Differential Equations

A Mathematical Approach to Understanding Volvox

Abstract This paper sheds light on the suitability of mathematical theories and models to unveil a variety of design solutions inherent to Volvox. Having evolved from the unicellular Chlamydomonas, Volvox demonstrates that multicellularity is of particular interest to improve the nutrient uptake per somatic cell. Also, randomness plays a role

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Mathematical Marvels of Foraminifera

Abstract Foraminifera are a family of marine unicellular eukaryotes whose fossils can be found throughout the world, from the deepest crevices of the ocean to the highest peaks of the Egyptian Pyramids. In this paper, we explore the mathematical models describing the optimization of common adaptations in foraminifera. Beginning with

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Exploring the Mathematics of Unicellular Green Algae (Chlamydomonas Reinhardtii)

Mathematics could be described as an area of knowledge involving the use of numbers, equations, and models to describe phenomena, but at its essence, mathematics is the language of the universe. Accordingly, every aspect of the natural world is governed by this “language,” and with each passing day, humanity draws…

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The Mathematics of Tardigrade Behavior and Development

Tardigrades are equipped with a plethora of features that, most notably, allow them to cope with very harsh conditions that very few organisms are known to be able to withstand. In addition to these tools themselves that they possess, tardigrades’ peculiarity can also be assessed by models that successfully represent…

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Mathematical Marine Models of Coral Polyps

While coral polyps have been extensively studied across various scientific perspectives, this paper will explore them from a Mathematical perspective. Coral’s spontaneous growth pattern was mathematically modelled and explained from a polyp-oriented perspective, showing how polyps contribute to growth patterns. Moreover, corals are heavily reliant on their environment which contributes…

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Magnetic Marvels: A Mathematical Exploration of Magnetotactic Bacteria

Order can be found within the seemingly complex, and perhaps even disordered, processes and shapes that constitute magnetotactic bacteria (MTB). This order can be explained by the concepts of mathematics. First and foremost, the crystalline structures within the magnetosomes of MTB can be modelled mathematically. Magnetite and greigite crystals consist…

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A Physical Analysis of Magnetotactic Bacteria: Nature’s Microscopic Compass as a Solution to a Motile Biotope

Figure 1: Magnetotactic Bacteria (Perduca, 2016). Magnetotactic bacteria (MTB) are unique aquatic microaerophiles that can align and move in the direction of the Earth’s magnetic field. In this paper, the basic physical properties of magnetosomes, some mechanisms, such as magnetotaxis, and phototaxis, involved in the MTB’s motion, and the role…

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Mathematical Modelling of Dinoflagellate Swimming, Population Dynamics and Interactions with Other Organisms

Mathematical models have been made to determine the vertical migration of dinoflagellates while considering the availability of nitrogen. Studies have shown that low nitrogen abundances lead to dinoflagellates avoiding sunlight, and not performing diel vertical migration. Dinoflagellate blooms take place under specific conditions of irradiance, temperature, and salinity. A model…

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Exploring Aquatic Fungi Through Mathematical Tools

 The beauty of mathematics lies in its ability to create models to simplify complex things in real life and give explanations to them. Models are a great way to study and analyze species in nature and it is the same for aquatic fungi. Mathematical models also help us predict their…

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Geometry is Key: Mathematical Modeling of Whiskers and Antennae

Abstract Rat whiskers can be  modeled by Euler spirals,  curves with linear change in curvature. One hypothesis explaining vibrissae shape is that the linear growth of rat whiskers creates linear curvature. Another hypothesis is that the Euler spiral is an optimal shape to satisfy its sensory needs. The patterning of…

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The Life Cycle of the Whiskers and Antennae of Animals and Insects 

This article explores the various chemical, cellular, and molecular mechanisms relevant to the life cycle of whiskers (barbels) and antennae. The growth of zebrafish barbel is characterized by elongation, vasculature development, and innervation of taste buds. Catfish barbels perform chemical and mechanical sensing; namely, their hyper-sensitive gustatory system enables catfish…

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Exploration of Mathematical Laws Governing Claws and their Applications within Flying Animals, Terrestrial Pests, and Amniotes

Claws are one of the most widely utilized tools within organisms, and for a good reason: their purposeful constructions, described by mathematical laws and correlations, allow a wide range of use. This research paper investigates these fascinating mathematical relationships, beginning with the connection between claw growth and logarithmic functions. Applying…

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