A one-dimensional momentum conservation equation for a straight jet driven by an electrical field is developed. It is presented in terms of a stress component, which can be applied to any constitutive relation o
The derivation of a discrete Helmholtz equation is outlined for the pressure in a fluid dynamic flow model with terrain following coordinates. Special attention is directed towards discrete gradient and divergence operators which are consistent with conservation of mass and momentum. A sketch of a ...
The corresponding principal (or “proper”) values Λ are obtained from the condition for consistency of equation (1), i.e. as the roots of the fourth degree equation (2)|Aik−λgik|=0, and are invariants of the tensor. Both the quantities λ and the eigenvectors correspondin...
From the laser illumination distribution, the optical force density distributed within the HR coating is simulated by the finite-difference time-domain (FDTD) method in two dimensions (2D)21. This method solves the electromagnetic-material momentum continuity equation in the experimental configuration of...
For a single particle we derived the equation (11.8)τex =dLdt relating the external torque to the rate of change of angular momentum. To extend this relation to a system of particles requires a somewhat involved and abstract derivation. To simplify the algebra without compromising the ...
Answer and Explanation:1 The first law of thermodynamics is a statement of a(d) conservation of energy. In equation form, we can write the first law of thermodynamics as: ...
(4.30) The magnetic pressure term 1 2 g(b, b) emerges naturally in the derivation, and its origin may traced back to the term b div u in the transport equation (4.24) for b. In a com- pressible fluid, whereas the fundamental magnetic flux β is simply Lie transported by the flow ...
This equation serves to connect the azimuthal vorticity and various streamfunction derivatives at the top of the boundary layer with those in the upper-level outflow of the tropical cyclone.17 In a well-developed tropical cyclone, the radius of maximum tangential wind is typically much smaller ...
Equation (1) means that the momentum imparted locally onto the moving object upon scattering is related to the expectation value of Qα for the specific input state |Ψin⟩ in the far field. A direct consequence of equation (1) is that if the input state |Ψin⟩ is chosen to be ...
(A3) . The velocity derivatives, un,1, in Equation (A2) were obtained using numerical derivation of the velocity waveform evaluated from Equation (A3). The system of Equation (A2) is overdetermined and only an approximate solution can be found. Moore–Penrose matrix inversion allows us to ...