Phase Transitions - Revision history

Tom: /* Agent Interactions */

2026-02-02T00:04:54Z

‎Agent Interactions

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2025-02-28T00:55:55Z

‎Agent Interactions

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‎Agent Interactions

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‎Agent Interactions

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‎Full Title or Meme

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Tom: /* Long Range */

2024-11-29T22:43:38Z

‎Long Range

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2024-11-29T22:42:52Z

‎Long Range

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‎Long Range

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‎Full Title

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 The actual world is disordered and many situations in the real world can be described as a large number of elementary agents that interact with each other. (See wiki page on [[Swarm Robotics]].) These interactions can be schematized with simple rules, but the results of their collective action are sometimes really unpredictable. The elementary agents can be spins, atoms or molecules, neurons, cells in general-but also websites, financial traders, stocks and shares, people, animals, components of ecosystems, and so on.
-Not all interactions between elementary agents generate dis- ordered systems. Disorder is born from the fact that certain elementary entities behave differently from others: some spins try to go in opposite directions; certain atoms are different from most others; certain financial actors sell shares that others are buying, some dinner guests actively dislike others who have been invited and want to sit as far away way from them as possible.
+Not all interactions between elementary agents generate disordered systems. Disorder is born from the fact that certain elementary entities behave differently from others: some spins try to go in opposite directions; certain atoms are different from most others; certain financial actors sell shares that others are buying, some dinner guests actively dislike others who have been invited and want to sit as far away way from them as possible.
 In all these disordered cases, the mathematical and conceptual tool I found is indispensable for tackling the problems associated with them. Recently, for example, we have achieved important results while trying to solve the problem of putting into a box as many different-sized solid spheres as possible. It's a very interesting problem because solid spheres of different sizes are used to construct models of liquids, of crystals, of colloidal systems, of granular and powder systems. Moreover, the "packaging" of solid spheres is correlated to important problems in information and optimization theory.

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 * [[Emergent Behavior]]: The collective behavior of agents emerges from their interactions. For instance, the alignment of tiny magnets in a ferromagnetic material leads to macroscopic magnetization.
-The actual world is disordered and many situations in the real world can be described as a large number of elementary agents that interact with each other. (See wiki page on [[Swarm Robotics]] These interactions can be schematized with simple rules, but the results of their collective action are sometimes really unpredictable. The elementary agents can be spins, atoms or molecules, neurons, cells in general-but also websites, financial traders, stocks and shares, people, animals, components of ecosystems, and so on.
+The actual world is disordered and many situations in the real world can be described as a large number of elementary agents that interact with each other. (See wiki page on [[Swarm Robotics]].) These interactions can be schematized with simple rules, but the results of their collective action are sometimes really unpredictable. The elementary agents can be spins, atoms or molecules, neurons, cells in general-but also websites, financial traders, stocks and shares, people, animals, components of ecosystems, and so on.
 Not all interactions between elementary agents generate dis- ordered systems. Disorder is born from the fact that certain elementary entities behave differently from others: some spins try to go in opposite directions; certain atoms are different from most others; certain financial actors sell shares that others are buying, some dinner guests actively dislike others who have been invited and want to sit as far away way from them as possible.

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 * [[Emergent Behavior]]: The collective behavior of agents emerges from their interactions. For instance, the alignment of tiny magnets in a ferromagnetic material leads to macroscopic magnetization.
-The actual world is disordered, and as we said at the start, many situations in the real world can be described as a large number of elementary agents that interact with each other. These interactions can be schematized with simple rules, but the results of their collective action are sometimes really unpredictable. The elementary agents can be spins, atoms or molecules, neurons, cells in general-but also websites, financial traders, stocks and shares, people, animals, components of ecosystems, and so on.
+The actual world is disordered and many situations in the real world can be described as a large number of elementary agents that interact with each other. (See wiki page on [[Swarm Robotics]] These interactions can be schematized with simple rules, but the results of their collective action are sometimes really unpredictable. The elementary agents can be spins, atoms or molecules, neurons, cells in general-but also websites, financial traders, stocks and shares, people, animals, components of ecosystems, and so on.
-Not all interactions between elementary agents generate dis- ordered systems. Disorder is born from the fact that certain ele- mentary entities behave differently from others: some spins try to go in opposite directions; certain atoms are different from most others; certain financial actors sell shares that others are buying, some dinner guests actively dislike others who have been invited and want to sit as far away way from them as possible.
+Not all interactions between elementary agents generate dis- ordered systems. Disorder is born from the fact that certain elementary entities behave differently from others: some spins try to go in opposite directions; certain atoms are different from most others; certain financial actors sell shares that others are buying, some dinner guests actively dislike others who have been invited and want to sit as far away way from them as possible.
 In all these disordered cases, the mathematical and conceptual tool I found is indispensable for tackling the problems associated with them. Recently, for example, we have achieved important results while trying to solve the problem of putting into a box as many different-sized solid spheres as possible. It's a very interesting problem because solid spheres of different sizes are used to construct models of liquids, of crystals, of colloidal systems, of granular and powder systems. Moreover, the "packaging" of solid spheres is correlated to important problems in information and optimization theory.

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 *Direct Interactions: For example, atoms in a crystal lattice are connected by bonds, and their vibrations affect neighboring atoms.
 * Indirect Interactions: Agents can influence each other even without direct contact. Think of how water molecules in a glass collectively form a cohesive liquid due to their mutual interactions.
-* Emergent Behavior: The collective behavior of agents emerges from their interactions. For instance, the alignment of tiny magnets in a ferromagnetic material leads to macroscopic magnetization.
+* [[Emergent Behavior]]: The collective behavior of agents emerges from their interactions. For instance, the alignment of tiny magnets in a ferromagnetic material leads to macroscopic magnetization.
 The actual world is disordered, and as we said at the start, many situations in the real world can be described as a large number of elementary agents that interact with each other. These interactions can be schematized with simple rules, but the results of their collective action are sometimes really unpredictable. The elementary agents can be spins, atoms or molecules, neurons, cells in general-but also websites, financial traders, stocks and shares, people, animals, components of ecosystems, and so on.

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 ==Full Title or Meme==
-[[Phase Transitions]] occur when a substance changes from one state (phase) to another due to variations in temperature, pressure,  composition , or other external factors.
+[[Phase Transitions]] occur when a substance changes from one state (phase) to another due to variations in temperature, pressure,  composition, or other external factors.
 ==Context==

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 ref Jona-Lasinio and Carlo Di Castro
-==Long Range==
+==Long Range Dependences==
 The wiki page on [[Stochastic Process with Memory]] describes the notion of long range dependence has, clearly, something to do with memory in a stochastic process. "The 'specialness' of long memory indicates that most stationary stochastic processes do not have it. it appears that connecting the notion of long range dependence to certain types of phase transitions is promising. It fits well with intuition of the term “long memory” describing a model that is out of
 the ordinary. Furthermore, it allows us to concentrate on the behavior of really important functionals. Much remains to be done to clarify both possible types of such [[Phase Transitions]] and the relevant boundaries for concrete families of stochastic processes."<ref>GENNADY SAMORODNITSKY ''Long Range Dependence'' Cornell (2007?) https://people.orie.cornell.edu/gennady/techreports/LRD-NOW.pdf</ref>

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 Clearly a photon that has originated in the early universe has a very long memory by now.
 ==References==
 [[Category: Physics]]

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 Clearly a photon that has originated in the early universe has a very long memory by now.
-==Full Title==
 The notion of long range dependence has, clearly, something to do with memory in a stochastic process. "The 'specialness' of long memory indicates that most stationary stochastic processes do not have it. it appears that connecting the notion of long range dependence to certain types of phase transitions is promising. It fits well with intuition of the term “long memory” describing a model that is out of
 the ordinary. Furthermore, it allows us to concentrate on the behavior of really important functionals. Much remains to be done to clarify both possible types of such phase transitions and the relevant boundaries for concrete families of stochastic processes."<ref>GENNADY SAMORODNITSKY ''Long Range Dependence'' Cornell (2007?) https://people.orie.cornell.edu/gennady/techreports/LRD-NOW.pdf</ref>