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Atomic Orbitals

Atomic Orbitals

An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

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Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.
The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Updated: Jan 22, 2026

Application of Deep Learning-Based Medical Image Segmentation via Orbital Computed Tomography

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Image encryption based on the pseudo-orbits from 1D chaotic map.

Erivelton G Nepomuceno¹, Lucas G Nardo¹, Janier Arias-Garcia²

¹Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei, MG 36307-352, Brazil.

Chaos (Woodbury, N.Y.)

|July 4, 2019

Summary

This summary is machine-generated.

This study introduces a new image encryption method using pseudo-orbits of 1D chaotic maps to generate secure random sequences. The novel approach enhances randomness and key space, overcoming limitations of previous chaotic image encryption techniques.

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Three-Dimensional Reconstruction of Orbital Fractures

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Area of Science:

Cryptography
Applied Mathematics
Computer Science

Background:

Chaotic systems are widely used for image encryption due to their inherent randomness.
A significant limitation of chaotic image encryption is dynamical degradation.
Existing methods often suffer from small key spaces, particularly those using 1D chaotic maps.

Purpose of the Study:

To propose a novel image encryption scheme that overcomes the dynamical degradation issue.
To enhance the randomness and key space limitations of 1D chaotic maps in image encryption.
To develop a secure and effective method for encrypting digital images.

Main Methods:

The proposed scheme utilizes the difference of two pseudo-orbits generated from 1D chaotic maps to create a random sequence.
The generated random sequence passed all National Institute of Standards and Technology (NIST) statistical tests for randomness.
Key space enhancement is achieved through a novel procedure involving multiple perturbations in the transient time, incorporating the plain image as a perturbation factor.

Main Results:

The generated random sequence demonstrated adequate randomness, passing all NIST tests.
Effective implementation of confusion and diffusion properties essential for secure encryption.
The key space was significantly improved compared to traditional 1D chaotic map-based methods.
The encryption scheme was successfully validated on standard test images like Lena, Baboon, and Barbara.

Conclusions:

The novel image encryption scheme based on pseudo-orbits of 1D chaotic maps effectively addresses dynamical degradation.
The method provides a robust random sequence with enhanced randomness and a significantly larger key space.
The proposed technique offers a secure and practical solution for digital image encryption.