Functional control of network dynamics using designed Laplacian spectra

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. Spectral graph theory has traditionally prioritized unweighted networks. Here, we introduce a complementary framework, providing a mathematically rigorous weighted graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer spectra can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces chimera states in Kuramoto-type oscillator networks, completely suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. Our approach can be generalized to design continuous band gaps through periodic extensions of finite networks.Comment: 9 pages, 5 figure

Autonomous actuation of zero modes in mechanical networks far from equilibrium

A zero mode, or floppy mode, is a non-trivial coupling of mechanical components yielding a degree of freedom with no resistance to deformation. Engineered zero modes have the potential to act as microscopic motors or memory devices, but this requires an internal actuation mechanism that can overcome unwanted fluctuations in other modes and the dissipation inherent in real systems. In this work, we show theoretically and experimentally that complex zero modes in mechanical networks can be selectively mobilized by non-equilibrium activity. We find that a correlated active bath actuates an infinitesimal zero mode while simultaneously suppressing fluctuations in higher modes compared to thermal fluctuations, which we experimentally mimic by high frequency shaking of a physical network. Furthermore, self-propulsive dynamics spontaneously mobilise finite mechanisms as exemplified by a self-propelled topological soliton. Non-equilibrium activity thus enables autonomous actuation of coordinated mechanisms engineered through network topology

Stochastic cycle selection in active flow networks

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models. Keywords: networks; active transport; stochastic dynamics; topologyNational Science Foundation (U.S.) (Award CBET-1510768

Ferromagnetic and antiferromagnetic order in bacterial vortex lattices.

Despite their inherent non-equilibrium nature1, living systems can self-organize in highly ordered collective states2,3 that share striking similarities with the thermodynamic equilibrium phases4,5 of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies6,7, microbial suspensions8,9 and tissues10 to the coherent macro-scale dynamics in schools of fish11 and flocks of birds12. Yet, the generic mathematical principles that govern the emergence of structure in such artificial13 and biological6-9,14 systems are elusive. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Here, we connect these two previously disparate regimes: Through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct phases of ferro- and antiferromagnetic order. The preferred phase can be controlled by tuning the vortex coupling through changes of the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents15,16, reminiscent of those in quantum systems17-19. Our experimental observations can be rationalized in terms of a generic lattice field theory, suggesting that bacterial spin networks belong to the same universality class as a wide range of equilibrium systems.EPSRCThis is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nphys360

Stochastic cycle selection in active flow networks.

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such nonequilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of biological and nonbiological far-from-equilibrium networks, including actively controlled information flows, and establishes a correspondence between active flow networks and generalized ice-type models.This is the accepted manuscript. It is currently embargoed pending publication

Stationarity, soft ergodicity, and entropy in relativistic systems

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.Comment: 4 page

Derivatives of spin dynamics simulations

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation and stability analysis of spin dynamics simulations and experiments. Keywords: NMR, EPR, simulation, analytical derivatives, optimal control, spin chemistry, radical pair.Comment: Accepted by The Journal of Chemical Physic

Formation of the planet around the millisecond pulsar J1719-1438

Context. Recently the discovery of PSR J1719-1438, a 5.8 ms pulsar with a companion in a 2.2 hr orbit, was reported. The combination of this orbital period and the very low mass function is unique. The discoverers, Bailes et al., proposed an ultracompact X-ray binary (UCXB) as the progenitor system. However, the standard UCXB scenario would not produce this system as the time required to reach this orbital period exceeds the current estimate of the age of the Universe. The detached state of the system aggravates the problem. Aims. We want to understand the evolutionary history of PSR J1719-1438, and determine under which circumstances it could have evolved from an UCXB. Methods. We model UCXB evolution varying the donor size and investigate the effect of a wind mass loss from the donor, and compare the results with the observed characteristics of PSR J1719-1438. Results. An UCXB can reach a 2.2 hr orbit within the age of the Universe, provided that 1) the millisecond pulsar can significantly heat and expand the donor by pulsar irradiation, or 2) the system loses extra orbital angular momentum, e.g. via a fast wind from the donor. Conclusions. The most likely scenario for the formation of PSR J1719-1438 is UCXB evolution driven by angular momentum loss via the usual gravitational wave emission, which is enhanced by angular momentum loss via a donor wind of ~3x10^-13 Msun/yr. Depending on the size of the donor during the evolution, the companion presently probably has a mass of ~1-3 Jupiter masses, making it a very low mass white dwarf as proposed by Bailes et al. Its composition can be either helium or carbon-oxygen. A helium white dwarf companion makes the long (for an UCXB) orbital period easier to explain, but the required inclination makes it a priori less likely than a carbon-oxygen white dwarf.Comment: 5 pages, 4 figures. Accepted for publication in Astronomy and Astrophysics. v2: Updated a referenc