Research

I am interested in the physics of complex systems. Most of my research is focused on the interface between biological networks, mechanical metamaterials, and electrical power grids.

Recent Research Highlights

Enhancing synchronization by optimal correlated noise

From the flashes of fireflies to Josephson junctions and power infrastructure, networks of coupled phase oscillators provide a powerful framework to describe synchronization phenomena in many natural and engineered systems. Most real-world networks are under the influence of noisy, random inputs, potentially inhibiting synchronization. While noise is unavoidable, here we show that there exist optimal noise patterns which minimize desynchronizing effects and even enhance order. Specifically, using analytical arguments we show that in the case of a two-oscillator model, there exists a sharp transition from a regime where the optimal synchrony-enhancing noise is perfectly anti-correlated, to one where the optimal noise is correlated. More generally, we then use numerical optimization methods to demonstrate that there exist anti-correlated noise patterns that optimally enhance synchronization in large complex oscillator networks. Our results may have implications in real-world networks such as power grids and neuronal networks, which are subject to significant amounts of correlated input noise.
Sherwood Martineau (W '22), Tim Saffold (W '22), Timothy Chang (W '23), H.R.
doi: 10.1103/PhysRevLett.128.098301, arXiv: 2107.08509.

Optimal elasticity of biological networks

Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in plant leaves, here we model networks of bending beams that capture the discrete and non-uniform nature of natural materials. Using the principle of maximal rigidity under natural resource constraints, we show that optimal discrete beam networks reproduce the structural features of real leaf venation. Thus, in addition to its ability to efficiently transport water and nutrients, the venation network also optimizes leaf rigidity using the same hierarchical reticulated network topology. We study the phase space of optimal mechanical networks, providing concrete guidelines for the construction of elastic structures. We implement these natural design rules by fabricating efficient, biologically inspired metamaterials.
H.R.
doi: 10.1103/PhysRevLett.126.038101, arXiv: 2006.01532.

Discontinuous transition to loop formation in optimal supply networks

The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding redundant edges to supply networks is costly, yet beneficial for resilience. Loops typically form when costs for new edges are small or inputs uncertain. Here, we shed further light on the transition to loop formation. We demonstrate that loops emerge discontinuously when decreasing the costs for new edges for both an edge-damage model and a fluctuating sink model. Mathematically, new loops are shown to form through a saddle-node bifurcation. Our analysis allows to heuristically predict the location and cost where the first loop emerges. Finally, we unveil an intimate relationship among betweenness measures and optimal tree networks. Our results can be used to understand the evolution of loop formation in real-world biological networks.
F. Kaiser, H.R., and D. Witthaut
doi: 10.1038/s41467-020-19567-2 arXiv: 2011.11960.

Active topolectrical circuits

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Building on a generic nonlinear oscillator representation, we demonstrate both theoretically and experimentally the emergence of self-organized protected edge states in ATCs. The good agreement between theory, simulations and experiment implies that ATCs can be realized in many different ways. Beyond topological protection, we also show how one can induce persistent localized bulk wave patterns by strategically placing defects in 2D lattice ATCs. These results lay the foundation for the practical implementation of autonomous electrical circuits with robust functionality in arbitrarily high dimensions.
T. Kotwal, F. Moseley, A. Stegmaier, S. Imhof, H. Brand, T. Kiessling, R. Thomale, H. Ronellenfitsch, J. Dunkel.
doi: 10.1073/pnas.2106411118. arXiv: 1903.10130.

Phenotypes of Vascular Flow Networks

Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold Physarum polycephalum as well as mammalian and plant venation. Adaptive rules are believed to guide development of these networks and lead to a reticulate, hierarchically nested topology that is both efficient and resilient against perturbations. However, as of yet, no mechanism is known that can generate such networks on all scales. We show how hierarchically organized reticulation can be constructed and maintained through spatially correlated load fluctuations on a particular length scale. We demonstrate that the network topologies generated represent a trade-off between optimizing transport efficiency, construction cost, and damage robustness and identify the Pareto-efficient front that evolution is expected to favor and select for. We show that the typical fluctuation length scale controls the position of the networks on the Pareto front and thus on the spectrum of venation phenotypes.
H. R., E. Katifori
doi: 10.1103/PhysRevLett.123.248101. arXiv: 1707.03074.

Inverse design of discrete mechanical metamaterials

Mechanical and phononic metamaterials exhibiting negative elastic moduli, gapped vibrational spectra, or topologically protected modes enable precise control of structural and acoustic functionalities. While much progress has been made in their experimental and theoretical characterization, the inverse design of mechanical metamaterials with arbitrarily programmable spectral properties and mode localization remains an unsolved problem. Here, we present a flexible computational inverse-design framework that allows the efficient tuning of one or more gaps at nearly arbitrary positions in the spectrum of discrete phononic metamaterial structures. The underlying algorithm optimizes the linear response of elastic networks directly, is applicable to ordered and disordered structures, scales efficiently in two and three dimensions, and can be combined with a wide range of numerical optimization schemes. We illustrate the broad practical potential of this approach by designing mechanical band-gap switches that open and close preprogrammed spectral gaps in response to an externally applied stimulus such as shear or compression. We further show that the designed structures can host topologically protected edge modes, and validate the numerical predictions through explicit three-dimensional finite-element simulations of continuum elastica with experimentally relevant material parameters. Generally, this network-based inverse design paradigm offers a direct pathway toward manufacturing phononic metamaterials, DNA origami structures, and topoelectric circuits that can realize a wide range of static and dynamic target functionalities.
H. Ronellenfitsch, N. Stoop, J. Yu, A. Forrow, and J. Dunkel
doi: 10.1103/PhysRevMaterials.3.095201. arXiv: 1802.07214v2.

Limits of multifunctionality in tunable networks

Nature is rife with networks that are functionally optimized to propagate inputs to perform specific tasks. Whether via genetic evolution or dynamic adaptation, many networks create functionality by locally tuning interactions between nodes. Here we explore this behavior in two contexts: strain propagation in mechanical networks and pressure redistribution in flow networks. By adding and removing links, we are able to optimize both types of networks to perform specific functions. We define a single function as a tuned response of a single “target” link when another, predetermined part of the network is activated. Using network structures generated via such optimization, we investigate how many simultaneous functions such networks can be programed to fulfill. We find that both flow and mechanical networks display qualitatively similar phase transitions in the number of targets that can be tuned, along with the same robust finite-size scaling behavior. We discuss how these properties can be understood in the context of constraint–satisfaction problems.J. W. Rocks* , H. Ronellenfitsch* , A. J. Liu, S. R. Nagel, and E. Katifori
doi: 10.1073/pnas.1806790116. arXiv: 1805.00504

Optimal Noise-Canceling Networks

Natural and artificial networks, from the cerebral cortex to large-scale power grids, face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant question of whether and how noise filtering can be hard wired directly into a network’s architecture. By considering generic phase oscillator arrays under cost constraints, we explore here analytically and numerically the design, efficiency, and topology of noise-canceling networks. Specifically, we find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. More broadly, our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks.
H. R., J. Dunkel, M. Wilczek
doi: 10.1103/PhysRevLett.121.208301. arXiv: 1807.08376

Autonomous Actuation of Zero Modes in Mechanical Networks Far from Equilibrium

A zero mode, or floppy mode, is a nontrivial 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 Letter, we show theoretically and experimentally that complex zero modes in mechanical networks can be selectively mobilized by nonequilibrium 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 mobilize finite mechanisms as exemplified by a self-propelled topological soliton. Nonequilibrium activity thus enables autonomous actuation of coordinated mechanisms engineered through network topology.
F. Woodhouse, H. R., J. Dunkel
doi: 10.1103/PhysRevLett.121.178001. arXiv: 1805.07728.

Dual Theory of Transmission Line Outages

A new graph dual formalism is presented for the analysis of line outages in electricity networks. The dual formalism is based on a consideration of the flows around closed cycles in the network. After some exposition of the theory is presented, a new formula for the computation of line outage distribution factors is derived, which is not only computationally faster than existing methods, but also generalizes easily for multiple line outages and arbitrary changes to line series reactance. In addition, the dual formalism provides new physical insight for how the effects of line outages propagate through the network. For example, in a planar network a single-line outage can be shown to induce monotonically decreasing flow changes, which are mathematically equivalent to an electrostatic dipole field.
H. R., D. Manik, J. Horsch, T. Brown, and D. Witthaut
doi: 10.1109/TPWRS.2017.2658022. arXiv: 1606.07276.

Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks

Highly optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is nonconvex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems, it is believed that such an optimal state is slowly achieved through natural selection. However, general coarse grained models for flow networks with local positive feedback rules for the vessel conductivity typically get trapped in low efficiency, local minima. In this work we show how the growth of the underlying tissue, coupled to the dynamical equations for network development, can drive the system to a dramatically improved optimal state. This general model provides a surprisingly simple explanation for the appearance of highly optimized transport networks in biology such as leaf and animal vasculature.
H. R., E. Katifori
doi: 10.1103/PhysRevLett.117.138301. arXiv: 1606.00331.