Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine

We demonstrate how three-dimensional fluid flow simulations can be carried out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for cellular-automata computations. The principal algorithmic innovation is the use of a lattice-gas model with a 16-bit collision operator that is specially adapted to the machine architecture. It is shown how the collision rules can be optimized to obtain a low viscosity of the fluid. Predictions of the viscosity based on a Boltzmann approximation agree well with measurements of the viscosity made on CAM-8. Several test simulations of flows in simple geometries -- channels, pipes, and a cubic array of spheres -- are carried out. Measurements of average flux in these geometries compare well with theoretical predictions.Comment: 19 pages, REVTeX and epsf macros require

Information Transmission Concept Based Model of Wave Propagation in Discrete Excitable Media

A new information transmission concept based model of excitable media with continuous outputs of the model’s cells and variable excitation time is proposed. Continuous character of the outputs instigates infinitesimal inaccuracies in calculations. It generates countless number of the cells’ excitation variants that occur in front of the wave even in the homogenous and isotropic grid. New approach allows obtain many wave propagation patterns observed in real world experiments and known simulation studies. The model suggests a new spiral breakup mechanism based on tensions and gradually deepening clefts that appear in front of the wave caused by uneven propagation speed of curved and planar segments of the wave. The analysis hints that the wave breakdown and daughter wavelet bursting behavior possibly is inherent peculiarity of excitable media with weak ties between the cells, short refractory period and granular structure. The model suggested is located between cellular automaton with discrete outputs and differential equation based models and gives a new tool to simulate wave propagation patterns in applied disciplines. It is also a new line of attack aimed to understand wave bursting, propagation and annihilation processes in isotropic homogenous media

Physics Without Physics: The Power of Information-theoretical Principles

David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a refoundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the observed regime is that of small wavevectors ...Comment: 34 pages, 8 figures. Paper for in memoriam of David Finkelstei

Mathematical modelling of anisotropy in fibrous connective tissue

We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial differential equations operating on a macroscopic scale. We show that a model consisting of a single extracellular matrix material aligned by fibroblasts via flux and stress exhibits behaviour that is incompatible with experimental observations. We extend the model to two matrix types and show that the results of this extended model are robust and consistent with experiment. The second model represents cells as discrete objects in a continuum of ECM. We show that this model predicts patterns of alignment on macroscopic length scales that are lost in a continuum model of the cell population

Entanglement Dynamics in 1D Quantum Cellular Automata

Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is required between arbitrarily distant pairs of lattice qubits. An alternative model of quantum computation based on quantum cellular automata (QCA) requires only homogeneous local interactions that can be implemented in parallel. This would be a huge simplification in an actual experiment. We find some minimal physical requirements for the construction of unitary QCA in a 1 dimensional Ising spin chain and demonstrate optimal pulse sequences for information transport and entanglement distribution. We also introduce the theory of non-unitary QCA and show by example that non-unitary rules can generate environment assisted entanglement.Comment: 12 pages, 8 figures, submitted to Physical Review