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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
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Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
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The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
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Diffusive transport on networks with stochastic resetting to multiple nodes.

Fernanda H González1, Alejandro P Riascos1, Denis Boyer1

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 Ciudad de México, México.

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Stochastic resetting enhances random walk efficiency on networks by improving target search and exploration. This study provides analytical tools to analyze resetting strategies on diverse network structures.

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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Markovian random walks are fundamental models for diffusive transport.
  • Stochastic resetting is a strategy to confine random walks to specific regions.
  • Analyzing search strategies on networks is crucial for various applications.

Purpose of the Study:

  • To develop a general formalism for analyzing random walks with stochastic resetting to multiple nodes.
  • To derive analytical expressions for key transport properties like occupation probability and first passage times.
  • To investigate the impact of resetting on network exploration and target search efficiency.

Main Methods:

  • Derivation of analytical expressions for stationary occupation probability and first passage times.
  • Utilizing spectral properties of the random walk without resetting.
  • Application of the formalism to specific network structures (rings, comb graphs) and walk types (normal, Lévy).

Main Results:

  • Analytical expressions for stationary occupation probability, mean first passage time, and global first passage time are deduced.
  • The study quantifies the effect of resetting on the efficiency of random walk-based search strategies.
  • Specific results are obtained for random walks and Lévy flights on rings and comb graphs.

Conclusions:

  • Stochastic resetting to multiple nodes can significantly enhance the efficiency of random walk-based search strategies.
  • The developed formalism provides a powerful tool for analyzing and optimizing such strategies on arbitrary networks.
  • The findings have implications for understanding and designing efficient search algorithms in various scientific domains.