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Related Concept Videos

Diffusion01:12

Diffusion

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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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Diffusion01:21

Diffusion

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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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Facilitated Diffusion01:16

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The plasma membrane, a critical structure in cellular biology, houses an array of transporters, or carrier proteins, interspersed within its lipid bilayer. These proteins play a crucial role in solute transport through facilitated diffusion, a form of passive diffusion that uses transporters to move the molecules across the membrane.
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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

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Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...
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Temperature Dependence on Reaction Rate02:55

Temperature Dependence on Reaction Rate

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The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
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Protein Diffusion in the Membrane01:24

Protein Diffusion in the Membrane

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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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Related Experiment Video

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Measuring Diffusion Coefficients via Two-photon Fluorescence Recovery After Photobleaching
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Backstepping-based boundary control design for a fractional reaction diffusion system with a space-dependent

Juan Chen1, Baotong Cui1, YangQuan Chen2

  • 1Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, PR China; School of IoT Engineering, Jiangnan University, Wuxi 214122, PR China.

ISA Transactions
|June 16, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a boundary feedback control for fractional reaction diffusion systems with varying diffusion rates. The backstepping method ensures stability for these complex systems, validated by numerical examples.

Keywords:
BacksteppingBoundary feedback controlFractional reaction diffusion system with space-dependent diffusivityMittag-Leffler stability

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Area of Science:

  • Control Theory
  • Partial Differential Equations
  • Fractional Calculus

Background:

  • Fractional reaction diffusion (FRD) systems are crucial in modeling complex phenomena.
  • Existing control methods often assume constant diffusion coefficients, limiting applicability.
  • Controlling FRD systems with space-dependent diffusivity presents significant challenges.

Purpose of the Study:

  • To design a boundary feedback controller for FRD systems with space-dependent diffusion coefficients.
  • To generalize existing backstepping control techniques to non-constant diffusivity scenarios.
  • To rigorously prove the stability of the controlled system.

Main Methods:

  • Utilized the backstepping method for controller design.
  • Employed an integral transformation to convert the control problem into solving a hyperbolic partial differential equation (PDE).
  • Applied fractional Lyapunov stability theory (Mittag-Leffler stability) for rigorous analysis.

Main Results:

  • Successfully designed and implemented a boundary feedback controller for FRD systems with non-constant diffusivity.
  • Demonstrated the well-posedness of the kernel PDE for the non-constant diffusivity case.
  • Proved the Mittag-Leffler stability of the closed-loop system.

Conclusions:

  • The proposed backstepping-based boundary feedback control is effective for FRD systems with space-dependent diffusivity.
  • The generalization of control methods to non-constant diffusion coefficients expands the applicability of FRD system control.
  • Numerical simulations confirm the controller's effectiveness and system stability.