Form Of Traveling Waves Research Articles

Ion Mobility Separations Using Cocentric Architecture.

Ion mobility separations, especially using drift tube ion mobility spectrometers, are usually performed in linear channels, which can have a large footprint when extended to achieve higher resolving powers. In this work, we explored the performance of an ion mobility device with a curved architecture, which can have a more compact form. The cocentric ion mobility spectrometer (CoCIMS) manipulates ions between two cocentric surfaces containing a serpentine track. The mobility separation inside the CoCIMS is achieved using traveling waveforms (TWs). We initially evaluated the device using ion trajectory simulations using SIMION, which indicated that when ions traveled circularly inside the CoCIMS they resulted in similar resolving powers and transmitted m/z range as traveling in a straight path. We then performed experimental validation of the CoCIMS in conjunction with a TOF MS. The CoCIMS was made of two flexible printed circuit board materials folded into cocentric cylinders separated by a gap of 2.8 mm. The device was about 50 mm diameter ×152 mm long and provided 1.846 m of serpentine path length. Three sets of mixtures (Agilent tune mixture, tetraalkylammonium salts, and an eight-peptide mixture) and four traveling waveform profiles (square, sine, triangle, and sawtooth) were used. The sawtooth TW profile produced a slightly higher resolving power for the Agilent tuning mixture and tetraalkylammonium ions. The average resolving power for Agilent tune mixture ions ranged from 37 (using sawtooth TW) to 27 (using square TW). The average resolving powers ranged from 45 (sawtooth TW) to 31 (square TW) for tetraalkylammonium ions. The resolving power of the peptide mixture ions was similar among the four TW profiles and ranged from 51 to 56. The average percent error in TWCCS for the peptide mixture ions was about 0.4%. The new device showed promising results, but improvements are needed to further increase the resolving power.

A mathematical model on the propagation of tau pathology in neurodegenerative diseases.

A system of partial differential equations is developed to study the spreading of tau pathology in the brain for Alzheimer's and other neurodegenerative diseases. Two cases are considered with one assuming intracellular diffusion through synaptic activities or the nanotubes that connect the adjacent cells. The other, in addition to intracellular spreading, takes into account of the secretion of the tau species which are able to diffuse, move with the interstitial fluid flow and subsequently taken up by the surrounding cells providing an alternative pathway for disease spreading. Cross membrane transport of the tau species are considered enabling us to examine the role of extracellular clearance of tau protein on the disease status. Bifurcation analysis is carried out for the steady states of the spatially homogeneous system yielding the results that fast cross-membrane transport combined with effective extracellular clearance is key to maintain the brain's healthy status. Numerical simulations of the first case exhibit solutions of travelling wave form describing the gradual outward spreading of the pathology; whereas the second case shows faster spreading with the buildup of neurofibrillary tangles quickly elevated throughout. Our investigation thus indicates that the gradual progression of the intracellular spreading case is more consistent with the clinical observations of the development of Alzheimer's disease.

On the dynamics of the (2+1)-dimensional chiral nonlinear Schrödinger model in physics

The nonlinear Schrödinger equation is one of the significant nonlinear complex models describing the optical solitons in dispersive media. In this study, the (2+1)-dimensional chiral nonlinear Schrödinger model has been investigated analytically which is of key importantance in the field of fluid sciences. A variety of exclusive travelling waveform solutions have been established for the complex dynamical model by employing a set of eminent analytical approaches namely the extended modified auxiliary equation mapping method, the improved F-expansion method, and the unified method, respectively. We obtained different forms of solitary types solutions with the help of these technique. The outcomes are a set of bell-shaped, single periodic, optical, and multi-periodic solutions. Finally, the stability of the developed results is also established to validate the computations. The study provides a very spectacular and appropriate way to put together several interesting wave demonstrations for more complex models of current era.

Novel Wentzel–Kramers–Brillouin Solutions to the Nonisentropic Helmholtz Equation in a Nonuniform Duct With Mean Temperature Gradient and Mean Flow

Abstract We derive the generalized Helmholtz equation (GHE) governing nonisentropic acoustic fluctuations in a quasi 1D duct with nonuniform cross section, mean temperature gradient, and nonuniform mean flow. Nonisentropic effects are included via heat conduction terms in the mean and fluctuating energy equations. To derive the Helmholtz equation exclusively in terms of the fluctuating pressure field, a relationship between density and pressure fluctuations is needed, which is shown to be a second-order differential equation for nonisentropic motions. Novel analytical solutions that are accurate for both low/high frequencies and small/large mean gradients are presented for the GHE based on the Wentzel–Kramers–Brillouin (WKB) method. WKB solutions are developed using the ansatz that the pressure fluctuation field has a travelling wave form, p^(x)=exp[∫0x(a+ib)dx], where x is the axial coordinate. Substituting this form into the Helmholtz equation yields coupled, nonlinear ordinary differential equations (ODEs) for a and b. Analytical solutions to the ODEs are obtained using the approximations of high frequency and slowly varying mean properties. This simplification allows us to obtain the lower order solutions b0 and a0. We then enhance solution accuracy by using a0 to solve for b1 without any approximations. Finally, b1 is employed to get a1, giving us the higher order solution. The p^ calculated from (a1, b1) is in good to excellent agreement with numerical solution of the GHE for both low and high frequencies and for a range of mean Mach numbers, including M¯≳1.

Traveling Wave Solutions to the Free Boundary Incompressible Navier‐Stokes Equations

AbstractIn this paper we study a finite‐depth layer of viscous incompressible fluid in dimension , modeled by the Navier‐Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving interface. A uniform gravitational field acts perpendicularly to the flat surface, and we consider the cases with and without surface tension acting on the free interface. In addition to these gravity‐capillary effects, we allow for a second force field in the bulk and an external stress tensor on the free interface, both of which are posited to be in traveling wave form, i.e., time‐independent when viewed in a coordinate system moving at a constant velocity parallel to the rigid lower boundary. We prove that, with surface tension in dimension and without surface tension in dimension , for every nontrivial traveling velocity there exists a nonempty open set of force and stress data that give rise to traveling wave solutions. While the existence of inviscid traveling waves is well‐known, to the best of our knowledge this is the first construction of viscous traveling wave solutions.Our proof involves a number of novel analytic ingredients, including: the study of an overdetermined Stokes problem and its underdetermined adjoint problem, a delicate asymptotic development of the symbol for a normal‐stress to normal‐Dirichlet map defined via the Stokes operator, a new scale of specialized anisotropic Sobolev spaces, and the study of a pseudodifferential operator that synthesizes the various operators acting on the free surface functions. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equations in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions. Some exact solutions in traveling wave forms are explicitly expressed by the proposed method for both the Korteweg-de Vries and modified Korteweg-de Vries equations.

A Green’s function approach for nonreciprocal vibrations of finite elastic structures with spatiotemporally modulated material properties

The spatiotemporal modulation of material properties in acoustic and elastic metamaterials is one way to realize dynamic nonreciprocity for mechanical wave propagation and vibration of finite systems. A recent study on nonreciprocal vibrations of finite elastic beams has shown that strong nonreciprocal input-output responses resulting from the spatiotemporal modulation only occur for a small subset of modulation parameters, which may complicate the design of nonreciprocal systems [Goldsberry et al., Phys. Rev. B 102 (2020)]. In this work, we derive a Green’s function approach for finite elastic systems with spatiotemporally modulated material properties, which mathematically describes the modulated system response for a given set of boundary conditions. As a case example, we investigate two-dimensional flexural vibrations of a plate whose stiffness is modulated in a traveling wave form. We then investigate the first order corrections to the unmodulated system by utilizing an asymptotic expansion in the small parameter defining the modulation strength. Finally, we find conditions on the material and modulation parameters that yield a large degree of nonreciprocity. The present analysis leads to potential applications in acoustic communications, vibration suppression, and energy harvesting. [Work supported by NSF EFRI.]

Traveling-wave control of the bending wave in a beam for high quality sound radiation

The bending wave generated by the actuator exciting a panel can be controlled to be in the traveling wave form void the structural resonances, which deteriorates the radiated sound if the panel is used as a speaker. Although such traveling-wave control method (TCM) yields a wider effective frequency range than the modal control method, the requirement of using many actuators is the practical problem yet. If a beam is employed instead of a plate as a panel speaker, the number of actuators can be reduced despite a smaller radiating surface than a plate. This study adopts three actuators for the beam control using TCM. An actuator excites the beam in the middle position, and the two actuators near the two edges are used to suppress the reflected waves from the boundaries. The control result shows that the driving-point mobility of the primary actuator is converted into that of an infinite beam, which means that the boundaries are changed into anechoic ones and the structural resonances are eliminated. Accordingly, the beam radiates a smooth sound spectrum without sharp peaks and troughs related to the resonant responses. Effects of material and dimension in determining the effective frequency range are also explored.

Responses and suppression of Joined-Wing UAV in wind field based on distributed model and active disturbance rejection control

For a Joined-Wing configuration UAV, the front and rear wing are joined at the wingtip, but they are far away at the roots, and their areas are comparable. These special geometric features make its behaviors quite different in wind field. So it's important to comprehend these behaviors accurately and to improve the safety of flight of Joined-Wing configurations. In this paper, firstly, a high-fidelity nonlinear distributed flight dynamics model coupling with distributed wind field are derived based on a distributed aerodynamics model. Base on this, the influence of gust on flight dynamics mode characteristics are analyzed. The mechanism that gust will significantly weaken the longitudinal stability of a UAV are derived. After that, the dynamic responses of a Joined-Wing UAV flying through a 3D wind field are studied by adopting centralized and distributed dynamics model respectively. Finally, a pitch controller is designed by Active Disturbance Rejection Control (ADRC) method for the Joined-Wing UAV in the 3D wind field environment, and the advantage of ADRC for the safety of flight is demonstrated by simulations. The results show that, with the help of the high-fidelity distributed model, a distinct traveling wave form excitation phenomenon is revealed while a Joined-Wing UAV flying through a 3D wind field. It's also can be found that, for the high-fidelity distributed model, the effect time of wind is longer, the disturbance of flight parameters is about twice more than the centralized model. More seriously, the initial response of pitch angle is reversed compared with that of the centralized model. With the traveling wave form excitation while flying through a 3D wind field, a traditional PID controller wouldn't ensure the safety of flight since the max pitch angle would reach to about 16 degrees. In comparison, the maximum pitch angle disturbance is suppressed to less than 3 degrees at the same conditions while applying the ADRC controller.

Kink dynamics in a nonlinear beam model

In this paper, we study the single kink and the kink-antikink collisions of a nonlinear beam equation bearing a fourth-derivative term. We numerically explore some of the key characteristics of the single kink both in its standing wave and in its traveling wave form. A point of emphasis is the study of kink-antikink collisions, exploring the critical velocity for single-bounce (and separation) and infinite-bounce (where the kink and antikink trap each other) windows. The relevant phenomenology turns out to be dramatically different than that of the corresponding nonlinear Klein-Gordon (i.e., ϕ4) model. Our computations show that for small initial velocities, the kink and antikink reflect nearly elastically without colliding. For an intermediate interval of velocities, the two waves trap each other, while for large speeds a single inelastic collision between them takes place. Lastly, we briefly touch upon the use of collective coordinates (CC) method and their predictions of the relevant phenomenology. When one degree of freedom is used in the CC approach, the results match well the numerical ones for small values of initial velocity. However, for bigger values of initial velocity, it is inferred that more degrees of freedom need to be self-consistently included in order to capture the collision phenomenology.

Oscillatory Rayleigh–Bénard Convection in elasto-viscoplastic gels

Abstract Rayleigh–Benard convection (RBC) is studied in an elasto-viscoplastic (EVP) gel, the widely used and studied Carbopol gel. The transition from conductive to convective regime is determined by the Schmidt–Milverton principle which leads to a critical value of the inverse of the Yield number 1 ∕ Y c . However, an oscillatory motion in the gel is observed below 1 ∕ Y c ≈ 60 when smooth and untreated walls are used. Particles within the gel describe periodical loops close to their initial positions for 16 . 5 1 ∕ Y 25 . For larger values of 1 ∕ Y ≈ 50 1 ∕ Y c , loops are still obtained but particles move away progressively from their initial position. The oscillations take the form of periodic traveling waves (TW). We demonstrate that elastic effects play the major role in the occurrence of oscillations.

Performance study of propulsion of N-link artificial Eukaryotic flagellum swimming microrobot within a fractional order approach: From simulations to hardware-in-the-loop experiments

The understanding of how bioinspired artificial microrobots propel themselves by propagating a planar wave along their flagellum is crucial to improve their mechanical design, as well as their performance. Likewise, the implementation of such a planar wave motion in N-link swimming microrobots involves several challenges, among with the motion control of actuators can be highlighted, whose load (viscous drag forces) does not only depend on their own link and motion, but also on their position along the flagellum. This paper proposes an improved locomotion for an N-link artificial Eukaryotic flagellum (AEF) swimming microrobot taking into account a fractional order approach for both the waveform design for propulsion and the control of the flagellum distributed dynamics. On the one hand, the novel way of swimming, based on a fractional order power law for the amplitude modulation, allows to preserve the motion properties obtained applying classical traveling waveforms, but presenting some benefits in terms of propulsion. On the other, a robust fractional order proportional-derivative (PDμ) controller is designed for the motion control of the microrobot. To demonstrate the advantages and validate both the waveform and the control strategy proposed, a hardware-in-the-loop (HIL) testbed for a 4-link robot is built. It consists of a microrobot simulator developed with the physical modeling tools in the MATLAB/Simulink environment and the embedded microcontroller Atmel ATmega32u4, where the control of the robot is programmed. The testbed, thanks to the simulator, allows to select different modes of swimming and geometry for the microrobot, as well as evaluating the performance of the locomotion in terms of propulsion, power efficiency or tracking. Experimental and simulation results are given to show that the best efficiency, with regard to both the way of swimming and the energy consumption with the control applied, is achieved with the proposed fractional approach.

Spatial genetic structure at the leading edge of a spruce budworm outbreak: The role of dispersal in outbreak spread

Outbreaking insects often undergo rapid population growth synchronously in multiple locations separated by large distances. Dispersal may play an essential role in synchronizing outbreaks over large geographic areas but its role in outbreak spread remains unclear. In our study, we used population genetics to assess how much dispersal contributes to the spread of a major forest pest, the spruce budworm (Choristoneura fumiferana Clemens). Using spatial analyses of genotypic data, we determined the extent to which dispersing individuals from epidemic populations in Quebec leave their genetic signature in adjacent, rising populations in New Brunswick and Maine. A lack of genetic differentiation between endemic and epidemic populations would indicate that outbreak spread depends on effective dispersal from epidemic to endemic regions. In contrast, endemic populations that are distinct from epidemic population would suggest that dispersal plays a reduced role in fomenting outbreak rise. An intermediate possibility with differentiation between epidemic and endemic population as a continuous spatial gradient might suggest a temporal lag in genetic differentiation that may take the form of a genetic travelling wave. PCA, cluster analyses, isolation by distance, and sPCA were used to characterize spatial genomic variation using 300 SBW larvae sampled in 2015 and genotyped at thousands of genome-wide SNPs. We found support for a genetic travelling wave pattern, matching the SBW density pattern. These results indicate that dispersal may trigger the transition of populations from the endemic to the epidemic state and thereby drive outbreak spread. By supplementing persisting endemic populations, migrants may drive populations to beyond levels that can be controlled by local biotic constraints. These results support the underlying justification of ongoing outbreak containment efforts in Atlantic Canada (i.e., the Early Intervention Strategy), although continued sampling as the outbreak progresses is needed confirm the temporal stability of the observed patterns.

On the propagation of temperature-rate waves and traveling waves in rigid conductors of the Graffi–Franchi–Straughan type

We examine second-sound phenomena in a theoretically-motivated class of rigid solids within which the flow of heat is described by a special case of the Maxwell–Catteneo flux law. Employing a combination of analytical and numerical methods, we examine both temperature-rate waves and thermal traveling waves in this class of solids, which have recently been termed Graffi–Franchi–Straughan type (thermal) conductors. The particular temperature-dependent form of the thermal relaxation time, which is the distinguishing feature of this class, gives rise to a variety of nonlinear effects; specifically, finite-time temperature-rate wave blow-up, ‘retrograde’ behavior, and temperature traveling waveforms that exhibit a ‘tongue’. The presentation concludes with a discussion of possible follow-on studies.

Semi-implicit methods for the dynamics of elastic sheets

Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints that arise in explicit methods while avoiding much of the complexity of fully-implicit approaches. For a triangular lattice discretization with stretching and bending springs, our semi-implicit approach involves discrete Laplacian and biharmonic operators, and is stable for all time steps in the case of overdamped dynamics. For a more general finite-difference formulation that can allow for general elastic constants, we use the analogous approach on a square grid, and find that the largest stable time step is two to three orders of magnitude greater than for an explicit scheme. For a model problem with a radial traveling wave form of the reference metric, we find transitions from quasi-periodic to chaotic dynamics as the sheet thickness is reduced, wave amplitude is increased, and damping constant is reduced.

Fault Analysis of High-Voltage Circuit Breakers Based on Coil Current and Contact Travel Waveforms Through Modified SVM Classifier

High-voltage circuit breakers (HVCBs) play a substantial protection role in power networks. The reliable operation of these critical components leads to an increment of resiliency and safety of power systems. It is essential to design a fault diagnostic system that detects the defects in preliminary levels and identify the origins to establish a precise maintenance task. This paper focuses on coil current and contact travel waveforms as significant signals that bear helpful information about the fault occurrence for a typical EDF, 72.5 kV, SF6 HVCB. Healthy and faulty signals simulated based on Michael Stanek's HVCB model in MATLAB, with performing some modifications in the actuating coil and operating mechanism. In the first step, to arrange an efficient fault recognition system, neural network and support vector machine (SVM) have been designed using the information of 475 simulated healthy and faulty HVCBs and verified for 200 new samples. In the second step, to improve the classification results, an additional distinction algorithm has been recommended for the cases in which two failure modes are detected by the classifier. Since any failure mode's impact on the selected features is different, the proposed diagnostic method makes a decision, between two classes of faults, based on the extracted pattern of each failure mode. The recommended method, which is a combination of commonly used classification techniques and the defined algorithm, leads to the more accurate diagnosis.

Maintenance of Oscillations in Three-Dimensional Traveling Waves in Plane Poiseuille Flows

Two solutions of three-dimensional Navier–Stokes equations are studied numerically. These solutions describe the fluid motion in a plane channel, are of the traveling-wave form, and are periodic in the streamwise and spanwise directions. It is shown that, in each solution, the oscillations arise as a result of linear instability in the streamwise averaged velocity field. This instability is due to the existence of streamwise streaks known as the regions where the velocity is higher or lower than the mean velocity. A mechanism for the maintenance of streamwise vortices causing the formation of streaks is revealed. The obtained results confirm and extend the existing knowledge about the mechanism for the formation of near-wall turbulent structures.

Complex modal analysis of the movements of swimming fish propelled by body and/or caudal fin

Most fish generate thrusts by undulating their body and/or caudal fin (BCF). The movement of a fish body can typically be described as a propulsive wave with an increasing amplitude. In this study, we decompose the midline motions of swimming fish into travelling and standing components based on the complex orthogonal decomposition (COD) analysis. The travelling index, i.e., the relative ratio between the magnitudes of the travelling and standing components, is employed to analyze the typical locomotion of BCF fish. Using existing biological data, we find that anguilliform swimmers prefer wave motions with high travelling index (0.74∼0.90), while the motions of thunniform fish are dominated by a standing wave with the travelling index around 0.36∼0.64. For subcarangiform and carangiform fish, their motions are mixed by the travelling and standing waves with a medium travelling index (0.52∼0.78). The locomotion of BCF fish can be broadly classified into three categories by the travelling index: the standing-wave form, the mixture wave form, and the travelling-wave form. The new criterion is firstly applied to classify the locomotion of BCF fish, different from the traditional classification based on the fraction of fish body with lateral displacement. Moreover, the travelling index can also be used to evaluate the swimming performance, and to analyze the fish swimming dynamics.

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.

The heat and mass transfer modeling with time delay

Nonlinear hyperbolic reaction-diffusion equations with a delay in time are investigated. All equations considered here contain one arbitrary function. Exact solutions are also presented for more complex nonlinear equations in which delay arbitrarily depends on time. Exact solutions with a generalized separation of variables are found. For special cases, new exact solutions in the form of a traveling waves are obtained, some of which can be represented in terms of elementary functions. All of these solutions contain free (arbitrary) parameters, so that one can use them to solve modeling problems of heat and mass transfer with relaxation phenomena.