31 research outputs found
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.Comment: Revised version; 25 pages; 7 figure
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 , whereas positive
values of 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.Comment: 14 pages, 9 figure
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.Comment: 11 pages, 6 figure
Solution of the Kirchhoff-Plateau problem
The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in
which a flexible filament in the form of a closed loop is spanned by a liquid
film, with the filament being modeled as a Kirchhoff rod and the action of the
spanning surface being solely due to surface tension. We establish the
existence of an equilibrium shape that minimizes the total energy of the system
under the physical constraint of non-interpenetration of matter, but allowing
for points on the surface of the bounding loop to come into contact. In our
treatment, the bounding loop retains a finite cross-sectional thickness and a
nonvanishing volume, while the liquid film is represented by a set with finite
two-dimensional Hausdorff measure. Moreover, the region where the liquid film
touches the surface of the bounding loop is not prescribed a priori. Our
mathematical results substantiate the physical relevance of the chosen model.
Indeed, no matter how strong is the competition between surface tension and the
elastic response of the filament, the system is always able to adjust to
achieve a configuration that complies with the physical constraints encountered
in experiments
Optimal efficiency of quantum transport in a disordered trimer
Disordered quantum networks, as those describing light-harvesting complexes,
are often characterized by the presence of peripheral ring-like structures,
where the excitation is initialized, and inner reaction centers (RC), where the
excitation is trapped. The peripheral rings display coherent features: their
eigenstates can be separated in the two classes of superradiant and subradiant
states. Both are important to optimize transfer efficiency. In the absence of
disorder, superradiant states have an enhanced coupling strength to the RC,
while the subradiant ones are basically decoupled from it. Static on-site
disorder induces a coupling between subradiant and superradiant states,
creating an indirect coupling to the RC. The problem of finding the optimal
transfer conditions, as a function of both the RC energy and the disorder
strength, is very complex even in the simplest network, namely a three-level
system. In this paper we analyze such trimeric structure choosing as initial
condition a subradiant state, rather than the more common choice of an
excitation localized on a site. We show that, while the optimal disorder is of
the order of the superradiant coupling, the optimal detuning between the
initial state and the RC energy strongly depends on system parameters: when the
superradiant coupling is much larger than the energy gap between the
superradiant and the subradiant levels, optimal transfer occurs if the RC
energy is at resonance with the subradiant initial state, whereas we find an
optimal RC energy at resonance with a virtual dressed state when the
superradiant coupling is smaller than or comparable with the gap. The presence
of dynamical noise, which induces dephasing and decoherence, affects the
resonance structure of energy transfer producing an additional 'incoherent'
resonance peak, which corresponds to the RC energy being equal to the energy of
the superradiant state.Comment: This article shares part of the introduction and most of Section II
with arXiv:1508.01613, the remaining parts of the two articles treat
different problem
Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids
We consider the free fall of slender rigid bodies in a viscous incompressible
fluid. We show that the dimensional reduction (DR), performed by substituting
the slender bodies with one-dimensional rigid objects, together with a
hyperviscous regularization (HR) of the Navier--Stokes equation for the
three-dimensional fluid lead to a well-posed fluid-structure interaction
problem. In contrast to what can be achieved within a classical framework, the
hyperviscous term permits a sound definition of the viscous force acting on the
one-dimensional immersed body. Those results show that the DR/HR procedure can
be effectively employed for the mathematical modeling of the free fall problem
in the slender-body limit.Comment: arXiv admin note: substantial text overlap with arXiv:1305.070
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.Comment: 8 pages; 1 figur
A theoretical framework for steady-state rheometry in generic flow conditions
open2siopenGiusteri, Giulio G.; Seto, RyoheiGiusteri, Giulio G.; Seto, Ryohe
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.Comment: Updated figures and included Supplemental materia