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Related Concept Videos

Relative Motion Analysis - Acceleration01:10

Relative Motion Analysis - Acceleration

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...
Shock Waves01:16

Shock Waves

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...
Tangential and Normal Components of Acceleration01:27

Tangential and Normal Components of Acceleration

In the study of particle motion, acceleration is often broken down into tangential and normal components to clarify how a particle's velocity changes over time. This approach relies on analyzing the geometry of the path and the dynamics of the motion. The tangential direction follows the path of motion and reflects changes in the particle's speed, while the normal direction points toward the center of curvature and captures changes in the direction of motion.The velocity of a particle moving...
Relative Motion Analysis using Rotating Axes - Acceleration01:22

Relative Motion Analysis using Rotating Axes - Acceleration

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Related Experiment Video

Updated: Jul 18, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Analytical study of diffusive relativistic shock acceleration.

Uri Keshet1

  • 1Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA. keshet@sns.ias.edu

Physical Review Letters
|December 13, 2006
PubMed
Summary

Particle acceleration in relativistic shocks depends on diffusion, impacting the particle spectral index. This study generalizes findings and can constrain shock models using observational data like gamma-ray bursts.

Area of Science:

  • Astrophysics
  • Plasma Physics
  • High-Energy Astrophysics

Background:

  • Relativistic shocks are crucial sites for particle acceleration in astrophysical phenomena.
  • Understanding particle acceleration mechanisms is key to interpreting high-energy emissions.

Purpose of the Study:

  • To analytically study particle acceleration in relativistic shocks.
  • To investigate the influence of arbitrary velocity-angle diffusion on particle spectra.
  • To generalize previous findings for isotropic diffusion.

Main Methods:

  • Analytical treatment in the test-particle, small-angle scattering limit.
  • Incorporation of an arbitrary velocity-angle diffusion function (D).
  • Numerical confirmation of analytical results.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System
10:52

Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System

Published on: August 7, 2018

Related Experiment Videos

Last Updated: Jul 18, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System
10:52

Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System

Published on: August 7, 2018

Main Results:

  • The particle spectral index (s) is sensitive to the diffusion function D.
  • Sensitivity is particularly noted downstream and at specific particle angles.
  • The analysis generalizes and confirms previous results for isotropic diffusion.

Conclusions:

  • The developed analytical framework can test collisionless shock models.
  • Observational data, such as gamma-ray burst afterglows, can constrain the diffusion function D.
  • Strongly anisotropic diffusion (forward or backward enhanced) downstream is observationally disfavored.