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As an example, consider the conjugate pair. The pressure acts as a generalized force – pressure differences force a change in volume, and their product is the energy lost by the system due to mechanical work. Pressure is the driving force, volume is the associated displacement, and the two form a pair of conjugate variables.
When stated in terms of temperature differences, Newton's law (with several further simplifying assumptions, such as a low Biot number and a temperature-independent heat capacity) results in a simple differential equation expressing temperature-difference as a function of time. The solution to that equation describes an exponential decrease of ...
Run-and-tumble motion is a movement pattern exhibited by certain bacteria and other microscopic agents. It consists of an alternating sequence of "runs" and "tumbles": during a run, the agent propels itself in a fixed (or slowly varying) direction, and during a tumble, it remains stationary while it reorients itself in preparation for the next run.
The difference between an idealized cycle and actual performance may be significant. [2] For example, the following images illustrate the differences in work output predicted by an ideal Stirling cycle and the actual performance of a Stirling engine:
The thermal displacement thickness, may be thought of in terms of the difference between a real fluid and a hypothetical fluid with thermal diffusion turned off but with velocity and temperature . With no thermal diffusion, the temperature drop is abrupt.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The equation of motion for the lattice vibration in terms of the displacement of atoms [d(jl,t): displacement vector of the j-th atom in the l-th unit cell at time t] is (,) = ′ ′ ( ′ ′) (′ ′,), where m is the atomic mass and Γ is the force constant tensor.
A temperature sensor attached to the swimmer would show temperature varying with time, simply due to the temperature variation from one end of the pool to the other. The material derivative finally is obtained when the path x ( t ) is chosen to have a velocity equal to the fluid velocity x ˙ = u . {\displaystyle {\dot {\mathbf {x} }}=\mathbf ...