Synopsys (Switzerland)

The leaning tower of Lire with variable block mass

Editor's Note: A classic block-stacking puzzle becomes more interesting when the blocks have different masses. Readers discover how changing thickness or density can make the total overhang shrink, grow slowly, or even increase linearly. The “Lire Tower Transform,” a neat way to...

A physical model of the sinc function: The center-of-mass spiral

The sinc function, defined as sinc(x)=sin(x)/x, is a fundamental tool in applied mathematics and physics, arising in fields ranging from signal processing to quantum mechanics. This paper presents a novel physical interpretation of the sinc function in the context of classical me...

THE KEPLERIAN HELICOID A Power-Law Helicoidal Surface

We identify a previously uncharacterized geometric surface — the Keplerian Helicoid — defined by z ∝ θ r^(3/2), which constitutes the envelope of planetary orbits when a gravitationally bound system is observed in a translating reference frame. This power-law helicoidal surface i...

MIND -FROM MOMENTUM COHERENCE TO TEMPORAL GEOMETRIC RESPONSE (Synopsis)

This synopsis presents the conceptual architecture of the MIND framework — Momentum in Inertial/Non-Inertial Dynamics — developed within the mathematical and conceptual structure of orthodox mechanics. The central proposition is that momentum is not merely a conserved quantity. I...

MIND -FROM MOMENTUM COHERENCE TO TEMPORAL GEOMETRIC RESPONSE (Synopsis)

This synopsis presents the conceptual architecture of the MIND framework — Momentum in Inertial/Non-Inertial Dynamics — developed within the mathematical and conceptual structure of orthodox mechanics. The central proposition is that momentum is not merely a conserved quantity. I...

THE QUANTUM MOMENTONIC ENERGY THEOREM The Missing Variable in Quantum Energy Accounting

The kinetic energy of every quantum system decomposes exactly into two terms: T_flow, the energy of net momentum flow, and T_org, the energy of momentum organization — the Quantum Momentonic Potential. This decomposition follows from the Madelung representation ψ = √ρ · exp(iS/ℏ)...

THE QUANTUM MOMENTONIC ENERGY THEOREM The Missing Variable in Quantum Energy Accounting

The kinetic energy of every quantum system decomposes exactly into two terms: T_flow, the energy of net momentum flow, and T_org, the energy of momentum organization — the Quantum Momentonic Potential. This decomposition follows from the Madelung representation ψ = √ρ · exp(iS/ℏ)...

MOMENTONICS: Momentum-Centered Science and Engineering of Dynamic Systems

Abstract Momentonics is proposed as a momentum-centered scientific and engineering framework for the analysis and architectural design of dynamic physical systems. The framework is based on a simple premise: momentum is not merely a consequence of force or motion, but a fundament...

From the Playground Swing to Andromeda

A child on a playground swing discovers, without equations, the principle that underlies this entire work: each push adds the same momentum, but produces more energy than the last — because the swing is already moving faster. The equation governing this observation, dK = v·dp, is...

MOMENTUM A Dynamical and Architectural Treatment of Momentum From Physical Quantity to Engineered Dynamic Resource

Momentum is one of the fundamental conserved quantities of classical mechanics, yet mechanical engineering is conventionally organized around force, energy, and power as its principal architectural variables. This work proposes a complementary framework: Momentum-First Engineerin...

MOMENTUM A Dynamical and Architectural Treatment of Momentum From Physical Quantity to Engineered Dynamic Resource

Momentum is one of the fundamental conserved quantities of classical mechanics, yet mechanical engineering is conventionally organized around force, energy, and power as its principal architectural variables. This work proposes a complementary framework: Momentum-First Engineerin...

Enterprise Knowledge Representation — Working Definition

Enterprise Knowledge Representation (EKR) is proposed as a technology-independent enterprise capability for creating, relating, governing and evolving purposeful representations of selected operational knowledge. This Working Definition V0.1 establishes the initial public definit...

A Two-step CFD Framework for Spray Combustion: Multiphase LES-based Droplet Prediction Coupled with Detailed Chemistry

Abstract Modeling fuel atomization in modern aircraft combustors remains challenging because liquid-gas interface dynamics, ligament formation, and droplet breakup are highly nonlinear. This study presents a systematic numerical framework for primary atomization and reactive flow...