陳聖
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier–Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical, i.e., there is a ‘scaling gap’ between what can be ...
Physical models—also known as white-box model—are based on the principles of physics and are often derived from first principles and expressed through derivative equations. These equations can manifest in various forms, ranging from intricate 3D finite element models to simplified lumped models, yie...
The kinematic restrictions which reject virtual and infrared corrections arise in our approach from a double-counting-exclusion (DCE) condition, which separates the LO and NLO contributions (see below). For the sake of definiteness and clarity, we hereafter will refer to this scheme as to NLO....
Whole-body 3D kinematic data were collected at 200 Hz using motion capture (8 cameras) and Vicon Nexus software v2.9.3 (Vicon, Oxford, UK). The laboratory coordinate system was oriented such that the x-, y-, and z-axes denoted the mediolateral (pointing towards the right side of the bo...
3 + √ 3/2 (9c) To remove ρ i from the previous equations, we multiply sin(θ i ) (respec- tively cos(θ i )) the equations in x (respectively in y) and we subtract the first one to the second one, to obtain three equations, sin(θ 1 )x −cos(θ 1 )y = 0 (10a...
and its kinematic and dynamic analysis is the basis of its kinematic control.The baffle module of the robot is an opened chain.The method of kinematic and dynamic analysis based on the screw theory is used to build up kinematic and dynamic equations of the robot by using the mathematic tools...
where is the (constant) fluid density, is the kinematic viscosity, and F = (fx , fy ) represents any external forces that act on the fluid. Notice that Equation 1 is actually two equations, because u is a vector quantity:Thus, we have three unknowns (u, v, and p) and thre...
which predict the behaviour of the physical structure functions as a function of the kinematic variableQ^2. The main advantage of Eq. (3) is that the evolution kernelsP_{ij}cannot depend on the factorization scheme nor on the factorization scale [13]: Being physical observables, the structure...
However, the kinematic quantities, which are absent from the governing equations, appear as Lagrange multipliers when solving the problem. The main strength of the lower bound principle is that it allows for a lower bound on the exact collapse multiplier to be computed, through constructing a ...