On a model mechanism for the spatial patterning of teeth primordia in the Alligator

We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986, 1987, 1990) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction-diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw ofA. mississippiensis. The results for the precise spatio-temporal sequence compare well with detailed developmental experiments

Locating Overlap Information in Quantum Systems

When discussing the black hole information problem the term ``information flow'' is frequently used in a rather loose fashion. In this article I attempt to make this notion more concrete. I consider a Hilbert space which is constructed as a tensor product of two subspaces (representing for example inside and outside the black hole). I discuss how the system has the capacity to contain information which is in NEITHER of the subspaces. I attempt to quantify the amount of information located in each of the two subspaces, and elsewhere, and analyze the extent to which unitary evolution can correspond to ``information flow''. I define the notion of ``overlap information'' which appears to be well suited to the problem.Comment: 25 pages plain LaTeX, no figures. Imperial/TP/93-94/2

On the torsional loading of elastoplastic spheres in contact

The mechanical interaction between two bodies involves normal loading in combination with tangential, torsional and rotational loading. This paper focuses on the torsional loading of two spherical bodies which leads to twisting moment. The theoretical approach for calculating twisting moment between two spherical bodies has been proposed by Lubkin [1]. Due to the complexity of the solution, this has been simplified by Deresiewicz for discrete element modelling [2]. Here, the application of a simplified model for elastoplastic spheres is verified using computational modelling. The single grain interaction is simulated in a combined finite discrete element domain. In this domain a grain can deform using a finite element formulation and can interact with other objects based on discrete element principles. For an elastoplastic model, the contact area is larger in comparison with the elastic model, under a given normal force. Therefore, the plastic twisting moment is stiffer. The results presented here are important for describing any granular system involving torsional loading of elastoplastic grains. In particular, recent research on the behaviour of soil has clearly shown the importance of plasticity on grain interaction and rearrangement

Quantum chaos, random matrix theory, and statistical mechanics in two dimensions - a unified approach

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory, and statistical mechanics. In the course of arguing for these connections, we observe sum rules associated with the outstanding counting problem in the theory of braid groups. We are able to show that the presented approach leads to the second law of thermodynamics.Comment: 23 pages, TeX typ

Monopole operators in three-dimensional N=4 SYM and mirror symmetry

We study non-abelian monopole operators in the infrared limit of three-dimensional SU(N_c) and N=4 SU(2) gauge theories. Using large N_f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators which are (anti-)chiral primaries and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified.Comment: 23 pages, LaTex; v2: section 3.4 modified, section 3.5 extended, references adde

Quantum Approach to a Derivation of the Second Law of Thermodynamics

We re-interprete the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas-subsystem" under consideration and its environment ("container"). The time-average of a purity-measure is found to equal the average over the respective path in Hilbert-space. We then show that for typical (degenerate or non-degenerate) thermodynamical systems almost all states within the allowed region of Hilbert-space have a local von Neumann-entropy S close to the maximum and a purity P close to its minimum, respectively. Typically thermodynamical systems should therefore obey the second law.Comment: 4 pages. Accepted for publication in Phys. Rev. Let

The foundations of statistical mechanics from entanglement: Individual states vs. averages

We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. We formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma.Comment: 12 pages, v3 title changed, v2 minor change

Information erasure and the generalized second law of black hole thermodynamics

We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle

Comparison between a μFE model and DEM for an assembly of spheres under triaxial compression

This paper presents a simple case of a Face Centred Cubic (FCC) array of 2,000 spheres under triaxial compression to compare the results obtained using the Discrete Element Method (DEM) and a micro finite element model (μFE). This μFE approach was developed so that the internal structure of the soil can be obtained using x-ray computed tomography and converted into a numerical fabric. The individual grains are represented as continuum deformable bodies and the inter-granular interaction based on the defined contact laws. In order to demonstrate the simple contact constitutive behaviour used in this μFE model, the response for two contacting elastic spheres is compared with theoretical equations. The strength at failure of the packing of 2,000 spheres is seen to yield similar values for DEM, μFE and the analytical solution. When comparing the evolving void ratio, a good agreement between the two numerical models was observed for very small strains but as the strain increases, the values start to diverge, which is believed to be related with the rigidity of the grains used in DEM