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Facilitated Transport01:19

Facilitated Transport

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The chemical and physical properties of plasma membranes cause them to be selectively permeable. Since plasma membranes have both hydrophobic and hydrophilic regions, substances need to be able to transverse both regions. The hydrophobic area of membranes repels substances such as charged ions. Therefore, such substances need special membrane proteins to cross a membrane successfully. In  facilitated transport, also known as facilitated diffusion, molecules and ions travel across a...
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Diffusion01:12

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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

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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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Primary Active Transport01:47

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In contrast to passive transport, active transport involves a substance being moved through membranes in a direction against its concentration or electrochemical gradient. There are two types of active transport: primary active transport and secondary active transport. Primary active transport utilizes chemical energy from ATP to drive protein pumps that are embedded in the cell membrane. With energy from ATP, the pumps transport ions against their electrochemical gradients—a direction...
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Gas Exchange and Transport01:20

Gas Exchange and Transport

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Gas exchange, the intake of molecular oxygen (O2) from the environment and the outflow of carbon dioxide (CO2) into the environment, is necessary for cellular function. Gas exchange during respiration occurs largely via the movement of gas molecules along pressure gradients. Gas travels from areas of higher partial pressure to areas of lower partial pressure. In mammals, gas exchange occurs in the alveoli of the lungs, which are adjacent to capillaries and share a membrane with them.
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Regulated mRNA Transport02:22

Regulated mRNA Transport

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In eukaryotes, transcription and translation are compartmentalized; an mRNA is first synthesized in the nucleus and then selectively transported to the cytoplasm for protein synthesis. Before transport, a pre-mRNA undergoes several steps of post-transcriptional modifications including splicing, 5' capping, and the addition of a poly-adenine tail. Various proteins bind to the pre-mRNA during these modifications. The mRNA transport takes place with the help of multiple proteins playing...
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Updated: Feb 6, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
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Published on: January 26, 2014

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Material barriers to diffusive and stochastic transport.

George Haller1, Daniel Karrasch2, Florian Kogelbauer3

  • 1Institute for Mechanical Systems, ETH Zürich, 8092 Zürich, Switzerland; georgehaller@ethz.ch.

Proceedings of the National Academy of Sciences of the United States of America
|August 29, 2018
PubMed
Summary
This summary is machine-generated.

Researchers identified material surfaces that minimize or maximize tracer transport in unsteady flows. These surfaces, computable from flow velocity, act as transport barriers or enhancers, even with vanishing diffusivity or in stochastic fields.

Keywords:
coherent structuresdiffusive transportstochastic transportturbulencevariational calculus

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Area of Science:

  • Fluid dynamics
  • Transport phenomena
  • Surface science

Background:

  • Understanding diffusive tracer transport in unsteady flows is crucial for various scientific and engineering applications.
  • Identifying surfaces that control transport (barriers and enhancers) is a key challenge.

Purpose of the Study:

  • To identify and characterize material surfaces that act as transport barriers or enhancers in general, unsteady fluid flow.
  • To develop a universal framework for detecting these transport-controlling surfaces.

Main Methods:

  • Formulated a universal, nondimensional transport functional to identify extremizing surfaces.
  • Computed the leading-order term of the functional from flow velocity.
  • Defined objective transport tensors to explicitly compute uniform transport extremizers as null surfaces.

Main Results:

  • Identified surfaces that minimize (barriers) or maximize (enhancers) diffusive tracer transport.
  • Demonstrated that these surfaces are extremizers of a universal transport functional.
  • Showed that these surfaces differ from previously known coherent structures, even in the vanishing diffusivity limit.
  • Extended the methodology to stochastic velocity fields, enabling detection under uncertainty.

Conclusions:

  • The study provides a robust method for identifying transport barriers and enhancers in complex fluid flows.
  • The findings are applicable to both deterministic and stochastic velocity fields, enhancing their practical utility.
  • This work offers new insights into controlling transport phenomena at material surfaces.