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A Kinetic Inductance Traveling Wave Amplifier (KIT) utilizes the nonlinear kinetic inductance of superconducting films, particularly niobium titanium nitride (NbTiN), for parametric amplification. These amplifiers achieve remarkable performance in terms of gain, bandwidth, and compression power and frequently approach the quantum limit for noise. However, most KIT demonstrations have been isolated from practical device readout systems. Using a KIT as the first amplifier in the readout chain of an unoptimized microwave SQUID multiplexer coupled to a transition-edge sensor microcalorimeter, we see an initial improvement in the flux noise [1]. One challenge in KIT integration is the considerable microwave pump power required to drive the non-linearity. To address this, we have initiated efforts to reduce the pump power by using thinner NbTiN films and an inverted microstrip transmission line design. In this article, we present the new transmission line design, fabrication procedure, and initial device characterization—including gain and added noise. These devices exhibit over 10 dB of gain with a 3 dB bandwidth of approximately 5.5–7.25 GHz, a maximum practical gain of 12 dB, and typical gain ripple under 4 dB peak to peak. We observe an appreciable impedance mismatch in the NbTiN transmission line, which is likely the source of the majority of the gain ripple. Finally, we perform an initial noise characterization and demonstrate system-added noise of three quanta or less over nearly the entire 3 dB bandwidth. [ABSTRACT FROM AUTHOR]

This article investigates the truncated time M-fractional paraxial wave equation. This model is frequently used to depict the activation of waves in utterly different physical frameworks, such as quantum mechanics and optics. Two trustworthy methodologies, the improved F-expansion and modified exponent function method, are used to obtain the different soliton solutions to the truncated time M-fractional paraxial wave equation. The obtained solutions offer a valuable understanding of the underlying physical events. Discussion is also had over the equation’s modulation instability, which confirms the given equation is stable. Several graphical charts, including 2D, 3D, density, and contour, are produced using symbolic software. These visual representations have a significant positive impact on qualitative evaluations of diverse natural occurrences. The evaluated findings showed that the approaches employed in this work to obtain inclusive and standard solutions are efficient and speedier in computing, they will be beneficial in addressing more difficult higher order nonlinear perturbed truncated time M-fractional models. [ABSTRACT FROM AUTHOR]

This article examines the nonlinear (2+1) complex conformable time fractional nonlinear Schrödinger equation and the soliton solutions that may be found by using the improved F-expansion method. Many novel solutions of concatenated model such as periodic wave, dark soliton, singular, hyperbolic, trigonometric and rational wave soliton solutions are retrieved using proposed method. The modulation instability of the selected model through stability analysis is also discussed. In order to display the retrieved soliton solutions graphically, 2D, 3D, density, and contour graphs have been utilized. The retrieved soliton solutions play a significant role in nonlinear optics. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. Also, these results are novel and provide invaluable insight into the fundamental physical phenomena. [ABSTRACT FROM AUTHOR]

This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high‐dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the unique stationary solution, they lack positivity, radial symmetry, and exponential decay. By employing variational and geometric approaches, along with perturbation theory, we establish the orbital (in)stability and strong instability of these traveling waves. [ABSTRACT FROM AUTHOR]

We consider solutions of the cubically nonlinear Schrödinger equation. For a certain class of solutions of the form with , we prove that they are nonexistent in the general case , , . In the three nongeneric cases (), ( , , ), and ( , ), we present a two-parameter set of solutions, for which we find the constraints specifying real bounded and unbounded solutions. [ABSTRACT FROM AUTHOR]

The opioid crisis in the United States is being fueled by the rapid emergence of new fentanyl analogs and precursors that can elude traditional library-based screening methods, which require data from known reference compounds. Since reference compounds are unavailable for new fentanyl analogs, we examined if fentanyls (fentanyl + fentanyl analogs) could be identified in a reference-free manner using a combination of electrospray ionization (ESI), high-resolution ion mobility (IM) spectrometry, high-resolution mass spectrometry (MS), and higher-energy collision-induced dissociation (MS/MS). We analyzed a mixture containing nine fentanyls and W-15 (a structurally similar molecule) and found that the protonated forms of all fentanyls exhibited two baseline-separated IM distributions that produced different MS/MS patterns. Upon fragmentation, both IM distributions of all fentanyls produced two high intensity fragments, resulting from amine site cleavages. The higher mobility distributions of all fentanyls also produced several low intensity fragments, but surprisingly, these same fragments exhibited much greater intensities in the lower mobility distributions. This observation demonstrates that many fragments of fentanyls predominantly originate from one of two different gas-phase structures (suggestive of protomers). Furthermore, increasing the water concentration in the ESI solution increased the intensity of the lower mobility distribution relative to the higher mobility distribution, which further supports that fentanyls exist as two gas-phase protomers. Our observations on the IM and MS/MS properties of fentanyls can be exploited to positively differentiate fentanyls from other compounds without requiring reference libraries and will hopefully assist first responders and law enforcement in combating new and emerging fentanyls. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with traveling wave phenomena of the inhomogeneous half-wave equation, which models the energy of a spin zero particle in the Coulomb field. We study the Gagliardo-Nirenberg and critical Hardy-Sobolev inequalities with velocity 0 < | v | < 1 and obtain the estimates for the best constants and optimizers of inequalities. Moreover, we establish the non-scattering results with small traveling wave for energy subcritical and critical cases. [ABSTRACT FROM AUTHOR]

We are concerned with the existence of traveling waves for density‐dependent diffusion reaction nonlinear convection equations with small time delay. We first study the existence and uniqueness of smooth and sharp‐type traveling wavefront solution of the wave speed c ≥ c∗ for equation without time delay, where c∗ is the minimal wave speed. Meanwhile, we construct a variational principle for c∗ from which the upper bound of c∗ is determined, while the lower bound of c∗ is attained by using the phase plane analysis. Then, we obtain the existence of smooth traveling wavefront solution for equation with small time delay for c > c∗ by applying the perturbation method and implicit function theorem. [ABSTRACT FROM AUTHOR]

Reaction–diffusion equations (RDEs) model the spatiotemporal evolution of a density field u(x,t)$u({x},t)$ according to diffusion and net local changes. Usually, the diffusivity is positive for all values of u$u$, which causes the density to disperse. However, RDEs with partially negative diffusivity can model aggregation, which is the preferred behavior in some circumstances. In this paper, we consider a nonlinear RDE with quadratic diffusivity D(u)=(u−a)(u−b)$D(u) = (u - a)(u - b)$ that is negative for u∈(a,b)$u\in (a,b)$. We use a nonclassical symmetry to construct analytic receding time‐dependent, colliding wave, and receding traveling wave solutions. These solutions are multivalued, and we convert them to single‐valued solutions by inserting a shock. We examine properties of these analytic solutions including their Stefan‐like boundary condition, and perform a phase plane analysis. We also investigate the spectral stability of the u=0$u = 0$ and u=1$u = 1$ constant solutions, and prove for certain a$a$ and b$b$ that receding traveling waves are spectrally stable. In addition, we introduce a new shock condition where the diffusivity and flux are continuous across the shock. For diffusivity symmetric about the midpoint of its zeros, this condition recovers the well‐known equal‐area rule, but for nonsymmetric diffusivity it results in a different shock position. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with traveling waves in a class of reaction–diffusion equations with nonlocal delays. By introducing new variables, we transform equations with nonlocal delays to non‐delayed system; the existence of traveling waves is obtained by means of Routh–Hurwitz criterion, and by considering the regularity of the Cauchy problem and using spectral theory, we investigate the global stability of traveling waves and then the uniqueness of wave speeds with the help of upper and lower solution method. Finally, our results are applied to two nonlocal delayed reaction–diffusion equations. [ABSTRACT FROM AUTHOR]

The vibrations of rotating joined conical–conical shells with classical supported conditions have been studied extensively. As a matter of fact, in some cases, these classical boundary conditions cannot exactly model actual situations. Moreover, theoretical frameworks on them are still limited. This research aims to investigate the fundamental frequencies and dynamic mode shapes of the traveling wave of the rotating porous metal material joined conical–conical thin shells (PJCS) with elastic supports. By utilizing artificial spring technology, arbitrary elastic supported boundary conditions and classical boundary conditions are achieved efficiently. A new dynamic model has been formulated with the help of the first-order shear deformation theory (FSDT) and Hamilton’s principle. By employing the generalized differential quadrature (GDQ) method along with stress boundary conditions and generalized eigenvalues, various factors such as porosity, semi-vertex angles and stiffness are analyzed for their impact on the fundamental frequencies of forward wave (FW), backward wave (BW) and mode shapes. The presented results are validated through the convergence and comparison studies from literatures. The interesting and novel results indicate that the in-plane displacement constraints have the most significant impact on the critical speed, while the lateral displacement constraint has the least effect. The vibrations are more easily excited for the part with a larger half vertex angle. Rotating PJCS with Type 1 has the biggest critical rotating speed. [ABSTRACT FROM AUTHOR]

In this paper, I consider a volume-filling chemotaxis model with a small cell diffusion coefficient and chemotactic sensitivity. By the geometric singular perturbation theory together with the center-stable and center unstable manifolds, one gets the existence of a positive traveling wave connecting the two constant steady states (0 , 0) and (b , α b β) with a small wave speed ϵc. In addition, the traveling wave is monotone for b ≥ 1 and is not monotone for 0 < b < 1. Moreover, by the spectral analysis it shows that the above traveling wave is spectrally unstable in some exponentially weighted spaces. [ABSTRACT FROM AUTHOR]

We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We examine the case of a shifting semi-infinite bad habitat connected to a semi-infinite good habitat. In this case we rigorously establish species persistence (non-persistence) if the habitat shift speed is less (greater) than the asymptotic spreading speed of the species in the good habitat. We also examine the case of a finite shifting patch of hospitable habitat, and find that the habitat shift speed must be less than the asymptotic spreading speed associated with the habitat and there is a critical patch size for species persistence. Spreading speeds and traveling waves are established to address species persistence. Our numerical simulations demonstrate the theoretical results and show the dependence of the critical patch size on the shift speed. [ABSTRACT FROM AUTHOR]

This paper focuses on the effects of environmental improvement and worsening on the spread and invasion of populations with birth pulse. We propose an impulsive reaction-diffusion model with a shifting environment to describe the dynamics of species with distinct reproduction stage and dispersal stage. First, the impulsive reaction-diffusion model is reduced to a discrete-time recursive system defined by a discrete map. Next, with the aid of the appropriate test function and comparison principle, we obtain some sufficient conditions on the nonexistence and uniqueness of nontrivial fixed points of the discrete map. This, combined with the abstract theory of spatially non-translation dynamical systems, enables us to establish the existence of traveling wave solutions and the asymptotic propagation properties of the model. [ABSTRACT FROM AUTHOR]

In this paper, a composite excitation method is used to optimize the design of an existing cantilevered cylindrical ultrasonic motor to avoid vibration interference. Modal and transient simulation analysis of the stator structure was carried out by the finite element method. Optimized stator structure is simpler than the original motor. Simulation analysis results show that the circumferential amplitude is increased by more than 35% with 55.7% reduction in ceramic usage. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical approach for studying the changes in pressure and temperature variables in flames. This conception extends beyond the traditional second-order Laplacian diffusion model by considering the p-Laplacian operator and a bi-stable reaction term, thereby providing a more generalized framework for flame diffusion analysis. Given the structure of our equations, we provide the boundedness and uniqueness of the solutions in a weak sense from both analytical and numerical approaches. We further reformulate the governing equations in the context of traveling wave solutions, applying singular geometric perturbation theory to derive the analytical expressions of these profiles. This theoretical development is complemented by numerical assessments, which not only validate our theoretical predictions, but also optimize the traveling wave speed to minimize the error between numerical and analytical solutions. Additionally, we explore self-similar structured solutions. The paper then concludes with a perspective on future research, with emphasis being placed on the need for experimental validation in laboratory settings. Such empirical studies could test the robustness of our model and allow for refinement based on actual measurements, thereby broadening the applicability and accuracy of our findings in practical scenarios. [ABSTRACT FROM AUTHOR]

We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the energy space for the standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions. We then characterize the solitary and traveling waves in the one dimensional case. [ABSTRACT FROM AUTHOR]

In this paper, the generalized Kudryashov (GK) approach and the sine-Gordon expansion approach are used for constructing new specific analytical solutions of the deoxyribonucleic acid model, which include the well-known bell-shaped soliton, kink, singular kink, periodic soliton, contracted bell-shaped soliton and anti-bell-shaped soliton. The efficacy of these strategies demonstrates their utility and efficiency in addressing a wide range of integer and fractional-order nonlinear evolution problems. The physical relevance of the demonstrated results has been proven using three-dimensional forms. It is interesting to mention that the solutions achieved here using the provided methods are extra-extensive and may be used to explain the internal interaction of the deoxyribonucleic acid model originating in mathematical biology. The suggested approach was utilized to get exact traveling wave solutions for fractional nonlinear partial differential equations appearing in nonlinear science. [ABSTRACT FROM AUTHOR]

In this paper, we first derive a theorem on the convergence of solutions to traveling waves in reaction-diffusion systems with equal diffusivities. Then we apply this theorem to some specific examples of predator-prey models which were studied recently in the literature. This gives a stability result for these traveling waves in the corresponding predator-prey system under certain perturbations of initial data. [ABSTRACT FROM AUTHOR]

We study a reaction-diffusion equation that describes the growth of a population with a strong Allee effect in a bounded habitat which shifts at a speed c > 0 . We demonstrate that the existence of forced positive traveling waves depends on habitat size L, and c ∗ , the speed of traveling wave for the corresponding reaction-diffusion equation with the same growth function all over the entire unbounded spatial domain. It is shown that for c ∗ > c > 0 there exists a positive number L ∗ (c) such that for L > L ∗ (c) there are two positive traveling waves and for L < L ∗ (c) there is no positive traveling wave. It is also shown if c > c ∗ for any L > 0 there is no positive traveling wave. The dynamics of the equation are further explored through numerical simulations. [ABSTRACT FROM AUTHOR]

In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but of different kinds. One is from the discontinuous second order term, the other from the obstacle. Existence, uniqueness, and regularity of the solution are obtained. We also prove that two free boundaries are C ∞. The asymptotic behavior of the solution is also considered: we show that it converges to a traveling wave solution when time goes to infinity. Moreover, numerical results are presented. [ABSTRACT FROM AUTHOR]

This paper proposed a double-sided staggered conical teeth traveling wave rotating ultrasonic motor based on in-plane bending mode, which reduces the difficulty of rotor preload application and improves the output characteristics of in-plane bending mode traveling wave rotating ultrasonic motor. The motor has four sets of drive teeth alternately distributed on both the inner and outer sides of the vibrator, with the drive teeth gap dedicated to accommodate the piezoelectric ceramic piece, and the staggered drive teeth on both sides of the vibrator are used to drive the rotor rotation. The motor operates in two in-plane third-order bending modes with the same frequency and orthogonal to each other, and is excited by four sets of piezoelectric ceramic disks spaced 90 degrees apart from the inner and outer sides. After the prototype was completed, its vibration characteristics and output performance were experimentally tested, and the actual effects of the three excitation schemes were compared. The experimental results show that the motor can provide a maximum output torque of 1.82N-mm and a maximum no-load speed of 96.4 rpm when the excitation voltage is 300 V and the excitation frequency is 20.60 kHz. [ABSTRACT FROM AUTHOR]

In this work, we investigate diverse analytical solutions and modulation instability of the nonlinear Schrödinger equation with an anti-cubic nonlinear term. We use the traveling wave transformation and the New Generalized Extended Direct Algebraic Method to perform a variety of exact traveling wave soliton-like solutions. The obtained solutions are among other trigonometric function solutions, complex soliton solutions, and rational solutions. A particular behavior has been depicted in self-focusing and defocusing nonlinearity where dark soliton changes to super rogue waves and breather soliton is obtained. We then use the linearizing scheme to get the growth rate of modulation instability. For a specific value of the excitation wave number and a specific time of simulation, diverse waveforms of the modulated waves are obtained. We have demonstrated that the combined dispersion and nonlinear terms, as well as the anti-cubic nonlinear term, can develop modulation instability. To confirm the predictions based on the analytical results, we use the direct numerical simulation, from which we have displayed a modulation wave of the growth rate modulation instability. It results equally that the anti-cubic nonlinearity is an important object to control the propagation of the solitonic waves in the nonlinear systems. [ABSTRACT FROM AUTHOR]

We are concerned with the existence and qualitative properties of traveling wave solutions for a quasilinear reaction‐diffusion equation on the real line. We consider a non‐Lipschitz reaction term of Fisher–KPP type and a discontinuous diffusion coefficient that allows for degenerations and singularities at equilibrium points. We investigate the joint influence of the reaction and diffusion terms on the existence and nonexistence of traveling waves, and assuming these terms are of power‐type near equilibria, we provide classification of solutions based on their asymptotic properties. Our approach provides a broad theoretical background for the mathematical treatment of rather general models not only in population dynamics but also in other applied sciences and engineering. [ABSTRACT FROM AUTHOR]

In order to improve the output torque of an in-plane bending mode traveling wave rotary ultrasonic motor, a double-sided tapered teeth traveling wave rotary ultrasonic motor was proposed. The motor is designed with three types of adaptive rotors that can be used for replacement in different output environments. Simulation analysis was conducted using ANSYS, and prototype production and experimental testing were conducted. The experimental results show that when the excitation voltage is 300 V and the excitation frequency is 22.665 kHz, the maximum output torque that the motor provide is 3.087 N·mm, and the maximum no-load speed is 295 rpm. [ABSTRACT FROM AUTHOR]

In order to simplify the motor structure, to reduce the difficulty of rotor pre-pressure application and to obtain better output performance, a new internal cone type rotating traveling wave ultrasonic motor is proposed. The parametric model of the internal cone type ultrasonic motor was established by the ANSYS finite element software. The ultrasonic motor consists of an internal cone type vibrator and a tapered rotor. The dynamic analysis of the motor vibrator is carried out, and two in-plane third-order bending modes with the same frequency and orthogonality are selected as the working modes. The other advantages of this motor are that pre-pressure can be imposed by the weight of the rotor. The prototype was trial-manufactured and experimentally tested for its vibration characteristics and output performance. When the excitation frequency is 22260.0 Hz, the pre-pressure is 0.1 N and the peak-to-peak excitation voltage is 300 V, the maximum output torque of the prototype is 1.06 N·mm, and the maximum no-load speed can reach 441.2 rpm. The optimal pre-pressure force under different loads is studied, and the influence of the pre-pressure force on the mechanical properties of the ultrasonic motor is analyzed. It is instructive in the practical application of this ultrasonic motor. [ABSTRACT FROM AUTHOR]

Weakly nonlinear longitudinal-torsional waves in rods are considered. The structure of discontinuities in the solutions of the hyperbolic system of equations describing these waves is studied. Previously, the authors studied discontinuity structures under more special assumptions about dissipative processes in these structures. In the present study, no constraints are imposed on the matrix of dissipative coefficients except for positive definiteness. Conditions are formulated for the existence of special discontinuities, that is, discontinuities with additional boundary conditions that are independent of conservation laws. [ABSTRACT FROM AUTHOR]

The bacterial colony is a powerful experimental platform for broad biological research, and reaction–diffusion models are widely used to study the mechanisms of its formation process. However, there are still some crucial factors that drastically affect the colony growth but are not considered in the current models, such as the non-homogeneously distributed nutrient within the colony and the substantially decreasing expansion rate caused by agar dehydration. In our study, we propose two plausible reaction–diffusion models (the VN and MVN models) based on the above two factors and validate them against experimental data. Both models provide a plausible description of the non-homogeneously distributed nutrient within the colony and outperform the classical Fisher–Kolmogorov equation and its variation in better describing experimental data. Moreover, by accounting for agar dehydration, the MVN model captures how a colony’s expansion slows down and the change of a colony’s height profile over time. Furthermore, we demonstrate the existence of a traveling wave solution for the VN model. [ABSTRACT FROM AUTHOR]

Analysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves (TWs) move. This value depends on the solution concept being considered. We analyze an extensive class of Fisher-type reaction–diffusion equations with flows in divergence form. We work with regular flows, which may not meet the standard elliptical conditions, but without other types of singularities. We show that the range of speeds at which classic TWs move is an interval unbounded to the right. Contrary to classic examples, the infimum may not be reached. When the flow is elliptic or over-elliptic, the minimum speed of propagation is achieved. The classic TW speed threshold is complemented by another value by analyzing an extension of the first-order boundary value problem to which the classic case is reduced. This singular minimum speed can be justified as a viscous limit of classic minimal speeds in elliptic or over-elliptic flows. We construct a singular profile for each speed between the minimum singular speed and the speeds at which classic TWs move. Under additional assumptions, the constructed profile can be justified as that of a TW of the starting equation in the framework of bounded variation functions. We also show that saturated fronts verifying the Rankine–Hugoniot condition can appear for strictly lower speeds even in the framework of bounded variation functions. [ABSTRACT FROM AUTHOR]

The phenomenon of overcompensation is widespread in ecology, and non-monotonic discrete-time map may admit complex dynamics. This paper focuses on the impact of overcompensation on the propagation of a spatially moving population with a birth pulse. We prove the upward convergence of the oscillating traveling wave when the birth function is a unimodal function. We establish the existence of monotone and non-monotone traveling wave solutions for the second iterative operator. Furthermore, we obtain the existence, uniqueness, and stability of the standing wave solutions for the second iterative operator. Numerical simulations are performed to illustrate and complement the theoretical results. [ABSTRACT FROM AUTHOR]

The faults in high voltage direct current (HVDC) transmission lines cause a sudden rise in DC, resulting in over-stressing of converter valves and transformer windings. DC line faults of longer duration, or permanent nature, will lead to a severe disturbance in the associated AC network as well. Thus, the HVDC line faults must be detected immediately to interrupt the fault current by initiating proper actions of control and protection. This paper implements a new method to detect the asymmetrical (pole-to-ground) faults in the conventional bipolar LCC-HVDC transmission system. The proposed method defines a Fault Indicating Parameter (FIP) based on the transient voltage and current elements of each pole. The transient elements are obtained based on single-end measurements. Single-end or non-unit measurements lead to the development of simple, cost-effective and fast protection criteria. Also, the method is applicable to faults close to the line boundary and of high resistivity. A two-terminal bipolar LCC-HVDC transmission system, based on ±500 kV, 1000 MW and 900 km length, is used to evaluate the performance of the proposed technique in offline mode, using MATLAB/Simulink software. Also, the results are validated using an OPAL-RT real-time simulator under divergent fault conditions. The simulation results prove the robustness, selectiveness and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

We study traveling waves in mass and spring dimer Fermi–Pasta–Ulam–Tsingou (FPUT) lattices in the long wave limit. Such lattices are known to possess nanopteron traveling waves in relative displacement coordinates. These nanopteron profiles consist of the superposition of an exponentially localized "core," which is close to a Korteweg–de Vries solitary wave, and a periodic "ripple," whose amplitude is small beyond all algebraic orders of the long wave parameter, although a zero amplitude is not precluded. Here we deploy techniques of spatial dynamics, inspired by results of Iooss and Kirchgässner, Iooss and James, and Venney and Zimmer, to construct mass and spring dimer nanopterons whose ripples are both exponentially small and also nonvanishing. We first obtain "growing front" traveling waves in the original position coordinates and then pass to relative displacement. To study position, we recast its traveling wave problem as a first‐order equation on an infinite‐dimensional Banach space; then we develop hypotheses that, when met, allow us to reduce such a first‐order problem to one solved by Lombardi. A key part of our analysis is then the passage back from the reduced problem to the original one. Our hypotheses free us from working strictly with lattices but are easily checked for FPUT mass and spring dimers. We also give a detailed exposition and reinterpretation of Lombardi's methods, to illustrate how our hypotheses work in concert with his techniques, and we provide a dialog with prior methods of constructing FPUT nanopterons, to expose similarities and differences with the present approach. [ABSTRACT FROM AUTHOR]

Clues about the organization of spinal networks responsible for rhythmic motor behaviors have come from the examination of reflex circuitry, lesioning studies, and single-cell recordings. Recently, more attention has been paid to extracellularly recorded multiunit signals thought to represent the general activity of local cellular potentials. Focusing on the gross localization of spinal locomotor networks, we used multiunit signals of the lumbar cord to classify the activation and organization of those networks. We employed power spectral analysis to compare multiunit power across rhythmic conditions and locations and to infer patterns of activation based on coherence and phase measures. We found greater multiunit power in midlumbar segments during stepping, supportive of previous lesioning studies isolating rhythm-generating capabilities to these segments. We also found much greater multiunit power during the flexion phase of stepping than during the extension phase for all lumbar segments. Greater multiunit power at flexion indicates increased neural activity during this phase and is suggestive of previously reported asymmetries between flexor- and extensor-related interneuronal populations of the spinal rhythm-generating network. Finally, the multiunit power showed no phase lag at coherent frequencies throughout the lumbar enlargement indicative of a longitudinal standing wave of neural activation. Our results suggest that the multiunit activity may be representative of the spinal rhythm-generating activity that is distributed in a rostrocaudal gradient. Additionally, our results indicate that this multiunit activity may operate as a flexor-dominant standing wave of activation that is synchronized throughout the rostrocaudal extent of the lumbar enlargement. NEW & NOTEWORTHY We report on the power spectral analysis of multiunit activity (MUA) of lumbar spinal interneurons during a locomotor task. In line with prior studies, we found evidence of greater power at the frequency of locomotion in high lumbar segments and during the flexion phase. Our results also confirm prior observations from our laboratory that the rhythmically active MUA behaves as a longitudinal standing wave of neural activation that is flexor dominant. [ABSTRACT FROM AUTHOR]

The bacterial traveling waves observed in experiments are of pulse type which is different from the monotone traveling waves of the Fisher–KPP equation. For this reason, the Keller–Segel equations are widely used for bacterial waves. Note that the Keller–Segel equations do not contain the population dynamics of bacteria, but the population of bacteria multiplies and plays a crucial role in wave propagation. In this paper, we consider the singular limits of a linear system with active and inactive cells together with bacterial population dynamics. Eventually, we see that if there are no chemotactic dynamics in the system, we only obtain a monotone traveling wave. This is evidence that chemotaxis dynamics are needed even if population growth is included in the system. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the spreading speed determinacy to an abstract time-periodic monotone semiflow, which is of monostable type with weak compactness and admits boundary equilibria in the phase space. The problem is challenging due to the existence of single spreading speed or multiple spreading speeds (fastest and slowest spreading speeds). We first study under what condition single spreading speed exists and establish necessary and sufficient conditions for linear and nonlinear selections of the spreading speed as well as the minimal wave speed of traveling wavefronts. In the case of multiple spreading speeds, the determinacy of each speed is further investigated based on the connection of wavefronts to the boundary equilibria. We apply our results to five time-periodic models: a delayed diffusive equation, a stream population model with a benthic zone, a nonlocal dispersal Lotka-Volterra model, and two cooperative systems. [ABSTRACT FROM AUTHOR]

Cooperation in a population system can result in the occurrence of a coexistence (win–win) equilibrium. When diffusion is incorporated, individual species possibly invade into far ends with different spreading speeds (co-speed or fast–slow speed). Predicting or determining them becomes challenging. This paper is devoted to the complete understanding of propagation dynamics to a cooperative Lotka–Volterra system, in addition of the determinacy of these speeds. The first major contribution of this paper is to establish a necessary and sufficient condition for the existence of a single spreading speed. In the existence of a single spreading speed (i.e., the two species share a common invasion speed), nonnegative traveling wave profiles, connecting the extinction equilibrium, exist, if the wave speed is not less than the common speed. We find that predicting or determining the invasion speed can be linked to the linearized system at the extinction state, and linear/nonlinear selections are established. The existence of multiple spreading speeds indicates new connections of traveling wave profiles into certain intermediate states. Due to this, the determinacy of multiple spreading speeds focuses not only on the extinction state but also on the corresponding intermediate states. Based on our constructions of upper–lower solutions, we also establish analytic criteria that can determine the fast–slow invasive speeds. Our speed selection mechanism can also help scientists greatly understand the movement of stacked fronts in cooperative systems with multiple species. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new traveling wave with a buffer zone, which is approached by an asymmetric credit migration model with fixed migration boundary. The asymptotic behavior of the solution of the model is discussed. By constructing two sets of sub and super solutions sequences, it is proved that the solution of the credit rating migration model approaches the new traveling wave with buffer zone as time goes to infinite in a direction. Additionally, some numerical results are presented. [ABSTRACT FROM AUTHOR]

In this article, the non-linear (2+1)-dimensional conformable time-fractional Schrödinger equation of order α where 0 < α ≤ 1, has been studied within introducing an appropriate fractional traveling wave transformation. The reliable and powerful method, namely the Improved Bernoulli sub equation function method, is applied to investigate some solitary wave, traveling wave and periodic solutions to the aforementioned model which is crucial significance because the model is in the fields of quantum mechanics and energy spectrum. The obtained solutions are new and significant in revealing the pertinent features of the physical phenomenon. Moreover, gotten solutions have been plotted in several kinds, such as in 3-D or 2-D. The impacts of the time evolution are offered in 2-D graphs for visual observation of the properties of the solutions. [ABSTRACT FROM AUTHOR]

The electro-thermo-convection of a dielectric liquid in a horizontal capacitor is investigated under the autonomous charge injection from the cathode and heating from above. In the case of a DC electric field, the linear stability analysis is carried out, and the thresholds of monotonic and oscillatory instability are determined. The finite difference method is used for the numerical simulation of the nonlinear behavior of electro-thermo-convective patterns: stationary convection and traveling waves. In the case of AC, electric field transient and permanent oscillations are analyzed. Two types of stable solutions are found. The modulated traveling waves are characterized by the quasiperiodic oscillations of convective characteristics. Another solution is modulated electroconvection (MEC). The patterns of MEC oscillate around some average flow synchronously with the external AC field and do not move laterally. The average intensity of convective mixing in modulated traveling waves is several times less than in modulated electroconvection. The spatiotemporal evolution of the stream function, temperature, and charge distributions for different types of transient and permanent solutions are analyzed. [ABSTRACT FROM AUTHOR]

We discuss numerical challenges in calculating stable and unstable steady states of widely used dynamic semiconductor laser models. Knowledge of these states is valuable when analyzing laser dynamics and different properties of the lasing states. The example simulations and analysis mainly rely on 1(time)+1(space)-dimensional traveling-wave models, where the steady state defining conditions are formulated as a system of nonlinear algebraic equations. The performed steady state calculations reveal limitations of the Lang-Kobayashi model, explain nontrivial bias threshold relations in lasers with several electrical contacts, or predict and explain transient dynamics when simulating such lasers. [ABSTRACT FROM AUTHOR]

We consider the reaction-diffusion competition system in the so-called critical competition case. The associated ODE system then admits infinitely many equilibria, which makes the analysis intricate. We first prove the nonexistence of ultimately monotone traveling waves by applying the phase plane analysis. Next, we study the large time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the "faster" species excludes the "slower" one (with a known spreading speed), but also provide a sharp description of the profile of the solution, thus shedding light on a new bump phenomenon. [ABSTRACT FROM AUTHOR]

Traveling wave solutions have played a vital role in demonstrating the wave character of nonlinear problems emerging in the field of mathematical sciences and engineering. To depict the nature of propagation of the nonlinear waves in nature, a range of nonlinear evolution equations has been proposed and investigated in the existing literature. In this article, solitary and traveling periodic wave solutions for the (2 + 1)‐dimensional modified KdV‐KP equation are derived by employing an ansatz method, named the enhanced (G′/G)‐expansion method. For this continued equation, abundant solitary wave solutions and nonlinear periodic wave solutions, along with some free parameters, are obtained. We have derived the exact expressions for the solitary waves that arise in the continuum‐modified KdV‐KP model. We study the significance of parameters numerically that arise in the obtained solutions. These parameters play an important role in the physical structure and propagation directions of the wave that characterizes the wave pattern. We discuss the relation between velocity and parameters and illustrate them graphically. Our numerical analysis suggests that the taller solitons are narrower than shorter waves and can travel faster. In addition, graphical representations of some obtained solutions along with their contour plot and wave train profiles are presented. The speed, as well as the profile of these solitary waves, is highly sensitive to the free parameters. Our results establish that the continuum‐modified KdV‐KP system supports solitary waves having different shapes and speeds for different values of the parameters. [ABSTRACT FROM AUTHOR]

Keller–Segel system models prototype of the population-based chemotaxis, which describes the oriented or partially oriented movement of cells in response to a chemical signal produced by the cells themselves. This paper focuses on dynamics of a class of Keller–Segel systems with a large diffusion. We obtain several different kinds of traveling waves and characterize their spectral stability. The main tools are geometric singular perturbation theory, qualitative theory and spectral analysis via the method of nonlocal eigenvalue problem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the traveling wave solutions of diffusive disease models with a general incidence rate, nonlocal interaction and transmission delay. We prove that a positive traveling wave solution exists if the wave speed is bigger than a threshold value and does not exist if the wave speed is smaller than this value. We also investigate the dependence of this critical wave speed on the diffusion coefficient of the infected population and average transmission delay. In the critical case when the wave speed equals the threshold value, we obtain the existence of nontrivial traveling waves without nonlocal interaction or transmission delay. We further develop numerical methods to simulate traveling wave solutions and estimate disease propagation speed. It is observed from numerical simulations that disease propagation speed is strictly less than the critical wave speed. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of circular ring traveling wave linear ultrasonic motor with incomplete teeth. The motor's movable slider is pressed against the end face of the tooth structure on the outer surface of the circular ring vibrator under a certain pre-pressure, four piezoelectric ceramic plates are evenly distributed at 90° intervals on the inner side of the circular structure, and four sets of driving teeth are arranged at 45° intervals from the position of the piezoelectric ceramic plates.When the motor is in operation, only one driving tooth works, and the life of the ultrasonic motor can be increased by rotating the different working teeth. The motor operates in two in-plane third-order bending modes that are orthogonal to each other at the same frequency. The dynamic design and simulation of the vibrator was carried out using ANSYS finite element software to analyze the effect of the structure on the mode. The principle prototype was fabricated, and the operating mode of the vibrator was measured using a laser Doppler vibrometer (LDV), and the vibration characteristics and output performance of the prototype were tested. Experimental results show that the motor runs smoothly at the excitation voltage of 240 V peak-to-peak, the excitation frequency of 30.459 kHz and the pre-pressure of 0.6 N, with the maximum output force of 90 mN and the motor no-load speed of 102 mm/s. [ABSTRACT FROM AUTHOR]

In this paper, we study new classes of differential equations of fractional order. The first considered problem involves the derivative of Caputo, while the second one involves conformable Khalil derivative. For the first class, we prove an existence and uniqueness result, then, we discuss an example to show the applicability of the result. For the second one, we apply the exp-function method to find new traveling wave solutions for a generalised conformable fractional partial differential equation, then some examples on Ostrovsky and KdV equations are given to illustrate the efficiency and accuracy of the method. Some graphs are plotted and discussed to show more the importance of the obtained results. [ABSTRACT FROM AUTHOR]

A key feature of (1 + 1) -dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave solutions for (1 + 1) -dimensional systems of nonlinear wave equations, given a certain asymptotic null condition and sufficient decay for the traveling wave. We first consider semilinear systems as a simpler model problem; we then proceed to treat more general quasilinear systems. [ABSTRACT FROM AUTHOR]

This paper proposes a prediction strategy for the hydrodynamic performance of bionic fish. The major challenges are meshing and building prediction model. The NACA0012 airfoil is used to replace the fish driven by the body and/or caudal fin (BCF), and a two-dimensional swimming geometric model is constructed. The geometric model is divided into hybrid meshes using the overset mesh method. The classical traveling wave model is studied using Matlab, and an improved self-propelled motion model is established. The hydrodynamic performance of the self-propelled model is numerically simulated based on computational fluid dynamics (CFD). In this strategy, the geometric model and the self-propelled motion model are integrated with user defined functions (UDF). The influences of the parameters such as inflow velocity, frequency, wavelength, and head fluctuation amplitude on the motion performance are studied. The results show that when inflow velocity is uniform, the self-propelled motion will eventually reach a quasi-steady state. According to the numerical simulation results, a hydrodynamic performance prediction model is established based on multilayer perceptron (MLP). The model is used to predict the performance of the optimized traveling wave parameters, and the error is within 3 %. The accuracy and generalization ability of the MLP prediction model is verified. [ABSTRACT FROM AUTHOR]

Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among the mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold, it is critical to consider the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes created by a local release of the infected mosquitoes. We develop and analyze PDE models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion with a bubble-shaped distribution, called the \critical bubble." The critical bubble is optimal in its release size compared to other spatial profiles in a one-dimensional landscape. The fraction of infection near the release center is higher than the threshold level for the corresponding homogeneously mixing ODE models. We show that the proposed spatial models give rise to the traveling waves of Wolbachia infection when above the threshold. We quantify how the threshold condition and traveling-wave velocity depend on the diffusion coefficients and other model parameters. Numerical studies for different scenarios are presented to inform the design of release strategies. [ABSTRACT FROM AUTHOR]