How fast is the concentration increasing at a distance of 1 centimeter from the center 3 seconds after the nutrient is introduced when suppose that 1 cubic centimeter of nutrient is placed at the center of circular petri dish filled with water. It might wonder how the nutrient is distributed after a time of t seconds. According to the classical theory of diffusion, the concentration of nutrient (in parts of nutrient per part of water) after time t is given by: u ( r , t ) = 1 4 π D t e − r 2 / ( 4 D t ) , Here, D is the diffusivity, which we will take to be 1 , and r is the distance from the center in centimeters.
How fast is the concentration increasing at a distance of 1 centimeter from the center 3 seconds after the nutrient is introduced when suppose that 1 cubic centimeter of nutrient is placed at the center of circular petri dish filled with water. It might wonder how the nutrient is distributed after a time of t seconds. According to the classical theory of diffusion, the concentration of nutrient (in parts of nutrient per part of water) after time t is given by: u ( r , t ) = 1 4 π D t e − r 2 / ( 4 D t ) , Here, D is the diffusivity, which we will take to be 1 , and r is the distance from the center in centimeters.
Solution Summary: The author calculates how fast the concentration increases at a distance of 1 centimeter from the center 3 seconds after the nutrient is introduced.
To calculate: How fast is the concentration increasing at a distance of 1 centimeter from the center 3 seconds after the nutrient is introduced when suppose that 1 cubic centimeter of nutrient is placed at the center of circular petri dish filled with water. It might wonder how the nutrient is distributed after a time of t seconds. According to the classical theory of diffusion, the concentration of nutrient (in parts of nutrient per part of water) after time t is given by:
u(r,t)=14πDte−r2/(4Dt),
Here, D is the diffusivity, which we will take to be 1, and r is the distance from the center in centimeters.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY