Nondimensionalization is the partial or full removal of physical dimensions from an equation involving physical quantities by a suitable substitution...

physics, however, this scruple may be set aside, by a process called nondimensionalization. The effective result is that many fundamental equations of physics...

if convection is present. The Fourier number arises naturally in nondimensionalization of the heat equation. The general definition of the Fourier number...

for which selected physical constants have been set to 1 through nondimensionalization of physical units. For example, the speed of light c may be set...

a\varepsilon _{r}\varepsilon _{0}k_{\text{B}}T}}=Z_{0}} To obtain the nondimensionalized differential equation and initial conditions, use the π {\displaystyle...

produced by lifting the fingers one at a time from bottom to top Nondimensionalization, the removal of units from a mathematical equation This disambiguation...

studentizing (e.g., Studentized residual). Another approach to nondimensionalization focuses on scaling by location rather than dispersion. The percent...

system of quantities is chosen in the speed of light, c, is used for nondimensionalization, so that, for example, seconds and lightseconds are interchangeable...

{\displaystyle \omega _{0}>0} describing the width of the distribution—cf. nondimensionalization. If the state is allowed to evolve in free space, then the time-dependent...

computing sets of dimensionless parameters from the given variables, or nondimensionalization, even if the form of the equation is still unknown. The Buckingham...

which can be used to simplify the problem. These can be found by nondimensionalization. The result is that, if energy is measured in units of ħω and distance...

types of turbines. To deal with this, nondimensionalization is applied to various qualities. Nondimensionalization allows one to make comparisons between...

)[x-(B^{3}t^{2}/6m^{2})]},} where, for simplicity (and nondimensionalization), choosing ħ = 1, m = 1/2, and B an arbitrary constant results in...

dimensionless critical shear stress τ c ∗ {\displaystyle \tau _{c}*} . The nondimensionalization is in order to compare the driving forces of particle motion (shear...

be reduced to this form.[citation needed] This is done through nondimensionalization. If the forcing function is f(t) = cos(ωt) = cos(ωtcτ) = cos(ωτ)...

for transformations with quantities named NondimensionalizationTransform that applies a nondimensionalization transform to an equation. Mathematica also...

{x}}} and, assuming high Reynolds number flow, it is possible to nondimensionalize the variables with the scalings: p d = ρ V 2 p d ′ , ∇ = L − 1 ∇ ′...

u ( r , t ) {\displaystyle \mathbf {q} _{u}(\mathbf {r} ,t)} are nondimensionalized noises. The choice of free energy function, f ( φ ) {\displaystyle...

spinodal time. The spinodal length and spinodal time can be used to nondimensionalize the equation of motion, resulting in universal scaling for spinodal...

quantities are normalized against like-dimensioned quantities (called nondimensionalization), resulting in only dimensionless quantities remaining. Physicists...

^{2}x^{2}\right)\psi (x)=E\psi (x).} Make a coordinate substitution to nondimensionalize the differential equation x   =   ℏ m ω q . {\displaystyle x\ =\ {\sqrt...

is often useful to separate these terms. Doing so completes the nondimensionalization of the range equation into fundamental design disciplines of aeronautics...

and P, normally called field quadratures in quantum optics. (See Nondimensionalization.) These operators are related to the position and momentum operators...

{1+\cos(\theta )}{2}},} and then expanding both dy⁄dx and γ(x) as a nondimensionalized Fourier series in θ with a modified lead term: d y d x = A 0 + A 1...

squared. The number is named after Henry Darcy and is found from nondimensionalizing the differential form of Darcy's law. This number should not be confused...

(note that the lines over the variables indicates that they have been nondimensionalized by dividing through by the chord): Z ¯ ( x ) = a [ ( b − 1 ) x ¯ 3...

the mass and frequency of the oscillator are equal to one (see nondimensionalization), the energy of the oscillator is H = 1 2 ( P 2 + X 2 ) . {\displaystyle...

densimetric Froude number is usually preferred by modellers who wish to nondimensionalize a speed preference to the Richardson number which is more commonly...

friction coefficient is a dimensionless skin shear stress which is nondimensionalized by the dynamic pressure of the free stream. The skin friction coefficient...

velocity scale (used for nondimensionalization), R 0 {\displaystyle R_{0}} , the length scale (used for nondimensionalization), R = R ( t ) = R 0 2 + 4...