https://htsod.github.io/ Recent content on ButterCat https://htsod.github.io/%3Clink%20or%20path%20of%20image%20for%20opengraph,%20twitter-cards%3E https://htsod.github.io/%3Clink%20or%20path%20of%20image%20for%20opengraph,%20twitter-cards%3E Hugo -- 0.123.7 en Tue, 17 Feb 2026 00:00:00 +0000 https://htsod.github.io/ee/suctionpump326m/ Sun, 01 Jun 2025 00:00:00 +0000 https://htsod.github.io/ee/suctionpump326m/ This article studies selected portions of the unit schematics, with particular focus on intermittent mode operation and the coordination between the bleed solenoid and dump solenoid to ensure patient safety. This blog serves as pedagogical material for understanding circuit operation and for developing structured troubleshooting strategies for Biomedical Equipment Technicians (BMETs). We begin with the intended clinical usage of the unit, followed by a discussion of its general functional architecture and mechanical components. https://htsod.github.io/ee/passivecomponent/ Fri, 30 Jan 2026 00:00:00 +0000 https://htsod.github.io/ee/passivecomponent/ Passive components—resistors, capacitors, and inductors—look deceptively simple on a schematic. Yet every analog circuit is built on the way these three elements enforce conservation laws and store or dissipate energy. This post takes a physics-forward route into passives: starting from charge flow and electromagnetic work, we motivate Kirchhoff’s current and voltage laws, connect them to Ohm’s law, and build intuition for why “voltage drops” and “current continuity” are more than rules-of-thumb. https://htsod.github.io/posts/percolation_network/ Tue, 07 Jan 2025 00:00:00 +0000 https://htsod.github.io/posts/percolation_network/ Site and bond percolation models exhibit a phase transition at a shared critical point, where both demonstrate self-similarity and scale invariance—hallmarks of continuous phase transitions. Using the Renormalization Group (RG) method in ( Citation: Sethna, 2020 Sethna,  J.  (2020).   Entropy, Order Parameters, and Complexity (2).   Clarendon Press. ) , which proposed a scaling procedure from the assumption of self-similar, we derive the scaling exponents for the percolation universality class. While this top-down approach offers pedagogical simplicity, it lacks the physical intuition provided by the Ginzburg-Landau framework. https://htsod.github.io/posts/small_world/ Sun, 06 Oct 2024 00:00:00 +0000 https://htsod.github.io/posts/small_world/ In this blog, we start with a qualitative overview of the small-world effect, also known as the “six degrees of separation,” followed by a quantitative analysis using computational methods, and finally, a description of the phenomenon through the framework of phase transitions and critical phenomena. From the surface level to deeper insights, I aim to explore the mechanics underlying this phenomenon and how this understanding can be extended to other large-scale phenomena. https://htsod.github.io/posts/maxwell_eqns_derive/ Mon, 19 Jun 2023 00:00:00 +0000 https://htsod.github.io/posts/maxwell_eqns_derive/ Can the order of physics discovery be differernt? From Zee Einstein’s Gravity in a nutshell, a hypothetical situation is proposed: a far away civilization where life was evolved from modular planet happen to understand the constancy of light before understanding electromagnetism. A brilliant physicist then could derived E.M. and gravity from the correct conception of space and time. The derivation was casted in a simplisitc manner: By placing the potential term either inside or outside the action square root, we obtain the familiar interactions of gravity or electromagnetism, with major concepts left unexplained. https://htsod.github.io/posts/fourier/ Wed, 27 Mar 2024 00:00:00 +0000 https://htsod.github.io/posts/fourier/ Group theory is powerful in analysis problem with symmetry. This blog aims at giving an example on how Fourier Theorem could be derived on the ground of group theory. https://htsod.github.io/posts/wave_particle/ Sun, 24 Mar 2024 00:00:00 +0000 https://htsod.github.io/posts/wave_particle/ Both the Schrödinger wave equation and the Heisenberg matrix method are fundamental approaches to quantum mechanics, each offering a unique perspective. To unify them, we recognize that while they approach the problem differently, they ultimately describe the same quantum phenomena. https://htsod.github.io/posts/ising_model/ Wed, 21 Jun 2023 00:00:00 +0000 https://htsod.github.io/posts/ising_model/ This blogh reprodcues the transfer matrix solution to one dimensional Ising model and the numerical solution to the two dimensional Ising model. https://htsod.github.io/posts/rg_method/ Sun, 11 Jun 2023 00:00:00 +0000 https://htsod.github.io/posts/rg_method/ Renormalization Group Approach in Dynamical System The renormalization group (RG) method is an approximation technique initially developed for solving strongly interacting many-body problems in quantum field theory, where perturbative solutions deviate from the actual solutions. The fundamental concept of the renormalization group approach is to eliminate irrelevant degrees of freedom in a physical system while preserving its essential characteristics ( Citation: P. Kopietz, 2010 P. Kopietz,  F.  (2010).   Introduction to the Functional Renormalization Group (1).