# Applications of Nonlinearity in Engineering and Finance

A nonlinear system is one in which the output is not proportional to the input. Its properties make it an interesting topic for engineers, mathematicians, biologists, and physicists. In fact, nonlinearity is common to most systems. Let’s look at some of the most common examples of nonlinear systems. This includes biotransformation and drug absorption. Nonlinearity also occurs in pricing simulations and engineering.

## Nonlinearity in drug absorption

Unlike dissolution, drug absorption does not follow a predictable pattern. It can be caused by changes in physiology, such as gastric emptying, increased or decreased GI blood flow, or binding sites saturating the enzyme. Nonlinearity in drug absorption is not dangerous unless the availability is affected. Some examples of nonlinear drug absorption include phenylbutazone, which has a finite number of binding sites on plasma proteins, and naproxen, which increases with blood concentrations.

Acidic and basic drugs have different pH-absorption curves. These different pH values cause the drug to ionize or diffuse differently through the GI tract. The pKa of these drugs is affected by the virtual pH, or microclimate pH. Several NSAIDs are affected by the pH. These differences are due to pH-dependent drug-ionisation. Some drugs, such as ionotherapy and diuretics, are highly soluble in these environments.

## Nonlinearity in biotransformation

A key aspect of biotransformation is its capacity-limited metabolism. Nonlinearity can occur for a number of reasons, including enzyme or cofactor saturation, inhibitory effect of metabolites, and pathological conditions such as hepatic toxicity. In physics, nonlinearity is defined as the opposite of a linear system, which means that its outputs do not change proportionally to its inputs. Scientists study this problem to better understand the process.

## Nonlinearity in pricing simulations

The Monte Carlo method is a widely used statistical tool for solving problems with discrete variables. In this book, we present five examples of applications of nonlinearity. Each example uses the standard Monte Carlo methodology, but incorporates nonlinearity by reformulating the physical observable or expectation. The MC method can be applied to various applications in finance, including those that involve complex geometry, null collisions, zero variance, and sensitivity analysis.

The main benefit of nonlinearity in pricing simulations is that it allows for flexible investment portfolios. Nonlinearity can create a seemingly chaotic situation in investments. Therefore, investors need to use different pricing simulations for these kinds of investments. Investors using these models will look for information on the Greeks. These factors help them manage risk and time entry points. However, investors should be aware of the limitations of nonlinearity in pricing simulations and be prepared for them.

## Nonlinearity in engineering

The concept of nonlinearity in engineering is the opposite of linearity, where the response of a system does not vary in proportion to its input. Nonlinear systems are more difficult to model and control than linear systems, because changes in one component of the system can have complex effects throughout the whole system. As a result, it is difficult to make accurate long-term forecasts using current technologies. Nonlinear systems also exhibit several other characteristics, such as being difficult to model.

Because of its inherent nature, nonlinear phenomena are common in all engineering systems, even in the simplest examples. While many people view nonlinearity as an inhibitor to system integration and performance improvement, research advances in nonlinear dynamics are continuously revealing its positive impacts on engineering systems. Nonlinearity can be beneficial to structure health monitoring, vibration control, energy harvesting, and other engineering systems. Nonlinearity is a promising topic in a wide range of engineering applications, including energy harvesting, structure health monitoring, and vibration control.