This paper presents the process optimization of some key parameters, such as beam spacing, flux density and optimal impedance load matching of magnetic coupled piezoelectric harvesters. In order to do this, the distributed parameters model of this structure, containing macro-fiber components (MFC) with homogenous material in the piezoelectric fiber layer, was determined. Next, the computational model of this structure was designed on the basis of the first-order shear theory (FOST). The performed analysis of the calculated voltage outputs on the basis of the theoretical approach and finite element model by various beam spacing allowed us to indicate that optimized parameters play an important role in enhancing the efficiency of the system. Experiments carried out in a laboratory stand for this structure, allowed for the verification of the numerical results. In the effect, it can be noted that magnetic coupled harvesters will be relevant for a wide range of application sectors, as well as useful for the evolving composite industry.

It is shown that the proton formation probabilities, extracted from experimental decay half-lives, can be well reproduced by a simple multilinear formula with only three parameters. The parameters obtained by considering the standard root mean square deviation and the mini-max criteria are very similar to each other. In addition, we applied Bayesian analysis to study the uncertainties of the parameters and the model predictions. In this way we explain the systematics of proton decay half-lives. The multilinearity of the model also provides a way to classify the relative hindrance of different proton decays. All the recent experimental data agree very well with the model prediction. Our Bayesian analysis suggests that those new data do help constrain the uncertainty of the model parameters.

The distributions of the temperature excess of alphas to protons (ε) were studied using Parker Solar Probe measurements for Encounters 2 through 14. The distributions were mapped based on heliographic distance, Coulomb number, plasma β, and Alfvén Mach number (M _A ). The importance of collisional effects in the thermalization of solar wind is observed for a wide range of Coulomb numbers. The distributions correlate better with N β and NM _A than just N. Furthermore, evidence was found for a narrow region immediately above the Alfvén surface (1 < M _A < 2) where ε has values much higher than the mass ratio.

We revisit the non-relativistic limit of the Dirac equation in finite scalar and vector potentials and derive a Schrödinger-like equation that retains leading spin–relativistic corrections in closed form. For general central potentials, we cast the radial equation into a quadratic eigenvalue problem (QEP) using a finite-difference discretization method and develop an open-source solver to address it. We study Coulomb, harmonic oscillator, Woods–Saxon, and Yukawa potentials. We further obtain first-order energy and wavefunction corrections for the three-dimensional isotropic harmonic oscillator and Coulomb potentials via perturbation theory. This framework provides a practical bridge between non-relativistic and fully relativistic treatments, enabling accurate quantification of relativistic effects without the computational cost of full four-component calculations.