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Search Results: 1 - 10 of 13205 matches for " Eric DeGiuli "
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Laws of Granular Solids. Geometry and Topology
Eric DeGiuli,Jim McElwaine
Physics , 2011, DOI: 10.1103/PhysRevE.84.041310
Abstract: In a granular solid, mechanical equilibrium requires a delicate balance of forces at the disordered grain scale. To understand how macroscopic rigidity can emerge in this amorphous solid, it is crucial that we understand how Newton's laws pass from the disordered grain scale to the laboratory scale. In this work, we introduce an exact discrete calculus, in which Newton's laws appear as differential relations at the scale of a single grain. Using this calculus, we introduce gauge variables which describe identically force- and torque-balanced configurations. In a first, intrinsic formulation, we use the topology of the contact network, but not its geometry. In a second, extrinsic formulation, we introduce geometry with the Delaunay triangulation. These formulations show, with exact methods, how topology and geometry in a disordered medium are related by constraints. In particular, we derive Airy's expression for a divergence-free, symmetric stress tensor in two and three dimensions.
On the Granular Stress-Geometry Equation
Eric DeGiuli,Christian Schoof
Physics , 2013, DOI: 10.1209/0295-5075/105/28001
Abstract: Using discrete calculus, we derive the missing stress-geometry equation for rigid granular materials in two dimensions, in the mean-field approximation. We show that (i) the equation imposes that the voids cannot carry stress, (ii) stress transmission is generically elliptic and has a quantitative relation to anisotropic elasticity, and (iii) the packing fabric plays an essential role.
Breakdown of continuum elasticity in amorphous solids
Edan Lerner,Eric DeGiuli,Gustavo Düring,Matthieu Wyart
Physics , 2013,
Abstract: We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale $\ell_c$ that diverges as unjamming is approached as $\ell_c \sim (z - 2d)^{-1/2}$, where $z \ge 2d$ is the mean coordination, and $d$ is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale $\ell_c$ is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of $\ell_c\sim (p_c-p)^{-1/4}$ with proximity to a critical internal stress $p_c$ at which soft elastic modes become unstable.
Effects of coordination and pressure on sound attenuation, boson peak and elasticity in amorphous solids
Eric DeGiuli,Adrien Laversanne-Finot,Gustavo Düring,Edan Lerner,Matthieu Wyart
Physics , 2014,
Abstract: Connectedness and applied stress strongly affect elasticity in solids. In various amorphous solids, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of elasticity that extends previous approaches by incorporating the effect of compression, of amplitude $e$, allowing one to describe quantitative features of sound propagation, transport, the boson peak, and elastic moduli near the elastic instability occurring at a compression $e_c$. The theory disentangles several frequencies characterizing the vibrational spectrum: the onset frequency $\omega_0\sim \sqrt{e_c-e}$ where strongly-scattered modes appear in the vibrational spectrum, the pressure-independent frequency $\omega_*$ where the density of states displays a plateau, the boson peak frequency $\omega_{BP}$, and the Ioffe-Regel frequency $\omega_{IR}$ where scattering length and wavelength become equal. We predict that sound attenuation crosses over from $\omega^4$ to $\omega^2$ behaviour at $\omega_0$. We predict that a frequency-dependent length scale $l_s(\omega)$ and speed of sound $\nu(\omega)$ characterize vibrational modes, and could be extracted from scattering data. One key result is the prediction of a flat diffusivity above $\omega_0$, in agreement with previously unexplained observations. We find that the shear modulus does not vanish at the elastic instability, but drops by a factor of 2. We check our predictions in packings of soft particles and study the case of covalent networks and silica. Overall, our approach unifies sound attenuation, transport and length scales entering elasticity in a single framework where disorder is not the main parameter controlling the boson peak, in agreement with observations. This framework leads to a phase diagram where various glasses can be placed, connecting microscopic structure to vibrational properties.
Theory of the Jamming Transition at Finite Temperature
E. DeGiuli,E. Lerner,M. Wyart
Physics , 2015, DOI: 10.1063/1.4918737
Abstract: A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature $T$ and pressure $p$. Variational arguments and effective medium theory identically predict a non-trivial temperature scale $T^*\sim p^{(2-a)/(1-a)}$ with $a \approx 0.17$ such that low-energy vibrational properties are hard-sphere like for $T \gtrsim T^*$, and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating $T$, $p$, and the packing fraction $\phi$, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of $T$ and $\phi$. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.
A Phase Diagram Unifies Energy Dissipation, Kinetics, and Rheology in Inertial Granular Flows
E. DeGiuli,J. N. McElwaine,M. Wyart
Physics , 2015,
Abstract: Flows of hard granular materials depend strongly on the interparticle friction coefficient $\mu_p$ and on the inertial number ${\cal I}$, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for $10^{-4} \lesssim {\cal I} \lesssim 0.1$: frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as $\mu_p$ increases from zero at constant ${\cal I}$. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress anisotropy both display non-monotonic behavior with $\mu_p$, corresponding to transitions between the three regimes of flow. We characterize the scaling properties of these regimes, show that energy balance yields scaling relations for each of them, and explain why friction qualitatively affects flow.
Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions
E. DeGiuli,G. Düring,E. Lerner,M. Wyart
Physics , 2014, DOI: 10.1103/PhysRevE.91.062206
Abstract: Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies {\it both} to suspensions and inertial flows of hard particles. We compare our predictions with the empirical literature, as well as with novel numerical data. Overall we find a very good agreement between theory and observations, except for frictional inertial flows whose scaling properties clearly differ from frictionless systems. For over-damped flows, more observations are needed to decide if friction is a relevant perturbation or not. Our analysis makes several new predictions on microscopic dynamical quantities that should be accessible experimentally.
The distribution of forces affects vibrational properties in hard sphere glasses
E. DeGiuli,E. Lerner,C. Brito,M. Wyart
Physics , 2014, DOI: 10.1073/pnas.1415298111
Abstract: We study theoretically and numerically the elastic properties of hard sphere glasses, and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero-temperature, we argue that the presence of certain pairs of particles interacting with a small force $f$ soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting $P(f)\sim f^{\theta_e}$ the force distribution of such pairs and $\phi_c$ the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale $\omega^*$, rising up to it as $D(\omega) \sim \omega^{2+a}$, and decaying above $\omega^*$ as $D(\omega)\sim \omega^{-a}$ where $a=(1-\theta_e)/(3+\theta_e)$ and $\omega$ is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with $\langle \delta R^2\rangle\sim1/\mu\sim (\phi_c-\phi)^{\kappa} $ where $\kappa=2-2/(3+\theta_e)$, and (iii) continuum elasticity breaks down on a scale $\ell_c \sim1/\sqrt{\delta z}\sim (\phi_c-\phi)^{-b}$ where $b=(1+\theta_e)/(6+2\theta_e)$ and $\delta z=z-2d$, where $z$ is the coordination and $d$ the spatial dimension. We numerically test (i) and provide data supporting that $\theta_e\approx 0.41$ in our bi-disperse system, independently of system preparation in two and three dimensions, leading to $\kappa\approx1.41$, $a \approx 0.17$, and $b\approx 0.21$. Our results for the mean-square displacement are consistent with a recent exact replica computation for $d=\infty$, whereas some observations differ, as rationalized by the present approach.
A Tale of Two Motives: Endogenous Time Preference, Cash-in-Advance Constraints and Monetary Policy  [PDF]
Eric Kam
Modern Economy (ME) , 2013, DOI: 10.4236/me.2013.46045

This paper demonstrates the effects of modeling an endogenous rate of time preference and two cash-in-advance constraints. If the constraint is levied on consumption and capital goods, time preference effects are neutral and cash-in-advance constraint effects invert the Tobin Effect. If the constraint applies solely to consumption goods, opposing motives are offsetting and monetary policy is super neutral.

Targeting Phosphodiesterase 4 to Block the Link between Acute Exacerbation of Chronic Obstructive Pulmonary Disease and the Metabolic Complications  [PDF]
Eric Cho
Journal of Biosciences and Medicines (JBM) , 2015, DOI: 10.4236/jbm.2015.311007
Abstract: The metabolic disorders such as obesity and diabetes are found to be more frequent in chronic obstructive pulmonary disease (COPD). The chronic systemic inflammation orchestrated by macrophages constitutes one critical pathophysiological process underlying both acute exacerbation of COPD (AECOPD) and its metabolic complications such as obesity and diabetes. The cyclic adenosine monophosphate (cAMP) signaling controlled by phosphodiesterase (PDE) 4 is a pivotal intracellular modulator for macrophages functions in immune inflammatory response underlying AECOPD as well as obesity and diabetes. Targeting PDE4/cAMP signaling has been suggested to be effective in treating AECOPD or the metabolic disorders of obesity and diabetes. It is therefore reasonable to hypothesize that the chronic systemic inflammation can be a critical link between AECOPD and the metabolic disorders and targeting the PDE4/cAMP signaling can be effective to block this link between AECOPD and the associated metabolic complications.
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