Non-classical computing: feasible versus infeasible

Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future

An investigation on flow field partitioning related to the rheological heterogeneities and its application to geological examples

Earth’s lithosphere is heterogeneous and composed of rheologically distinct elements at various scales of observations. This causes the flow of rocks to vary with space and time, which may influence the formation of various kinds of geological rock records. This thesis provides quantitative solutions to some first-order problems in structural geology regarding this heterogeneous flow variation and thereby the development of various geological rock records at different scales of observations. Pressure in a rheologically heterogeneous element may deviate from its ambient value and if significant, may influence the metamorphic assemblages. This might cause problems in the routine use of geothermobarometry-based pressure estimates from mineral assemblages as a proxy for depth in geodynamic models of geological processes. A micromechanics-based multiscale model called Multi Order Power Law Approach (MOPLA) is applied to simulate pressure deviation in and around a rheologically distinct rock element embedded in a rock medium of a non-linear viscous anisotropic rheology. The results show that the pressure deviations are in the same order as the deviatoric stress levels and hence limited by the strength of rocks. Flow variation can influence c-axis fabrics from quartz aggregate within feldspar-mica matrix in the natural high strain zones. If such effect is not accounted for, crucial geological information such as deformation temperature, deformation history and shear sense obtained using c-axis fabrics can be seriously misinterpreted. A multiscale approach coupling MOPLA with Viscoplastic Self-consistent (VPSC) model is used to simulate c-axis fabrics under partitioned flow. The results show that the quartz c-axis fabric variation showing apparent opposite senses of shear within a single thin section, can be explained by partitioned flow within the quartz domains and reflect finite strain gradient rather than a reversal of vorticity sense as previously thought. Flow variation can form flanking structures around a cross-cutting element like a vein or a dyke that may provide kinematic information such as ‘shear sense’ and ‘finite strain’. Their correct interpretations are critical for understanding regional tectonics. A micromechanics-based modeling approach is used to simulate 3-D flanking structures and demonstrate how the flanking structure may vary with the cutting element’s shape, orientation, and rheological contrast to the ambient medium. A reverse-dynamic modeling approach is applied to quantitatively estimate kinematic vorticity number, viscosity contrast of the cutting element to the ambient medium, and finite strain from natural flanking structures

Applicability of the Eshelby Formalism to Viscous Power-Law Materials: A Numerical Validation

Fabric is important for the interpretation of tectonic evolutions. In the process of extrapolating small-scale fabric to tectonics, modeling frameworks are needed. Neither the early kinematic models nor the contemporary computational geodynamics are able to capture the complexities of the fabric development in natural deformation systems. Eshelby proposed a formalism in micro-mechanics, and it is now well understood that this formalism works well for the linear viscous deformations. However, given that most of the natural rocks are power-law materials, the Eshelby Formalism cannot be directly applied to geological problems. This problem was largely solved when Lebensohn and Tom (1993, Acta Metallurgica et Materialia, vol 41, 2611-2624) incorporated a linearization scheme with Eshelby Formalism, known as the Tangent Linearization. The purpose of this project is to validate the applicability of the Eshelby Formalism with Tangent Linearization (EFTL) or with Secant Linearization (EFSL) to power-law material deformations. Two types of simulations are proceeded, one is based on EFTL / EFSL, while the other one based on 2D finite difference geodynamic method. Comparisons of the two simulations show that even in the most general situation of power-law material deformations, EFSL has major differences with the simulated power-law behavior while EFTL has only an approximately 10% deviation. Through this project, EFTL is validated to be a new, sufficient framework for fabric modeling, which marks a new era of fabric interpretation both in theoretical simulations and in field work practice

The New Science of Complexity

Deterministic chaos, and even maximum computational complexity, have been discovered within Newtonian dynamics. Economists assume that prices and price changes can also obey abstract mathematical laws of motion. Sociologists and other postmodernists advertise that physics and chemistry have outgrown their former limitations, that chaos and complexity provide new holistic paradigms for science, and that the boundaries between the hard and soft sciences, once impenetrable, have disappeared like the Berlin Wall. Three hundred years after the deaths of Galileo, Descartes, and Kepler, and the birth of Newton, reductionism appears to be on the decline, with holistic approaches to science on the upswing. We therefore examine the evidence that dynamical laws of motion may be discovered from empirical studies of chaotic or complex phenomena, and also review the foundation of reductionism in invariance principle

Cargese Lectures on Extra Dimensions

I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible relevance to the hierarchy problem.Comment: 56 pages, 11 figures, lectures given at Cargese School "Particle Physics and Cosmology: the Interface'', August 200