arXiv subjects

Marco Morandotti

Publications and source records attributed to Marco Morandotti.

At least 19 recordsLinked to original sources

arXiv2026

Effective Dynamics of Disclination Pairs

The dissipative dynamics of a pair of wedge disclinations with opposite Frank angles confined to a circular domain is investigated under the assumption of radially symmetric motion. Two distinct dynamical regimes are identified: a diverging-disclination regime and an annihilating-dipole regime. The stationary points associated with both regimes are determined and fully characterized in terms of their stability, and quantitative estimates for the characteristic evolution times in their vicinity are derived. In the annihilating-dipole regime, it is shown that, after a suitable time rescaling, the resulting law of motion for the dipole coincides with that of an edge dislocation.

math.DS↗

arXiv2026

Equilibrium and Interaction Regimes in Mixed Disclination-Dislocation Systems

We investigate equilibrium configurations and dissipative dynamics of simplified disclination--dislocation systems in planar elasticity. We consider an edge dislocation interacting with a fixed wedge disclination in a circular domain. We derive the reduced interaction energy, characterize the equilibrium states and their stability, and study the associated dissipative evolution. The analysis reveals characteristic length scales and collision times arising from the competition between the dislocation and disclination contributions. In particular, the presence of the disclination produces a nontrivial modification of the dislocation dynamics and can hinder its motion. This behavior is consistent with experimental observations and provides a simple mathematical description of the interaction between rotational and translational defects.

math.DS↗

arXiv2026

Minimizers of one-dimensional regularization problems with linear and nonlinear total variation

A study of the minimizers of one-dimensional Rudin-Osher-Fatemi-type functionals with linear or nonlinear total variation and fidelity term is undertaken. Conditions on the input datum and the parameters of the functional are found that force the input itself to be the minimizer or not. In the linear setting the discriminating conditions on the parameters are complementary highlighting the sharpness of the results. The nonlinear setting is substantially different: while the non-minimality of the datum is treated in analogy with the linear case, for the minimality of the input only partial answers are found. The results in the nonlinear setting hinge on auxiliary constrained or penalized minimization problems investigating the behavior of optimal transitions with prescribed height. Additionally, they are complemented by some numerical examples.

math.CA↗

arXiv2026

Stabilization of solutions to a model of Langmuir-Blodgett films

We show stabilisation of solutions to one-dimensional advective Cahn-Hilliard equation modeling the Langmuir-Blodgett thin films. This problem has the structure of a gradient flow perturbed by a linear term $\beta u_x$. Through application of an abstract result by Carvalho-Langa-Robinson, we show that for small $\beta$ the equation has the structure of gradient flow in a weak sense. Combining this with the finite number of steady states implies stabilization of solutions.

math.AP↗

arXiv2026

Purcell swimmer near a wall

We study the effects of hydrodynamic interactions between a wall and the Purcell three-link swimmer in the two-dimensional case. After deriving the equations of motion in a low Reynolds number regime using Resistive Force Theory with suitably modified drag coefficients, we show, by means of criteria from Geometric Control Theory, that the system is controllable at configurations that are nearly parallel to the wall. Furthermore, we study configurations that are tilted, and we show net displacement with respect to the initial orientation. Some numerical experiments illustrate the analytical results.

physics.flu-dyn↗

arXiv2025

A general perspective on CBO methods with stochastic rate of information

This paper studies a class of Consensus-Based Optimization (CBO) models featuring an additional stochastic rate of information, modeling the agents' knowledge of the environment and energy landscape. The well-posedness of the stochastic system is proved, together with its finite-particle approximation and the mean-field convergence to a kinetic PDE. Particles are shown to concentrate around the consensus point under mild assumptions on the initial spatial distribution and initial level of knowledge. In particular, the analysis unveils that a positive, however small, initial level of knowledge is enough for convergence to consensus to happen. The framework presented is general enough to include the first instances of CBO proposed in the literature.

math.OC↗

arXiv2025

Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects

A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy, over a compact metric space. The evolution is governed by a non-local interaction mechanism and by stochastic effects acting on the spatial component of the state. The well-posedness of the multi-agent system and that of a certain McKean--Vlasov stochastic differential equation are proved. Eventually, a propagation of chaos result is obtained, which guarantees that the former model converges to the latter as the number of agents goes to infinity.

math.AP↗

arXiv2025

A Comprehensive Approach via Global Relaxation to the Variational Modelling of Hierarchical Structured Deformations

The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of such changes and for the variational determination of the corresponding energetic response. The research in this article provides substantial refinements and broadenings of the mathematical setting both for the underlying geometrical structure and for the variational analysis of energetic response. The mathematical tools employed in this research include the global method for relaxation and establish the equivalence of a relaxed energy obtained via relaxation under simultaneous geometrical changes at all levels and a relaxed energy obtained via iterated relaxations proceeding from the deepest submacroscopic level successively to the macroscopic level.

math.CA↗

arXiv2025

Variational formulation of planar linearized elasticity with incompatible kinematics

We present a variational characterization of mechanical equilibrium in the planar strain regime for systems with incompatible kinematics. For non-simply connected domains, we show that the equilibrium problem for a non-liftable strain-stress pair can be reformulated as a well-posed minimization problem for the Airy potential of the system. We characterize kinematic incompatibilities on internal boundaries as rotational or translational mismatches, in agreement with Volterra's modeling of disclinations and dislocations. Finally, we establish that the minimization problem for the Airy potential can be reduced to a finite-dimensional optimization involving cell formulas.

math.OC↗

arXiv2025

Replicator dynamics as the large population limit of a discrete Moran process in the weak selection regime: A proof via Eulerian specification

We study the large population limit of a multi-strategy discrete-time Moran process in the weak selection regime. We show that the replicator dynamics is interpreted as the large-population limit of the Moran process. This result is obtained by interpreting the discrete process in its Eulerian specification, proving a compactness result in the Wasserstein space of probability measures for the law of the proportions of strategies, and passing to the limit in the continuity equation that describes the evolution of the proportions.

math.AP↗

arXiv2024

Geometrically constrained walls in three dimensions

We study geometrically constrained magnetic walls in a three dimensional geometry where two bulks are connected by a thin neck. Without imposing any symmetry assumption on the domain, we investigate the scaling of the energy as the size of the neck vanishes. We identify five significant scaling regimes, for all of which we characterise the energy scaling and identify the asymptotic behaviour of the domain wall. Finally, we notice the emergence of sub-regimes that are not present in the previous works due to restrictive symmetry assumptions.

math.AP↗

arXiv2024

Controllability and kinetic limit of spherical particles immersed in a viscous fluid

This paper deals with systems of spherical particles immersed in a viscous fluid. Two aspects are studied, namely the controllability of such systems, with particular attention to the case of one active particle and either one or two passive ones, and the kinetic limit of such systems as the number of particles diverges. The former issue is tackled in the framework of geometric control theory, whereas the latter resorts to Boltzmann-type formulations of the system of interacting particles.

math.AP↗

arXiv2024

Space-time evolution of Volterra disclinations

The dynamics of a system of particles subject to a 4th order potential field modeling the space-time evolution of wedge disclinations is studied, focusing on finite systems of disclinations within a circular domain. Existence theorems for the trajectories of these disclinations are presented, considering both the dynamics without predefined preferred directions of motion in an isotropic medium and the dynamics in which the disclinations move parallel to predefined directions, modeling a crystalline material. The analysis is illustrated with a number of numerical solutions to demonstrate various relevant configurations.

math.DS↗

arXiv2024

Calibrating the Heston model with deep differential networks

We propose a gradient-based deep learning framework to calibrate the Heston option pricing model (Heston, 1993). Our neural network, henceforth deep differential network (DDN), learns both the Heston pricing formula for plain-vanilla options and the partial derivatives with respect to the model parameters. The price sensitivities estimated by the DDN are not subject to the numerical issues that can be encountered in computing the gradient of the Heston pricing function. Thus, our network is an excellent pricing engine for fast gradient-based calibrations. Extensive tests on selected equity markets show that the DDN significantly outperforms non-differential feedforward neural networks in terms of calibration accuracy. In addition, it dramatically reduces the computational time with respect to global optimizers that do not use gradient information.

q-fin.CP↗

arXiv2024

Semi-discrete modeling of systems of wedge disclinations and edge dislocations via the Airy stress function method

We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge dislocations, which we model as the solutions to minimum problems for isotropic elastic energies under the constraint of kinematic incompatibility. Operating under the assumption of planar linearized kinematics, we formulate the mechanical equilibrium problem in terms of the Airy stress function, for which we introduce a rigorous analytical formulation in the context of incompatible elasticity. Our main result entails the analysis of the energetic equivalence of systems of disclination dipoles and edge dislocations in the asymptotics of their singular limit regimes. By adopting the regularization approach via core radius, we show that, as the core radius vanishes, the asymptotic energy expansion for disclination dipoles coincides with the energy of finite systems of edge dislocations. This proves that Eshelby's kinematic characterization of an edge dislocation in terms of a disclination dipole is exact also from the energetic standpoint.

math.AP↗

arXiv2024

Control of Microparticles Through Hydrodynamic Interactions

The controllability of passive microparticles that are advected with the fluid flow generated by an actively controlled one is studied. The particles are assumed to be suspended in a viscous fluid and well separated so that the far-field Stokes flow solutions may be used to describe their interactions. Applying concepts from geometric control theory, explicit moves characterized by a small amplitude parameter $\varepsilon$ are devised to prove that the active particle can control one or two passive particles. The leading-order (in $\varepsilon$) theoretical predictions of the particle displacements are compared with those obtained numerically and it is found that the discrepancy is small even when $\varepsilon\approx 1$. These results demonstrate the potential for a single actuated particle to perform complex micromanipulations of passive particles in a suspension.

physics.flu-dyn↗

arXiv2024

Gait controllability of length-changing slender microswimmers

Controllability results of four models of two-link microscale swimmers that are able to change the length of their links are obtained. The problems are formulated in the framework of Geometric Control Theory, within which the notions of fiber, total, and gait controllability are presented, together with sufficient conditions for the latter two. The dynamics of a general two-link swimmer is described by resorting to Resistive Force Theory and different mechanisms to produce a length-change in the links, namely, active deformation, a sliding hinge, growth at the tip, and telescopic links. Total controllability is proved via gait controllability in all four cases, and illustrated with the aid of numerical simulations.

math.OC↗

arXiv2024

Characterizing BV- and BD-ellipticity for a class of positively 1-homogeneous surface energy densities

Lower semicontinuity of surface energies in integral form is known to be equivalent to BV-ellipticity of the surface density. In this paper, we prove that BV-ellipticity coincides with the simpler notion of biconvexity for a class of densities that depend only on the jump height and jump normal, and are positively 1-homogeneous in the first argument. The second main result is the analogous statement in the setting of bounded deformations, where we show that BD-ellipticity reduces to symmetric biconvexity. Our techniques are primarily inspired by constructions from the analysis of structured deformations and the general theory of free discontinuity problems.

math.AP↗