Novelant Scientific Research Inc.

Our recent research publications:
Analytical Resolution of the Dark Night Sky (Olbers’) Paradox by Zaki Harari
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Explanation :
Imagine a puzzle as old as humanity: why is the night sky dark if there are countless stars out there? This paper delves into that age-old mystery, showing that although the universe contains an immense number of stars, the sky appears relatively dark to human eyes because of a fascinating interplay between how our vision works, how starlight is distributed in our galactic neighborhood, and how this light is projected onto the celestial sphere as seen from Earth. In dark conditions, the human eye functions much like a camera with a “shutter” time of about 650 milliseconds, or a shutter speed of roughly 1/1.5 seconds. This is the effective exposure time that determines how much light the eye can collect in a single moment. As with a camera, only objects bright enough to register within that exposure become visible. Thus, although the sky is filled with stars, only a small fraction emit enough light to excite the retina strongly enough to be processed by the brain, while most remain unseen. This biological limitation highlights why it is important to account for the parameters of our light-detection system when considering the brightness of the night sky. The image our eyes form is far from an objective measure of all the starlight available—just as a short-exposure camera photo captures only a fraction of what a longer exposure would reveal. In practice, both our eyes and even our most powerful telescopes can only register a tiny part of the cosmos, constrained by detection limits and available observation time. Reflecting on the dark night sky paradox, one realises that if the question had always been posed as “Why does the night sky appear dark to our eyes if there are countless stars out there?”, the resolution might have suggested itself more readily.
Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations by Zaki Harari
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Explanation :
Our research reveals a subtle yet significant deviation from Newton's third law of motion in the derivation of the iconic Tsiolkovsky Rocket Equation, a cornerstone of rocket propulsion science since its introduction in 1903. We employ a dynamic model in which the propellant generates forward momentum through self-combustion and expansion, leading to the development of the Revised Tsiolkovsky Rocket Equation. This work illuminates the intricate interplay between detonation and retonation waves generated in a rocket combustion chamber, essential for better understanding the source of combustion instability, a critical factor in catastrophic rocket engine failures. We also show that it is imprecise to describe a rocket as a mass ejection-reaction machine because a rocket is propelled forward when the gas pressure inside the combustion chamber is made higher than the gas pressure at the exhaust nozzle, and that the rearward mass ejection is merely the visible after-effect of the expended pressurized gases being released, not the cause of rocket propulsion. Our findings aim to contribute to the design of more efficient rocket engines and offer valuable insights into the intricate realm of combustion engineering.
Investigating the Mathematical Foundations of the Euler and Navier-Stokes Equations by Zaki Harari
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Explanation :
In this study, we explore the mathematical foundations of the Euler and Navier-Stokes equations in fluid dynamics and identify inconsistencies in the definitions of flow velocity and the material derivative. We argue that flow velocity should be treated as a parametric function of time, rather than a bivariate function of initial position and time, revealing mathematical inconsistencies in the standard material derivative formulation. Our findings also indicate that in non-unidirectional flows, the relationship between parcel position and flow velocity becomes ambiguous, suggesting that flow velocity is not a valid function of position in both Lagrangian and Eulerian descriptions under these conditions. This raises questions about the feasibility of obtaining a solution to the Euler and Navier-Stokes equations by integrating these equations spatially when flow is non-unidirectional. Through our analysis, we also highlight other limitations of the Eulerian approach, particularly for gases and low-viscosity liquids. We advocate for a shift towards Lagrangian-based solutions to better capture complex flow behaviors, aiming to enhance our understanding and modeling capabilities across various application areas such as atmospheric sciences and oceanography.
NEW The Geometric Quadrature Method (GQM): A Singularity-Free Spatial Formulation for Constrained Motion on Arbitrary Planar Curves by Zaki Harari
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Explanation :
Imagine a particle rolling along a wildly curving track — a loop, a spiral, a cubic ramp with a hump in it — and you want to know exactly how fast it's going, how hard it's pressing on the rail, and when it will reach any given point; the usual way engineers solve this is to grind through Newton's laws in x-y coordinates, but that approach chokes and blows up wherever the track goes vertical, so this paper proposes a cleaner path by measuring everything in terms of distance traveled along the curve itself and using a self-orienting compass frame that never flips or breaks, even at kinks like inflection points where the track bends the other way. Using this trick, the paper shows that the particle's speed and the rail's push on it can be computed exactly and instantly from nothing but the shape's height profile, with no simulation needed at all; only the question of "how long will it take to get there" resists an exact formula (a fact of mathematics, not a flaw in the method) and must be estimated numerically, but this single remaining calculation can be done once, to extreme precision, and then reused indefinitely to reconstruct the particle's motion far into the future without the slow, creeping errors that plague standard step-by-step simulations — a distinction verified on both a swinging pendulum and a friction-laden curved ramp, and one that matters wherever engineers need trustworthy predictions of contact forces and long-term motion on curved paths, from rail systems to roller coasters to orbital mechanics.
NEW Solid Angle and the Fine-Structure Constant: A Geometric View of Hydrogen Length Scales by Zaki Harari
Explanation:
Picture a hydrogen atom two ways: as a tiny ball roughly a tenth of a nanometer across (the Bohr radius, the size of the electron's home orbit), and as the light swallowed when that electron is ripped away entirely — a photon whose wavelength, about 91 nanometers, is a couple thousand times bigger than the atom itself. In textbooks the ratio of those two lengths is noted only in passing as "roughly 1/α²," where α ≈ 1/137 is the fine-structure constant that sets the strength of electromagnetism, but here it is shown that the ratio is not approximate at all: it is exactly 4π/α, or 1722.045…, and it is obtained from four lines of standard algebra using nothing but the ordinary CODATA definitions of the constants involved. The cute part is where the 4π comes from, since it splits into 2π (from writing Planck's constant as h = 2πℏ, one full cycle of phase) times 2 (from the virial theorem, which says a Coulomb-bound electron's kinetic energy is exactly half its binding energy) — and those are precisely the two factors obtained by integrating around a sphere to find that it subtends 4π steradians, so the ratio can be read as a solid angle divided by α. This resemblance is stressed to be formal and dependent on bookkeeping convention, not evidence of any real angular integration, and no new physics is claimed; the value lies in the teaching, plus a clean exact scaling law for heavier hydrogen-like ions and a zero-parameter check on future measurements of α.