125 research outputs found
On the Role of Viscosity in Early Cosmology
We present a discussion of the effects induced by bulk viscosity on the very
early Universe stability. The viscosity coefficient is assumed to be related to
the energy density via a power-law of the form
(where ) and the behavior of the density contrast in
analyzed.
In particular, we study both Einstein and hydrodynamic equations up to first
and second order in time in the so-called quasi-isotropic collapsing picture
near the cosmological singularity. As a result, we get a power-law solution
existing only in correspondence to a restricted domain of . The
particular case of pure isotropic FRW dynamics is then analyzed and we show how
the asymptotic approach to the initial singularity admits an unstable
collapsing picture.Comment: 4 pages, no figur
Structure of force networks in tapped particulate systems of disks and pentagons I Clusters and loops
The force network of a granular assembly, defined by the contact network and the corresponding contact
forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic et al., Phys. Rev. E 93, 062903 (2016)], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network’s topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.Fil: Pugnaloni, Luis. UTN (Universidad Tecnológica Nacional). Departamento de Ingeniería Mecánica. GMG. CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas); ArgentinaFil: Carlevaro, Manuel. UTN (Universidad Tecnológica Nacional). Facultad Regional Buenos Aires. UDB Física. CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas); ArgentinaFil: Kramar, M. Rutgers University. Department of Mathematics; USAFil: Mischaikow, K. Rutgers University. Department of Mathematics; USAFil: Kondic, L. New Jersey Institute of Technology. Department of Mathematical Sciences; USAPeer Reviewe
Structure of force networks in tapped particulate systems of disks and pentagons II Persistence analysis
In the companion paper [Pugnaloni et al., Phys. Rev. E 93, 062902 (2016)], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.Fil: Kondic, L. New Jersey Institute of Technology. Department of Mathematical Sciences; USAFil: Kramar, M. Rutgers University. Department of Mathematics; USAFil: Pugnaloni, Luis. UTN (Universidad Tecnológica Nacional). Departamento de Ingeniería Mecánica. GMG. CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas); ArgentinaFil: Carlevaro, Manuel. UTN (Universidad Tecnológica Nacional). Facultad Regional Buenos Aires. UDB Física. CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas); ArgentinaFil: Mischaikow, K. Rutgers University. Department of Mathematics; USAPeer Reviewe
Structure of force networks in tapped particulate systems of disks and pentagons. II. Persistence analysis
In the companion paper [Pugnaloni, Phys. Rev. E 93, 062902 (2016)10.1103/PhysRevE.93.062902], we use classical measures based on force probability density functions (PDFs), as well as Betti numbers (quantifying the number of components, related to force chains, and loops), to describe the force networks in tapped systems of disks and pentagons. In the present work, we focus on the use of persistence analysis, which allows us to describe these networks in much more detail. This approach allows us not only to describe but also to quantify the differences between the force networks in different realizations of a system, in different parts of the considered domain, or in different systems. We show that persistence analysis clearly distinguishes the systems that are very difficult or impossible to differentiate using other means. One important finding is that the differences in force networks between disks and pentagons are most apparent when loops are considered: the quantities describing properties of the loops may differ significantly even if other measures (properties of components, Betti numbers, force PDFs, or the stress tensor) do not distinguish clearly or at all the investigated systems.Instituto de Física de Líquidos y Sistemas Biológico
Structure of force networks in tapped particulate systems of disks and pentagons : I. Clusters and loops
The force network of a granular assembly, defined by the contact network and the corresponding contact forces, carries valuable information about the state of the packing. Simple analysis of these networks based on the distribution of force strengths is rather insensitive to the changes in preparation protocols or to the types of particles. In this and the companion paper [Kondic, Phys. Rev. E 93, 062903 (2016)10.1103/PhysRevE.93.062903], we consider two-dimensional simulations of tapped systems built from frictional disks and pentagons, and study the structure of the force networks of granular packings by considering network's topology as force thresholds are varied. We show that the number of clusters and loops observed in the force networks as a function of the force threshold are markedly different for disks and pentagons if the tangential contact forces are considered, whereas they are surprisingly similar for the network defined by the normal forces. In particular, the results indicate that, overall, the force network is more heterogeneous for disks than for pentagons. Such differences in network properties are expected to lead to different macroscale response of the considered systems, despite the fact that averaged measures (such as force probability density function) do not show any obvious differences. Additionally, we show that the states obtained by tapping with different intensities that display similar packing fraction are difficult to distinguish based on simple topological invariants.Instituto de Física de Líquidos y Sistemas Biológico
The Jeans Instability in Presence of Viscous Effects
An analysis of the gravitational instability in presence of dissipative
effects is addressed. In particular, the standard Jeans Mechanism and the
generalization in treating the Universe expansion are both analyzed when bulk
viscosity affects the first-order Newtonian dynamics. As results, the
perturbation evolution is founded to be damped by dissipative processes and the
top-down mechanism of structure fragmentation is suppressed. In such a scheme,
the value of the Jeans Mass remains unchanged also in presence of viscosity.Comment: 13 pages, 2 figure
Intruder in a two-dimensional granular system: statics and dynamics of force networks in an experimental system experiencing stick-slip dynamics
In quasi-two-dimensional experiments with photoelastic particles confined to
an annular region, an intruder constrained to move in a circular path halfway
between the annular walls experiences stick-slip dynamics. We discuss the
response of the granular medium to the driven intruder, focusing on the
evolution of the force network during sticking periods. Because the available
experimental data does not include precise information about individual contact
forces, we use an approach developed in our previous work (Basak et al, J. Eng.
Mechanics (2021)) based on networks constructed from measurements of the
integrated strain magnitude on each particle. These networks are analyzed using
topological measures based on persistence diagrams, revealing that force
networks evolve smoothly but in a nontrivial manner throughout each sticking
period, even though the intruder and granular particles are stationary.
Characteristic features of persistence diagrams show identifiable changes as a
slip is approaching, indicating the existence of slip precursors. Key features
of the dynamics are similar for granular materials composed of disks or
pentagons, but some details are consistently different. In particular, we find
significantly larger fluctuations of the measures computed based on persistence
diagrams, and therefore of the underlying networks, for systems of pentagonal
particles
On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity
We analyze the effects induced by the bulk viscosity on the dynamics
associated to the extreme gravitational collapse. Aim of the work is to
investigate whether the presence of viscous corrections to the evolution of a
collapsing gas cloud influence the fragmentation process. To this end we study
the dynamics of a uniform and spherically symmetric cloud with corrections due
to the negative pressure contribution associated to the bulk viscosity
phenomenology. Within the framework of a Newtonian approach (whose range of
validity is outlined), we extend to the viscous case either the Lagrangian,
either the Eulerian motion of the system and we treat the asymptotic evolution
in correspondence to a viscosity coefficient of the form ( being the cloud density and ). We show how,
in the adiabatic-like behavior of the gas (i.e. when the politropic index takes
values ), density contrasts acquire, asymptotically, a
vanishing behavior which prevents the formation of sub-structures. We can
conclude that in the adiabatic-like collapse the top down mechanism of
structures formation is suppressed as soon as enough strong viscous effects are
taken into account. Such a feature is not present in the isothermal-like (i.e.
) collapse because the sub-structures formation is yet present
and outlines the same behavior as in the non-viscous case. We emphasize that in
the adiabatic-like collapse the bulk viscosity is also responsible for the
appearance of a threshold scale beyond which perturbations begin to increase.Comment: 13 pages, no figur
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