Eleni Katifori

Max Planck Institute for Dynamics and Self-Organization

Existing theories of structural adaptation in biological flow networks are largely concerned with steady flows. However, biological networks are composed of elastic vessels, and many are driven by a pulsatile or periodic source, leading to spatiotemporal variations in the pressure and flow fields on short time-scales within each vessel. Here, we in...

In stochastic exploration of geometrically embedded graphs, intuition suggests that providing a shortcut between a pair of nodes reduces the mean first passage time of the entire graph. Counterintuitively, we find a Braess’s paradox analog. For regular diffusion, shortcuts can worsen the overall search efficiency of the network, although they bridg...

Immersed nonlinear elements are prevalent in biological systems that require a preferential flow direction, such as the venous and the lymphatic system. We investigate here a certain class of models where the fluid is driven by peristaltic pumping and the nonlinear elements are ideal valves that completely suppress backflow. This highly nonlinear s...

Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individ...

Latency is a microbial strategy for persistence. For Toxoplasma gondii the ability of the bradyzoite stage to form long-lived cysts is critical for transmission, while their presence in neurons is considered important for immune evasion. Development of a mathematical model highlighted that immune pressure on bradyzoites should contribute to dynamic...

Interactions between commuting individuals can lead to large-scale spreading of rumors, ideas, or disease, even though the commuters have no net displacement. The emergent dynamics depend crucially on the commuting distribution of a population, that is how the probability to travel to a destination decays with distance from home. Applying this idea...

Truss structures at macro-scale are common in a number of engineering applications and are now being increasingly used at the micro-scale to construct metamaterials. In analyzing the properties of a given truss structure, it is often necessary to understand how stress waves propagate through the system and/or its dynamic modes under time dependent...

Fluid flow networks are ubiquitous and can be found in a broad range of contexts, from human-made systems such as water supply networks to living systems like animal and plant vasculature. In many cases, the elements forming these networks exhibit a highly non-linear pressure-flow relationship. Although we understand how these elements work individ...

Interactions between commuting individuals can lead to large-scale spreading of rumors, ideas, or disease, even though the commuters have no net displacement. The emergent dynamics depend crucially on the commuting distribution of a population, that is how the probability to travel to a destination decays with distance from home. Applying this idea...

In the stochastic exploration of geometrically embedded graphs, intuition suggests that providing a shortcut between a pair of nodes reduces the mean first passage time of the entire graph. Counterintuitively, we find a Braess paradox analog. For regular diffusion, shortcuts can worsen the overall search efficiency of the network, although they bri...

The mechanical properties of a thin, planar material, perfused by an embedded flow network, have been suggested to be potentially changeable locally and globally by fluid transport and storage, which can result in both small- and large-scale deformations such as out-of-plane buckling. In these processes, fluid absorption and storage eventually caus...

Existing models of adaptation in biological flow networks consider their constituent vessels (e.g. veins and arteries) to be rigid, thus predicting a non physiological response when the drive (e.g. the heart) is dynamic. Here we show that incorporating pulsatile driving and properties such as fluid inertia and vessel compliance into a general adapt...

The mechanical properties of a thin, planar material, perfused by an embedded flow network, can be changed locally and globally by the fluid transport and storage, resulting in small or large-scale deformation, such as out-of-plane buckling. Fluid absorption and storage eventually cause the material to locally swell. Different parts can hydrate and...

Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies, but controlling the often asymmetric and apparently stochastic wrinkles that result remains an elusive goal. Her...

The dense populations that inhabit global coastlines have an uncertain future due to increased flooding, storms, and human modification. The channel networks of deltas and marshes that plumb these coastlines present diverse architectures, including well‐studied dendritic topologies. However, the quasi‐stable loops that exist in nearly all coastal n...

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g., the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states...

Flow networks efficiently transport nutrients and other solutes in many physical systems, such as plant and animal vasculature. In the case of the animal circulatory system, an adequate oxygen and nutrient supply is not guaranteed everywhere: as nutrients travel through the microcirculation and get absorbed, they become less available at the venous...

Leaf hydraulic networks play an important role not only in fluid transport but also in maintaining whole-plant water status through transient environmental changes in soil-based water supply or air humidity. Both water potential and hydraulic resistance vary spatially throughout the leaf transport network, consisting of xylem, stomata and water-sto...

The dynamics of flow within a material transport network is dependent upon the dynamics of its power source. Responding to a change of these dynamics is critical for the fitness of living flow networks, e.g. the animal vasculature, which are subject to frequent and sudden shifts when the pump (the heart) transitions between different steady states....

A generic flow distribution network typically does not deliver its load at a uniform rate across a service area, instead oversupplying regions near the nutrient source while leaving downstream regions undersupplied. In this Letter we demonstrate how a local adaptive rule coupling tissue growth with nutrient density results in a flow network that se...

Global coastlines and their dense populations have an uncertain future due to increased flooding, storms, and human modification. The distributary channel networks of deltas and marshes that plumb these coastlines present diverse architectures, including well-studied dendritic topologies. However, the quasi-stable loops that are frequent in many co...

Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a nonlinear relation between current and pressure difference, and can be applied to networks of arbitrary topology. The model displays complex dynamics, including self-sustained oscillation...

Transport networks are typically optimized, either by evolutionary pressures in biological systems, or by human design, in engineered structures. In the case of systems such as the animal vasculature, the transport of fluids is not only hindered by the inherent resistance to flow but also kept in a dynamic state by the pulsatile nature of the heart...

The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges, organisms robustly control the propagation of inputs to perform specific tasks. However, a fundamental discon...

Thin elastic membranes form complex wrinkle patterns when put on substrates of different shapes. Such patterns continue to receive attention across science and engineering. This is due, in part, to the promise of lithography-free micropatterning, but also to the observation that similar patterns arise in biological systems from growth. The challeng...

Highlight Our data suggest a model that defines the capacity of incipient leaf vascular cells to develop based on the relative strength of both auxin biosynthesis and auxin transport. Abstract Our current understanding of vein development in leaves is based on canalization of the plant hormone auxin into self-reinforcing streams which determine the...

A generic flow distribution network typically does not deliver its load at a uniform rate across a service area, instead oversupplying regions near the nutrient source while leaving downstream regions undersupplied. In this work we demonstrate how a local adaptive rule coupling tissue growth with nutrient density results in a flow network that self...

Complex networks encountered in biology are often characterized by significant structural diversity. Whether due to differences in the three-dimensional structure of allosteric proteins, or the variation among the microscale structures of organisms' cerebral vasculature systems, identifying relationships between structure and function often poses a...

Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be applied to networks of arbitrary topology. The model displays complex dynamics, including self-sustained oscillatio...

We present a model for flow networks with non-linear conductance that allows for internal accumulation/depletion of volume. In the absence of any time dependence in the pressure input and output we observe emerging dynamics in the form of self-sustained waves which travel through the system. These spontaneously emerging fluctuations persist for a b...

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 perturba...

The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges, organisms can robustly control the propagation of inputs to perform specific tasks. However, a fundamental di...

Inspired by protein folding, we smooth out the complex cost function landscapes of two processes: the tuning of networks and the jamming of ideal spheres. In both processes, geometrical frustration plays a role—tuning pressure differences between pairs of target nodes far from the source in a flow network impedes tuning of nearby pairs more than th...

The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these microclots affect the large-scale blood flow or to what extent they decrease functionality. Moti...

Significance Functionally optimized networks are ubiquitous in nature, e.g., in allosteric proteins that change conformation upon binding to a ligand or vascular networks that distribute oxygen and nutrients in animals or plants. Many of these networks are multifunctional, with proteins that can catalyze more than one substrate or vascular networks...

Inspired by protein folding, we introduce funnels into the complex cost function landscapes of two processes, the tuning of networks, and the jamming of ideal spheres. In both processes, geometrical frustration plays a role -- tuning pressure differences between pairs of target nodes far from the source in a flow network impedes tuning of nearby pa...

The ability to reroute and control flow is vital to the function of many biological transport networks. By tuning the conductance of edges, many flow networks robustly control the propagation of inputs in order to achieve a wide variety of specific tasks. However, recent evidence suggests that network architectures used to achieve such tasks demons...

Modern leaves, the energy factories of plants, are the products of a 400-million-year evolutionary race towards improved efficiency and robustness. As such they have evolved two sophisticated transport systems, the xylem and the phloem, which irrigate the surface of the leaf blade, distribute water and nutrients, and collect the products of photosy...

Distribution networks—from vasculature to urban transportation pathways—are spatially embedded networks that must route resources efficiently in the face of pressures induced by the costs of building and maintaining network infrastructure. Such requirements are thought to constrain the topological and spatial organization of these systems, but at t...

Additional figures, further description of methods, and supplementary analyses. The supplementary text includes figures showing examples of the different kinds of mycelial networks and vasculature networks examined in this study. It also provides more in-depth descriptions and formal definitions of the standard topological graph metrics utilized in...

Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a fluid substrate. Floating shells spontaneously buckle to accommodate the natural excess of projected area and, de...

Nature is rife with networks that are functionally optimized to propagate inputs in order 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 pressu...

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 pert...

Background The analysis of complex networks both in general and in particular as pertaining to real biological systems has been the focus of intense scientific attention in the past and present. In this paper we introduce two tools that provide fast and efficient means for the processing and quantification of biological networks like Drosophila tra...

Distribution networks -- from vasculature to urban transportation systems -- are prevalent in both the natural and consumer worlds. These systems are intrinsically physical in composition and are embedded into real space, properties that lead to constraints on their topological organization. In this study, we compare and contrast two types of biolo...

A trophallaxis inspired model for distributed transport between randomly interacting agents Trophallaxis, the regurgitation and mouth to mouth transfer of liquid food between members of eusocial insect societies, is an important process that allows the fast and efficient dissemination of food in the colony. Trophallactic systems are typically treat...

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 non-convex and characterized by many local extrema. In general, finding the global, or nearly global optimum is difficult. In biological systems,...

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus c...

The leaves of angiosperms contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We describe a new phenotypic trait of reticulate vascular networks based on the topology of the nested loops. This phenotypic trait encodes information orthogonal to widely used geometric phenotypic traits, and thus c...

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical s...

The phloem vascular system facilitates transport of energy-rich sugar and signaling molecules in plants, thus permitting long range communication within the organism and growth of non-photosynthesizing organs such as roots and fruits. The flow is driven by osmotic pressure, generated by differences in sugar concentration between distal parts of the...

Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function. Yet, the set of tools that can characterize such a weighted cycle-rich architecture in a physically relevant, ma...

Supply and transport networks support much of our technical infrastructure as well as many biological processes. Their reliable function is thus essential for all aspects of life. Transport processes involving quantities beyond the pure loads exhibit alternative collective dynamical options compared to processes exclusively characterized by loads....

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical s...

Thin, doubly curved shells occur commonly in nature and their mechanical properties and modes of deformation are very important for engineering structures of all scales. Although there has been substantial work on the stability and modes of failure of thin shells, relatively little work has been done to understand the conditions that promote contin...

Systematic studies of phenotypic diversity-required for understanding evolution-lag behind investigations of genetic diversity. Here we develop a quantitative approach to studying behavioral diversity, which we apply to swimming of the ciliate Tetrahymena. We measure the full-lifetime behavior of hundreds of individual organisms at high temporal re...

Various monocotyledon pollen grains have a geometric design. They are constituted by a stiff thin shell with an n-fold rotationally symmetric softer sector. The mechanic response of these inhomogeneous shells can be approximated as an open shell. Isometric modes are known to be energetically favorable for thin shells when they are possible. Althoug...

Many biological systems employ complex networks of vascular tubes to facilitate transport of solute nutrients, examples include the vascular system of plants (phloem), some fungi, and the slime-mold Physarum. It is believed that such networks are optimized through evolution for carrying out their designated task. We propose a set of hydrodynamic go...

We study the dynamics of the classical and quantum mechanical scattering of a wave packet from an oscillating barrier. Our main focus is on the dependence of the transmission coefficient on the initial energy of the wave packet for a wide range of oscillation frequencies. The behavior of the quantum transmission coefficient is affected by tunneling...

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of approaches have be...

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Nature provides us with many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture. Although a number of methods have been proposed to measure aspects of the structu...

Distribution and structural networks permeate virtually all life, from the cellular to the organismic level. They have allowed organisms to grow in size and complexity by ensuring efficient distribution of nutrients and structural support. Given their importance, these vascular and structural webs have been under strong evolutionary selection and t...

Several configurations, such as d-cones, minimal ridges, and developable patches, occur regularly in the configuration of elastic sheets. We dub such features "building blocks." Here, we study elastic sheets confined in a manner that prohibits the sheet from taking on a single-buckle shape. We find not only building blocks where stress focuses, rem...

We study the behavior of thin elastic sheets that are bent and strained under a weak, smooth confinement. We show that the emerging shapes exhibit the coexistence of two types of domains. A focused-stress patch is subject to a geometric, piecewise-inextensibility constraint, whereas a diffuse-stress region is characterized by a mechanical constrain...

Upon release from the anther, pollen grains of angiosperm flowers are exposed to a dry environment and dehydrate. To survive this process, pollen grains possess a variety of physiological and structural adaptations. Perhaps the most striking of these adaptations is the ability of the pollen wall to fold onto itself to prevent further desiccation. R...

An elastic sheet subject to uniaxial compression will buckle out of plane. In order to minimize the bending energy, the wrinkled shape that is created will have as large a wavelength as possible. This behavior can be frustrated by constraining one edge of the sheet to smaller amplitude, as is often the case with curtains, which forces a shorter wav...

Leaf venation is a pervasive example of a complex biological transport network that is necessary for the survival of land plants. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However, dicotyledon leaf venation has a large number of functional closed loops. Inspired by leaf venation, we study two possible r...

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e., loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in t...

Hydrostatically pressurized circular rings confined to two dimensions (or cylinders constrained to have only z-independent deformations) undergo Euler type buckling when the outside pressure exceeds a critical value. We perform a stability analysis of rings with arc-length dependent bending moduli and determine how weakened bending modulus segments...

It has been shown that four dimensional N=2 gauge theories, softly broken to N=1 by a superpotential term, can accommodate metastable non-supersymmetric vacua in their moduli space. We study the SU(2) theory at high temperatures in order to determine whether a cooling universe settles in the metastable vacuum at zero temperature. We show that the c...

This thesis examines the effects of defects in three different systems in soft matter physics. First, we discuss the interaction of vortex filaments in type II superconductors with a curved line defect in thin superconducting slabs. The equilibrium probability density for an isolated fluctuating line and an array of vortices attracted to a particul...

In the hard core limit, interacting vortices in planar type II superconductors can be modeled as non-interacting one dimensional fermions propagating in imaginary time. We use this analogy to derive analytical expressions for the probability density and imaginary current of vortex lines interacting with an isolated bent line defect and to understan...

To better understand vortex pinning in thin superconducting slabs, we study the interaction of a single fluctuating vortex filament with a curved line defect in (1+1) dimensions. This problem is also relevant to the interaction of scratches with wandering step edges in vicinal surfaces. The equilibrium probability density for a fluctuating line att...