What happens when characteristic curves intersect?

The characteristic curves intersect the initial curve Γ more than once, leading to inconsis- tencies. The characteristic curves intersect one another at a point in the domain. The initial curve, Γ, corresponds exactly to a characteristic curve. In this case the problem is not fully determined.

What is the characteristic curve Who invented it?

It is used to describe the contrast characteristics of a photographic film for a particular range of exposure. The exposure needed to produce an image is also determined. It is also called Hurter and Driffield curve (or H & D curve), named after Ferdinand Hurter and Vero Charles Driffield who first developed it.

What is method of characteristics in aerodynamics?

The Method of Characteristics is a very convenient tool to calculate isentropic portions within a supersonic flows. This is a numerical method, but the merit is that the method itself determines the grid (or mesh) it requires.

What are characteristic points?

[‚kar·ik·tə′ris·tik ′pȯint] (mathematics) The characteristic point of a one-parameter family of surfaces corresponding to the value u0 of the parameter is the limit of the point of intersection of the surfaces corresponding to the values u0, u1, and u2 of the parameter as u1 and u2 approach u0 independently.

What are characteristics curves?

A characteristic curve is a graph of the relationship between the amount of exposure given a film and it’s corresponding density after processing. 1. A typical film characteristic curve is made by plotting density produced, against the log of exposure given (Log E).

When can you use method of characteristics?

In mathematics, the method of characteristics is a technique for solving partial differential equations. Typically, it applies to first-order equations, although more generally the method of characteristics is valid for any hyperbolic partial differential equation.

Can characteristic curves cross?

The right hand side of the equation is constant, indicating that the characteristic curves will be straight lines, as in the constant coefficient advection equation case. The characteristics are straight lines, but the lines do not all have the same slope, so it is possible for the characteristics to intersect.

How do you find the characteristic curve?

For a PDE a(x,y,z)zx+b(x,y,z)zy=c(x,y,z), you can obtain the characteristic by solving the ODE’s dxds=a(x,y,z), dyds=b(x,y,z) dzds=c(x,y,z).

WHAT IS curve characteristics?

A curve plotted on a graph from two axes, exposure and density, used to describe the characteristics and performance of sensitive emulsions. A characteristic curve is a graph of the relationship between the amount of exposure given a film and it’s corresponding density after processing.

What is the importance of the characteristic curve?

I-V characteristic curves are generally used as a tool to determine and understand the basic parameters of a component or device and which can also be used to mathematically model its behaviour within an electronic circuit.