Following the evolution of a star cluster is among the most computer-intensive and delicate problems in science, let alone stellar dynamics. The main challenges are to deal with the extreme discrepancy of length and time scales, the need to resolve the very small deviations from thermal equilibrium that drive the evolution of the system, and the sheer number of computations involved. Though numerical algorithms of many kinds are used, this is not an exercise in numerical analysis: the choice of algorithm and accuracy are dictated by the need to simulate the physics faithfully rather than to solve the equations of motion as exactly as possible.

Length/time scale problem

Simultaneous close encounters between three or more stars have to be modelled accurately, since they determine the exchange of energy and angular momentum between internal and external degrees of freedom (Chapter 23). Especially the energy flow is important, since the generation of energy by double stars provides the heat input needed to drive the evolution of the whole system, at least in its later stages (Chapter 27). Unfortunately, the size of the stars is a factor 109 smaller than the size of a typical star cluster. If neutron stars are taken into account, the problem is worse, and we have a factor of 1014 instead, for the discrepancy in length scales.

The time scales involved are even worse, a close passage between two stars taking place on a time scale of hours for normal stars, milliseconds for neutron stars (Table 3.1).

Third source of controlled experimental data

Laboratory experiments and well data serve as main sources of controlled experimental data where a number of physical properties are measured on the same samples at varying conditions, such as saturation and pressure. Chapter 2 discusses how these data are used to derive theoretical models as well as establish the relevance of these models to rock types.

Computational rock physics, also called digital rock physics or DRP, is the third such source. The principle of this technique is “image and compute”: image the pore structure of rock and computationally simulate various physical processes in this space, including single-phase viscous fluid flow for absolute permeability; multiphase flow for relative permeability; electrical flow for resistivity; and loading and stress computation for the elastic properties.

The principle of DRP is simple but its implementation is not. It requires at least three main steps: imaging; image processing and segmentation; and physical property simulation.

Three-dimensional imaging of a rock sample is usually performed in a CT scanning machine by rotating the sample relative to an X-ray source. The actual 3D geometry is reconstructed tomographically from these raw data and the image appears in shades of gray. The brightness of a voxel in such a 3D image is directly affected by the effective atomic number of the material and is approximately proportional to its density. For example, dense pyrite will appear bright while less dense quartz will appear light gray. The empty pore space will be black and parts of it illed with, for example, water or bitumen will be dark gray. To image very small features present in shale or micrite in carbonates, even the sharpest CT resolution may not be enough. A different technique, the so-called FIB-SEM, is used where the focused ion beam gradually shaves off thin slices of the sample and the exposed 2D surface is imaged (photographed) by the scanning electron microscope to produce a stack of closely spaced 2D images.

Quantum computation and quantum information is a field of fundamental interest because we believe quantum information processing machines can actually be realized in Nature. Otherwise, the field would be just a mathematical curiosity! Nevertheless, experimental realization of quantum circuits, algorithms, and communication systems has proven extremely challenging. In this chapter we explore some of the guiding principles and model systems for physical implementation of quantum information processing devices and systems.

We begin in Section 7.1 with an overview of the tradeoffs in selecting a physical realization of a quantum computer. This discussion provides perspective for an elaboration of a set of conditions sufficient for the experimental realization of quantum computation in Section 7.2. These conditions are illustrated in Sections 7.3 through 7.7, through a series of case studies, which consider five different model physical systems: the simple harmonic oscillator, photons and nonlinear optical media, cavity quantum electrodynamics devices, ion traps, and nuclear magnetic resonance with molecules. For each system, we briefly describe the physical apparatus, the Hamiltonian which governs its dynamics, means for controlling the system to perform quantum computation, and its principal drawbacks.