Statistical and Biological Physics

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Soft Condensed Matter

Within the last few years, the physics of soft condensed matter has become a rapidly expanding branch of science. This is mainly due to the recognition that seemingly disparate phenomena in materials such as colloids, polymers and liquid crystals, may be described by unified concepts taking into account the importance of thermal fluctuations in these systems. The softness of interactions in these systems leads to complex phase behavior and dynamical phenomena which not only present challenges to fundamental science, but which are also of enormous technological importance, such as for the processing of ceramics, food, and paint, for the stability and delivery of drugs and for the processing and design of biocompatible materials.

Introductory Review Articles


Current Research

  • pattern_induced_symmetry_breaking_resized

    Pattern-induced local symmetry breaking in active matter systems

    The emergence of both macroscopic order and spatiotemporal patterns are hallmarks of active-matter systems. In conceptual theoretical models, the symmetry of the ordered states, such as polar traveling waves and nematic bands, has been linked to that of the underlying microscopic interaction between the constituent particles. Recently, this close link was challenged by experiments with actomyosin motility assays (Huber et al, Science, 2018). There it was observed that patterns of polar and nematic symmetries can be firmly intertwined: they can coexist, interact and even dynamically transform into each other. However, a theoretical understanding of this fascinating phenomenon of the dynamic coexistence of ordered states with different symmetries is lacking. more

  • bacillus

    New class of turbulence in active systems

    Turbulence is a fundamental and ubiquitous phenomenon in nature, ranging from astrophysical to biophysical scales. At the same time, it is widely acknowledged as one of the key unsolved problems in modern physics. While in the past, most theoretical work in this area has been devoted to simple fluids as described by the Navier-Stokes equations, there is now a growing awareness for the need to extend the research focus to systems with multiscale drive and/or dissipation. This includes various types of complex fluids, plasmas, as well as active systems. One very interesting example of this kind is "low Reynolds number turbulence" in dense bacterial suspensions. Recently, a continuum model has been proposed to describe the experimentally observed flows. It is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem, e.g., Swift-Hohenberg terms to represent the drive/dissipation as well as an additional Toner-Tu-type cubic nonlinearity which can interact with the quadratic Navier-Stokes nonlinearity. While developed in the context of living fluids, it is expected to be applicable to many other systems. The present work represents the first systematic study of turbulence described by this model. Our combined numerical and analytical analysis reveals, in particular, that the energy spectrum exhibits a power law at large scales as reported in [1], but that it is not universal and that its slope depends both on finite-size effects of the simulation domain as well as on system parameters. Further investigations even provide a quantitative expression for this dependence which is reinforced by numerical simulations. more

  • polarpattern_naturecover

    Polar pattern formation in driven filament systems requires non-binary particle collisions

    It has been exactly 20 years since the first physical studies which attempted to connect macroscopic collective behaviours in biological active matter systems to phase transitions and nonequilibrium physics. During the years, it has become clear that the precise knowledge of the interaction among the constituents is the key for understanding the emergence of order. In recent years, Boltzmann equations for propelled particles have been developed in order to connect the microscopic dynamics of the individual constituents to the meso- or macroscopic behaviour of the system. However due to the lack of quantitative experimental data, all models relied on very crude assumption of the interaction – most times simple digital interaction were assumed: collisions below 90 degrees align, above they are unaffected by the collision. more

  • rndburstcut

    Random bursts determine dynamics of active filaments

    Active matter is a fascinating new field in soft matter physics aiming to understand how macroscopic properties of interacting active particles emerge from properties of the constituent particles as well as their interactions. To this end, kinetic theory has been successfully applied to connect the physics at the microscopic scale with the corresponding macroscopic description; it was able to predict the emergent patterns and collective dynamics for interacting propelled particle systems. One central finding is that the degree of alignment of colliding active particles competes with the strength of randomness of the individual’s persistent random walks. This randomness arises from the inherent active fluctuations of each particle, i.e. the non-thermal and local input and dissipation of energy. more

  • active_defects_cover_homepage

    Defect-Mediated Phase Transitions in Active Soft Matter

    In this letter we study how topological defects affect the degree of polar and crystalline order in active matter at high densities. To this end, we analyze a generic agent-based model, which accounts for both polar alignment and shorted-ranged repulsive interaction.
    We show that, while defects still play a decisive role, the emerging defect dynamics and phase behavior differ qualitatively from their equilibrium analogues. In active systems, the non-equilibrium steady states include different types of polycrystalline phases, and an intriguing crystalline phase with quasi-long-range translational order but completely devoid of any topological defects. Moreover, we find that absence of defects and polar order are mutually exclusive features. When alignment forces dominate over repulsive forces, polar states are favored. The resulting collective particle flux makes the system highly susceptible to the spontaneous formation of grain boundaries and thereby repeatedly creates small crystalline patches. These spontaneous fracture-like processes are accompanied by propagating sound waves. In contrast, in systems with strong repulsive forces the formation of a crystalline state precludes the formation of collectively moving
    clusters. Surprisingly, the phonon modes in this active crystalline state lead to quasi-long-range order but the fluctuations generated by the active particle motion do not create topological defects. more

  • pic

    Long-range Ordering of Vibrated Disks

    The emergence of collective motion in fish schools and bird flocks constitutes a ubiquitous and fascinating phenomenon in nature. One reason might be the emergence of highly dynamic, coherently moving spatial patterns such as clusters, swirls or waves, and the fact that the patterns commonly extend over length scales much larger than the size of the individuals. more

  • christoph_nature

    Modeling swarms with agent-based simulations

    The emergence of collective motion such as exhibited by systems ranging from flocks of animals, self-propelled microorganisms or the cytoskeleton is an ubiquitous and fascinating self-organization phenomenon. All these systems display similar phenomenologies, even though the particular underlying physics is genuinely different, ranging from hydrodynamic interaction to steric or inelastic repulsion, attraction, to more complex interactions mediated by linker proteins or molecular motors. Examples for similarities are the inherent polarity of the constituents, a density-dependent transition to ordered phases or the existence of huge density fluctuations. This suggests universal organizing principles underlying pattern formation; an idea followed by hydrodynamic models valid on large scales. more

  • poly_single

    Excluded volume effects on semiflexible ring polymers

    One aim of modern biotechnology is the controlled assembly and manipulation of structures. The simplest building blocks for constructing structures are rodlike polymers. The next higher level of complexity concerning building blocks is achieved with ringlike polymers. On the nano scale level the effective shape of such building blocks is governed by the interplay of entropic forces on the one hand and elastic stiffness and steric hindrance of the polymer segments on the other hand. Entropic forces lead to a coiled, cigar-like shape. This is opposed by elastic bending stiffness, which favors non-curved conformations. This poses the question how strong each of these molecular based forces contribute and how they affect the resulting shape of the building blocks. more

  • prl_100_240604_a

    Anisotropic Memory Effects in Confined Colloidal Diffusion

    Understanding and controlling the transport of colloidal microcarriers
    through a fluid is one of the main challenges in cell biology, and related
    lab-on-a-chip approaches. With the miniaturization of such technologies,
    particularly microfluidics, the colloid's motion is increasingly
    confined, and the influence of boundaries becomes non-negligible. Any
    deviation from its well-understood free Brownian motion, will give us
    information on the particle's surroundings. more

  • microscale-thermoviscose

    Microscale fluid flow induced by thermoviscous expansion along a traveling wave

    Recently, flow at the scale of millimeters and below has attracted significant attention, stimulated by the rapid advances to manipulate and to control small-scale devices. In our Letter we propose a novel mechanism to generate net flow in a thin fluid chamber, i.e. a viscous liquid confined between two plates separated by a distance of the order of a few micrometers. more

  • Microtubule dynamics depart from wormlike chain model

    Microtubules are cytoskeletal protein filaments that play an essential role in a multitude of cell functions in all eucaryotes. While specialized structures such as cilia, flagellae and axons require microtubule lengths of up to several hundred micrometers, fundamental tasks like cell division and intracellular transport involve microtubules with lengths that are comparable to or smaller than typical eucaryotic cell sizes (10-20 micrometer).The standard model for semiflexible polymers is the wormlike chain which envisions a homogeneous, isotropic, continuously flexible rod characterized by its bending stiffness. We have shown that this standard model fails for microtubules, mainly due to the highly anisotropic molecular architecture where protofilaments are arranged in parallel to form a hollow tube of 25 nanometer in diameter. more

  • The shape of semiflexible polymer rings

    Following the trajectory of a random walk or likewise a flexible polymer one finds that the typical overall shape is cigar-like, prolate. Intuitively one would assume a spherical appearance, but this implies rotational averaging. Flexible and moreover semiflexible polymers are the building blocks of various biological processes, since DNA and cytoskeletal filaments belong to the class of semiflexible polymers. The shape of a polymer is important for its mobility in heterogeneous media like the cytoplasm, the depletion forces between larger complexes in polymer solution or the accessibility of specific sites along the polymer to enzymes. Our recent work shows that semiflexible polymer rings such as DNA plasmids or viral DNA exhibit distinct shapes depending on their flexibility. more

  • Optimal flexibility for conformational transitions in macromolecules

    Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized "hinge". Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo" attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices. more

  • Coupling of transverse and longitudinal response in stiff polymers

    For a comprehensive picture of the viscoelasticity of cellular material a thorough understanding of single molecule properties is necessary, in particular of the response of single filaments under force. Biological examples include cytoskeletal polymers such as actin or microtubules, but also stretched DNA, which by now is almost ubiquitious in single-molecule experiments. The large bending stiffness of these polymers makes their static and dynamic features highly anisotropic: fluctuations and response are larger in the transverse direction (perpendicular to the local tangent) than in the longitudinal one. However, these filaments are also nearly inextensible, and motion in the two directions is therefore not independent. We show that beyond the linear level, where the coupling between transverse and longitudinal dynamics is not yet relevant, the dynamic response to transverse forces becomes nonlinearly coupled to the longitudinal one, even in the weakly-bending limit of an almost straight contour. more

  • Mechanics of bundled semiflexible polymer networks

    To ensure adaptability of cytoskeletal organization cells exploit the dynamic interplay between semi-flexible filamentous polymers such as microtubules or F-actin using a multitude of associated binding proteins. In particluar, the local elastic properties are regulated by the activation of auxiliary proteins which e.g. cross-link and/or bundle the filamentous networks into complex scaffolds. In this Letter we show that above a critical concentration of the actin binding protein (ABP) fascin, a solution of actin filaments organizes into a homogeneous network whose building blocks are bundles only. more

  • Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains: The wormlike bundle model

    The wormlike chain (WLC) has emerged as the standard model for the description of semiflexible polymers. The defining property of a WLC is a mechanical bending stiffness that is an intrinsic material constant of the polymer. Within this framework, numerous correlation and response functions have been calculated, providing a comprehensive picture of the equilibrium and dynamical properties of WLCs. Another important emerging class of semiflexible polymers consists of bundles of WLCs. Unlike standard WLCs, wormlike bundles (WLB) have a state-dependent bending stiffness that derives from a generic interplay between the high stiffness of the individual filaments and their soft relative sliding motion. We demonstrate that this state-dependence gives rise to fundamentally new behavior that cannot be reproduced trivially using existing relations for WLCs. In an article just published in PRL we explore the consequences of a state-dependent bending stiffness on the statistical mechanics of isolated WLBs, as well as on the scaling behavior of their entangled solutions and crosslinked networks. more

  • Floppy modes and non-affine deformations in random fiber networks

    Materials as different as granular matter, colloidal suspensions or lithospheric block systems share the common property that they may exist in a highly fragile state. While in principle able to withstand static shear stresses, small changes in the loading conditions may lead to large scale structural rearrangements or even to the complete fluidization of the material. To understand the extraordinary mechanical properties of these systems new concepts have to be developed that go beyond the application of classical elasticity theory and that sufficiently reflect the presence of the microstructure. more

  • Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length

    We find that microtubules, essential structural elements in living cells, grow stiffer as they grow longer, an unexpected property that could lead to advances in nano-materials development. more

  • molecular_crystals

    "Soft Molecular Crystals" - Hard Matter Physics with Soft Matter Systems

    Superimposing optical interference patterns to two-dimensional colloidal systems generates versatile soft matter systems which allow to study the subtle interplay between thermal fluctuations, intermolecular interactions and external potentials on the ordering of the colloidal particles. These systems serve as model systems to study hard matter physics: the interfering laser patterns mimic the substrate potential of a crystalline surface and the assemblies of colloidal particles in the potential minima mimic molecules of various symmetries. Depending on the strength of the fluctuations, the symmetry of the laser patterns and the soft colloidal molecules novel phases emerge. more