What is the physical meaning of second derivative?

Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of an object with respect to time is the instantaneous acceleration of the object, or the rate at which the velocity of the object is changing with respect to time …

What can be the use of the second time derivative of a physical variable?

It tells you the (instantaneous) change rate of (instantaneous) change rate of f. Let f(t) be the travelled distance for example. Then the first derivative gives you the velocity and the second derivative gives you the change rate of velocity, namely the acceleration.

What is second spatial derivative?

By taking the second spatial derivative (SSD) of a series of local field potentials (LFPs) generated by the superposition of synaptic events (Cottaris & Elfar, 2009), CSD analysis allows identification of the laminar sources of currents, based on a characteristic pattern of current sources and sinks.

What is D in diffusion equation?

D is the diffusion coefficient or diffusivity. Its dimension is area per unit time. φ (for ideal mixtures) is the concentration, of which the dimension is amount of substance per unit volume.

What does first derivative physically mean?

Derivative – First Order. The first order derivative of a function represents the rate of change of one variable with respect to another variable. For example, in Physics we define the velocity of a body as the rate of change of the location of the body with respect to time.

What do second order partial derivatives tell us?

The unmixed second-order partial derivatives, f x x and , f y y , tell us about the concavity of the traces. The mixed second-order partial derivatives, f x y and , f y x , tell us how the graph of twists.

What is physical interpretation?

Physical interpretation of an equation means the act of understanding the relation between the physical quantities in the equation and how we can expect the system to behave at extreme or normal conditions.

What is the physical meaning of derivative?

The derivative is defined as an instantaneous rate of change at a given point. We usually differentiate two kinds of functions, implicit and explicit functions. Explicit functions are the functions in which the known value of the independent variable “x” directly leads to the value of the dependent variable “y”.

What are the 2 variables in the denominator of Fick’s law of diffusion?

It states that ‘the rate of diffusion is proportional to both the surface area and concentration difference and is inversely proportional to the thickness of the membrane’.

How do you find the space-time fractional diffusion equation?

Thus, the space-time fractional diffusion equation is obtained by replacing the first-order time derivative and second-order space derivative in the standard diffusion equation by a fractional derivative of order α and β, respectively.

How do fractional diffusion equations describe anomalous diffusion?

As in [14, 183], fractional diffusion equations describe anomalous diffusion on fractals (physical objects of fractional dimension, like some amorphous semiconductors or strongly porous materials). In normal diffusion described by, such as the heat equation, the mean square displacement of a diffusive particle behaves like const · t for t → ∞.

Why is the Caputo fractional derivative used to solve FDEs?

As stated earlier, the Caputo fractional derivative is generally used to solve FDEs because it allows traditional initial and boundary conditions to be included in the formulation in a standard way, whereas models based on other fractional derivatives may require the values of the fractional derivative terms at the initial time. Xiao Jun Yang,