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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]

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]

The shallow-water wave equations with different forms of delays are presented in this work, such as no delay, local delay and nonlocal delay, which are described in the form of convolutions with different kernels. These shallow-wave equations satisfy the asymptotic integrability condition and include the Korteweg-de Vries equation, Camassa-Holm equation and Degasperis-Procesi equation as particular cases. The existence and non-existence of solitary wave are established by the invariant manifold theory and geometric singular perturbation theory. It is found that different delays have various effects on the existence of solitary waves. In particular, the Melnikov functions with divergence free or not are derived for different delays to measure the separation of stable and unstable manifolds, so that the existence of solitary waves could be justified. [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]

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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]

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]

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]

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]

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]

When overhead lines are impacted by lightning, the traveling wave of the fault contains a wealth of fault information. The accurate extraction of feature quantities from transient components and their classification are fundamental to the identification of lightning faults. The extraction process may involve modal aliasing, optimal wavelet base issues, and inconsistencies between the lightning strike distance and the fault point. These factors have the potential to impact the effectiveness of recognition. This paper presents a method for identifying lightning strike faults by utilizing Kullback–Leibler (KL) divergence enhanced Variational Mode Decomposition (VMD) and Symmetric Geometry Mode Decomposition (SGMD) improved with Permutation Entropy (PE) to address the aforementioned issues. A model of a 220 kV overhead line is constructed using real faults to replicate scenarios of winding strike, counterstrike, and short circuit. The three-phase voltage is chosen and then subjected to Karenbaren decoupling in order to transform it into zero mode, line mode 1, and line mode 2. The zero-mode voltage is decomposed using KL-VMD and PE-SGMD methods, and the lightning identification criteria are developed based on various transient energy ratios. The research findings demonstrate that the criteria effectively differentiate between winding strike, counterstrike, and short-circuit faults, thus confirming the accuracy and efficacy of the lightning fault identification criteria utilizing KL-VMD and PE-SGMD. [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]

This article deals with the existence of traveling wave solutions of a spatial diffusion predator-prey model that includes the Allee effect on prey and the simplified Holling type Ⅲ functional response function. Moreover, we assume that the wave speed is much greater than the diffusion rate of the prey and that the growth rate of the prey is much greater than the growth rate of the predator. In this case, the geometric singular perturbation theory is an important tool to analyze such a singularly perturbed equation. The existence of relaxation oscillations, canard cycles, canard explosions and inverse canard explosions phenomena of the system restricted to the critical manifold are illustrated by means of entry-exit functions, Fenichel's theory and normal form theory. Furthermore, we establish sufficient conditions for the existence of the monotone traveling waves, non-monotone traveling waves and periodic wave trains. The coexistence of two isolated periodic wave trains is also discussed in this article. And some simulation figures are introduced to support these results. Above all, we show the generation and disappearance of the periodic wave trains due to the canard explosion and the inverse canard explosion. [ABSTRACT FROM AUTHOR]

AbstractWe 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]

We solve the traveling wave solution for the explicit-time nonlinear photorefractive dynamics equation. Nonlinearity comes from the support of linear and quadratic electro-optic effects. We investigate two cases, i.e., the wave assumes to be in low amplitude and without such an assumption. In this step, we apply the direct solution method by setting the ansatz of the wave solution from the start. The first case relies on the Taylor series expansion to integrate the equations of these results and get an exact solution for the traveling wave. In the second case, we thoroughly evaluate the original dynamic equation. It reduces to a first-order differential equation that provides the initial conditions for a numerical evaluation. The exact solution shows the propagation wave traveling in the positive and negative directions in the diffraction axis direction. An angle between the traveling wave and the center of the propagation plane decreases as the value of the displacement constant in the solution increases. In addition, we also study the power of the traveling wave, and the numerical solution gives a kink-like traveling wave. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the (2+1)-dimensional Hirota system of equations, which is essential for modeling physical events since it contains the NLS equation and the cmKdV equation. We apply the Jacobi elliptic function method to obtain new results. By using some ansatz in terms of finite Jacobi elliptic functions, we have obtained various exact solutions, such as dark solitons, bright solitons, and periodic solutions. Moreover, for some reductions as α=0,β=1 and α=1,β=0, we obtain the exact solutions for the (2+1)-dimensional NLS equation and the (2+1)-dimensional cmKdV equation. The dynamics of the obtained solutions are presented in the figures. We also analyze the phase portraits of the (2+1)-dimensional Hirota system.

Due to the discontinuous wave impedance, uneven line parameters, and complex and changeable fault transient traveling waves of overhead-cable hybrid transmission lines, the traditional double-ended traveling wave ranging method will produce large errors. Aiming at this problem, this paper proposes a fault location method for multi-point hybrid transmission lines based on Hilbert-Huang transform (HHT). First, the effective identification of the traveling wave head is completed at both ends of the line and at the connection point between the overhead line and the cable line, and then the HHT is used to extract the time when the fault traveling wave head reaches the measurement point, and finally it is substituted into the multi-point ranging equation to calculate the fault. The result of the ranging. The simulation results of MATLAB/PSCAD show that the method proposed in this paper avoids the influence of traveling wave velocity on the ranging accuracy, and is not affected by the line structure. Compared with the traditional double-ended ranging method, its ranging accuracy is higher. At the same time, it can also meet the requirements of engineering practice positioning accuracy within 200m.

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]

In this paper, we investigate the dynamical behavior of traveling waves for a generalized Vakhnenko-Parkes-modified Vakhnenko-Parkes (VP-mVP) equation with non-homogeneous power law nonlinearity. By the dynamical systems approach and the singular traveling wave theory, the existence of all possible bounded traveling wave solutions is discussed, including smooth solutions (solitary wave solutions, periodic wave solutions and breaking wave solutions) and non-smooth solutions (solitary cusp wave solutions and periodic cusp wave solutions). We not only obtain all the explicit parametric conditions for the existence of 5 kinds of bounded traveling wave solutions, but also give their exact explicit expressions. Moreover, we qualitatively analyze the dynamical behavior of these traveling waves by using the bifurcation of phase portraits under different parameter conditions, and strictly prove the evolution of different traveling waves with their exact expressions. [ABSTRACT FROM AUTHOR]

Approximation and analysis are used for investigating accurate soliton solutions of the ill-posed Boussinesq (IPB) equation. The investigated model explains shallow-water gravitational waves. It examines one-dimensional nonlinear strings and lattices. IPB explains small-amplitude surface waves on nonlinear strings and lattices. We provide unique analytical solutions to analyze numerical beginning and boundary conditions. A solution's quality is judged by its divergence from analytical predictions. Physical wave properties are illustrated. [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 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]

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]

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]

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]

Many systems in life sciences have been modeled by reaction–diffusion equations. However, under some circumstances, these biological systems may experience instantaneous and periodic perturbations (e.g. harvest, birth, release, fire events, etc) such that an appropriate formalism like impulsive reaction–diffusion equations is necessary to analyze them. While several works tackled the issue of traveling waves for monotone reaction–diffusion equations and the computation of spreading speeds, very little has been done in the case of monotone impulsive reaction–diffusion equations. Based on vector-valued recursion equations theory, we aim to present in this paper results that address two main issues of monotone impulsive reaction–diffusion equations. Our first result deals with the existence of traveling waves for monotone systems of impulsive reaction–diffusion equations. Our second result tackles the computation of spreading speeds for monotone systems of impulsive reaction–diffusion equations. We apply our methodology to a planar system of impulsive reaction–diffusion equations that models tree–grass interactions in fire-prone savannas. Numerical simulations, including numerical approximations of spreading speeds, are finally provided in order to illustrate our theoretical results and support the discussion. [ABSTRACT FROM AUTHOR]

The article considers methods for measuring grain moisture. The authors carried out the analysis and selected significant parameters that affect the measurement of grain moisture. Methods and ways of grain moisture control are investigated. Modern technological methods of production of agricultural products are largely related to moisture content. The excess or lack of moisture in the material affects its physico-chemical, physico-mechanical and operational properties, as well as quality indicators. Quick and accurate determination of water content in a particular material, both in the production process and during operation, is the most important task. The accuracy and measurement errors of moisture content of moisture meters significantly depend on the density of materials and the parameters of the measurement medium. The optimal method for the most accurate measurement of humidity has been determined. Growing requirements for the quality and competitiveness of domestic agricultural products put forward new requests for the devices and facilities for express moisture control in most technological processes. Modern technological processes require universal devices that control the moisture content of a wide range of agricultural materials. Having analyzed in detail and determined the significant parameters that affect the measurement of grain moisture, the paper proposes mathematical model of ultra-high-frequency measuring transformation of the moisture of grain crops, the essence of which is to measure the power of this signal at the output of the waveguide when the grain moisture changes by using a traveling wave. By means of the analysis, carried out, the authors suggested the structural diagram of ultra-high-frequency humidity meter of cereal crops which realizes the mathematical model, proposed in the paper. [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]

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]

In this paper we investigate traveling waves for a generalized two-component rotation b-family (R-b-family) system with b > 1 . Based on qualitative theory and bifurcation method of dynamical systems, the traveling wave problem is converted into the dynamical analysis of the corresponding traveling wave system with 5 parameters and 2 distinct singular lines. We systematically analyze this traveling wave system with the help of the three-step method to obtain 6 bifurcation curves of its phase portraits, which enables us to draw all the phase portraits. Combining these phase portraits, we get that the R-b-family system has exactly 6 kinds of bounded traveling wave solutions and give all the explicit conditions for their existence as well as their expressions and coexistence. Finally, discussing dynamical behavior of these traveling waves, we not only provide the bifurcation wave velocities for solitary wave solutions of peak and valley type, for solitary cusp wave solutions of peak and valley type and for periodic cusp wave solutions of peak and valley type, respectively, but also find 3 other types of traveling wave evolution, namely kink wave bifurcation, solitary cusp bifurcation and periodic wave bifurcation. [ABSTRACT FROM AUTHOR]

A mathematical model of the effect of axial current in plasma on cylindrical nonrelativistic nonlinear oscillations is constructed. As a result of the coordinated interaction of electromagnetic fields and particles, plasma oscillations are transformed into a nonlinear traveling wave. For its initialization, the method for constructing the missing initial conditions based on solving a linear problem in the form of Fourier–Bessel integrals is proposed. A traveling wave is numerically simulated using the scheme of the finite difference method of the second order of accuracy. It is shown that the wave velocity increases with an increase in the magnitude of the current, which contributes to the removal of energy from the initial region of localization of oscillations. For this reason, the breaking effect is realized much later in time; i.e., the stabilization of oscillations is observed. [ABSTRACT FROM AUTHOR]