15 research outputs found
Statistical mechanics of thin spherical shells
We explore how thermal fluctuations affect the mechanics of thin amorphous
spherical shells. In flat membranes with a shear modulus, thermal fluctuations
increase the bending rigidity and reduce the in-plane elastic moduli in a
scale-dependent fashion. This is still true for spherical shells. However, the
additional coupling between the shell curvature, the local in-plane stretching
modes and the local out-of-plane undulations, leads to novel phenomena. In
spherical shells thermal fluctuations produce a radius-dependent negative
effective surface tension, equivalent to applying an inward external pressure.
By adapting renormalization group calculations to allow for a spherical
background curvature, we show that while small spherical shells are stable,
sufficiently large shells are crushed by this thermally generated "pressure".
Such shells can be stabilized by an outward osmotic pressure, but the effective
shell size grows non-linearly with increasing outward pressure, with the same
universal power law exponent that characterizes the response of fluctuating
flat membranes to a uniform tension.Comment: 16 pages, 6 figure
Thermal Excitations of Warped Membranes
We explore thermal fluctuations of thin planar membranes with a frozen spatially varying background metric and a shear modulus. We focus on a special class of D-dimensional “warped membranes” embedded in a d-dimensional space with d≥D+1 and a preferred height profile characterized by quenched random Gaussian variables , , in Fourier space with zero mean and a power-law variance . The case D=2, d=3, with could be realized by flash-polymerizing lyotropic smectic liquid crystals. For the elastic constants are nontrivially renormalized and become scale dependent. Via a self-consistent screening approximation we find that the renormalized bending rigidity increases for small wave vectors q as , while the in-hyperplane elastic constants decrease according to . The quenched background metric is relevant (irrelevant) for warped membranes characterized by exponent , where is the scaling exponent for tethered surfaces with a flat background metric, and the scaling exponents are related through .Molecular and Cellular BiologyPhysic
Phase behavior and morphology of multicomponent liquid mixtures
Multicomponent systems are ubiquitous in nature and industry. While the
physics of few-component liquid mixtures (i.e., binary and ternary ones) is
well-understood and routinely taught in undergraduate courses, the
thermodynamic and kinetic properties of -component mixtures with have
remained relatively unexplored. An example of such a mixture is provided by the
intracellular fluid, in which protein-rich droplets phase separate into
distinct membraneless organelles. In this work, we investigate equilibrium
phase behavior and morphology of -component liquid mixtures within the
Flory-Huggins theory of regular solutions. In order to determine the number of
coexisting phases and their compositions, we developed a new algorithm for
constructing complete phase diagrams, based on numerical convexification of the
discretized free energy landscape. Together with a Cahn-Hilliard approach for
kinetics, we employ this method to study mixtures with and
components. We report on both the coarsening behavior of such systems, as well
as the resulting morphologies in three spatial dimensions. We discuss how the
number of coexisting phases and their compositions can be extracted with
Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally,
we discuss how one can reverse engineer the interaction parameters and volume
fractions of components in order to achieve a range of desired packing
structures, such as nested `Russian dolls' and encapsulated Janus droplets.Comment: 16 pages, 11 figures + hyperlinks to 7 video
Mechanical Properties of Warped Membranes
We explore how a frozen background metric affects the mechanical properties of planar membranes with a shear modulus. We focus on a special class of “warped membranes” with a preferred random height profile characterized by random Gaussian variables h(q) in Fourier space with zero mean and variance and show that in the linear response regime the mechanical properties depend dramatically on the system size L for . Membranes with could be produced by flash polymerization of lyotropic smectic liquid crystals. Via a self-consistent screening approximation we find that the renormalized bending rigidity increases as for membranes of size L, while the Young and shear moduli decrease according to resulting in a universal Poisson ratio. Numerical results show good agreement with analytically determined exponents.Molecular and Cellular BiologyPhysic
Non-uniform growth and surface friction determine bacterial biofilm morphology on soft substrates
During development, organisms acquire three-dimensional shapes with important
physiological consequences. While the basic mechanisms underlying morphogenesis
are known in eukaryotes, it is often difficult to manipulate them in vivo. To
circumvent this issue, here we present a study of developing Vibrio cholerae
biofilms grown on agar substrates in which the spatiotemporal morphological
patterns were altered by varying the agar concentration. Expanding biofilms are
initially flat, but later experience a mechanical instability and become
wrinkled. Whereas the peripheral region develops ordered radial stripes, the
central region acquires a zigzag herringbone-like wrinkle pattern. Depending on
the agar concentration, the wrinkles initially appear either in the peripheral
region and propagate inward (low agar concentration) or in the central region
and propagate outward (high agar concentration). To understand these
experimental observations, we developed a model that considers diffusion of
nutrients and their uptake by bacteria, bacterial growth/biofilm matrix
production, mechanical deformation of both the biofilm and the agar, and the
friction between them. Our model demonstrates that depletion of nutrients
beneath the central region of the biofilm results in radially-dependent growth
profiles, which in turn, produce anisotropic stresses that dictate the
morphology of wrinkles. Furthermore, we predict that increasing surface
friction (agar concentration) reduces stress anisotropy and shifts the location
of the maximum compressive stress, where the wrinkling instability first
occurs, toward the center of the biofilm, in agreement with our experimental
observations. Our results are broadly applicable to bacterial biofilms with
similar morphologies and also provide insight into how other bacterial biofilms
form distinct wrinkle patterns.Comment: 16 pages, 4 figures + supplementary information (36 pages, 14
figures