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Related Concept Videos

The Periodic Table03:25

The Periodic Table

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As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping includes lithium (Li), sodium (Na), and potassium (K). All of these elements are shiny, conduct heat and electricity well, and have similar chemical properties. A second grouping includes calcium (Ca), strontium (Sr), and barium (Ba), which also are shiny, good conductors of heat and electricity, and have chemical properties in common. However,...
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The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their electron configurations are added to the table, a periodic recurrence of similar electron configurations in the outer shells of these elements is observed. Because they are in the outer shells of an atom, valence electrons play the most important role in chemical reactions. The outer electrons have the highest energy of the electrons in an atom...
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In biological systems, most metabolic pathways are interconnected. The cellular respiration processes that convert glucose to ATP—such as glycolysis, pyruvate oxidation, and the citric acid cycle—tie into those that break down other organic compounds. As a result, various foods—from apples to cheese to guacamole—end up as ATP. In addition to carbohydrates, food also contains proteins and lipids—such as cholesterol and fats. All of these organic compounds are used...
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Hydronium and hydroxide ions are present both in pure water and in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion product of water (Kw). The concentrations of these ions in a solution are often critical determinants of the solution’s properties and the chemical behaviors of its other solutes. Two different solutions can differ in their hydronium or hydroxide ion concentrations by a million, billion, or even trillion times. A common means of...
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Effective Value of a Periodic Waveform01:07

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The concept of effective value, the root mean square (RMS) value, is crucial in understanding electrical circuits and power delivery. This idea emerges from the necessity to measure the effectiveness of a voltage or current source in supplying power to a resistive load.
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Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Updated: Jan 28, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Self-organizing scale-free patterns in a phase-modulated periodic connecting system.

Tsutomu Matsunaga1, Masaaki Muramatsu2

  • 1Research and Development Headquarters, NTT DATA Corporation, 3-3-9, Toyosu, Koto-ku, Tokyo, 135-8671, Japan. Tsutomu.Matsunaga@nttdata.com.

BMC Research Notes
|March 7, 2019
PubMed
Summary

This study reveals how phase-modulated periodic systems self-organize into scale-free patterns, offering a new model for understanding natural and social distributions. The findings suggest dynamic equilibrium arises from adaptive connectivity and spatiotemporal balance.

Keywords:
Dynamic equilibrium stateOscillating fluctuationSelf-organizing scale-free pattern

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Area of Science:

  • Complex Systems
  • Network Theory
  • Statistical Physics

Background:

  • Scale-free patterns are common in diverse systems like word frequency, city sizes, and gene expression.
  • Existing models, often based on 'rich-get-richer' mechanisms, conflict with observed local interaction behaviors.
  • Understanding the emergence of these universal patterns is of significant scientific interest.

Purpose of the Study:

  • To propose and validate a novel computational model for generating scale-free patterns.
  • To investigate the role of local constraints and periodic modulations in self-organization.
  • To explain the mechanisms behind the common emergence of rank-size regularity.

Main Methods:

  • Implementation of a computational model for resource distribution.
  • Inspiration drawn from word connectivity and local interaction constraints.
  • Inclusion of periodic and phase modulatory features in the system's connectivity.

Main Results:

  • Empirical demonstration that a phase-modulated periodic connecting system achieves a dynamic equilibrium.
  • Self-organizing scale-free patterns emerge as the most probable outcome.
  • The observed regularity is linked to configurational balance in spatiotemporal inequity and adaptive connectivity.

Conclusions:

  • Phase-modulated periodic systems provide a viable mechanism for generating scale-free patterns.
  • Dynamic equilibrium and self-organization arise from adaptive, constrained connectivity.
  • Further research into oscillating fluctuations can illuminate autoregulatory dynamics in such systems.