Applied mathematics articles within Nature Physics

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  • Article |

    Many recent experiments have stored quantum information in bosonic modes, such as photons in resonators or optical fibres. Now an adaptation of the classical spherical codes provides a framework for designing quantum error correcting codes for these platforms.

    • Shubham P. Jain
    • , Joseph T. Iosue
    •  & Victor V. Albert

  • Article |

    Cytoplasmic flows in the fruit fly oocyte can reorganize cellular components. These structured vortical flows arise through self-organizing dynamics of microtubules, molecular motors and cytoplasm.

    • Sayantan Dutta
    • , Reza Farhadifar
    •  & Michael J. Shelley

  • Article |

    Although using low-rank matrices is the go-to approach to model the dynamics of complex systems, its validity remains formally unconfirmed. An analysis of random networks and real-world data now sheds light on this low-rank hypothesis and its implications.

    • Vincent Thibeault
    • , Antoine Allard
    •  & Patrick Desrosiers

  • News & Views |

    Physical networks, composed of nodes and links that occupy a spatial volume, are hard to study with conventional techniques. A meta-graph approach that elucidates the impact of physicality on network structure has now been introduced.

    • Zoltán Toroczkai

  • Article |

    Physical networks are systems composed of physical entities, which conventional graph-based approaches fail to capture. Theoretical work now introduces a meta-graph technique to uncover the impact of physicality on the structure of networks.

    • Márton Pósfai
    • , Balázs Szegedy
    •  & Albert-László Barabási

  • Article |

    Network geometry is an emerging framework used to describe several topological and organizational features of complex networks. Now this approach has been extended to directed networks, which contain both symmetric and asymmetric interactions.

    • Antoine Allard
    • , M. Ángeles Serrano
    •  & Marián Boguñá

  • Article |

    Quantum computers are believed to exponentially outperform classical computers at some tasks, but it is hard to make guarantees about the limits of classical computers. It has now been proven that classical computers cannot efficiently simulate most quantum circuits.

    • Ramis Movassagh

  • Comment |

    An analysis of representations of fluid flows in classical paintings reveals scientific inaccuracies. Some of these misrepresentations might be caused by a limited understanding of fluid dynamics and others by deliberate artistic choices.

    • Rouslan Krechetnikov

  • Article |

    Wrinkling happens because of mechanical instabilities arising from length mismatches. A theory now describes wrinkling in confined elastic shells and is expected to be relevant for the controlled design of complex wrinkle patterns.

    • Ian Tobasco
    • , Yousra Timounay
    •  & Eleni Katifori

  • Article |

    Network models rarely fix the number of connections of each node during evolution, despite this being needed in real-world applications. Addressing this need, a new approach can grow scale-free networks without preferential attachment.

    • Shubha R. Kharel
    • , Tamás R. Mezei
    •  & Zoltan Toroczkai

  • Perspective |

    Network representations of complex systems are limited to pairwise interactions, but real-world systems often involve higher-order interactions. This Perspective looks at the new physics emerging from attempts to characterize these interactions.

    • Federico Battiston
    • , Enrico Amico
    •  & Giovanni Petri

  • Measure for Measure |

    What does it mean for an individual to be ‘important’ or for a connection to be ‘outstanding’? The answer depends on context, as Sarah Shugars and Samuel V. Scarpino explain.

    • Sarah Shugars
    •  & Samuel V. Scarpino

  • Measure for Measure |

    The assembly of the more than a million single parts of the ITER tokamak requires large-scale three-dimensional precision metrology. John Villanueva Jr gives us insights into the complexity of this project.

    • John Villanueva Jr

  • Article |

    The authors investigate the relationship between the volume of malignant tumours and their metabolic processes using a large dataset of patients with cancer. They find that cancers follow a superlinear metabolic scaling law, which implies that the proliferation of cancer cells accelerates with increasing volume.

    • Víctor M. Pérez-García
    • , Gabriel F. Calvo
    •  & Ana M. García Vicente

  • Letter |

    Knowledge of the spreading mechanisms of contagions is important for understanding a range of epidemiological and social problems. A study now shows that so-called simple and complex contagions cannot be told apart if there is more than one simple contagion traversing the population at the same time.

    • Laurent Hébert-Dufresne
    • , Samuel V. Scarpino
    •  & Jean-Gabriel Young

  • Perspective |

    This Perspective argues that ergodicity — a foundational concept in equilibrium statistical physics — is wrongly assumed in much of the quantitative economics literature. By asking the extent to which dynamical problems can be replaced by probabilistic ones, many economics puzzles are resolved in a natural and empirically testable fashion.

    • Ole Peters

  • News & Views |

    It is generally difficult to know in advance if a sheet of paper can be folded into an origami shape, but for quadrilateral crease patterns a tiling approach can identify all possible ways of folding them.

    • Christian Santangelo

  • News & Views |

    The mechanics of many materials can be modelled by a network of balls connected by springs. A bottom-up approach based on differential geometry now captures changes in mechanics upon network growth or merger, going beyond the linear deformation regime.

    • A. Souslov
    •  & V. Vitelli

  • Article |

    A bottom-up mathematical approach provides a framework for the design of mechanical networks of two- or three-dimensional frames composed of freely rotating rods and springs that achieve any desired coordinate motion.

    • Jason Z. Kim
    • , Zhixin Lu
    •  & Danielle S. Bassett

  • Perspective |

    Rich data are revealing that complex dependencies between the nodes of a network may not be captured by models based on pairwise interactions. Higher-order network models go beyond these limitations, offering new perspectives for understanding complex systems.

    • Renaud Lambiotte
    • , Martin Rosvall
    •  & Ingo Scholtes

  • Comment |

    Modern physics edged mechanics out into the wilds of engineering. But multidisciplinary interest in pattern formation has moved it back into the mainstream, bringing with it interest from other fields — as this summer’s Solvay Workshop demonstrated.

    • Pedro M. Reis
    • , Fabian Brau
    •  & Pascal Damman

  • Editorial |

    In praise of the Fields Medal.

  • Measure for Measure |

    Solid angle is an ancient notion with modern relevance. A one-page primer by Ben Kravitz.

    • Ben Kravitz

  • Letter |

    Knotted lines representing torus knot and figure-eight knot are produced in the polarization profile of optical beams, leading to a topological characterization of the structure of the polarization field.

    • Hugo Larocque
    • , Danica Sugic
    •  & Ebrahim Karimi

  • Letter |

    The organization of small clusters of connected cells confined to an egg chamber during early development can be mapped onto a tree packing problem. Entropically preferred packing configurations are shown to arise more readily in experiment.

    • Jasmin Imran Alsous
    • , Paul Villoutreix
    •  & Jörn Dunkel

  • Article
    | Open Access

    Complex networks are not obviously renormalizable, as different length scales coexist. Embedding networks in a geometrical space allows the definition of a renormalization group that can be used to construct smaller-scale replicas of large networks.

    • Guillermo García-Pérez
    • , Marián Boguñá
    •  & M. Ángeles Serrano

  • Article |

    Controlled wave propagation in disordered media is a challenge because of scattering processes. Now it is shown that for speckled targets much larger than the wavelength, long-range correlations between the speckles enhance wave propagation control.

    • Chia Wei Hsu
    • , Seng Fatt Liew
    •  & A. Douglas Stone

  • Letter |

    Critical phenomena are well understood in a wide range of physical systems. The dynamics of snap-through instabilities, a widespread phenomenon in their own right, are now shown to display critical scaling properties.

    • Michael Gomez
    • , Derek E. Moulton
    •  & Dominic Vella

  • News & Views |

    Going around an exceptional point in a full circle can be a non-adiabatic, asymmetric process. This surprising prediction is now confirmed by two separate experiments.

    • Dieter Heiss

  • Letter |

    The common policy of replacing infected individuals with healthy substitutes can have the effect of accelerating disease transmission. A dynamic network model suggests that standard modelling approaches underplay the effect of network structure.

    • Samuel V. Scarpino
    • , Antoine Allard
    •  & Laurent Hébert-Dufresne

  • Article |

    Knots have been observed in a variety of classical systems, but so far not in the quantum regime. Knot solitons have now been created in a spinor Bose–Einstein condensate, exhibiting interesting topological structures, including Hopf fibration.

    • D. S. Hall
    • , M. W. Ray
    •  & M. Möttönen

  • News & Views |

    The myriad creatures that inhabit the waters of our planet all swim using different mechanisms. Now, a simple relation links key physical observables of underwater locomotion, on scales ranging from millimetres to tens of metres.

    • Johannes Baumgart
    •  & Benjamin M. Friedrich

  • Letter |

    Nonlinear inertial flows usually influence the motion of swimming organisms, but most studies focus on the tractable case of swimmers too small to feel such effects. A mechanistic principle now unifies the varied dynamics of macroscopic swimmers.

    • Mattia Gazzola
    • , Médéric Argentina
    •  & L. Mahadevan

  • Letter |

    Connecting complex networks is known to exacerbate perturbations and lead to cascading failures, but natural networks of networks are surprisingly stable. A theory now proposes that network structure holds the key to understanding this paradox.

    • Saulo D. S. Reis
    • , Yanqing Hu
    •  & Hernán A. Makse

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