plants at the beginning of invasive spread is important as it can help practitioners eradicate harmful species more efficiently. In our work the propagation regime of the invasive plant species is studied at the short-time scale before a travelling wave is established and advances into space at a constant speed. The integro-difference framework has been employed to deal with a stage-structured population, and a short-distance dispersal mode has been considered in the homogeneous environment and when a road presents in the landscape. It is explained in the paper how nonlinear spatio-temporal dynamics arise in a transient regime where the propagation speed depends on the detection threshold population density. Furthermore, we investigate the question of whether the transient dynamics become different when the homogeneous landscape is transformed into the heterogeneous one. It is shown in the paper how invasion slows down in a transient regime in the presence of a road. [ABSTRACT FROM AUTHOR]

We study traveling wave solutions for a reaction–diffusion model, introduced in the article Calvez et al. (Regime switching on the propagation speed of travelling waves of some size-structured myxobacteriapopulation models, 2023), describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely, a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted by k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to + ∞ . For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio θ ⋆ between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below θ ⋆ , the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above the critical threshold, the critical spreading speed becomes strictly greater than the linear speed. [ABSTRACT FROM AUTHOR]

We focused on solitonic phenomena in substrate-supported graphene sheets by learning the solitons of fractional thermophoretic motion equation, which was extracted from wrinkle wave motions. By utilizing the analytical technique and selecting suitably the improved tan (ϕ / 2) -expansion method involved in the nonlinear ODE form, the new exact solutions are attained. Soliton, bright–dark soliton and periodic are studied with usage of symbolic computation. In addition, more symbolic computation by transformed to ODE for governing model is considered. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of single soliton and periodic wave solutions are explained all right. The findings demonstrate the investigated model’s broad variety of explicit solutions. As a result, the exact solitary wave solutions to the studied issues, including solitary, single soliton, and periodic wave solution are found. It is shown that the Paul-Painlevé approach is practical and flexible in mathematical physics. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering. [ABSTRACT FROM AUTHOR]

Abstract We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions to a generalized breaking soliton system by the Hirota bilinear form and a mixture of exponentials and trigonometric functions are presented. Periodic-soliton, breather wave and periodic are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of double-periodic soliton and breather wave solutions are explained all right. The findings demonstrate the investigated model’s broad variety of explicit solutions. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering.

Abstract This study presents a comprehensive analysis of a nonlinear telecommunications model, exploring bifurcation, stability, and wave solutions using Hamiltonian and Jacobian techniques. The investigation begins with a thorough examination of bifurcation behavior, identifying critical points and their stability characteristics, leading to the discovery of diverse bifurcation scenarios. The stability of critical points is further assessed through graphical and numerical methods, highlighting the sensitivity to parameter variations. The study delves into the derivation of both numerical and analytical wave solutions, aligning them with energy orbits depicted in phase portraits, revealing a spectrum of wave behaviors. Additionally, the analysis extends to traveling wave solutions, providing insights into wave propagation dynamics. Notably, the study underscores the efficacy of the planar dynamical approach in capturing system behavior in harmony with phase portrait orbits. The findings have significant implications for telecommunications engineers and researchers, offering insights into system behavior, stability, and signal propagation, ultimately advancing our understanding of complex nonlinear dynamics in telecommunications networks.

• Alpha oscillations propagate anterior-to-posterior in healthy controls in a behavioral task. • The propagation of alpha oscillations is disrupted in patients with schizophrenia. • Our results support the disconnection syndrome hypothesis regarding schizophrenia. Propagation of electroencephalogram (EEG) oscillations, often referred to as traveling waves, reflects the role of brain oscillations in neural information transmission. This propagation can be distorted by brain disorders such as schizophrenia that features disconnection of neural information transmission (i.e., disconnection syndrome). However, this possibility of the disruption of EEG oscillation propagation in patients with schizophrenia remains largely unexplored. Using a publicly shared dataset (N = 19 and 24; patients with schizophrenia and healthy controls, respectively), we investigated EEG oscillation propagation by analyzing the local phase gradients (LPG) of alpha (8–12 Hz) oscillations in both healthy participants and patients with schizophrenia. Our results showed significant directionality in the propagation of alpha oscillations in healthy participants. Specifically, alpha oscillations propagated in an anterior-to-posterior direction along mid-line and a posterior-to-anterior direction laterally. In patients with schizophrenia, some of alpha oscillation propagation were notably disrupted, particularly in the central midline area where alpha oscillations propagated from anterior to posterior areas. Our finding lends support to the hypothesis of a disconnection syndrome in schizophrenia, underscoring a disruption in the anterior-to-posterior propagation of alpha oscillations. This study identified disruption of alpha oscillation propagation observed in scalp EEG as a biomarker for schizophrenia. [ABSTRACT FROM AUTHOR]

In this research, the solitary wave solutions, the periodic type, and single soliton solutions are attained. The coupled fractional Lakshmanan–Porsezian–Daniel (LPD) equation is depicted the wave pulses' physical properties in birefringent optical fibres containing two vector solitons. Here, the Paul–Painlevé operator is employed to investigate kink soliton solutions. Also, the new modified exponential Jacobi technique is used to find periodic wave and soliton, bright-dark soliton. By utilizing symbolic computation and the applied methods, the mentioned system is successfully investigated. The coupled fractional LPD model is exhibited the travelling waves, as shown by the research in the current paper. Through three-dimensional graph, contour graph, density graph, complex-plot, and two-dimensional design using Maple, the physical features of single soliton and periodic wave solutions are explained all right. The findings the investigated model's broad variety of explicit solutions are demonstrated. As a result, the exact solitary wave solutions to the studied issues, including solitary, single soliton, and periodic wave solution are found. It is shown that the approach is practical and flexible in mathematical physics. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the propagation dynamics of stochastic reaction–diffusion equations, including the existence of travelling wave solution and asymptotic wave speed. Based on the stochastic Feynman–Kac formula and comparison principle, the boundedness of the solution of stochastic reaction–diffusion equations can be obtained so that we can construct a sup-solution and a sub-solution to estimate the upper bound and the lower bound of wave speed. [ABSTRACT FROM AUTHOR]

This article discusses the solitons as well as additional solutions to the modified nonlinear Schrödinger equation, which appears in the study of optical waveguide and rogue waves in ocean. One theorem is analyzed and and also is investigated by obtaining one solution as exact optical soliton solution from the modified NLSE utilizing the Paul-Painlevé technique. Accurate traveling wave solutions are obtained using the generalized G-expansion equation method and the tan (ϕ / 2) -expansion method. In addition, semi-inverse variational principle method is used to finding the periodic wave, soliton and breather wave solution to mentioned nonlinear model. Restraint conditions for the occurrence of soliton and periodic wave solutions are also established. By selecting suitable values for the parameters involved in the solutions, 3D graphs, 2D density graphs and line graphs are presented to provide graphical demonstration of the results. The reported results will be helpful to design new and better optical devices. The findings of this research may also help in problems arising in ocean engineering or nonlinear optics. [ABSTRACT FROM AUTHOR]

Traveling wave rotary ultrasonic motors (TRUSMs) have been applied in optical systems, robotics, biomedical and other fields. However, the disadvantages such as short working life, driving performance degradation, and low energy utilization significantly limit the long-term and stable operation of TRUSMs in advanced fields like aerospace mechanisms. To address the above issues, a novel rotary ultrasonic motor based on multiple Langevin transducers is proposed in this paper. First, the structural design, driving principle and general design criteria are described in detail. Then, the structural parameters are optimized by finite element simulation analysis. Second, a prototype is assembled controllably. Subsequently, the impedance test and vibration measurement are carried out. The results show that the traveling wave is successfully generated on the tooth-ring, and all the Langevin transducers are excited to the first-order longitudinal vibration modes, which strongly verify the correctness of design principle. Finally, the driving performance experiment is carried out. The experimental results show that the no-load speed is 62 r min−1 under the pre-pressure of 10 N. The stalling torque is 0.94 N m at the driving voltage of 500 Vp-p. The response characteristics show that the start/stop time are 4.6/5.5 ms, and the angular displacement resolution of clockwise/counterclockwise driving are 6.7/10.2 μ rad. The motor proposed in this paper not only exhibits relatively high output performance with excellent vibration characteristics, but also maintains compactness of the structure. The sandwiched structure design effectively avoids the problem that the bonded-type piezoceramic rings in conventional TRUSMs are prone to damage or fall-off when vibrating for a long time. Furthermore, the general design criteria provide a new approach to develop high performance rotary ultrasonic motors. The proposed novel ultrasonic motor is expected to meet the demand for long-term and stable operation in aerospace mechanisms. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of beam deflection type that involves nonlinear equations with sequential Caputo fractional derivatives. Under flexible/fixed end-conditions, two main theorems on the existence and uniqueness of solutions are proved by using two fixed point theorems. Some examples are discussed to illustrate the applications of the existence and uniqueness of solution results. Another main result on the Ulam–Hyers stability of solutions for the introduced system is also discussed. Some examples of stability are discussed. New travelling wave solutions are obtained for another conformable coupled system of beam type that has a connection with the first considered system. A conclusion follows at the end. [ABSTRACT FROM AUTHOR]

This paper proposes a new solution for the classification of short-circuits in medium-voltage distribution grids. The solution requires the measurements of the phase voltages at the time of the short-circuit and the voltage amplitudes of the short-circuit wave resulting from the fault. The values of the voltage before the short-circuit are used to calculate the expected values of the short-circuit wave amplitudes for the different types of short circuits. These calculations are based on an analysis of the charge flow between the capacitances of the power line due to the disturbance. The short-time matrix pencil method was used to detect the incoming short-circuit waves. Tests of the algorithm were carried out on the IEEE 34-bus Feeder model, taking into account the influence of voltage sensors on the measured signal values. The classification algorithm uses only non-zero components due to their relatively low attenuation. Despite that, it achieves high performance in the classification of single- and two-phase short-circuits.

Far distant wind farms are integrated nowadays with the help of Voltage Source Converter (VSC)-based HVDC grids. Rapid fault current is very common in VSC-based HVDC grids and, therefore, quick fault detection and fast executing protection methods are critical for the existence of the HVDC grids. This paper proposes a rise time-based fault detection method using local measurement data and Travelling Wave (TW) characteristics of incoming fault TW. Dominating frequency of the primary wavefront is computed by the rise time of incoming fault TW. With the help of auto-updating transmission line parameters and the dominating frequency of incoming TW, the fault location is identified. The performance of the proposed method has been observed in PSCAD Simulation with a 4-Terminal HVDC test grid in multiple scenarios and compared with the existing fault detection methods on multiple levels. The results show that the proposed method is very fast, and accurate and can complete the whole Fault Location process within a few microseconds just after the Inception of the fault. [ABSTRACT FROM AUTHOR]

In this paper, the solitary wave solutions, the periodic type, and single soliton solutions are acquired. Here, the Hirota bilinear operator is employed to investigate single soliton, periodic wave solutions and the asymptotic case of periodic wave solutions. By utilizing symbolic computation and the applied method, generalized (3+1)-dimensional shallow water wave (GSWW) equation is investigated. The variational principle scheme to case periodic forms is studied. The (3+1)-GSWW model exhibits travelling waves, as shown by the research in the current paper. Through three-dimensional design, contour design, density design, and two-dimensional design using Maple, the physical features of single soliton and periodic wave solutions are explained all right. The findings demonstrate the investigated model’s broad variety of explicit solutions. As a result, exact solitary wave solutions to the studied issues, including solitary, single soliton, and periodic wave solution, are found. The phase plane is quickly examined after establishing the Hamiltonian function. The effects of wave velocity and other free factors on the wave profile are also investigated. It is shown that the approach is practical and flexible in mathematical physics. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering. [ABSTRACT FROM AUTHOR]

This work investigates the efficiency of Travelling Wave (TW) based fault detection and locationing for multi-sectional cross-bonded export cable for offshore wind farm applications. The cables, instrument transformers and the offshore wind farm are modelled according to the TW method and practical conditions. In order to correctly reflect the offshore collection grid dynamics, an aggregation method that preserves the frequency response of the wind farm impedance is implemented. The result of the EMT simulation of the developed offshore system model is played back on an actual TW relay to test the reliability of the current-based TW FDL method. A simulation of TW FDL using wavelet transform is performed to verify the relay response. Through cross-validation with the relay testing result, the paper provides another aspect of the applicability of TW relay for offshore applications.

The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as its polarization, dispersion, and interactions with other waves or boundaries. The fractional differential Duffing problem refers to the mathematical modelling of nonlinear, damped oscillations of a system with fractional derivatives. It is a generalization of the classical Duffing equation, which describes the behaviour of a nonlinear, damped oscillator (the equation becomes symmetric under time-reversal). The fractional derivatives allow for a more accurate description of the system's memory and hereditary properties. The solution of the fractional Duffing equation can provide insight into the complex dynamic behaviour of various physical, biological, and engineering systems. We are concerned with studying a new differential Duffing fractional problem. It involves some sequential Caputo derivatives with an infinite series of Riemann-Liouville integrals and some other functions. We begin by proving a first existence and uniqueness result, then we discuss two types of stability for the obtained uniqueness result. An illustrative examples is given to show the applicability of the result. We are also concerned with applying the Tanh method to obtain new classes of travelling wave solutions for three important classes of (Khalil) fractional conformable problems; the generalized equation of Duffing, the Landau-Ginzburg-Higgs equation and the Sine-Gordon one. Some numerical simulations are plotted and a conclusion is given at the end. [ABSTRACT FROM AUTHOR]

MHD flow equations are non-linear partial differential equations. In this essay,we have considered the flow of an incompressible fluid through a porous medium and have employed a strategy based on the traveling wave solution. By utilizing wave parameters, the non-linear equations are transformed into ordinary differential equations. In this approach, all the fluid parameters, initially functions of (x, y, t), are now represented by a single variable 'z' through the transformation z = bx + ay + ct. Finally, expressions for the pressure function, magnetic field, vorticity, velocity components, and other parameters are derived for two different cases, and comparisons are drawn with previously known results. [ABSTRACT FROM AUTHOR]

This paper focuses on the numerical and experimental investigation of the small-scale power generator. The travelling wave thermoacoustic power generator is numerically analyzed and experimentally tested. The cyclic analysis is used to carry out numerical analysis of the power generator. The system is operated on atmospheric pressure, which allows the manufacturing of an acoustic feedback loop using Polyvinyl chloride piping. The acoustic power generated inside the generator is harnessed by the low-cost linear alternator, i.e., loudspeaker. The effect of regenerator wire mesh on performance of the power generator is numerically analyzed and validated experimentally. The numerical analysis identifies the temperature variation, pressure fluctuation, volume flow rate inside the system, and acoustic power distribution. The maximum electric power experimentally generated by the small-scale power generator is around 45 W with overall efficiency 8.30%. The alternator generates the maximum electric power at the optimum location, i.e. 2.30 m away from the engine core.

In this paper, we concentrate on the propagation dynamics of stochastic reaction–diffusion equations, including the existence of travelling wave solution and asymptotic wave speed. Based on the stochastic Feynman–Kac formula and comparison principle, the boundedness of the solution of stochastic reaction–diffusion equations can be obtained so that we can construct a sup-solution and a sub-solution to estimate the upper bound and the lower bound of wave speed.

Abstract Considering that no current limiting inductances (CLIs) are installed at the end of the DC line in the flexible DC distribution grid, the protections relying on line boundary are no longer applicable. To overcome this problem, the paper proposes a single‐ended protection method independent of line boundary. Firstly, the Peterson equivalent circuit is applied to analyze the amplitude‐time ratio of initial voltage travelling wave (ARIVTW) under internal and external faults. Secondly, the fault direction criterion based on the fault component current and the fault type criterion based on the pole voltage are built. Subsequently, the fault identification criterion is constructed by using the ARIVTW, and the corresponding protection method is formed. Finally, the flexible DC distribution grid is built in PSCAD to verify the proposed method. The simulation results show that the method is robust to fault resistance and noise. Besides, the method realizes the protection of the whole line, which has good selectivity and engineering applicability.

Some discrete models for a simplified (compared to that published earlier in JODEA, 28 (1) (2020), 1 – 42) initial boundary value problem for a 1D linear degenerate wave equation, posed in a space-time rectangle and solved earlier exactly (JODEA, 30 (1) (2022), 89 – 121), have been considered. It has been demonstrated that the correct evaluation of the degenerate grid flux can be possible.

The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as its polarization, dispersion, and interactions with other waves or boundaries. The fractional differential Duffing problem refers to the mathematical modelling of nonlinear, damped oscillations of a system with fractional derivatives. It is a generalization of the classical Duffing equation, which describes the behaviour of a nonlinear, damped oscillator (the equation becomes symmetric under time-reversal). The fractional derivatives allow for a more accurate description of the system's memory and hereditary properties. The solution of the fractional Duffing equation can provide insight into the complex dynamic behaviour of various physical, biological, and engineering systems. We are concerned with studying a new differential Duffing fractional problem. It involves some sequential Caputo derivatives with an infinite series of Riemann–Liouville integrals and some other functions. We begin by proving a first existence and uniqueness result, then we discuss two types of stability for the obtained uniqueness result. An illustrative examples is given to show the applicability of the result. We are also concerned with applying the Tanh method to obtain new classes of travelling wave solutions for three important classes of (Khalil) fractional conformable problems; the generalized equation of Duffing, the Landau–Ginzburg–Higgs equation and the Sine–Gordon one. Some numerical simulations are plotted and a conclusion is given at the end.

The (2 + 1)-dimensional Konopelchenko-Dubrovsky (KD) model and the modified version of the new Kudryashov (MVNK) technique are chosen in the current research to obtain the traveling wave solutions (TWSs). The obtained solutions represent the rich range of explicit solutions to the studied model. As a result, TWSs to the stated model are expressed as the different types of wave profiles such as the kink shape, bell shape, anti-bell shape, and W-shape wave profiles. The Hamiltonian function is found from the stated model and shown it as three dimensional, contour and phase plane in this manuscript. The effects of wave velocity and other parameters on the wave profile are also discussed. The obtained wave profiles are typically useful in applications how waves interact with high-dimensional systems in new, specialized structures. Additionally, the direction and position of solitons for changing other parameters can offer a clear-cut explanation of all the different features of wind and water waves. It is seen that the mentioned scheme is effective, potential and easy in mathematical physics. Finally, this study may be opened up brand-new avenues for further study and application in the fields of mathematical physics.

We explore the spatial spread of vector-borne infections with conditional vector preferences, meaning that vectors do not visit hosts at random. Vectors may be differentially attracted toward infected and uninfected hosts depending on whether they carry the pathogen or not. The model is expressed as a system of partial differential equations with vector diffusion. We first study the non-spatial model. We show that conditional vector preferences alone (in the absence of any epidemiological feedback on their population dynamics) may result in bistability between the disease-free equilibrium and an endemic equilibrium. A backward bifurcation may allow the disease to persist even though its basic reproductive number is less than one. Bistability can occur only if both infected and uninfected vectors prefer uninfected hosts. Back to the model with diffusion, we show that bistability in the local dynamics may generate travelling waves with either positive or negative spreading speeds, meaning that the disease either invades or retreats into space. In the monostable case, we show that the disease spreading speed depends on the preference of uninfected vectors for infected hosts, but also on the preference of infected vectors for uninfected hosts under some circumstances (when the spreading speed is not linearly determined). We discuss the implications of our results for vector-borne plant diseases, which are the main source of evidence for conditional vector preferences so far. [ABSTRACT FROM AUTHOR]

We studied travelling waves in N nonlinear differential equations with a delay and large parameter. This system is important because it can be regarded as a phenomenological model of N-coupled neuron-like oscillators with delay. The problem of the existence of travelling-wave-type solutions was reduced to the study of the dynamics of an auxiliary equation with two delays. Using a special asymptotic method for the large parameter we proved that this equation has a relaxation cycle, studied its properties (amplitude, period and asymptotics) and found the sufficient stability conditions. Based on this periodic solution the travelling waves of the initial model were constructed. [ABSTRACT FROM AUTHOR]

The presented article deals with a model of flame propagation in porous medium. We depart from previously reported models in flame propagation, and we propose a new modelling conception based on a p-Laplacian operator. Such an operator is intended to extend the conceptions for reproducing the diffusion given in porous media. In addition, we introduce a nonlinear reaction term that generalizes the classical KPP-Fisher model of typical use in combustion. Our analysis shows first the boundedness and uniqueness of weak solutions. Afterward, we reformulate the driving equations using the travelling wave technique; and we introduce a density and flux ansatz to analyse the stability of a critical point. We obtain asymptotic profiles of travelling wave solutions, by making use of the Geometric Perturbation Theory. Eventually, we obtain upper solutions under selfsimilar forms for finite support propagating flames. This is particularly applicable for flames departing from compactly supported initial pressure–temperature distributions.

This mini review focuses on the opportunities provided by current and emerging separation techniques for mass spectrometry metabolomics. The purpose of separation technologies in metabolomics is primarily to reduce complexity of the heterogeneous systems studied, and to provide concentration enrichment by increasing sensitivity towards the quantification of low abundance metabolites. For this reason, a wide variety of separation systems, from column chemistries to solvent compositions and multidimensional separations, have been applied in the field. Multidimensional separations are a common method in both proteomics applications and gas chromatography mass spectrometry, allowing orthogonal separations to further reduce analytical complexity and expand peak capacity. These applications contribute to exponential increases in run times concomitant with first dimension fractionation followed by second dimension separations. Multidimensional liquid chromatography to increase peak capacity in metabolomics, when compared to the potential of running additional samples or replicates and increasing statistical confidence, mean that uptake of these methods has been minimal. In contrast, in the last 15 years there have been significant advances in the resolution and sensitivity of ion mobility spectrometry, to the point where high-resolution separation of analytes based on their collision cross section approaches chromatographic separation, with minimal loss in sensitivity. Additionally, ion mobility separations can be performed on a chromatographic timescale with little reduction in instrument duty cycle. In this review, we compare ion mobility separation to liquid chromatographic separation, highlight the history of the use of ion mobility separations in metabolomics, outline the current state-of-the-art in the field, and discuss the future outlook of the technology. “Where there is one, you’re bound to divide it. Right in two”, James Maynard Keenan.

Considering that no current limiting inductances (CLIs) are installed at the end of the DC line in the flexible DC distribution grid, the protections relying on line boundary are no longer applicable. To overcome this problem, the paper proposes a single‐ended protection method independent of line boundary. Firstly, the Peterson equivalent circuit is applied to analyze the amplitude‐time ratio of initial voltage travelling wave (ARIVTW) under internal and external faults. Secondly, the fault direction criterion based on the fault component current and the fault type criterion based on the pole voltage are built. Subsequently, the fault identification criterion is constructed by using the ARIVTW, and the corresponding protection method is formed. Finally, the flexible DC distribution grid is built in PSCAD to verify the proposed method. The simulation results show that the method is robust to fault resistance and noise. Besides, the method realizes the protection of the whole line, which has good selectivity and engineering applicability. [ABSTRACT FROM AUTHOR]

In this study, we used the generalised exponential rational function method (GERF method) to find a new family of solitary wave solutions of the modified chemotaxis equation accounting for short-range and long-range diffusion. The presented solutions exhibit various classes of solitary waves, i.e. bell-shaped and kink–antikink solitary wave solutions under certain constraint relations. We have used a different source function for the attractant as well as species density taking inspiration from the existing models. We have also presented 3D and 2D plots to explain the behaviour of the obtained family of solutions. [ABSTRACT FROM AUTHOR]

The separation of variables based solution to a simplified (compared to that published earlier in JODEA, 28 (1) (2020), 1 – 42) initial boundary value problem for a 1D linear degenerate wave equation, posed in a space-time rectangle, has been presented in a fully complete form. Degeneracy of the equation is due to vanishing its coefficient in an interior point of the spatial segment being the side of the rectangle. For the sake of convenience, the solution is interpreted as a vibrating ‘string’. The solution obtained in the case of weak degeneracy is smooth and bounded, whereas that in the case of strong degeneracy is piece-wise smooth, piece-wise continuous and unbounded in a neighborhood of the point of degeneracy, nevertheless being satisfied some regularity conditions, including square-integrability. In both cases the travelling waves pass through the point of degeneracy, and this phenomenon is referred to as an ability of the ‘string’ to hear itself. The total energy of the ‘string’ is shown to conserve in both cases of degeneracy, provided the ends of the ‘string’ are fixed, though the above vibrating ‘string’ analogy fails in the case of strong degeneracy. The total energy conservation implies the uniqueness of the solution to the problem in both cases of degeneracy

We look for travelling wave fields E (x , y , z , t) = U (x , y) cos (k z + ω t) + U ~ (x , y) sin (k z + ω t) , (x , y , z) ∈ R 3 , t ∈ R satisfying Maxwell's equations in a nonlinear medium which is not necessarily cylindrically symmetric. The nonlinearity of the medium enters Maxwell's equations by postulating a nonlinear material law D = ε E + χ (x , y , ⟨ | E | 2 ⟩) E between the electric field E, its time averaged intensity ⟨ | E | 2 ⟩ and the electric displacement field D. We derive a new semilinear elliptic problem for the profiles U , U ~ : R 2 → R 3 L u - V (x , y) u = f (x , y , u) with u = U U ~ , for (x , y) ∈ R 2 , where f (x , y , u) = ω 2 χ (x , y , | u | 2) u . Solving this equation we can obtain exact travelling wave solutions of the underlying nonlinear Maxwell equations. We are able to deal with super quadratic and subcritical focusing effects, e.g. in the Kerr-like materials with the nonlinear susceptibility of the form χ (x , y , ⟨ | E 2 | ⟩ E) = χ (3) (x , y) ⟨ | E | 2 ⟩ E . A variational approach is presented for the semilinear problem. The energy functional associated with the equation is strongly indefinite, since L contains an infinite dimensional kernel. The methods developed in this paper may be applicable to other strongly indefinite elliptic problems and other nonlinear phenomena. [ABSTRACT FROM AUTHOR]

Mathematical and computational models are used to describe biomechanical processes in multicellular systems. Here, we develop a model to analyse how two types of epithelial cell layers interact during tissue invasion depending on their cellular properties, i.e., simulating cancer cells expanding into a region of normal cells. We model the tissue invasion process using the cellular Potts model and implement our two-dimensional computational simulations in the software package CompuCell3D. The model predicts that differences in mechanical properties of cells can lead to tissue invasion, even if the division rates and death rates of the two cell types are the same. We also show how the invasion speed varies depending on the cell division and death rates and the mechanical properties of the cells. [ABSTRACT FROM AUTHOR]

Beta oscillations in human sensorimotor cortex are hallmark signatures of healthy and pathological movement. In single trials, beta oscillations include bursts of intermittent, transient periods of high-power activity. These burst events have been linked to a range of sensory and motor processes, but their precise spatial, spectral, and temporal structure remains unclear. Specifically, a role for beta burst activity in information coding and communication suggests spatiotemporal patterns, or travelling wave activity, along specific anatomical gradients. We here show in human magnetoencephalography recordings that burst activity in sensorimotor cortex occurs in planar spatiotemporal wave-like patterns that dominate along two axes either parallel or perpendicular to the central sulcus. Moreover, we find that the two propagation directions are characterised by distinct anatomical and physiological features. Finally, our results suggest that sensorimotor beta bursts occurring before and after a movement can be distinguished by their anatomical, spectral, and spatiotemporal characteristics, indicating distinct functional roles.

In order to provide quick and accurate fault detection in a DC microgrid, a new protection strategy is developed in this study. It is based on the multi-resolution analysis of travelling waves. The multi-resolution analysis of travelling waves is carried out using discrete wavelet transform (DWT). The dyadic filter bank theory is used to obtain the DWT coefficient of the voltage travelling wave. The energy of the DWT coefficient is then determined, and the fault will be identified if this energy content exceeds the predetermined threshold value. Initially, the efficacy of the proposed algorithm is verified on a 500 V ring-type bipolar DC microgrid test model, which is developed with MATLAB/Simulink environment. Then the results obtained were later validated with the real-time simulator Opal-RT. The various simulation results indicate that the proposed algorithm can successfully be implemented in both modes, i.e., grid-integrated and islanded. It can also provide protection against high resistance fault (HRF) up to 900 Ω in grid-integrated mode, and up to 1,300 Ω in islanded mode. The operating time of the proposed algorithm is also quite fast, i.e., 0.64 m.

High-performance computations (HPC) require switching structures to operate at high input powers with minimum latency and lower penalties. Keeping in view these challenges along with the restriction in existing modules and components, we present a response investigation of the proposed 3-stage 8 × 8 Wideband Travelling Wave Semiconductor Optical Amplifier (TW-SOA) based switch. The switch operation is better in terms of Bit Error Rate (BER) of e−13 to e−16, Extinction Ratio (ER) of 17.99794 dB, power penalty of 0.15–0.30 dB, and (Optical Signal-to-Noise Ratio) OSNR of 25.92411 dB. It is observed that increasing power per bit leads to interference of cross-port data that can be controlled by varying biasing conditions of SOA. A short response time of 0.61596 ns is achieved by utilizing small transient time values of cross-phase modulation occurring in SOA. To investigate the impairments that occurred during modulation of signal in TW-SOA loops by control signals, the switch performance is optimized for parameters at various input powers and injection currents to offer it an improved solution to switching challenges for HPC systems. [ABSTRACT FROM AUTHOR]

Richards equation describes water transport in soils, but requires as input, soil material property functions specifically relative hydraulic conductivity and relative diffusivity typically obtained from the soil–water retention curve (SWRC) function (involving capillary suction head). These properties are often expressed via particular functional forms, with different soil types from sandstones to loams represented within those functional forms by a free fitting parameter. Travelling wave solutions (profile of height ξ ^ against moisture content Θ ) of Richards equation using van Genuchten's form of the soil material property functions diverge to arbitrarily large height close to full saturation. The value of relative diffusivity itself diverges at full saturation owing to a weak singularity in the SWRC. If, however, soil material property data are sparse near full saturation, evidence for the nature of that divergence may be limited. Here we rescale the relative diffusivity to approach unity at full saturation, removing a singularity from the original van Genuchten SWRC function by constructing a convex hull around it. A piecewise SWRC function results with capillary suction head approaching zero smoothly at full saturation. We use this SWRC with the Brooks–Corey relative hydraulic conductivity to develop a new relative diffusivity function and proceed to solve Richards equation. We obtain logarithmic relationships between height ξ ^ and moisture content Θ close to saturation. Predicted ξ ^ values are smaller than profile heights obtained when solving using the original van Genuchten's soil material property functions. Those heights instead exhibit power law behaviour. [ABSTRACT FROM AUTHOR]

The repeated emergence of SARS-CoV-2 escape mutants from host immunity has obstructed the containment of the current pandemic and poses a serious threat to humanity. Prolonged infection in immunocompromised patients has received increasing attention as a driver of immune escape, and accumulating evidence suggests that viral genomic diversity and emergence of immune-escape mutants are promoted in immunocompromised patients. However, because immunocompromised patients comprise a small proportion of the host population, whether they have a significant impact on antigenic evolution at the population level is unknown. We consider an evolutionary epidemiological model that combines antigenic evolution and epidemiological dynamics. Applying this model to a heterogeneous host population, we study the impact of immunocompromised hosts on the evolutionary dynamics of pathogen antigenic escape from host immunity. We derived analytical formulae of the speed of antigenic evolution in heterogeneous host populations and found that even a small number of immunocompromised hosts in the population significantly accelerates antigenic evolution. Our results demonstrate that immunocompromised hosts play a key role in viral adaptation at the population level and emphasize the importance of critical care and surveillance of immunocompromised hosts. [ABSTRACT FROM AUTHOR]

We present the design and simulation methodology of a superconducting ridge-gap waveguide (RGWG) as a potential basis for mm-wave kinetic inductance travelling wave parametric amplifiers (KI-TWPAs). A superconducting RGWG was designed using Ansys HFSS to support a quasi-TEM mode of transmission over a bandwidth of 20–120 GHz with its internal dimensions optimised for integration with W-band rectangular waveguide. A design of an impedance loaded travelling wave structure incorporating periodic perturbations of the ridge was described. A method to simulate the nonlinear kinetic inductance via user-defined components in Keysight's ADS was outlined, which yielded the power dependent S-parameters and parametric signal gain. A RGWG with a 30 nm NbTiN coating and 5 μ m conductor spacing, corresponding to a kinetic inductance fraction α ∼ 60 % was used for the description of a KI-TWPA with 900 perturbations equivalent to a physical length 25 cm that achieved more than 10 dB of signal gain over a 75–110 GHz bandwidth via 4-wave mixing (4WM). [ABSTRACT FROM AUTHOR]

A differential equation that models the motion of a domain wall is considered. For this equation, in the case of constant coefficients, there exists a solution in the form of a travelling wave which describes the transition from one equilibrium to another. For an equation with slowly varying coefficients, we construct an asymptotic one-phase solution. The phase is found from the Hamilton–Jacobi equation whose coefficients are taken from the asymptotics of the unperturbed wave at infinity. The asymptotic construction is based on the requirement that the first correction is small as compared to the leading term uniformly over a wide range of independent variables. [ABSTRACT FROM AUTHOR]

Hybrid high voltage direct current systems utilized for bulk-power transmission have recently attracted more attention. The overhead lines (OHLs) are mainly used for the implementation of such systems due to their outstanding economic advantages. However, OHLs are vulnerable to temporary faults, jeopardizing the safe and reliable operation of the network. The resiliency to the line faults is of considerable significance to the power transmission. This paper proposes a fault property identification strategy based on the Pearson correlation coefficient for the LCC-MMC hybrid HVDC system which can differentiate temporary and permanent faults. To achieve this, a voltage signal is injected into the faulty line by decreasing the firing angles of the LCC-based rectifier. Based on the established OHLs model and the injected signal, an estimated backward travelling wave can be accurately calculated. The fault property is identified by comparing the wave difference of the real backward travelling wave and the estimated backward travelling wave. The proposed strategy has a high accuracy since all influencing factors including the fault resistance, fault distance, and line parameters have been taken into account. Finally, to verify the efficacy of the proposed algorithm, several simulations have been performed using PSCAD/EMTDC. The simulation results show that the proposed algorithm can effectively distinguish the fault property. [ABSTRACT FROM AUTHOR]

The existing semi-fluidisation devices are described by high-energy consumption during operation, heavy metal structure, and complexity of the drive mechanism. Therefore, the search for effective heat exchange schemes in low-temperature processing of fruit and vegetable products, provided that its damage and energy consumption for the process are minimised, constitutes the relevance of this study. The purpose of this study was to determine and substantiate the amplitude-frequency and power mode parameters of the vibration wave driving organ of the semi-fluidisation machine for freezing fruit and berry products, the regularities of changes in the main characteristics of low-frequency vibrations in the process under study. To perform these tasks, an experimental model of a semi-fluidisation machine with a vibration wave driving organ was developed and a set of special devices was manufactured in the form of a microcontroller system that provides measurement and automatic adjustment of the main parameters of the process under study. Intensification of heat exchange in the process of fluidisation freezing in the conditions of a pseudo-suspended state of products is described by a high heat transfer coefficient, which can exceed typical convective processes by several orders of magnitude; an increase in the active heat exchange surface up to 100% is observed; the contact surface with the energy carrier increases proportionally, which leads to a decrease in the active temperature difference; there is a 2-3 times decrease in internal friction in the mass of products and, accordingly, the technological resistance in the mass of loading is reduced, which is a potential for increasing the technical and economic characteristics of the low-temperature processing under study. The practical value of this study can be attributed to the application of vibro-slush freezing of the proposed structure with a vibration-wave product driver and a spatial elastic system for levelling out parasitic vibrations, which allows simplifying the structure, reducing power loads and, accordingly, energy costs

This paper proposes three techniques for locating lightning strikes in a 115 kV transmission system over 88.5 km, based on the arrival time of a transient wave obtained from a discrete wavelet transform (DWT). The first technique calculates the location based on the ‘type D’ travelling wave method. The second technique analyses the first arrival time and same reflected-back wave arrival time between two substations. In the third technique, two sensors are installed to record arrival times at each sensor. Case studies of direct lightning strikes to phase conductors (shielding failure) are simulated using the ‘Alternative Transients Program/Electromagnetic Transients Program’ (ATP/EMTP). The influences of three parameters are considered: inception angles, the phase of the conductor, and the position at which the lightning struck the transmission system. By performing an operation scheme for all techniques, a positive sequence current is calculated, using a three-phase current from the ATP/EMTP program which is converted using Clark’s transform. A positive sequence current is extracted to several scales using the DWT, and the orders of arrival times for both substations are determined. After the arrival times are obtained, each technique uses a different order of arrival time for calculating the lightning location. By comparing the average error among the three techniques, it is shown that the arrival time of the two sensors’ technique is less than that of the other techniques.

Based on the fact that the incubation periods of epidemic disease in asymptomatically infected and infected individuals are inevitable and different, we propose a diffusive susceptible, asymptomatically infected, symptomatically infected and vaccinated (SAIV) epidemic model with delays in this paper. To see whether epidemic disease can propagate spatially with a constant speed, we focus on the travelling wave solution for this model. When the basic reproduction number of the corresponding spatial-homogenous delayed differential system is greater than one and the wave speed is greater than or equal to the critical speed, we prove that this model admits nontrivial positive travelling wave solutions. Our theoretical results are of benefit to the prevention and control of epidemic. [ABSTRACT FROM AUTHOR]