arXiv subjects

Arezki Boudaoud

Publications and source records attributed to Arezki Boudaoud.

At least 19 recordsLinked to original sources

arXiv2025

Geometry-driven jets underlie dispersal of plants and fungi by raindrops

The impact of droplets on concave surfaces is poorly understood, although it is relevant to a mode of dispersal that has evolved independently in several species of plants and fungi. This mode relies on splash-cups, specialized organs that use raindrops to disperse reproductive units away from the parent organism. We investigated the impact of droplets on conical cavities that mimic splash-cups and we found that such impact may lead to the formation of two types of jets, which appear essential for dispersal in nature. We built a minimal kinematic model that explains jet formation, involving the motion of fluid particles along geodesics (shortest paths) on the cone surface and we predicted cone angles that optimize jet formation, consistent with the geometries of natural splash-cups

physics.flu-dyn↗

arXiv2025

Mechanics of pressurized cellular sheets

Everyday experience shows that cellular sheets are stiffened by the presence of a pressurized gas: from bicycle inner tubes to bubble wrap, the presence of an internal pressure increases the stiffness of otherwise floppy structures. The same is true of plants, with turgor pressure (due to the presence of water) taking the place of gas pressure; indeed, in the absence of water, many plants wilt. However, the mechanical basis of this stiffening is somewhat opaque: simple attempts to rationalize it suggest that the stiffness should be independent of the pressure, at odds with everyday experience. Here, we study the mechanics of sheets that are a single cell thick and show how a pressure-dependent bending stiffness may arise. Our model rationalizes observations of turgor-driven shrinkage in plant cells and also suggests that turgor is unlikely to provide significant structural support in many monolayer leaves, such as those found in mosses. However, for such systems, turgor does provide a way to control leaf shape, in accordance with observations of curling upon drying of moss leaves. Guided by our results, we also present a biomimetic actuator that un-curls upon pressurization.

cond-mat.soft↗

arXiv2023

Multiscale modelling and analysis of growth of plant tissues

How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links between microscopic and macroscopic tissue properties, we perform a multiscale analysis of a model of growing plant tissue with subcellular resolution. We use homogenization to rigorously derive the corresponding macroscopic tissue scale model. Tissue scale mechanical properties are computed from microscopic structural and material properties, taking into account deformation by the growth field. We then consider case studies and numerically compare the detailed microscopic model and the tissue-scale model, both implemented using finite element method. We find that the macroscopic model can be used to efficiently make predictions about several configurations of interest. Our work will help making links between microscopic measurements and macroscopic observations in growing tissues.

math.AP↗

arXiv2023

Predicting the mechanical properties of spring networks

The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, either representing finite material elements or even the molecular bonds of a system. However, to date, there is no direct derivation of the relation between a general discrete spring network\blu{, with arbitrary geometry,} and it's corresponding elastic continuum. Furthermore, understanding the network's mechanical response requires simulations that may be expensive computationally. Here we report a method to derive the exact elastic continuum model of any discrete network of springs, requiring network geometry and topology only. We identify and calculate the so-called "non-affine" displacements. Explicit comparison of our calculations to simulations of different crystalline and disordered configurations, shows we successfully capture the mechanics even of auxetic materials. Our method is valid for residually stressed systems with non-trivial geometries, and is an essential step in generalizing active stresses on such discrete systems. It is easily generalizable to other discrete models, and opens the possibility of a rational design of elastic systems.

cond-mat.soft↗

arXiv2022

The Structure of Fluctuating Thin Sheets Under Random Forcing

We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the Föppl-von Kármán equations from elasticity theory with techniques from out-of-equilibrium statistical physics to obtain a nonlinear strongly coupled $ϕ^{4}$-Langevin field equation with spatially varying kernel. With the aid of the self-consistent expansion (SCE), this equation is analytically solved for the structure factor of a fluctuating sheet. In contrast to previous research which has suggested that the structure factor follows an anomalous power-law, we find that the structure factor in fact obeys a logarithmically corrected rational function. Numerical simulations of our model confirm the accuracy of our analytical solution.

cond-mat.soft↗

arXiv2022

Nonlinear clogging of a rectangular slit by a spherical soft particle

The capture of a soft spherical particle by a rectangular slit leads to a non-monotonic pressure-flow rate relation at low Reynolds number. In the presence of the trapped particle the flow-induced deformations focus the streamlines and pressure drop to a small region. This increases the resistance to flow by several orders of magnitude as the driving pressure is increased. As a result two regimes are observed: a flow-dominated regime for small particle deformations, where flow rate increases with pressure, and an elastic-dominated regime in which solid deformations block the flow.

cond-mat.soft↗

arXiv2022

Compression of a pressurized spherical shell by a spherical or flat probe

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere, or compression between two plates. Previously, different theoretical approaches have been developed to retrieve material parameters (e.g. elastic modulus) or state variables (e.g. pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.

physics.bio-ph↗

arXiv2021

Cellular Fourier analysis for geometrically disordered materials

Many media are divided into elementary units with irregular shape and size, as exemplified by domains in magnetic materials, bubbles in foams, or cells in biological tissues. Such media are essentially characterized by geometrical disorder of their elementary units, which we term cells. Cells set a reference scale at which are often assessed parameters and fields reflecting material properties and state. Here, we consider the spectral analysis of spatially varying fields. Such analysis is difficult in geometrically disordered media, because space discretization based on standard coordinate systems is not commensurate with the natural discretization into geometrically disordered cells. Indeed, we found that two classical spectral methods, the Fast Fourier Transform and the Graph Fourier transform, fail to reproduce all expected properties of spectra of plane waves and of white noise. We therefore built a method, which we call Cellular Fourier Transform (CFT), to analyze cell-scale fields, which comprise both discrete fields defined only at cell level and continuous fields smoothed out from their sub-cell variations. Our approach is based on the construction of a discrete operator suited to the disordered geometry and on the computation of its eigenvectors, which, respectively, play the same role as the Laplace operator and sine waves in Euclidean coordinate systems. We show that CFT has the expected behavior for sinusoidal fields and for random fields with long-range correlations. Our approach for spectral analysis is suited to any geometrically disordered material, such as a biological tissue with complex geometry, opening the path to systematic multiscale analyses of material behavior.

physics.bio-ph↗

arXiv2019

Patterns of polar domains in a spatiotemporal model of interacting polarities

Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical model that generalizes classical spin models on a lattice by incorporating effective transport of polarity molecules between neighboring sites. We account for an external field and for ferromagnetic interactions between sites and prescribe the time-evolution of the system using two distinct dissipative classes for non-conserved and conserved variables representing polarity orientation and magnitude, respectively. We observe two main types of steady-state configurations --disordered configurations and patterns of highly polar spots surrounded by regions with low polarity-- and we characterise patterns and transitions between configurations. Our results may provide alternative pattern-generating mechanisms for materials endowed with polarity fields.

physics.bio-ph↗

arXiv2018

Elongation and shape changes in organisms with cell walls: a dialogue between experiments and models

The generation of anisotropic shapes occurs during morphogenesis of almost all organisms. With the recent renewal of the interest in mechanical aspects of morphogenesis, it has become clear that mechanics contributes to anisotropic forms in a subtle interaction with various molecular actors. Here, we consider plants, fungi, oomycetes, and bacteria, and we review the mechanisms by which elongated shapes are generated and maintained. We focus on theoretical models of the interplay between growth and mechanics, in relation with experimental data, and discuss how models may help us improve our understanding of the underlying biological mechanisms.

q-bio.CB↗

arXiv2016

Leaf growth is conformal

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Based on the mapping we predict the local displacement field in the leaf blade and find it to agree with the experimentally measured displacement field to 92%. This approach is applicable to any two-dimensional system with locally isotropic growth, enabling the deduction of the whole growth field just from observation of the tissue contour.

q-bio.TO↗

arXiv2013

Path-memory induced quantization of classical orbits

A droplet bouncing on a liquid bath can self-propel due to its interaction with the waves it generates. The resulting "walker" is a dynamical association where, at a macroscopic scale, a particle (the droplet) is driven by a pilot-wave field. A specificity of this system is that the wave field itself results from the superposition of the waves generated at the points of space recently visited by the particle. It thus contains a memory of the past trajectory of the particle. Here, we investigate the response of this object to forces orthogonal to its motion. We find that the resulting closed orbits present a spontaneous quantization. This is observed only when the memory of the system is long enough for the particle to interact with the wave sources distributed along the whole orbit. An additional force then limits the possible orbits to a discrete set. The wave-sustained path memory is thus demonstrated to generate a quantization of angular momentum. Because a quantum-like uncertainty was also observed recently in these systems, the nonlocality generated by path memory opens new perspectives.

cond-mat.soft↗

arXiv2013

A comparative study of crumpling and folding of thin sheets

Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly ine cient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than 6 or 7 times. Here we show that the sti ness that builds up in the two processes is of the same nature, and therefore simple folding models allow to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We nd that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.

cond-mat.soft↗

arXiv2010

Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system.

cond-mat.soft↗

arXiv2010

Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators

Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting on a soft foundation creates a regular pattern of sinusoidal wrinkles with a broad distribution of energy. Here, we study the energy distribution for highly confined membranes and show the emergence of a new morphological instability triggered by a period-doubling bifurcation. A periodic self-organized focalization of the deformation energy is observed provided an up-down symmetry breaking, induced by the intrinsic nonlinearity of the elasticity equations, occurs. The physical model, exhibiting an analogy with parametric resonance in nonlinear oscillator, is a new theoretical toolkit to understand the morphology of various confined systems, such as coated materials or living tissues, e.g., wrinkled skin, internal structure of lungs, internal elastica of an artery, brain convolutions or formation of fingerprints. Moreover, it opens the way to new kind of microfabrication design of multiperiodic or chaotic (aperiodic) surface topography via self-organization.

cond-mat.mtrl-sci↗

arXiv2009

Statics and inertial dynamics of a ruck in a rug

We consider the familiar problem of a bump, or ruck, in a rug. Under lateral compression, a rug bends out of the plane forming a ruck -- a localized region in which it is no longer in contact with the floor. We show that when the external force that created the ruck is removed, the ruck flattens out unless the initial compression is greater than a critical value, which we determine. We also study the inertial motion of a ruck that is generated when one end of the rug is moved rapidly. We show that the equations of motion admit a travelling ruck solution for which a linear combination of the tension and kinetic energy is determined by the ruck size. We confirm these findings experimentally. We end by discussing the potential implications of our work for the analogous propagation of localized slip pulses in the sliding of two bodies in contact.

cond-mat.soft↗

arXiv2008

Energy distributions and effective temperatures in the packing of elastic sheets

The packing of elastic sheets is investigated in a quasi two-dimensional experimental setup: a sheet is pulled through a rigid hole acting as a container, so that its configuration is mostly prescribed by the cross-section of the sheet in the plane of the hole. The characterisation of the packed configuration is made possible by using refined image analysis. The geometrical properties and energies of the branches forming the cross-section are broadly distributed. We find distributions of energy with exponential tails. This setup naturally divides the system into two sub-systems: in contact with the container and within the bulk. While the geometrical properties of the sub-systems differ, their energy distributions are identical, indicating 'thermal' homogeneity and allowing the definition of effective temperatures from the characteristic scales of the energy distributions.

physics.class-ph↗

arXiv2008

Observation of wave turbulence in vibrating plates

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small lengthscales. Here, wave turbulence is observed in experiments on a vibrating plate. The frequency power spectra of the normal velocity of the plate may be rescaled on a single curve, with power-law behaviors that are incompatible with the weak turbulence theory of D{ü}ring et al. [Phys. Rev. Lett. 97, 025503 (2006)]. Alternative scenarios are suggested to account for this discrepancy -- in particular the occurrence of wave breaking at high frequencies. Finally, the statistics of velocity increments do not display an intermittent behavior.

nlin.CD↗