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.

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.

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.

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.

The Periodic Table needs negative orbitals in order to eliminate quantum weirdness: a new quantum chemistry mathematics

A consensus among quantum experts is that the quantum world is not properly understood. It is a mistake to think we can cure quantum weirdness by tinkering with superficial aspects of quantum mechanics (QM). We propose that nature uses (–ψ) as its wave function, whereas QM uses (+ψ). We propose therefore that the Periodical Table should be changed to negative orbitals (–ψ). Surprisingly, this change makes almost no difference to chemistry on a practical level. The Born rule takes the absolute square of an amplitude to obtain a probability to test in chemistry lab P=|–ψ|2=|+ψ|2. We propose a new math based on (–ψ) that is the mirror image of quantum mathematics. We call it the Theory of Elementary Waves (TEW). The negative sign is not an electrical charge. It has nothing to do with Coulomb’s law. Valence electrons are unchanged. Ions, covalent bonds, dipoles, metals, hydrogen bonding and the hydrogen 21 cm line are unchanged. The octet rule and rules for drawing dot structures of molecules do not change. Amino acids, sugars and DNA do not change their handedness. We cite abundant experimental evidence showing that TEW is correct and QM is wrong.

Solution of the Riemann problem for an ideal polytropic dusty gas in magnetogasdynamics

The main aim of this paper is, to obtain the analytical solution of the Riemann problem for a quasi-linear system of equations, which describe the one-dimensional unsteady flow of an ideal polytropic dusty gas in magnetogasdynamics without any restriction on the initial data. By using the Rankine-Hugoniot (R-H) and Lax conditions, the explicit expressions of elementary wave solutions (i. e., shock waves, simple waves and contact discontinuities) are derived. In the flow field, the velocity and density distributions for the compressive and rarefaction waves are discussed and shown graphically. It is also shown how the presence of small solid particles and magnetic field affect the velocity and density across the elementary waves. It is an interesting fact about this study that the results obtained for the Riemann problem are in closed form.