Elementary Waves Research Articles

Stimulation of Waves and Instabilities in Response to Irradiation of Electromagnetic Fields into Plasmas

Plasma is a unique phase of matter constituting positively or negatively charged atoms, excited atoms, neutral atoms, electrons, radicals, etcetera displaying a unique role in the nuclear fusion research besides studying electrical discharges in the domain of switching devices and biomedical applications lately. We discuss in this extensive proposition the fundamental plasma characteristics such as Debye length, plasma oscillations, plasma sheath and condition for sustainability and confinement of plasmas, besides examining the elementary waves in plasmas namely zero waves, electron plasma wave and ion plasma wave. The inherent electron plasma wave and ion plasma wave is associated with the driving of plasma currents which in turn depends upon the density perturbation and thermal velocities of the electrons and ions. The application of external electromagnetic radiation such as laser (pump wave) into the plasma modifies the dispersion relations of electron and ion plasma wave, respectively. The laser stimulates a plethora of waves in the plasma and undergoes remarkable physical phenomena such as self-focusing and filamentation of laser beams. The excitation of sideband waves of the laser beams into the plasma plays a key role in imparting ponderomotive force on the electron plasma waves leading to turbulence in the plasmas due to coupling of the waves. The oscillatory velocity of the electron due to pump wave, plasma density perturbation, ponderomotive force and current densities are associated with the excitation of instabilities in the plasma. Conclusively, such waves and instabilities in unmagnetized and magnetized plasma is comprehensively studied and concluded by proposing the investigation of unexplored twisted electromagnetic wave-plasma interaction.

Nonlinear stability of diffusive contact wave for a chemotaxis model

We consider a 2×2 system of hyperbolic-parabolic balance laws. Our system is the converted form under inverse Hopf-Cole transformation of a Keller-Segel type chemotaxis model with logistic growth, logarithmic sensitivity, non-diffusive chemical signal and density-dependent production/consumption rate. We study Cauchy problem when the Cauchy data are near a diffusive contact wave. The contact wave connects two different end-states as x→±∞, reflecting the situation when the logarithmic singularity plays an intrinsic role in the original chemotaxis model. We establish global existence of solution and study time asymptotic behavior of the solution. Consequently, we obtain nonlinear stability of the diffusive contact wave. Our result shows a significant difference when comparing our model to Euler equations with damping. In our case, there exists a secondary wave in the asymptotic ansatz. Therefore, the solution to Cauchy problem converges to the diffusive contact wave slower than in the case of Euler equations with damping. Besides its own physical relevance, our model is a prototype of a general system of hyperbolic-parabolic balance laws. Our results shed light on the future study of nonlinear stability of elementary waves for a general system.

Conical Statistical Optimal Near-Field Acoustic Holography with Combined Regularization.

For the sound field reconstruction of large conical surfaces, current statistical optimal near-field acoustic holography (SONAH) methods have relatively poor applicability and low accuracy. To overcome this problem, conical SONAH based on cylindrical SONAH is proposed in this paper. Firstly, elementary cylindrical waves are transformed into those suitable for the radiated sound field of the conical surface through cylinder-cone coordinates transformation, which forms the matrix of characteristic elementary waves in the conical spatial domain. Secondly, the sound pressure is expressed as the superposition of those characteristic elementary waves, and the superposition coefficients are solved according to the principle of superposition of wave field. Finally, the reconstructed conical pressure is expressed as a linear superposition of the holographic conical pressure. Furthermore, to overcome ill-posed problems, a regularization method combining truncated singular value decomposition (TSVD) and Tikhonov regularization is proposed. Large singular values before the truncation point of TSVD are not processed and remaining small singular values representing high-frequency noise are modified by Tikhonov regularization. Numerical and experimental case studies are carried out to validate the effectiveness of the proposed conical SONAH and the combined regularization method, which can provide reliable evidence for noise monitoring and control of mechanical systems.

Wave dispersion analysis in auxetic rods

Very few works have dealt with the wave propagation in auxetic rods. They mainly considered the effect of density changes on the longitudinal wave velocity. To this goal, the elementary one-dimensional wave propagation equation has been modified to include the high variation in material density that occurs in auxetic materials. In this work, we are mainly interested in analysing wave dispersion in auxetic rods. To this purpose, the three-dimensional Pochhammer-Chree equation is solved, for a Poisson’s ratio ν ranging from −1 to 0.5, using the regula-falsi method. We mainly show that the Poisson’s ratio controls the wave dispersion in rods through two effects: radial inertia and shear stiffness. Increasing the module of the Poisson’s ratio leads to an increase in radial inertia thus reducing wave velocity. This happens at low frequencies or large wavelengths. Consequently, the wave velocity within this range is mainly governed by the Poisson’s ratio module. On the opposite, in the high frequencies range (short wavelengths range) the wave velocity is rather governed by the shear stiffness of the auxetic rod. The wave velocity at vanishing wavelengths converges to the velocity of Rayleigh waves, which increases as the Poisson’s ratio decreases. In the high frequencies range, wave velocity is sensitive to the algebraic value of the Poisson’s ratio. In this work, we have also dealt with higher modes (higher solutions). Namely, the Pochhammer-Chree equation have been solved for the second and third modes; and analytical approximations were proposed for both low and high wavenumber ranges.

The invariant domain of Riemann solution for 1D non-isentropic gas dynamics equations

In this paper, we get the invariant domain of 1D non-isentropic gas dynamics equations. First of all, we construct the elementary waves with the characteristic analysis method. According to the characteristic of elementary waves, we divide the u–p plane into five areas. By analyzing the structure of Riemann solutions in each area, we find a new convex bounded domain where if the Riemann data belong to the domain, then the Riemann solutions also belong to the domain. Moreover, it is used to prove the uniform boundedness of approximate solutions built by the difference scheme, so it is the basis for the Riemann problem to be applied to the Cauchy problem.

Common-Sense Rejected by Physicists:

We propose a new integration of relativity and quantum mechanics (QM). Your cell phone or smart phone is a rich source of empirical information about relativity. It tells time based on a system called Coordinated Universal Time (UTC) which assumes absolute simultaneity: all observers in all inertial frames observe the same sequence of all events. You must choose whether to trust the time on your cell phone, or trust Einstein’s incompatible ideas about a space-time continuum. As concerns QM, the existence of “weirdness” means a mistake was made in QM’s starting assumptions. This article finds and corrects that mistake and presents for the first time, a quantum world free of all weirdness. There is another half to nature, previously unrecognized. It is devoid of energy and matter, namely zero-energy Elementary Waves which move within the medium of aether. We derive the linear wave PDE’s. There is evidence that Elementary Waves are in control of nature, despite their lack of energy. The existence of UFO’s (Unidentified Flying Objects) suggests that someone has learned how to control Elementary Waves. If we could learn from the UFO’s, we might acquire a decisive advantage in our battle against climate change.

The Sound Monad: A Philosophical Perspective on Sound Design

Abstract This article aims at sketching a philosophical theory of sound based on the perspective of sound designers: unique agents blurring the boundaries between engineering, music, acoustics and sound-based art. After having introduced the general framing in Section 1, focusing on a short history of the theory and practice of sound design, in Section 2 we propose a reading of sound as monad. We derive such intuition from the technology of digital sampling of audio signals, based on the decomposition of complex sound waves in a number of elementary sinusoidal waves. Thus, in Section 3, we attempt at grounding the resulting “sound-atom” on Leibniz’s notion of monad, intended both as a “simple substance without parts” and as a “nucleus of forces in statu possibilitatis.” The insight is resumed and further discussed in Section 4, where we draw our conclusions by demonstrating the fitness of such framing with regards to the standpoint of sound design, while accounting for the work of sound artists Carsten Nicolai and Ryoji Ikeda.

Interaction of elementary waves for the Aw–Rascle traffic flow model with variable lane width

Interaction of elementary waves for the Aw–Rascle traffic flow model with variable lane width

Numerical implementation of the Neumann-Michell theory incorporating with the analytical panel integral for ship waves

The numerical implementation approach (named NM_LSA) of the Neumann-Michell (NM) theory by using the Linear-semi-analytical method for panel integral is established to solve ship waves. The NM theory is a boundary-integral equation method, which is discretized by using 4-node isoparametric elements with linear flow potential distribution in this paper. To overcome the difficulty of panel integral of wave component in the Green function, the NM_LSA employs the analytical panel integral related to the elementary wave. The filter function based on parabolic extrapolation within a layer bordering the free surface is used to remove unwanted short waves. The analytical panel integral of elementary wave over a triangular panel is derived and applied to compute the spatial integral of wave potential.In addition, another numerical implementation approach (named NM_LG) of the NM theory by using Linear-gauss method for panel integral is established. Two sets of filter parameters and five hulls are selected to validate the above mentioned numerical methods. The simulation results obtained by different numerical methods show good agreement with experimental measurements. Moreover, the time consumption of wave drag computation per Froude number via the NM_LSA is reduced by about 40 % compared to that via the NM_LG.

Interactive exploration of a hierarchical spider web structure with sound

3D spider webs exhibit highly intricate fiber architectures and owe their outstanding performance to a hierarchical organization that spans orders of magnitude in length scale from the molecular silk protein, to micrometer-sized fibers, and up to cm-scale web. Similarly, but in a completely different physical manifestation, music has a hierarchical structure composed of elementary sine wave building blocks that can be combined with other waveforms to create complex timbres, which are then arranged within larger-scale musical compositions. Although apparently different, spider webs and music have many similarities, as we point out in this work. Here, we propose an intuitive and interactive way to explore and visualize a 3D Cyrtophora citricola spider web geometry that has been digitally modeled with micron-scale details from full-scale laboratory experiments. We use model-based sonification to translate the web architecture into sound, allowing for aural perception and interpretation of its essential topological features. We implement this sonification using Unity3D and Max/MSP to create an interactive spider web environment in which a user travels through a virtual spider web. Each silk fiber in their field of view is sonified using different sine waves. Together, the sonified fibers create new and more complex timbres that reflects the architecture of 3D spider webs. These concepts are implemented into a spider web-based instrument for live performances, art installations and data exploration. It provides an unprecedented and creative way to immerse the composer, audience and user in an immersive multimedia experience generated by the complexity of a 3D spider web.

PDE boundary conditions that eliminate quantum weirdness: a mathematical game inspired by Kurt Gödel and Alan Turing

Although boundary condition problems in quantum mathematics (QM) are well known, no one ever used boundary conditions technology to abolish quantum weirdness. We employ boundary conditions to build a mathematical game that is fun to learn, and by using it you will discover that quantum weirdness evaporates and vanishes. Our clever game is so designed that you can solve the boundary condition problems for a single point if-and-only-if you also solve the “weirdness” problem for all of quantum mathematics. Our approach differs radically from Dirichlet, Neumann, Robin, or Wolfram Alpha. We define domain Ω in one-dimension, on which a partial differential equation (PDE) is defined. Point α on ∂Ω is the location of a boundary condition game that involves an off-center bi-directional wave solution called Æ, an “elementary wave.” Study of this unusual, complex wave is called the Theory of Elementary Waves (TEW). We are inspired by Kurt Gödel and Alan Turing who built mathematical games that demonstrated that axiomatization of all mathematics was impossible. In our machine quantum weirdness vanishes if understood from the perspective of a single point α, because that pinpoint teaches us that nature is organized differently than we expect.

On the stability of the improved Aw–Rascle–Zhang model with Chaplygin pressure

In this paper, we mainly study the stability of Riemann problem for the improved Aw–Rascle–Zhang model which describes the formation and dynamics of traffic jams. First of all, we construct the classical Riemann solutions by elementary waves with the method of characteristic analysis. With the generalized Rankine–Hugoniot and entropy conditions, we prove the existence and uniqueness of δ-shock wave for arbitrary convex F(u) in this model. Then through a small perturbation, we analyze the wave interactions of different kinds of waves. As a result, we get the stability for the Riemann problem by letting the perturbed parameter ε→0.

Shock-Capturing Anomaly in the Interaction of Unsteady Disturbances with a Stationary Shock

Shock-capturing methods for numerical fluid dynamics are capable of correctly representing the flow conditions across shocks. However, there is no guarantee that the methods remain equally applicable for unsteady problems of shock–disturbance interaction. Based on the results of wide parametric computations, this paper demonstrates an inherent weakness of shock-capturing methods related to an ambiguous station of a stationary shock on a grid cell. To this end, the interaction of stationary shocks of different intensities with elementary waves of acoustic and nonacoustic nature is investigated in a simplified formulation. The computations reveal unpredictable postshock amplitudes of disturbances unless the viscous structure of the shock is sufficiently resolved. A shock resolution criterion and possible cures are suggested and discussed.

Self-consistent Equation Method for Solving Problems of Wave Diffraction on Scatter Systems

The paper considers one of the numerical methods to solve problems of scattering electromagnetic waves on the systems formed by parallel-oriented cylindrical elements – two-dimensional photonic crystals. The method is based on the classical partition approach used for solving the wave equation. Тhe method principle is to represent the field as the sum of the primary field and the unknown secondary field scattered on the medium elements. The mathematical expression for the latter is written as the infinite series according to elementary wave functions with unknown coefficients. In particular, the N elements-scattered field is found as the sum of N diffraction series in which one of the series is composed of the wave functions of one body and the wave functions in the remaining series are expressed in terms of the eigenfunctions of the first body using addition theorems. Further, to meet the boundary conditions, on the surface of each element, we obtain systems of linear algebraic equations with the infinite number of unknowns – the required expansion coefficients, which are solved by standard methods. A feature of the method is the use of analytical expressions to describe diffraction on a single element of the system. In contrast to most numerical methods, this approach allows one to obtain information on the amplitude-phase or spectral characteristics of the field only at the local points of the structure. The high efficiency of this method stems from the fact that there is no need to determine the field parameters in the entire area of space occupied by the multi-element system under consideration. The paper compares the calculated results of the transmission spectra of two-dimensional photonic crystals using the considered method with the experimental data and numerical results, obtained by other approaches, and demonstrates their good agreement.

Nonlinear Wave Interactions in a Macroscopic Production Model

In this article, we study the exhaustive analysis of nonlinear wave interactions for a 2 × 2 homogeneous system of quasilinear hyperbolic partial differential equations (PDEs) governing the macroscopic production. We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations. Furthermore, we study the interaction between simple waves in detail through exact solution of general initial value problem. Finally, we discuss the all possible interaction of elementary waves using the solution of Riemann problem.

Four-Quadrant Riemann Problem for a 2×2 System II

In previous work, we considered a four-quadrant Riemann problem for a 2×2 hyperbolic system in which delta shock appears at the initial discontinuity without assuming that each jump of the initial data projects exactly one plane elementary wave. In this paper, we consider the case that does not involve a delta shock at the initial discontinuity. We classified 18 topologically distinct solutions and constructed analytic and numerical solutions for each case. The constructed analytic solutions show the rich structure of wave interactions in the Riemann problem, which coincide with the computed numerical solutions.

Six Reasons to Discard Wave Particle Duality: Thereby Opening New Territory for Young Scientists to Explore

Wave particle duality is a cornerstone of quantum chemistry and quantum mechanics (QM). But there are experiments it cannot explain, such as a neutron interferometer experiment. If QM uses Ψ as its wavefunction, several experiments suggest that nature uses -Ψ instead. The difference between -Ψ and +Ψ is that they describe entirely different pictures of how nature is organized. For example, with -Ψ quantum particles follow waves backwards, which is incompatible with wave-particle-duality, obviously. We call the -Ψ proposal the Theory of Elementary Waves (TEW). It unlocks opportunities for young scientists with no budget to conduct the basic research for a new, unexplored science. This is a dream come true for young scientists: the discovery of uncharted territory. We show how TEW explains the double slit, Pfleegor Mandel and Davisson Germer experiments, Feynman diagrams and the Bell test experiments. We provide innovative research designs for which -Ψ and +Ψ would predict divergent outcomes. What makes QM so accurate is its probability predictions. But Born’s law would yield the same probabilities if it were changed from P = |+Ψ |2 to P = |-Ψ |2. This article is accompanied by a lively YouTube video, “6 reasons to discard wave particle duality.”

Four-Quadrant Riemann Problem for a 2 × 2 System Involving Delta Shock

In this paper, a four-quadrant Riemann problem for a 2×2 system of hyperbolic conservation laws is considered in the case of delta shock appearing at the initial discontinuity. We also remove the restriction in that there is only one planar wave at each initial discontinuity. We include the existence of two elementary waves at each initial discontinuity and classify 14 topologically distinct solutions. For each case, we construct an analytic solution and compute the numerical solution.

Interaction of the elementary waves for shallow water equations with discontinuous topography

The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears when the water depth changes, especially when there exists a bottom step. In this paper, we are mainly concerned with the interaction between a stationary wave with either a shock wave or a rarefaction wave. By using the characteristic analysis methods, the evolution of waves is described during the interaction process. The solution in large time scale is also presented in each case. The results may contribute to research on more complicated wave interaction problems.

Wave Interactions for Chaplygin Gas with Combustion

The elementary wave interactions for the Chapman-Jouguet model with combustion are investigated. We obtain the unique solution of the initial value problem under the global entropy conditions. We analyze the elementary wave interactions in the phase plane and construct uniquely the solution of this initial value problem. It is found that the combustion wave solution of the corresponding Riemann may be extinguished after perturbation which shows that the unburnt gas is unstable.