arXiv subjects

Ren-Zun Lian

Publications and source records attributed to Ren-Zun Lian.

3 recordsLinked to original sources

arXiv2026

First-Principles-Based Grand Unified Theory (GUT) for Micro-Macro Modal Quantization (MQ) -- Part V: Planck-Einstein-de Broglie Eigen-Relations, Act 1

As a continuation of our previous papers, the Planck-Einstein eigen-relation (or alternatively called Lagrange-Hamilton eigen-relation) and de Broglie eigen-relation in macroscopic electrodynamics are revealed in this paper. Using the macroscopic Planck-Einstein eigen-relation, the generalized quality factor defined in our previous papers can be derived naturally and rigorously. These above provide a solid physical and mathematical foundation for defining the concept of generalized quality factor, whose physical meaning is the reciprocal of normalized free-photon number. Using the above these, we also derive a novel and effective calculation formulation for the generalized quality factor. Based on the macroscopic Planck-Einstein eigen-relation and generalized quality factor, a series of conclusions regarding macroscopic modal quantization (MMQ) are also derived, for example: the physical meaning of eigen-value is further clarified from several different points of view; a natural normalization method for eigenmodal quanta is obtained; a generalized Parseval identity is formulated; the lower bound of generalized quality factor is revealed.

physics.gen-ph↗

arXiv2021

Work-Energy Principle Based Characteristic Mode Theory for Yagi-Uda Array Antennas

Work-energy principle (WEP) governing the work-energy transformation process of Yagi-Uda array antennas is derived. Driving power as the source to sustain a steady work-energy transformation is introduced. Employing WEP and driving power, the essential difference between the working mechanisms of scattering objects and Yagi-Uda array antennas is revealed. The difference exposes that the conventional characteristic mode theory (CMT) for scattering objects cannot be directly applied to Yagi-Uda array antennas. Under WEP framework, this paper proposes a generalized CMT for Yagi-Uda antennas. By orthogonalizing driving power operator (DPO), the WEP-based CMT can construct a set of energy-decoupled characteristic modes (CMs) for an objective Yagi-Uda antenna, and then can provide an effective modal analysis for the Yagi-Uda antenna. In addition, a uniform interpretation for the physical meaning of the characteristic values / modal significances (MSs) of metallic, material, and metal-material composite Yagi-Uda antennas is also obtained by employing the WEP-based modal decomposition and the field-current interaction expression of driving power.

physics.app-ph↗

arXiv2021

Energy-Viewpoint-Based Electromagnetic Modal Analysis

In computational physics and mathematical physics, modal analysis method has been one of important study topics. The central purposes of this Post-Doctoral Concluding Report are (1) to reveal the core position of energy viewpoint in the realm of electromagnetic modal analysis; (2) to show how to do energy-viewpoint-based modal analysis for various electromagnetic structures. The major conclusions of this report are that: energy conservation law governs the energy utilization processes of various electromagnetic structures, and its energy source term sustains the steady energy utilization processes; the whole modal space of an electromagnetic structure is spanned by a series of energy-decoupled modes (DMs), which don't have net energy exchange in any integral period; the DMs can be effectively constructed by orthogonalizing energy source operator, which is just the operator form of the energy source term. Specifically speaking: in classical electromagnetism, energy conservation law has five different manifestation forms, that are power transport theorem (PTT), partial-structure-oriented work-energy theorem (PS-WET), entire-structure-oriented work-energy theorem (ES-WET), Poynting's theorem (PtT), and Lorentz's reciprocity theorem (LRT) forms; the energy source terms in the first four forms are formulated as input power operator (IPO), partial-structure-oriented driving power operator (PS-DPO), entire-structure-oriented driving power operator (ES-DPO), and Poynting's flux operator (PtFO); the DMs of wave-port-fed, lumped-port-driven, externally-incident-field-driven, and energy-dissipating/self-oscillating electromagnetic structures can be constructed by orthogonalizing IPO, PS-DPO, ES-DPO, and PtFO; LRT guarantees that the obtained DMs satisfy some useful Em-Hn orthogonality relations, where the Em and Hn represent the electric field of the m-th DM and the magnetic field of the n-th DM.

physics.class-ph↗