I'm using the RK method to calculate the thin film profile. there is a complex interface curvature term, as shown in 1, κ. The final formula is a fourth-order ordinary differential equation which requires the first and second curvature derivative terms, they are also listed in 1. However, I don't understand how it was simplified. Specifically, I don't know where does ln(r) come from. Can anybody explain it to me?
2026-03-25 20:36:38.1774470998
Simplification of the derivative of the mean curvature
77 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
Related Questions in ORDINARY-DIFFERENTIAL-EQUATIONS
- The Runge-Kutta method for a system of equations
- Analytical solution of a nonlinear ordinary differential equation
- Stability of system of ordinary nonlinear differential equations
- Maximal interval of existence of the IVP
- Power series solution of $y''+e^xy' - y=0$
- Change of variables in a differential equation
- Dimension of solution space of homogeneous differential equation, proof
- Solve the initial value problem $x^2y'+y(x-y)=0$
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Derive an equation with Faraday's law
Related Questions in DERIVATIVES
- Derivative of $ \sqrt x + sinx $
- Second directional derivative of a scaler in polar coordinate
- A problem on mathematical analysis.
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Holding intermediate variables constant in partial derivative chain rule
- How would I simplify this fraction easily?
- Why is the derivative of a vector in polar form the cross product?
- Proving smoothness for a sequence of functions.
- Gradient and Hessian of quadratic form
Related Questions in CURVATURE
- Sign of a curve
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- A closed manifold of negative Ricci curvature has no conformal vector fields
- CAT(0) references request
- Why is $\kappa$ for a vertical line in 2-space not undefined?
- Discrete points curvature analysis
- Local computation of the curvature form of a line bundle
- Closed surface embedded in $\mathbb R^3$ with nonnegative Gaussian curvature at countable number of points
- What properties of a curve fail to hold when it is not regular?
Related Questions in RUNGE-KUTTA-METHODS
- Sensitivity (gradient) of function solved using RK4
- Solve fourth order ODE using fourth order Runge-Kutta method
- Prove that Runge Kutta Method (RK4) is of Order 4
- Applying second-order differential operator vs applying first-order differential operator twice?
- Adaptive step size Runge Kutta: getting a specific value
- PYTHON RK2 (Midpoint Method)
- Runge-Kutta Order Question
- fourth-order Runge-Kutta method producing values for $f(x)=\int_0^x e^{-t^2}$ (confusing answer key)
- Adaptive Step Size in RK45 for Second-Order ODE
- Runge kutta method for order 4 for ODE x'=f(t)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?