@ghostnshell_ @ghostnshell_

From a single point source, light or other radiation spreads over ever-larger spheres, causing intensity to follow the inverse square law. For source S the surface intensity equals total power S divided by the sphere area, giving I_r = S / (4πr²). When distance reaches 2r intensity falls to one quarter; at 3r to one ninth, as shown by the labeled concentric spheres and ray bundles. It is used to calculate exposure times in photography or maintain safe distances around X-ray machines.

In real engineering, the Navier–Stokes equations are rarely solved exactly. Exact analytical solutions are possible only for very simple flows. Most real flows are too complex because they involve changing velocity, pressure, viscosity, turbulence, heat, and interaction with solid surfaces. For this reason, engineers usually solve the equations approximately using numerical methods such as finite difference, finite volume, finite element, and spectral methods. This practical use of the equations forms the foundation of Computational Fluid Dynamics, or CFD. In aerospace engineering, CFD based on the Navier–Stokes equations is essential for predicting how air moves around aircraft and spacecraft. It helps engineers study lift, drag, shock waves, flow separation, turbulence, heating, and aircraft stability. NASA’s studies on aircraft such as the F/A-18 used three-dimensional thin-layer Navier–Stokes computations and compared the results with flight and wind-tunnel data. This shows how the equations connect mathematical fluid dynamics with real aircraft performance. The equations are also important in hypersonic flight, where vehicles move many times faster than the speed of sound. At such speeds, air behaves in extreme ways. Navier–Stokes simulations are used to study real-gas aerothermodynamics, shock interactions, and heating. NASA CFD research has shown that in shock–shock interactions, peak heating can exceed stagnation heating by up to a factor of two. This is a critical issue in hypersonic vehicle design because excessive heating can damage or destroy a vehicle’s surface. In modern aircraft design, Reynolds-averaged Navier–Stokes equations are widely used in optimization workflows. These methods allow engineers to improve aircraft shapes and performance before building expensive physical prototypes. NASA Langley research notes that Euler and Reynolds-averaged Navier–Stokes optimization methods have become important parts of the aerospace design cycle. Adjoint methods also help make large-scale design optimization computationally practical. The Navier–Stokes equations are not limited to aircraft and spacecraft. They are also central to weather prediction. The atmosphere is treated as a moving fluid, and numerical weather prediction uses equations based on fluid motion on a rotating Earth. These include local acceleration, nonlinear advection, the Coriolis force, pressure gradients, friction, and gravity. In this way, the same basic physics used to study airflow over aircraft is also used to model winds, storms, and large-scale atmospheric circulation. In medicine, the Navier–Stokes equations are used in cardiovascular CFD. Blood flow through the heart and blood vessels can be modeled using conservation of momentum, leading to velocity and pressure fields in complex patient-specific geometries. This is especially useful in studying congenital heart disease and planning surgical procedures. By simulating blood flow, researchers and doctors can better understand how changes in anatomy or surgery may affect circulation. The significance of the Navier–Stokes equations comes from this wide practical range. They are not only theoretical equations in fluid mechanics. They are working tools in aerospace engineering, hypersonic flight, aircraft design, weather prediction, and medical research. Their exact mathematical behavior remains difficult, but their numerical use has become one of the most important foundations of modern engineering and applied science.

Only Have a Schematic? Turn It into a Real PCB! Grab a $200 coupon: jlcpcb.com/coupon-center?… No layout experience? Let JLCPCB layout engineers handle the routing. Upload your schematic, get production-ready Gerber files, and bring ideas to life faster!

Mastering All Design Patterns in C A detailed guide to implementing design patterns in C, exploring how to apply object-oriented design principles and common patterns in a procedural language.

Bilgisayar bilimi için açık kaynak “lisans müfredatı” varsa, Elektronik Mühendisliği için neden olmasın? GitHub’da devre analizinden dijital elektroniğe, sinyaller ve sistemlerden mikroişlemcilere, kontrolden haberleşmeye kadar Elektrik-Elektronik Mühendisliği müfredatını adım adım sıralayan açık kaynak öğrenme rotaları bulunuyor. Üstelik kaynakların önemli bir bölümü MIT, Stanford ve benzeri üniversitelerin ücretsiz derslerinden oluşuyor. Tek fark şu: Bilgisayar bilimi bilgisayar başında öğrenilebilir. Elektronik mühendisliği ise devre kurmadan öğrenilemez. Bu yüzden açık derslerin yanına breadboard, multimetre, mikrodenetleyici ve gerçek projeler eklemek gerekiyor. Diploma vermiyorlar. Ama bir mühendislik bölümünde hangi konuyu, hangi sırayla öğrenmeniz gerektiğini ücretsiz gösteriyorlar. Üniversite müfredatları artık yalnızca üniversite duvarlarının içinde değil. github.com/Artoriuz/OSEE

Maxwell completed Ampère's law by including the effect of changing electric fields. The differential form of the Ampère-Maxwell law is ∇ × B = μ₀ (J + ε₀ ∂E/∂t). The left side shows the curl of the magnetic field B in teslas. The right side combines the conduction current density J in amperes per square meter with the displacement current density ε₀ ∂E/∂t, scaled by the permeability of free space μ₀. Arrows in the equation point out the vector nature of the del operator and fields, along with the units for each quantity. It is used to determine the magnetic fields surrounding charging capacitors and in the design of high-frequency circuits.

Insane image of a cave on Mars, located in the Elysium Valley. Photographed by NASA's MRO

Force balance on any sub-volume of a solid directly yields its local stress equilibrium rule. Starting from ∭_V0 P_i dV + ∬_S0 σ_vi dS = 0, with surface traction σ_vi = σ_ij α_vj, the divergence theorem converts it to ∭_V0 (P_i + ∂σ_ij/∂x_j) dV = 0. For arbitrary V0 this requires P_i + ∂σ_ij/∂x_j = 0 everywhere. It is used to calculate internal forces in loaded parts such as aircraft wings or pressure pipes for failure prevention.

Did some experiments with local models In this example, all requests are handled by Gemma 4. It generates a new circuit as JSON based on the prompt Edited out the waiting times from the clip. It usually takes around 5 - 10s More details ↓

Unlock the Power of One IC: Generate Square, Triangle & Sine Waves 🧠⚡ Did you know the LM324 packs four operational amplifiers into a single chip? That’s like having a tiny signal-processing lab in one component. 🧪 Here’s how it works step by step → 🔹 Op‑amp 1 (Comparator) → produces a square wave 👉 Controlled by resistors + a potentiometer for tuning 🔹 Op‑amp 2 (Integrator) → turns the square wave into a triangle wave 👉 Using capacitor charge/discharge cycles 🔹 Op‑amp 3 (Filter) → shapes the triangle wave into a smooth sine wave Why this matters: You can generate and transform fundamental waveforms using simple, low‑cost components. Perfect for learning analog signal conditioning, function generators, or DIY audio projects. 💡 Have you ever built a waveform generator using basic op‑amps? What was your biggest insight? 👇 Let’s discuss in the comments. #OpAmp #ElectronicsEngineering #AnalogCircuits #LM324 #SignalProcessing #EmbeddedSystems

Geometric construction of the trigonometric functions.

Pi and e emerge naturally from integrating these functions across all real numbers. The Gaussian f(x) = e^{-x^2} has integral √π from -∞ to +∞. The function f(x) = 1/(x^2 + 1) integrates to π. The sinc function f(x) = sin(x)/x integrates to π. The function f(x) = cos(x)/(1 + x^2) integrates to π/e. The plots show each function's shape with shading marking the relevant areas under the curves. These exact values are used in probability theory to define standard distributions and in engineering for frequency domain analysis of signals.

Most people use devices powered by CMOS every day — but few know what makes it so powerful. Here's a quick breakdown for anyone diving into VLSI or semiconductor design: 👇 What is CMOS? Complementary Metal-Oxide-Semiconductor (CMOS) is the technology backbone of virtually every digital chip today — from your phone's processor to data center servers. Its secret? Pairing PMOS and NMOS transistors to work in opposition. The Core Idea (Simpler Than It Sounds) → NMOS turns ON when input = 1 → PMOS turns ON when input = 0 Because only one conducts at a time, static power consumption drops to near zero. That's the "complementary" magic. The CMOS Inverter — Small Gate, Big Importance Input 0 → Output 1 Input 1 → Output 0 It sounds trivial, but this single building block is the foundation of every logic circuit in existence. Why CMOS Has Dominated for Decades ✦ Ultra-low power consumption ✦ High noise immunity ✦ Scales to billions of transistors on a single chip ✦ Consistently reliable across process nodes Power Breakdown ⚡ Dynamic Power: P = C · V² · f (the dominant concern in modern design) 💤 Static Power: Minimal — though leakage is a growing challenge at smaller nodes Design Structure Pull-Up Network (PMOS) → drives output to VDD Pull-Down Network (NMOS) → drives output to GND Always designed as complements of each other — hence the name. CMOS isn't just a technology. It's the reason we can pack billions of transistors into a chip the size of a fingernail and still keep it cool enough to hold. If you're studying VLSI, this is where everything starts. What concept in VLSI would you like broken down next? Drop it in the comments 👇 #VLSI #CMOS #SemiconductorDesign #ChipDesign #Electronics #EmbeddedSystems #Engineering

How a swiich mode power supply works

The right tool makes the job easier, cleaner, and safer.

🫧♻️ Transformando RESIDUOS de cocina en #JABÓN casero ¡100% hecho a mano! #OficiosPerdidos 🎥 #Documental COMPLETO (5 minutos) de este resumen: youtu.be/tN6EjrNzG2U

nTop and PhysicsX show what a closed-loop AI design pipeline looks like in production. nTop generated 100+ drone configurations with zero geometry failures. The parametric model and live parameter updates were created in nTop, and the design exploration was run in the PhysicsX Optimizer.

Golden ratio proportions align with circular geometry to link phi and pi. A diagonal line marks points at 1/φ ≈ 0.618033..., then the value 1, and φ ≈ 1.618033.... Circles each spanning a vertical diameter of 1 demonstrate pi ≈ 3.141592... as their circumference divided by diameter yields this constant. It is used to model natural growth patterns alongside circular motions in biology, art, and mechanical engineering.

Every successful electronic product starts with a solid PCB foundation. These FR-4 2-layer boards have completed fabrication and passed inspection. The next step is SMT assembly, where components will be placed and soldered to bring the design to life. #pcb #pcba

Open sourcing KENSAT 🤖🛰️ KENSAT is a 2U CubeSat that runs an LLM in orbit. AI inference is run on a NVIDIA Jetson and downlinked to Earth with RF. Launching on the SpaceX Falcon9 in October. The repo includes everything - from its firmware, schematics and PCBs.

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