arXiv subjects

Mohamed Warda

Publications and source records attributed to Mohamed Warda.

5 recordsLinked to original sources

arXiv2026

Shape-space dynamics and geometric pattern formation in nonreciprocal slender bodies

Nonreciprocal interactions in active solids violate action-reaction symmetry and produce a net response to strain. Assuming invariance under Euclidean symmetries, we derive a shape-space formulation for the elastohydrodynamics of nonreciprocal slender bodies that separates intrinsic deformation from rigid motion. The resulting nonlinear reaction-advection-diffusion system represents a geometric flow whose activity-driven instabilities generate steady, oscillatory, and chaotic patterns. These manifest as rigid, swimming, and chaotic motion, linking nonreciprocal elastohydrodynamics to geometric pattern formation and unifying recent observations in slender active structures.

cond-mat.soft↗

arXiv2026

Weakly nonlinear analysis of Hopf bifurcations in the elastohydrodynamics of Cosserat rods

We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a non-self-adjoint linear operator, produces stable limit-cycle oscillations in the fully nonlinear overdamped dynamics. Here we derive an analytical description of the emergence of this limit cycle near threshold. Working close to the critical follower force, we perform a multiple-scale expansion about the compressed straight base state and systematically remove secular growth at higher orders. Solvability at cubic order, enforced using the adjoint eigenmode of the non-Hermitian operator, yields a Stuart-Landau amplitude equation for the critical oscillatory mode. The Landau coefficients are expressed as explicit inner products involving the critical eigenmode, its adjoint, and quadratic corrections. The resulting reduced theory predicts a supercritical Hopf bifurcation with a steady-state tip oscillation amplitude scaling as the square root of the distance from threshold. These predictions rationalize the near-threshold scaling observed in nonlinear simulations and provide an analytical normal form for the onset of self-sustained beating in pressure-driven soft robotic arms at low Reynolds number.

math-ph↗

arXiv2025

Geometric Field Theory for Elastohydrodynamics of Cosserat Rods

Slender structures are ubiquitous in biological and physical systems, from bacterial flagella to soft robotic arms. The Cosserat rod provides a mathematical framework for slender bodies that can stretch, shear, twist and bend. In viscous fluid environments at low Reynolds numbers - as encountered in soft matter physics, biophysics, and soft continuum robotics - inertial effects become negligible, and hydrodynamic forces are well approximated by Stokes friction. We demonstrate that the resulting elastohydrodynamic equations of motion, when formulated using Cartan's method of moving frames, possess the structure of a geometric field theory in which the configuration field takes values in SE(3), the Lie group of rigid body motions. This geometric formulation yields coordinate-independent equations that are manifestly invariant under spatial isometries and naturally suited to constitutive modeling based on Curie's principle. We derive integrability conditions that determine when constitutive laws can be derived from an energy functional, thereby distinguishing between passive and active material responses. We also obtain the beam limit for small deformations. Our results establish a unified geometric framework for the nonlinear mechanics of slender structures in slow viscous flow and enable efficient numerical solutions.

cond-mat.soft↗

arXiv2025

Elastohydrodynamic instabilities of a soft robotic arm in a viscous fluid

The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here we show that this interplay leads to novel elastohydrodynamic instabilities in a clamped soft robotic arm driven terminally by a constant pressure in a viscous fluid. We model the arm as a Cosserat rod that can stretch, shear and bend. We obtain invariant, geometrically exact, non-linear equations of motion by using Cartan's method of moving frames. Stability to small perturbations of a straight rod is governed by a non-Hermitian linear operator. Eigenanalysis shows that stability is lost through a Hopf bifurcation with the increase of pressure above a first threshold. A surprising return to stability is obtained with further increase of pressure beyond a second threshold. Numerical solutions of the non-linear equations, using a geometrically exact spectral method, confirms stable limit-cycle oscillations between these two pressure thresholds. An asymptotic analysis in the beam limit rationalizes these results analytically. This counterintuitive sequence of bifurcations underscores the subtle nature of the elastohydrodynamic coupling in Cosserat rods and emphasizes their importance for the control of the viscous dynamics of soft robots.

cond-mat.soft↗

arXiv2021

Graphene Field Effect Transistors: A Review

The past decade has seen rapid growth in the research area of graphene and its application to novel electronics. With Moore's law beginning to plateau, the need for post-silicon technology in industry is becoming more apparent. Moreover, existing technology is insufficient for implementing terahertz detectors and receivers, which are required for a number of applications including medical imaging and security scanning. Graphene is considered to be a key potential candidate for replacing silicon in existing CMOS technology as well as realizing field effect transistors for terahertz detection, due to its remarkable electronic properties, with observed electronic mobilities reaching up to $2 \times 10^5$ cm$^2$ V$^{-1}$ s$^{-1}$ in suspended graphene samples. This report reviews the physics and electronic properties of graphene in the context of graphene transistor implementations. Common techniques used to synthesize graphene, such as mechanical exfoliation, chemical vapor deposition, and epitaxial growth are reviewed and compared. One of the challenges associated with realizing graphene transistors is that graphene is semimetallic, with a zero bandgap, which is troublesome in the context of digital electronics applications. Thus, the report also reviews different ways of opening a bandgap in graphene by using bilayer graphene and graphene nanoribbons. The basic operation of a conventional field effect transistor is explained and key figures of merit used in the literature are extracted. Finally, a review of some examples of state-of-the-art graphene field effect transistors is presented, with particular focus on monolayer graphene, bilayer graphene, and graphene nanoribbons.

cond-mat.mes-hall↗