An acinus (plural, acini; adjective, acinar or acinous) refers to any cluster of cells that resembles a many-lobed "berry", such as a raspberry (acinus is Latin for berry). The berry-shaped termination of an exocrine gland, where the secretion is produced, is acinar in form, as is the alveolar sac containing multiple alveoli in the lungs.
Lichtenberg figures (Lichtenberg-Figuren (German), or "Lichtenberg dust figures") are branching electric discharges that sometimes appear on the surface or the interior of insulating materials. Lichtenberg figures are often associated with the progressive deterioration of high voltage components and equipment. The study of planar Lichtenberg figures along insulating surfaces and 3D electrical trees within insulating materials often provides engineers with valuable insights for improving the long-term reliability of high voltage equipment. Lichtenberg figures are now known to occur on or within solids, liquids, and gases during electrical breakdown.
Lichtenberg figures are named after the German physicist Georg Christoph Lichtenberg, who originally discovered and studied them. When they were first discovered, it was thought that their characteristic shapes might help to reveal the nature of positive and negative electric "fluids". In 1777, Lichtenberg built a large electrophorus to generate high voltagestatic electricity through induction. After discharging a high voltage point to the surface of an insulator, he recorded the resulting radial patterns by sprinkling various powdered materials onto the surface. By then pressing blank sheets of paper onto these patterns, Lichtenberg was able to transfer and record these images, thereby discovering the basic principle of modern xerography.
This discovery was also the forerunner of the modern day science of plasma physics. Although Lichtenberg only studied two-dimensional (2D) figures, modern high voltage researchers study 2D and 3D figures (electrical trees) on, and within, insulating materials. Lichtenberg figures are now known to be examples of fractals.
Reaction–diffusion systems are mathematical models which explain how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.
The endoplasmic reticulum ( ER) is an organelle of cells in eukaryotic organisms that forms an interconnected network of membrane vesicles. According to the structure, the endoplasmic reticulum is classified into two types, rough endoplasmic reticulum (RER) and smooth endoplasmic reticulum (SER). The rough endoplasmic reticulum is studded with ribosomes on the cytosolic face.
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. (not to be confused with Edward Witten) and L.M. Sander in 1981, is applicable to aggregation in any system where diffusion is the primary means of transport in the system. DLA can be observed in many systems such as electrodeposition, Hele-Shaw flow, mineral deposits, and dielectric breakdown.
The clusters formed in DLA processes are referred to as Brownian trees. These clusters are an example of a fractal. In 2-D these fractals exhibit a dimension of approximately 1.71 for free particles that are unrestricted by a lattice, however computer simulation of DLA on a lattice will change the fractal dimension slightly for a DLA in the same embedding dimension. Some variations are also observed depending on the geometry of the growth, whether it be from a single point radially outward or from a plane or line for example. Two examples of aggregates generated using a microcomputer by allowing random walkers to adhere to an aggregate (originally (i) a straight line consisting 1300 particles and (ii) one particle at center) are shown on the right.
Computer simulation of DLA is one of the primary means of studying this model. Several methods are available to accomplish this. Simulations can be done on a lattice of any desired geometry of embedding dimension, in fact this has been done in up to 8 dimensions, or the simulation can be done more along the lines of a standard molecular dynamics simulation where a particle is allowed to freely random walk until it gets within a certain critical range at which time it is pulled onto the cluster. Of critical importance is that the number of particles undergoing Brownian motion in the system is kept very low so that only the diffusive nature of the system is present.
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