445 research outputs found

    Protein folding and the robustness of cells

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    The intricate intracellular infrastructure of all known life forms is based on proteins. The folded shape of a protein determines both the proteinā€™s function and the set of molecules it will bind to. This tight coupling between a proteinā€™s function and its interconnections in the molecular interaction network has consequences for the molecular course of evolution. It is also counter to human engineering approaches. Here we report on a simulation study investigating the impact of random errors in an abstract metabolic network of 500 enzymes. Tight coupling between function and interconnectivity of nodes is compared to the case where these two properties are independent. Our results show that the model system under consideration is more robust if function and interconnection are intertwined. These findings are discussed in the context of nanosystems engineering

    Sparse robot swarms: Moving swarms to real-world applications

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    Robot swarms are groups of robots that each act autonomously based on only local perception and coordination with neighbouring robots. While current swarm implementations can be large in size (e.g. 1000 robots), they are typically constrained to working in highly controlled indoor environments. Moreover, a common property of swarms is the underlying assumption that the robots act in close proximity of each other (e.g. 10 body lengths apart), and typically employ uninterrupted, situated, close-range communication for coordination. Many real-world applications, including environmental monitoring and precision agriculture, however, require scalable groups of robots to act jointly over large distances (e.g. 1000 body lengths), rendering the use of dense swarms impractical. Using a dense swarm for such applications would be invasive to the environment and unrealistic in terms of mission deployment, maintenance and post-mission recovery. To address this problem, we propose the sparse swarm concept, and illustrate its use in the context of four application scenarios. For one scenario, which requires a group of rovers to traverse, and monitor, a forest environment, we identify the challenges involved at all levels in developing a sparse swarmā€”from the hardware platform to communication-constrained coordination algorithmsā€”and discuss potential solutions. We outline open questions of theoretical and practical nature, which we hope will bring the concept of sparse swarms to fruition

    On the co-existence of transonic buffet and separation-bubble modes for the OALT25 laminar-flow wing section

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    Transonic buffet is an unsteady flow phenomenon that limits the safe flight envelope of modern aircraft. Scale-resolving simulations with span-periodic boundary conditions are capable of providing new insights into its flow physics. The present contribution shows the co-existence of multiple modes of flow unsteadiness over an unswept laminar-flow wing section, appearing in the following order of increasing frequency: (a) a low-frequency transonic buffet mode, (b) an intermediate-frequency separation bubble mode, and (c) high-frequency wake modes associated with vortex shedding. Simulations are run over a range of Reynolds and Mach numbers to connect the lower frequency modes from moderate to high Reynolds numbers and from pre-buffet to established buffet conditions. The intermediate frequency mode is found to be more sensitive to Reynolds-number effects compared to those of Mach number, which is the opposite trend to that observed for transonic buffet. Spectral proper orthogonal decomposition is used to extract the spatial structure of the modes. The buffet mode involves coherent oscillations of the suction-side shock structure, consistent with previous studies including global mode analysis. The laminar separation-bubble mode at intermediate frequency is fundamentally different, with a phase relationship between separation and reattachment that does not correspond to a simple `breathing' mode and is not at the same Strouhal number observed for shock-induced separation bubbles. Instead, a Strouhal number based on separation bubble length and reverse flow magnitude is found to be independent of Reynolds number within the range of cases studied

    Connecting transonic buffet with incompressible low-frequency oscillations on aerofoils

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    Self-sustained low-frequency flow unsteadiness over rigid aerofoils in the transonic regime is referred to as transonic buffet. Although the exact physical mechanisms underlying this phenomenon are unclear, it is generally assumed to be unique to the transonic regime. This assumption is shown to be incorrect here by performing large-eddy simulations of flow over a NACA0012 profile for a wide range of flow conditions. At zero incidence and sufficiently high freestream Mach numbers, M, transonic buffet occurs with shock waves present in the flow. However, self-sustained oscillations that occur at similar frequencies are observed at lower M for which shock waves are absent and the entire flow field remains subsonic at all times. At higher incidences, the oscillations are sustained at progressively lower M. Oscillations were observed for M as low as 0.3, where compressibility effects are small. A spectral proper orthogonal decomposition shows that the spatial structure of these oscillations (i.e., mode shapes) are essentially the same for all cases. These results indicate that buffet on aerofoils does not necessarily require the presence of shock waves. Furthermore, the trend seen with increasing incidence angles suggests that transonic buffet on aerofoils and low-frequency oscillations reported in the incompressible regime (Zaman et al., 1989, J. Fluid Mech., vol. 202, pp. 403--442) have similar origins. Thus, models which rely specifically on shock waves to explain transonic buffet are incorrect. These insights could be useful in understanding the origins of ``transonic" buffet and reformulating mitigation strategies by shifting the focus away from shock waves.Comment: 28 pages, 20 figure

    Transfer Matrices and Excitations with Matrix Product States

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    We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network states. In particular, we show that the Matrix Product State Transfer Matrix (MPS-TM) - a central object in the computation of static correlation functions - provides important information about the location and magnitude of the minima of the low energy dispersion relation(s) and present supporting numerical data for one-dimensional lattice and continuum models as well as two-dimensional lattice models on a cylinder. We elaborate on the peculiar structure of the MPS-TM's eigenspectrum and give several arguments for the close relation between the structure of the low energy spectrum of the system and the form of static correlation functions. Finally, we discuss how the MPS-TM connects to the exact Quantum Transfer Matrix (QTM) of the model at zero temperature. We present a renormalization group argument for obtaining finite bond dimension approximations of MPS, which allows to reinterpret variational MPS techniques (such as the Density Matrix Renormalization Group) as an application of Wilson's Numerical Renormalization Group along the virtual (imaginary time) dimension of the system.Comment: 39 pages (+8 pages appendix), 14 figure

    Symmetry Breaking and the Geometry of Reduced Density Matrices

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    The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding quantum correlations in many body systems and in this work we show how symmetry breaking can be understood from this wavefunction centered point of view. We demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions. The surfaces of those convex bodies exhibit non-analytic behavior in the form of ruled surfaces, which turn out to be the defining signatures for the emergence of symmetry breaking and of an associated order parameter. We illustrate this by plotting the convex sets arising in the context of three paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model in transverse magnetic field, exhibiting a second order quantum phase transition; the classical Ising model at finite temperature in two dimensions, which orders below a critical temperature TcT_c; and a system of free bosons at finite temperature in three dimensions, exhibiting the phenomenon of Bose-Einstein condensation together with an associated order parameter āŸØĻˆāŸ©\langle\psi\rangle. Remarkably, these convex sets look all very much alike. We believe that this wavefunction based way of looking at phase transitions demystifies the emergence of order parameters and provides a unique novel tool for studying exotic quantum phenomena.Comment: 5 pages, 3 figures, Appendix with 2 pages, 3 figure
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