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The Symplectic Penrose Kite

Fiammetta Battaglia, Elisa Prato
2010 Communications in Mathematical Physics  
The purpose of this article is to view the Penrose kite from the perspective of symplectic geometry.  ...  The Penrose kite, however, is the most elementary and beautiful example of a simple convex polytope that is not rational.  ...  The Penrose Kite and Dart Let us now recall the procedure for obtaining the Penrose kite and dart from the pentagram.  ... 
doi:10.1007/s00220-010-1103-y fatcat:wavtu3tr6fhg7ppzcw6xvaiifi

P.d.e.'s which imply the Penrose conjecture [article]

Hubert L. Bray, Marcus A. Khuri
2009 arXiv   pre-print
In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved.  ...  In addition, our techniques suggest a more general Penrose conjecture and generalized notions of apparent horizons and trapped surfaces, which are also of independent interest.  ...  (Notation: We adopt the convention that Greek indices always range from 0 to 3 and Latin indices always range from 1 to 3.  ... 
arXiv:0905.2622v1 fatcat:dicybrhmr5a3hjvh6nenw53yfe

On Supertwistors, the Penrose-Ward Transform and N=4 super Yang-Mills Theory [article]

Alexander D. Popov, Christian Saemann
2006 arXiv   pre-print
Furthermore, we extend the picture to the full N=4 SYM theory and, by using the known supertwistor description of this case, we show that the corresponding constraint equations are (gauge) equivalent to  ...  This hCS theory in turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions.  ...  Some mathematical definitions Interior product. For the interior product of a vector V with a one-form A, we use the notation V A := V, A . A second common notation for this product is i V A.  ... 
arXiv:hep-th/0405123v5 fatcat:mohuihy66vfuzd6mmimc26e7oi

P. D. E.'s Which Imply the Penrose Conjecture

Hubert L. Bray, Marcus A. Khuri
2011 Asian Journal of Mathematics  
In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved.  ...  In addition, we discuss the Carrasco-Mars counterexample to the Penrose conjecture for generalized apparent horizons (added since the first version of this paper was posted on the arXiv) and instead conjecture  ...  (Notation: We adopt the convention that Greek indices always range from 0 to 3 and Latin indices always range from 1 to 3.  ... 
doi:10.4310/ajm.2011.v15.n4.a5 fatcat:k7wio235o5cxjf5tjhc3qher74

Proof of the Riemannian Penrose Conjecture Using the Positive Mass Theorem [article]

Hubert L. Bray
1999 arXiv   pre-print
This result improves upon the beautiful work of Huisken and Ilmanen, who used inverse mean curvature flows of surfaces to show that the total mass is at least the mass contributed by the largest black  ...  We prove the Riemannian Penrose conjecture, an important case of a conjecture made by Roger Penrose in 1973, by defining a new flow of metrics.  ...  We will continue with the same notation as defined in section 4.  ... 
arXiv:math/9911173v1 fatcat:avhbsentdfdq5lrj5orufqwsku

On supertwistors, the Penrose--Ward transform and $\CN=4$ super-Yang--Mills theory

Alexander D. Popov, Christian Sämann
2005 Advances in Theoretical and Mathematical Physics  
Some mathematical definitions 983 Appendix C. The twistor geometry in the Kleinian case ε = +1 986 Appendix D.  ...  The map PW: h → f is called the Penrose-Ward transform. Of course, one can also consider the inverse map PW −1 : f → h.  ...  Acknowledgments We are grateful to O. Lechtenfeld, S. Uhlmann and M. Wolf for many useful comments. This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG).  ... 
doi:10.4310/atmp.2005.v9.n6.a2 fatcat:kx67khwoi5cn5jqclltdigplfu

The Gap Labelling Integrated Density of States for a Quasi Crystal Universe Is Identical to the Observed 4.5 Percent Ordinary Energy Density of the Cosmos

Mohamed S. El Naschie
2014 Natural Science  
Condense matter methods and mathematical models used in solving problems in solid state physics are transformed to high energy quantum cosmology in order to estimate the magnitude of the missing dark energy  ...  Looking at the problem from this novel viewpoint was rewarded by a rather unexpected result, namely that the gap labelling method of integrated density of states for three dimensional icosahedral quasicrystals  ...  Landi's K-Analysis of the Penrose Tiling As noted by Landi [12] , the K-theory of Penrose universe treated as x-space by Connes [26] is straight forward and leads via Bratteli diagram and the fact that  ... 
doi:10.4236/ns.2014.616115 fatcat:d37uxuf4vvhb5js2hc7j5b4tku

DisCoPy for the quantum computer scientist [article]

Alexis Toumi, Giovanni de Felice, Richie Yeung
2022 arXiv   pre-print
In particular, the diagram data structure allows to encode various kinds of quantum processes, with functors for classical simulation and optimisation, as well as compilation and evaluation on quantum  ...  DisCoPy (Distributional Compositional Python) is an open source toolbox for computing with string diagrams and functors.  ...  We look forward to welcoming new contributors!  ... 
arXiv:2205.05190v1 fatcat:izzrcumgl5dtxpumwfgudna6dm

On Math, Matter and Mind

Piet Hut, Mark Alford, Max Tegmark
2006 Foundations of physics  
Others suspect that no single framework, from physics or other sources, will ever capture reality.  ...  The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math.  ...  ACKNOWLEDGMENTS The authors are grateful to the Institute for Advanced Study in Princeton for providing the stimulating environment for our early discussions, which over the past eight years evolved into  ... 
doi:10.1007/s10701-006-9048-x fatcat:7xgzxc4kdveypnndvt7ivijexa

Twistors and amplitudes

Andrew Hodges
2015 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
One contribution of 13 to a theme issue 'New geometric concepts in the foundations of physics' .  ...  Penrose [5] had in fact derived the early twistor diagrams from a consideration of twistor Hamiltonians.  ...  A further question lay in discerning what rule might be expected to generate the diagrams, analogous to the derivation of the Feynman rules from a Lagrangian.  ... 
doi:10.1098/rsta.2014.0248 pmid:26124244 fatcat:e5rx6rh7l5ajzpmmtxdrnhq44i

Climbing Escher's stairs: a way to approximate stability landscapes in multidimensional systems [article]

Pablo Rodríguez-Sánchez, Egbert H. van Nes, Marten Scheffer
2019 arXiv   pre-print
These landscapes can be calculated from the system's dynamical equations using the physical concept of scalar potential.  ...  The non-gradient to gradient ratio can be used to estimate the local error introduced by our approximation.  ...  Penrose and Penrose (1958) for details). Penrose and Penrose (1958) is a classical example of an impossible object.  ... 
arXiv:1903.05615v2 fatcat:fjgcsjdrwrg5zbr5xmfbizoyx4

Cubulating rhombus groups

David Janzen, Daniel Wise
2013 Groups, Geometry, and Dynamics  
Our viewpoint relates Sageev's dual cube complexes to de Bruijn's approach to the Penrose tilings. Mathematics Subject Classification (2010). 20F67.  ...  We are grateful to the referee for corrections that improved the exposition.  ...  In [dB81] , de Bruijn had previously discovered this viewpoint on the Penrose rhombus tiling of E 2 and it led him to beautiful explanations of the construction and behavior of the Penrose tilings, as  ... 
doi:10.4171/ggd/188 fatcat:mhnestbrtjazxpv6zb7uetb6iu

The Black Hole Firewall Transformation and Realism in Quantum Mechanics

Gerard 't 't Hooft
2021 Universe  
domains in the Penrose diagram is a primary example.  ...  The proposal requires that one starts off with the entire Penrose diagram for the eternal black hole as the background metric, after which one has to invoke the antipodal identification in order to see  ...  However, the Penrose diagram is not. A time boost for far-away regions in I and I I corresponds to a Lorentz transformation at the origin of the Penrose diagram.  ... 
doi:10.3390/universe7080298 fatcat:tkt5e7ux6zhlddzn75funkp3by

A Unified Mathematical Language for Medicine and Science [article]

Patrick St-Amant
2014 arXiv   pre-print
A unified mathematical language for medicine and science will be presented.  ...  It can also serve as a basis for exploring ideas related to what could be called metascience.  ...  Acknowledgement I would like to thank Véronique Pagé and Nathalie Patenaude for their help and encouragement.  ... 
arXiv:1409.5045v1 fatcat:jy6gzxyq4bdcpf3kf5m7ajqux4

An introduction to the surface science of quasicrystals

P.A. Thiel
2004 Progress in Surface Science  
diagram'' [12] .  ...  Mathematical constructions such as the Fibonacci sequence, or the Penrose tiling, stop short of answering the famous question, ''Where are the atoms?''  ... 
doi:10.1016/j.progsurf.2004.05.012 fatcat:fimerhejpza75mnw2rnk24w4mu
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