Chemical networks with inflows and outflows: a positive linear differential inclusions approach

David Angeli1, Patrick De Leenheer, Eduardo D Sontag

  • 1Dept. of Electrical and Electronic Engineering, Imperial College, London, UK. angeli@dsi.unifi.it

Related Concept Videos

Indefinite Integrals01:25

Indefinite Integrals

The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...
Mesh Analysis01:20

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Mesh Analysis with Current Sources01:10

Mesh Analysis with Current Sources

Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law (KVL)...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Surface Integrals of Vector Fields: Flux01:22

Surface Integrals of Vector Fields: Flux

Understanding the movement of air masses is fundamental to meteorological analysis and atmospheric modeling. A key component in this process is quantifying the total mass of air that flows into or out of a defined region over a specified period of time. This is achieved by evaluating the mass flux across a boundary surface, a conceptual tool that simplifies the complex dynamics of atmospheric systems.To begin, an imaginary boundary surface S is introduced, enclosing the region of interest. The...