arXiv subjects

Giulio G. Giusteri

Publications and source records attributed to Giulio G. Giusteri.

At least 19 recordsLinked to original sources

arXiv2026

A numerical study to analyze the interplay of Weissenberg number and viscosity ratio in a log-strain tensorial model for viscoelastic fluids

We present a computational study aimed at exploring the different and independent roles of the Weissenberg number and of the ratio between the polymeric and solvent viscosity contributions in a viscoelastic fluid model. The tensorial model under investigation, recently proposed, is based on a logarithmic relation between the elastic (or recoverable) strain and the elastic stress. In this model, the elastic strain plays the role of a conformation tensor and its evolution equation inherently preserves its determinant and positive definiteness. These properties are also enforced in the computational method employed in the study. A finite-difference discretization in time is combined with a stabilized mixed finite element formulation based on the Variational Multiscale method for the spatial discretization and with a generalized Lie derivative approach for the advection terms. The behavior of the model is analyzed in paradigmatic pressure-driven flows and we find that the value of the viscosity ratio is crucial in determining to which extent non-Newtonian flow profiles are observed upon increasing the Weissenberg number. By comparing the solutions of the log-strain tensorial model with those of a suitable Generalized Newtonian Fluid model, we show that flow-type dependence plays a significant role even in the simple planar flow past a cylinder.

cond-mat.soft↗

arXiv2026

Inertial motion of incompressible continua

We study the inertial motion of incompressible continua within a geometric and variational framework, extending the classical Arnold-Ebin-Marsden theory from the group of volume-preserving diffeomorphisms of a fixed domain to configuration spaces of deformations with variable image. In the latter case, the lack of a group structure requires proving some results that are instead immediate in the classical setting. We show that the orientation-preserving deformations with suitable regularity constitute a Hilbert manifold and that volume-preserving deformations form a submanifold with tangent vectors that are mapped onto divergence-free vector fields by the Lagrangian-to-Eulerian-picture correspondence. In so doing, we also present the geometric structure corresponding to compressible continua. The kinetic energy of the continuum gives rise to both a Lagrangian action, from which the equations of inertial motion are deduced, and a metric, with geodesics that are identified precisely by inertial motions. While the inertial motion can coincide with a physical one only for incompressible perfect fluids, it can be used to provide a natural parametrization of the configuration manifold for generic continua. We obtain a general result of local-in-time existence of solutions for the geodesic flow equation and we present explicit examples showing that, for the same initial data, the geodesic followed by the continuum in the compressible case can leave the manifold of admissible deformations in finite time, while the corresponding incompressible geodesic exists for all times.

math-ph↗

arXiv2026

Morphogenesis driven by nematic defects in active biological networks

Cellular morphogenesis, the process by which biological tissues acquire shape and structure, remains a fundamental challenge in understanding pattern formation and the coordinated remodeling of cellular assemblies. Under appropriate conditions, cytoskeletal filaments can organize into a nematic phase exhibiting partial orientational order. Topological defects within this nematic organization generate localized mechanical stresses that destabilize the tissue and promote deformation and structural rearrangements to relieve internal stresses. We develop a continuum framework that models living tissues as active biological networks represented as nematic polymer networks capable of heterogeneous growth and remodeling. The model captures macroscopic effects through spatial variations in the fiber order parameter which drives the system away from equilibrium. Morphogenesis is described as a sequence of quasi-static equilibrium states governed by the coupling between nematic order, elasticity, stress-driven growth, and adaptive relaxation. Finite element simulations illustrate Hydra regeneration and development when topological defects are prescribed according to the mature organism's expected morphology. The results show that defect topology controls stress localization and shape evolution: $+1$ defects drive protrusion formation, while $-1/2$ defects act as structural stabilizers with minimal growth. By varying the initial defect configuration, we model diverse morphogenetic outcomes, including uniaxial regeneration, tentacle formation, and biaxial development.

cond-mat.soft↗

arXiv2026

Modelling the passive and active response of skeletal muscles within the adapted Voigt representation framework

We present a constitutive model for the passive and active response of skeletal muscles. At variance with more classical approaches, the model is developed exploiting adapted Voigt representations of strain and stress tensors within the context of nonlinear Cauchy elasticity. This framework allows us to identify non-trivial stress-strain relations in a rather direct way from experimental data, enhancing the mechanical interpretability of the material functions that describe the tissue response and obtaining additional insight on the distinct role of the contractile fibres and of the surrounding extracellular matrix. We propose a two-material model, with an additive splitting of the stress contributions, in which only one component depends on an activation parameter. The constitutive model for the passive behaviour satisfactorily predicts the nonlinear stress response to elongation at different relative orientations with respect to the fibre direction and highlights the dominant role of the extracellular matrix. The activation model, essentially determined by the mechanics of the contractile fibres, captures well the isometric stress response through the prescription of an elasto-plastic evolution of the along-fibre active strain.

cond-mat.soft↗

arXiv2026

Quantum trajectories and reduced dynamics in time-correlated environments

The stochastic Schrödinger equation (SSE) provides a trajectory-level route to simulate the dynamics of open quantum systems with applications ranging from molecular processes to quantum technologies. We study a colored-noise extension of the SSE based on an Ornstein-Uhlenbeck (OU) noise drive, and benchmark its ensemble-averaged dynamics against the standard white-noise SSE and against a fluctuating OU random Hamiltonian. When the environment exhibits a finite correlation time, averaging over pure-state trajectories yields master equations that are generally open-form and not of Lindblad type, yet remain positive by construction. By considering the differential of the OU process, we define an effective correlated noise, whose properties we analyze and use to formulate an SSE unraveling of its associated open-form quantum master equation. We show that the averaged dissipator separates into a Lindblad contribution stemming from the white-noise component, and additional correlation terms arising from the fluctuations of the OU Hamiltonian. To obtain a practical closed description and physical intuition, we introduce a Redfield-inspired perturbative closure for these correlation terms, providing an effective master equation for the colored SSE. For a two-level system, the resulting dynamics exhibit long-lived coherences, nontrivial stationary (including oscillatory) states, and multi-timescale relaxation, rationalized through the components of a time-dependent Redfield tensor.

quant-ph↗

arXiv2026

On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians

Stochastic evolution underpins several approaches to the dynamics of open quantum systems, such as random modulation of Hamiltonian parameters, the stochastic Schrodinger equation (SSE), and the stochastic Liouville equation (SLE). These approaches replace the explicit system-environment coupling with an effective system-only dynamics, where dissipative behavior emerges from ensemble averaging. Stochastic Hamiltonians, in particular, have long served as phenomenological tools in physical chemistry to include environmental effects without recourse to an explicit microscopic derivation. In this work, we aim at a self-contained and accessible presentation of these approaches to further elaborate on their common roots in essential concepts of stochastic calculus and to delineate the conditions under which they are equivalent. We also discuss how different formulations naturally lead to different numerical time-integration schemes, better suited for either classical simulation platforms, based on finite-difference approximations, or quantum algorithms, that employ random unitary maps. Our analysis aims at providing a unified perspective and actionable recipes for classical and quantum implementations of stochastic evolution in the simulation of open quantum systems.

quant-ph↗

arXiv2025

Shape instabilities driven by topological defects in nematic polymer networks

Liquid crystalline networks (LCNs) are stimuli-responsive materials formed from polymeric chains cross-linked with rod-like mesogenic segments, which, in the nematic phase, align along a non-polar director. A key characteristic of these nematic systems is the existence of singularities in the director field, known as topological defects or disclinations, and classified by their topological charge. In this study, we address the open question of modeling mathematically the coupling between mesogens disclination and polymeric network by providing a mathematical framework describing the out-of-plane shape changes of initially flat LCN sheets containing a central topological defect. Adopting a variational approach, we define an energy associated with the deformations consisting of two contributions: an elastic energy term accounting for spatial director variations, and a strain-energy function describing the elastic response of the polymer network. The interplay between nematic elasticity, which seeks to minimize distortions in the director field, variations in the degree of order, with the consequent tendency of monomers in the polymer chains to distribute anisotropically in response to an external stimulus, and mechanical stiffness, which resists deformation, determines the resulting morphology. We analyze the transition to instability of the ground-state flat configuration and characterize the corresponding buckling modes.

cond-mat.soft↗

arXiv2024

Evolution of local relaxed states and the modelling of viscoelastic fluids

We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant material parameters is able to qualitatively reproduce a number of experimental observations in both simple shear and extensional flows, including linear viscoelastic properties, the rate dependence of steady-state material functions, the stress overshoot in incipient shear flows, and the difference in shear and extensional rheological curves. Furthermore, by allowing the relaxation time of the model to depend on the total strain, we can reproduce some experimental observations of the non-attainability of steady flows in uniaxial extension, and link this to a concept of polymeric jamming or effective solidification. Remarkably, this modelling framework helps in understanding the interplay between different mechanisms that may compete in determining the rheology of non-Newtonian materials.

cond-mat.soft↗

arXiv2024

Viscoelasticity, logarithmic stresses, and tensorial transport equations

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally belong to a multiplicative group of linear transformations, to stresses, that are additive elements of a linear space of tensors. As regards the viscous stresses, we simply assume a Newtonian constitutive law, but the presence of elasticity and plastic relaxation makes the materials non-Newtonian. Our aim is to discuss the existence of weak solutions for the corresponding systems of partial differential equations in the nonlinear large-deformation regime. The main difficulties arise in the analysis of the transport equations necessary to describe the evolution of tensorial measures of strain. For the solid model, we only need to consider the equation for the left Cauchy-Green tensor, while for the fluid model we add an evolution equation for the elastically-relaxed strain. Due to the tensorial nature of the fields, available techniques cannot be applied to the analysis of such transport equations. To cope with this, we introduce the notion of charted weak solution, based on non-standard a priori estimates, that lead to a global-in-time existence of solutions for the viscoelastic models in the natural functional setting associated with the energy inequality.

math.AP↗

arXiv2022

Periodic rhomboidal cells for symmetry-preserving homogenization and isotropic metamaterials

In the design and analysis of composite materials based on periodic arrangements of sub-units it is of paramount importance to control the emergent material symmetry in relation to the elastic response. The target material symmetry plays also an important role in additive manufacturing. In numerous applications it would be useful to obtain effectively isotropic materials. While these typically emerge from a random microstructure, it is not obvious how to achieve isotropy with a periodic order. We prove that arrangements of inclusions based on a rhomboidal cell that generates the Face-Centered Cubic lattice do in fact preserve any material symmetry of the constituents, so that spherical inclusions of isotropic materials in an isotropic matrix produce effectively isotropic composites.

math-ph↗

arXiv2022

Efficient light harvesting and photon sensing via engineered cooperative effects

Efficient devices for light harvesting and photon sensing are fundamental building blocks of basic energy science and many essential technologies. Recent efforts have turned to biomimicry to design the next generation of light-capturing devices, partially fueled by an appreciation of the fantastic efficiency of the initial stages of natural photosynthetic systems at capturing photons. In such systems extended excitonic states are thought to play a fundamental functional role, inducing cooperative coherent effects, such as superabsorption of light and supertransfer of photoexcitations. Inspired by this observation, we design an artificial light-harvesting and photodetection device that maximally harnesses cooperative effects to enhance efficiency. The design relies on separating absorption and transfer processes (energetically and spatially) in order to overcome the fundamental obstacle to exploiting cooperative effects to enhance light capture: the enhanced emission processes that accompany superabsorption. This engineered separation of processes greatly improves the efficiency and the scalability of the system.

physics.optics↗

arXiv2021

A multi-scale method for complex flows of non-Newtonian fluids

We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable interaction potentials at the micro-scale. Compared to previous proposals, our approach takes into account the fact that the material response can depend strongly on the local flow type and we show that this is a necessary feature to correctly capture the macroscopic dynamics. In particular, we highlight the importance of extensional rheology in simulating generic flows of polymeric fluids.

physics.flu-dyn↗

arXiv2021

Shear jamming and fragility of suspensions in a continuum model with elastic constraints

Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension can turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases. We show that, to reproduce the phenomenology of shear jamming in generic geometries, it is necessary to link this effect to the elastic response supported by the suspension microstructure rather than to a divergence of the viscosity.

cond-mat.soft↗

arXiv2018

Normal stress differences in dense suspensions

The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_1$, whereas positive values of $N_1$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limit. Furthermore, we found that the stress anisotropy induced by the planarity of the simple shear flow vanishes as the volume fraction approaches the jamming point for frictionless particles, while it remains finite for the case of frictional particles.

cond-mat.soft↗

arXiv2018

A theoretical framework for steady-state rheometry in generic flow conditions

We introduce a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions, which include extensional flows, simple shear flows, and any type of mixed flows. Such a basis is determined solely by the symmetric part of the velocity gradient and allows for a straightforward interpretation of the non-Newtonian response in any local flow conditions. In steady homogeneous flows, the material functions that represent the components of the stress on the adapted basis generalize and complete the classical set of viscometric functions used to characterize the response in simple shear flows. Such a general decomposition of the stress is effective in coherently organizing and interpreting rheological data from laboratory measurements and computational studies in non-viscometric steady flows of great importance for practical applications. The decomposition of the stress in terms with clearly distinct roles is also useful in developing constitutive models.

physics.flu-dyn↗

arXiv2017

Importance and effectiveness of representing the shapes of Cosserat rods and framed curves as paths in the special Euclidean algebra

We discuss how the shape of a special Cosserat rod can be represented as a path in the special Euclidean algebra. By shape we mean all those geometric features that are invariant under isometries of the three-dimensional ambient space. The representation of the shape as a path in the special Euclidean algebra is intrinsic to the description of the mechanical properties of a rod, since it is given directly in terms of the strain fields that stimulate the elastic response of special Cosserat rods. Moreover, such a representation leads naturally to discretization schemes that avoid the need for the expensive reconstruction of the strains from the discretized placement and for interpolation procedures which introduce some arbitrariness in popular numerical schemes. Given the shape of a rod and the positioning of one of its cross sections, the full placement in the ambient space can be uniquely reconstructed and described by means of a base curve endowed with a material frame. By viewing a geometric curve as a rod with degenerate point-like cross sections, we highlight the essential difference between rods and framed curves, and clarify why the family of relatively parallel adapted frames is not suitable for describing the mechanics of rods but is the appropriate tool for dealing with the geometry of curves.

math-ph↗

arXiv2017

Microstructure and thickening of dense suspensions under extensional and shear flows

Dense suspensions are non-Newtonian fluids which exhibit strong shear thickening and normal stress differences. Using numerical simulation of extensional and shear flows, we investigate how rheological properties are determined by the microstructure which is built under flows and by the interactions between particles. By imposing extensional and shear flows, we can assess the degree of flow-type dependence in regimes below and above thickening. Even when the flow-type dependence is hindered, nondissipative responses, such as normal stress differences, are present and characterise the non-Newtonian behaviour of dense suspensions.

cond-mat.soft↗

arXiv2017

Continuum balances from extended Hamiltonian dynamics

The classical procedure devised by Irving and Kirkwood in 1950 and completed slightly later by Noll produces counterparts of the basic balance laws of standard continuum mechanics starting from an ordinary Hamiltonian description of the dynamics of a system of material points. Post-1980 molecular dynamics simulations of the time evolution of such systems use extended Hamiltonians such as those introduced by Andersen, Nosé, and Parrinello and Rahman. The additional terms present in these extensions affect the statistical properties of the system so as to capture certain target phenomenologies that would otherwise be beyond reach. We here propose a physically consistent application of the Irving-Kirkwood-Noll procedure to extended Hamiltonian systems of material points. Our procedure produces balance equations at the continuum level featuring non-standard terms, because the presence of auxiliary degrees of freedom gives rise to additional fluxes and sources that influence the thermodynamic and transport properties of the continuum model. Being aware of the additional contributions may prove crucial when designing multiscale computational schemes in which information is exchanged between the atomistic and continuum levels.

math-ph↗