Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

The Asymptotic Approach to the Description of Two-Dimensional Symmetric Soliton Patterns

The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe stationary moving symmetric wave patterns consisting of two plane solitary waves of equal amplitudes moving at an angle to each other. The results obtained within the approximate asymptotic theory are validated by comparison with the exact two-soliton solution of the Kadomtsev–Petviashvili equation (KP2-equation). The suggested approach is equally applicable to a wide class of non-integrable equations too. As an example, the asymptotic theory is applied to the description of wave patterns in the 2D Benjamin–Ono equation describing internal waves in the infinitely deep ocean containing a relatively thin one of the layers.

Selective actuation and sensing of antisymmetric ultrasonic waves using shear-deforming piezoelectric transducers

Structural health monitoring of thin plate and beam structures using ultrasonic guided wave techniques has been widely studied and demonstrated advanced capabilities dependent on detailed analysis of specific guided wave modes. A common setup employs the d31 electromechanical coupling of piezoelectric wafer active sensors mounted on the surface of a beam or plate. Analysis of output signals from these basic systems is complicated because they represent multiple superposed ultrasonic wave modes that propagate at different velocities, are dispersive, and undergo reflection, refraction, and mode conversion. Multiple techniques have been pursued to overcome this complication. This article presents recent research into the use of shear-deforming lead zirconate titanate piezoelectric transducers, employing the d15 electromechanical coupling property, embedded within beam-like structures to selectively actuate and sense specific ultrasonic wave modes. The internally located transducers actuated and sensed transverse shear, coupled to bending and antisymmetric waves. A combination of results from finite element simulations and experiments found that d15 transducers located at the neutral axis of a beam exclusively coupled to antisymmetric wave modes and did neither directly actuate nor sense symmetric wave modes. Further study was performed to evaluate the effects of off-neutral-axis location on the mode selectivity and found that off axis location of the d15 transducer did not diminish the coupling to antisymmetric wave modes, but introduced coupling to symmetric wave modes. Additional study was performed to assess the ability of structural health monitoring systems employing shear-deforming d15 lead zirconate titanates located at the neutral axis to detect common forms of damage in laminate structures. The combination of selective actuation and selective sensing provides a powerful tool for signal analysis in ultrasonic structural health monitoring of thin plates and beams.

Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy

In this paper the dynamics of a submerged axi-symmetric wave energy converter are studied, through mathematical models and wave basin experiments. The device is disk-shaped and taut-moored via three inclined tethers which also act as a power take-off. We focus on parasitic yaw motion, which is excited parametrically due to coupling with heave. Assuming linear hydrodynamics throughout, but considering both linear and nonlinear tether geometry, governing equations are derived in 6 degrees of freedom (DOF). From the linearized equations, all motions, apart from yaw, are shown to be contributing to the overall power absorption. At higher orders, the yaw governing equation can be recast into a classical Mathieu equation (linear in yaw), or a nonlinear Mathieu equation with cubic damping and stiffness terms. The well-known stability diagram for the classical Mathieu equation allows prediction of onset/occurrence of yaw instability. From the nonlinear Mathieu equation, we develop an approximate analytical solution for the amplitude of the unstable motions. Comparison with regular wave experiments confirms the utility of both models for making relevant predictions. Additionally, irregular wave tests are analysed whereby yaw instability is successfully correlated to the amount of parametric excitation and linear damping. This study demonstrates the importance of considering all modes of motion in design, not just the power-producing ones. Our simplified 1 DOF yaw model provides fundamental understanding of the presence and severity of the instability. The methodology could be applied to other wave-activated devices.

Study of Axi-Symmetric Vibrations in a Micropolar Transversely Isotropic Layer

The present investigation deals with the propagation of circular crested Lamb waves in a homogeneous micropolar transversely isotropic medium. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation are computed numerically for magnesium as a material and the dispersion curves, amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented graphically to evince the effect of anisotropy. Some special cases of interest are also deduced.