Search

We developed a model for oil production on the basis of simple physical considerations. The model provides a basic understanding of Hubbert’s empirical observation that the production rate for an oil-producing region reaches its maximum when approximately half the recoverable oil has been produced. According to the model, the oil production rate at a large field must peak before drilling peaks. We use the model to investigate the effects of several drilling strategies on oil production. Despite the model’s simplicity, predictions for the timing and magnitude of peak production match data on oil production from major oil fields throughout the world.

We demonstrate the control of chaos in a nonlinear circuit constructed from readily available electronic components. Control is achieved using recursive proportional feedback, which is applicable to chaotic dynamics in highly dissipative systems and can be implemented using experimental data in the absence of model equations. The application of recursive proportional feedback to a simple electronic oscillator provides an undergraduate laboratory problem for exploring proportional feedback algorithms used to control chaos.

When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.

Just over fifty years ago, Hubbert correctly predicted that US oil production in the lower-48 states would soon peak, despite substantially rising production at the time. Hubbert based his prediction on the empirical observation that the production rate at oil reservoirs typically follows a bell-shaped curve that peaks near the midpoint of production. We present a highly simplified physical model of oil production that gives insight into Hubbert’s success. This toy model relates the total area of active wells to future production and allows for several interesting analytical conclusions. We show analytically, contrary to intuition but consistent with historical data, the number of active wells at any given field must peak after the production rate peaks. Since oil production is pressuredriven, the toy model treats an oil reservoir as a sealed container filled with liquid oil and highly pressurized gas. A pipe extends into the container with a cross-sectional area, which represents the total area of wells and changes continuously over time. As gas expands, it forces liquid out of the container through the pipe but also drops in pressure, eventually limiting production. We assume the flow obeys Bernoulli’s principle and the gas expands isothermally, which leads to a nonlinear ordinary differential equation for the velocity of fluid exiting the container. For most reasonable choices of the area function, the differential equation requires a numerical solution. However, it is possible to specify a plausible area function for which the model yields an analytical expression for the production rate that corresponds to the bell-shaped curve used by Hubbert to predict the peak in US oil production.

We investigate a novel bursting state in inclined layer thermal convection in which convection rolls exhibit intermittent, localized, transverse bursts. With increasing temperature difference, the bursts increase in duration and number while exhibiting a characteristic wavenumber, magnitude, and size. We propose a mechanism which describes the duration of the observed bursting intervals and compare our results to bursting processes in other systems., Comment: 4 pages, 8 figures