arXiv subjects

Alain Goriely

Publications and source records attributed to Alain Goriely.

At least 37 records · Page 2Linked to original sources

arXiv2024

Decomposing force fields as flows on graphs reconstructed from stochastic trajectories

Disentangling irreversible and reversible forces from random fluctuations is a challenging problem in the analysis of stochastic trajectories measured from real-world dynamical systems. We present an approach to approximate the dynamics of a stationary Langevin process as a discrete-state Markov process evolving over a graph-representation of phase-space, reconstructed from stochastic trajectories. Next, we utilise the analogy of the Helmholtz-Hodge decomposition of an edge-flow on a contractible simplicial complex with the associated decomposition of a stochastic process into its irreversible and reversible parts. This allows us to decompose our reconstructed flow and to differentiate between the irreversible currents and reversible gradient flows underlying the stochastic trajectories. We validate our approach on a range of solvable and nonlinear systems and apply it to derive insight into the dynamics of flickering red-blood cells and healthy and arrhythmic heartbeats. In particular, we capture the difference in irreversible circulating currents between healthy and passive cells and healthy and arrhythmic heartbeats. Our method breaks new ground at the interface of data-driven approaches to stochastic dynamics and graph signal processing, with the potential for further applications in the analysis of biological experiments and physiological recordings. Finally, it prompts future analysis of the convergence of the Helmholtz-Hodge decomposition in discrete and continuous spaces.

cond-mat.stat-mech↗

arXiv2024

A Mechanical Model for the Failure of Reconstructive Breast Implant Surgery Due to Capsular Contracture

Capsular contracture is a pathological response to implant-based reconstructive breast surgery, where the ``capsule'' (tissue surrounding an implant) painfully thickens, contracts and deforms. It is known to affect breast-cancer survivors at higher rates than healthy women opting for cosmetic cosmetic breast augmentation with implants. We model the early stages of capsular contracture based on stress-dependent recruitment of contractile and mechanosensitive cells to the implant site. We derive a one-dimensional continuum spatial model for the spatio-temporal evolution of cells and collagen densities away from the implant surface. Various mechanistic assumptions are investigated for linear versus saturating mechanical cell responses and cell traction forces. Our results point to specific risk factors for capsular contracture, and indicate how physiological parameters, as well as initial states (such as inflammation after surgery) contribute to patient susceptibility.

q-bio.CB↗

arXiv2024

A network aggregation model for the dynamics and treatment of neurodegenerative diseases at the brain scale

Neurodegenerative diseases are associated with the assembly of specific proteins into oligomers and fibrillar aggregates. At the brain scale, these protein assemblies can diffuse through the brain and seed other regions, creating an autocatalytic protein progression. The growth and transport of these assemblies depend on various mechanisms that can be targeted therapeutically. Here, we use spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain to study the effect of different drugs on whole-brain Alzheimer's disease progression.

math.DS↗

arXiv2024

Controllable Deformations in Compressible Isotropic Implicit Elasticity

For a given material, \emph{controllable deformations} are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, \emph{universal deformations} are those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress $\boldsymbolσ$ and the left Cauchy-Green strain $\mathbf{b}$, have the implicit form $\boldsymbol{\mathsf{f}}(\boldsymbolσ,\mathbf{b})=\mathbf{0}$. We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is permissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations.

cond-mat.mtrl-sci↗

arXiv2024

Minimal activation with maximal reach: Reachability clouds of bio-inspired slender manipulators

In the field of soft robotics, flexibility, adaptability, and functionality define a new era of robotic systems that can safely deform, reach, and grasp. To optimize the design of soft robotic systems, it is critical to understand their configuration space and full range of motion across a wide variety of design parameters. Here we integrate extreme mechanics and soft robotics to provide quantitative insights into the design of bio-inspired soft slender manipulators using the concept of reachability clouds. For a minimal three-actuator design inspired by the elephant trunk, we establish an efficient and robust reduced-order method to generate reachability clouds of almost half a million points each to visualize the accessible workspace of a wide variety of manipulator designs. We generate an atlas of 256 reachability clouds by systematically varying the key design parameters including the fiber count, revolution, tapering angle, and activation magnitude. Our results demonstrate that reachability clouds not only offer an immediately clear perspective into the inverse problem of control, but also introduce powerful metrics to characterize reachable volumes, unreachable regions, and actuator redundancy to quantify the performance of soft slender robots. Our study provides new insights into the design of soft robotic systems with minimal activation and maximal reach with potential applications in medical robotics, flexible manufacturing, and the autonomous exploration of space.

cs.RO↗

arXiv2024

Classical Non-Relativistic Fractons

We initiate the study of the classical mechanics of non-relativistic fractons in its simplest setting - that of identical one dimensional particles with local Hamiltonians characterized by by a conserved dipole moment in addition to the usual symmetries of space and time translation invariance. We introduce a family of models and study the $N$ body problem for them. We find that locality leads to a ``Machian" dynamics in which a given particle exhibits finite inertia only if within a specified distance of at least another one. For well separated particles this leads to immobility, much as for quantum models of fractons discussed before. For two or more particles within inertial reach of each other at the start of motion we get an interesting interplay of inertia and interactions. Specifically for a solvable ``inertia only" model of fractons we find that $N=2$ particles always become immobile at long times. Remarkably $N =3$ particles generically evolve to a late time state with one immobile particle and two that oscillate about a common center of mass with generalizations of such ``Machian clusters" for $N > 3$ . Interestingly, Machian clusters exhibit physical limit cycles in a Hamiltonian system even though mathematical limit cycles are forbidden by Liouville's theorem.

cond-mat.str-el↗

arXiv2024

Minimal design of the elephant trunk as an active filament

One of the key problems in active materials is the control of shape through actuation. A fascinating example of such control is the elephant trunk, a long, muscular, and extremely dexterous organ with multiple vital functions. The elephant trunk is an object of fascination for biologists, physicists, and children alike. Its versatility relies on the intricate interplay of multiple unique physical mechanisms and biological design principles. Here we explore these principles using the theory of active filaments and build, theoretically, computationally, and experimentally, a minimal model that explains and accomplishes some of the spectacular features of the elephant trunk.

cond-mat.soft↗

arXiv2024

Soft cells and the geometry of seashells

A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat faces. However, many tilings in Nature are characterized by shapes with curved edges, non-flat faces, and few, if any, sharp corners. An important question is then to relate prototypical sharp tilings to softer natural shapes. Here, we solve this problem by introducing a new class of shapes, the \textit{soft cells}, minimizing the number of sharp corners and filling space as \emph{soft tilings}. We prove that an infinite class of polyhedral tilings can be smoothly deformed into soft tilings and we construct the soft versions of all Dirichlet-Voronoi cells associated with point lattices in two and three dimensions. Remarkably, these ideal soft shapes, born out of geometry, are found abundantly in nature, from cells to shells.

physics.app-ph↗

arXiv2023

Surface wrinkling of a film coated to a graded substrate

We study the surface wrinkling of a stiff thin elastic film bonded to a compliant graded elastic substrate subject to compressive stress generated either by compression or growth of the bilayer. Our aim is to clarify the influence of the modulus gradient on the onset and surface pattern in this bilayers. Within the framework of finite elasticity, an exact bifurcation condition is obtained using the Stroh formulation and the surface impedance matrix method. Further analytical progress is made by focusing on the case of short wavelength limit for which the Wentzel-Kramers-Brillouin method can be used to resolve the eigenvalue problem of ordinary differential equations with variable coefficients. An explicit bifurcation condition is obtained from which asymptotic the critical buckling load and the critical wavelength are derived. In particular, we consider two distinct situations depending on the ratio $β$ of the shear modulus at the substrate surface to that at infinity. If $β$ is of $\mathcal{O}(1)$ or small, the parameters related to modulus gradient all appear in the high order terms and play an insignificant role in the bifurcation. In that case, it is the modulus ratio between the film and substrate surface that governs the onset of surface wrinkling. If, however, $β\gg1$, the modulus gradient affects the critical condition through leading-order terms. Through our analysis we unravel the influence of different material and geometric parameters, including the modulus gradient, on the bifurcation threshold and the associated wavelength which can be of importance in many biological and technological settings.

cond-mat.mtrl-sci↗

arXiv2023

Brain Chains as Topological Signatures for Alzheimer's Disease

We propose a topological framework to study the evolution of Alzheimer's disease, the most common neurodegenerative disease. The modeling of this disease starts with the representation of the brain connectivity as a graph and the seeding of a toxic protein in a specific region represented by a vertex. Over time, the accumulation of toxic proteins at vertices and their propagation along edges are modeled by a dynamical system on this graph. These dynamics provide an order on the edges of the graph according to the damage created by high concentrations of proteins. This sequence of edges defines a filtration of the graph. We consider different filtrations given by different disease seeding locations. To study this filtration we propose a new combinatorial and topological method. A filtration defines a maximal chain in the partially ordered set of spanning subgraphs ordered by inclusion. To identify similar graphs, and define a topological signature, we quotient this poset by graph homotopy equivalence, which gives maximal chains in a smaller poset. We provide an algorithm to compute this direct quotient without computing all subgraphs and then propose bounds on the total number of graphs up to homotopy equivalence. To compare the maximal chains generated by this method, we extend Kendall's $d_K$ metric for permutations to more general graded posets and establish bounds for this metric. We then demonstrate the utility of this framework on actual brain graphs by studying the dynamics of tau proteins on the structural connectome. {We show that the proposed topological brain chain equivalence classes distinguish different simulated subtypes of Alzheimer's disease.

q-bio.NC↗

arXiv2023

Active shape control by plants in dynamic environments

Plants are a paradigm for active shape control in response to stimuli. For instance, it is well-known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimulus, proprioception. These effects can be modulated when a potted plant is additionally rotated along the plant's axis, as in a rotating clinostat, leading to intricate shapes. We use a morphoelastic model for the response of growing plants to study the joint effect of both stimuli at all rotation speeds. In the absence of rotation, we identify a universal planar shape towards which all shoots eventually converge. With rotation, we demonstrate the existence of a stable family of three-dimensional dynamic equilibria where the plant axis is fixed in space. Further, the effect of axial growth is to induce steady behaviors, such as solitary waves. Overall, this study offers new insight into the complex out-of-equilibrium dynamics of a plant in three dimensions and further establishes that internal stimuli in active materials are key for robust shape control.

physics.bio-ph↗

arXiv2023

Cooperative melting in double-stranded peptide chains through local mechanical interactions

Under an external field a double-stranded peptide chain can separate in a fragile or ductile transition. It is usually believed that these two regimes are driven either by chemical and thermal fields, or through non-local mechanical interactions. Here, we show explicitly that local mechanical interactions regulates the stability and reversibility of the cooperative/non-cooperative melting transition, which is described by a single parameter depending on an internal length scale. Our theory is applicable to a wide range of biological examples such as DNA, protein secondary structures, and the microtubules and tau proteins, for which we are able to predict the critical melting force as a function of the chain length.

cond-mat.soft↗

arXiv2022

Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial

Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan's classical study of the 1970s through to contemporary agent-based models. Of the many factors that regulate spheroid growth, mechanical effects are perhaps some of the least studied, both theoretically and experimentally, though experimental enquiry has established their significance to tumour growth dynamics. In this tutorial, we formulate a hierarchy of mathematical models of increasing complexity to explore the role of mechanics in spheroid growth, all the while seeking to retain desirable simplicity and analytical tractability. Beginning with the theory of morphoelasticity, which combines solid mechanics and growth, we successively refine our assumptions to develop a somewhat minimal model of mechanically regulated spheroid growth that is free from many unphysical and undesirable behaviours. In doing so, we will see how iterating upon simple models can provide rigorous guarantees of emergent behaviour, which are often precluded by existing, more complex modelling approaches. Perhaps surprisingly, we also demonstrate that the final model considered in this tutorial agrees favourably with classical experimental results, highlighting the potential for simple models to provide mechanistic insight whilst also serving as mathematical examples.

q-bio.TO↗

arXiv2022

Stability of topological descriptors for neuronal morphology

The topological morphology descriptor of a neuron is a multiset of intervals associated to the shape of the neuron represented as a tree. In practice, topological morphology descriptors are vectorized using persistence images, which can help classify and characterize the morphology of broad groups of neurons. We study the stability of topological morphology descriptors under small changes to neuronal morphology. We show that the persistence diagram arising from the topological morphology descriptor of a neuron is stable for the 1-Wasserstein distance against a range of perturbations to the tree. These results guarantee that persistence images of topological morphology descriptors are stable against the same set of perturbations and reliable.

q-bio.NC↗

arXiv2022

Barcodes distinguish morphology of neuronal tauopathy

The geometry of neurons is known to be important for their functions. Hence, neurons are often classified by their morphology. Two recent methods, persistent homology and the topological morphology descriptor, assign a morphology descriptor called a barcode to a neuron equipped with a given function, such as the Euclidean distance from the root of the neuron. These barcodes can be converted into matrices called persistence images, which can then be averaged across groups. We show that when the defining function is the path length from the root, both the topological morphology descriptor and persistent homology are equivalent. We further show that persistence images arising from the path length procedure provide an interpretable summary of neuronal morphology. We introduce {topological morphology functions}, a class of functions similar to Sholl functions, that can be recovered from the associated topological morphology descriptor. To demonstrate this topological approach, we compare healthy cortical and hippocampal mouse neurons to those affected by progressive tauopathy. We find a significant difference in the morphology of healthy neurons and those with a tauopathy at a postsymptomatic age. We use persistence images to conclude that the diseased group tends to have neurons with shorter branches as well as fewer branches far from the soma.

q-bio.NC↗

arXiv2021

Instabilities in liquid crystal elastomers

Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low stress. Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. We investigate the following two problems: First, how do instabilities in nematic bodies change from those found in purely elastic solids? Second, how are these phenomena modified if the material constants fluctuate? To answer these questions, we present a systematic study of instabilities occurring in nematic liquid crystal elastomers, and examine the contribution of the nematic component and of fluctuating model parameters that follow probability laws. This combined analysis may lead to more realistic estimations of subsequent mechanical damage in nematic solid materials.

cond-mat.soft↗

arXiv2020

The role of clearance mechanisms in the kinetics of toxic protein aggregates involved in neurodegenerative diseases

Protein aggregates in the brain play a central role in cognitive decline and structural damage associated with neurodegenerative diseases. For instance, in Alzheimer's disease the formation of Amyloid-beta plaques and tau proteins neurofibrillary tangles follows from the accumulation of different proteins into large aggregates through specific mechanisms such as nucleation and elongation. These mechanisms have been studied in vitro where total protein mass is conserved. However, in vivo, clearance mechanisms may play an important role in limiting the formation of aggregates. Here, we generalise classical models of protein aggregation to take into account both production of monomers and the clearance of protein aggregates. Depending on the clearance model, we show that there may be a critical clearance value above which aggregation does not take place. Our result offers further evidence in support of the hypotheses that clearance mechanisms play a potentially crucial role in neurodegenerative disease initiation and progression; and as such, are a possible therapeutic target.

q-bio.BM↗

arXiv2020

Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death

Neurodegenerative diseases, such as Alzheimer's or Parkinson's disease, show characteristic degradation of structural brain networks. This degradation eventually leads to changes in the network dynamics and degradation of cognitive functions. Here, we model the progression in terms of coupled physical processes: The accumulation of toxic proteins, given by a nonlinear reaction-diffusion transport process, yields an evolving brain connectome characterized by weighted edges on which a neuronal-mass model evolves. The progression of the brain functions can be tested by simulating the resting-state activity on the evolving brain network. We show that while the evolution of edge weights plays a minor role in the overall progression of the disease, dynamic biomarkers predict a transition over a period of 10 years associated with strong cognitive decline.

nlin.AO↗