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When a body is in motion, it encounters resistance because the body interacts with its surroundings. This resistance is known as friction, a common yet complex force whose behavior is still not completely understood. Friction opposes relative motion between systems in contact, but also allows us to move. Friction arises in part due to the roughness of surfaces in contact. For one object to move along a surface, it must rise to where the peaks of the surface can skip along the bottom of the...
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One of the simpler characteristics of sliding friction is that it is parallel to the contact surfaces between systems, and is always in a direction that opposes the motion or attempted motion of the systems relative to each other. If two systems are in contact and moving relative to one another, then the friction between them is called kinetic friction. For example, kinetic friction slows a hockey puck sliding on ice.
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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Types of Friction Problems01:27

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Friction is an essential concept in physics, engineering, and everyday life. It is the force that opposes the relative motion or tendency of such motion between two surfaces in contact. One of the most common types of friction encountered in various applications is dry friction. Dry friction problems can be broadly categorized into three types, each with unique characteristics and challenges.
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First Law: Particles in Two-dimensional Equilibrium01:18

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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Linear momentum is a fundamental concept in physics that describes the motion of an object. It is a vector quantity, having a magnitude equal to the product of its mass and its velocity, and direction along the object's velocity. On the other hand, linear impulse, also known as momentum impulse, is a concept in physics related to the change in the linear momentum of an object. Impulse is a vector quantity defined as the product of force and the time over which the force is applied.
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Active noise-driven particles under space-dependent friction in one dimension.

D Breoni1, H Löwen1, R Blossey2

  • 1Institut für Theoretische Physik II: Weiche Materie, Heinrich Heine-Universität Düsseldorf, Universitässtraße 1, 40225 Düsseldorf, Germany.

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This study explores particle motion with space-dependent friction and active noise. Researchers found that friction and potential changes influence particle behavior, leading to diverse probability density functions (PDFs).

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Soft Matter Physics

Background:

  • Stochastic processes are fundamental in describing systems with inherent randomness.
  • Understanding particle dynamics in complex environments is crucial for fields like biophysics and materials science.
  • Nonequilibrium systems, driven by active noise, exhibit unique behaviors not seen in equilibrium.

Purpose of the Study:

  • To investigate the dynamics of a particle in one dimension under space-dependent friction, confining potentials, and active noise.
  • To analyze both short-time particle dynamics and long-time stationary probability density functions (PDFs).
  • To explore how varying friction coefficients and potential forms affect particle behavior and PDF characteristics.

Main Methods:

  • Utilized a Langevin equation to model the particle's stochastic motion.
  • Employed analytical and numerical methods to study particle dynamics.
  • Investigated specific forms of space-dependent friction (γ(x) = γ₀ + γ₁|x|ᵖ) and potentials (U(x) ∝ |x|ⁿ) with varying exponents (p=1,2; n=0,1,2).

Main Results:

  • Short-time dynamics exhibited both diffusive and ballistic regimes.
  • Stationary PDFs showed unique features dependent on the exponents (p,n).
  • Observed PDFs interpolated between Laplacian, Gaussian, and bimodal distributions, tunable via the friction strength ratio (γ₀/γ₁).

Conclusions:

  • The interplay of space-dependent friction, potentials, and active noise leads to rich particle dynamics.
  • The friction strength ratio is a key parameter for controlling the nature of the stationary probability density functions.
  • The model provides insights into the behavior of molecular motors and confined colloidal particles.