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## Présentée pour obtenir le grade de DOCTEUR DE L’UNIVERSITE ́ PARIS–EST Domaine: Physique

### Citations

1612 |
Computer Simulation of Liquids
- Allen, Tildesley
- 1987
(Show Context)
Citation Context ...velocities of the particles at time t it permits us to compute at the second order of the positions and velocities at time t+ δt, with δt a fixed time step. It is based on the following two equations =-=[67]-=-: (i) the Taylor series expansion of the particle position ~r(t) which reads at second order: ~r(t+ δt) = ~r(t) + δt ~v(t) + 1 2 δt2 ~a(t) +O(δt3) (2.2) with ~a the acceleration; and (ii) the time exp... |

705 |
Theory of Simple Liquids
- Hansen, McDonald
- 1986
(Show Context)
Citation Context .... . . d~rN exp(−U(~r1, . . . , ~rN )/kBT ) ρ2 ∫ d~r1 . . . d~rN exp(−U(~r1, . . . , ~rN )/kBT ) (3.4) where ∫ d~r1 . . . d~rN exp(−U(~r1, . . . , ~rN )/kBT ) is the partition function of the ensemble =-=[73]-=-. For an isotropic and homogeneous system the distribution function depends only on the inter-particle distance rij = ‖~rj − ~ri‖, and is then called the “radial distribution function”, g(r). For a sy... |

497 |
The Structure and Rheology of Complex Fluids
- Larson
- 1999
(Show Context)
Citation Context ... colloidal suspensions the glass transition is reached by increasing the volume fraction occupied by the particles. This effect can be illustrated by considering a model system: the hard sphere fluid =-=[19]-=-, which presents a liquid structure for volume fraction φ . 0.49. The crystal formation can be avoided by a quick increase of the volume fraction beyond φ ∼ 0.56, that traps the particles and brings t... |

485 |
The determination of the elastic field of an ellipsoidal inclusion, and related problems
- Eshelby
- 1957
(Show Context)
Citation Context ...ion from where its flip occurs. Argon then proposes to compute the free energy barrier as the elastic energy required to deform a zone up to some yield strain motivated by the earlier work of Eshelby =-=[44]-=-. Finally, he writes down an equation for the strain rate as a balance between forward flips (occurring in the direction of, and thus releasing, external forcing) and a “back flux” (due to flips occur... |

395 |
The Art of Molecular Dynamics Simulations
- Rapaport
- 1995
(Show Context)
Citation Context ...or of the small (large) particles. Numerical results We present in Fig. 3.2 the values of gab(r) (a and b denote the type of particles: S or L) for several temperatures as measured following protocol =-=[74]-=-. For the sake of clarity each curve is shifted vertically upwards from its preceding higher temperature curve. We see: (i) gab(r) rapidly dampens to unity and (ii) it changes very little with decreas... |

266 |
G.: Statistical mechanics of non equilibrium liquids
- Evans, Morris
- 1990
(Show Context)
Citation Context ...equations can be rewritten as ~̇ri(t) = ~pi(t) m + êxγ̇yi(t) (2.12) ~̇pi(t) = −~∇U(~r, t)− êxγ̇pyi(t) (2.13) with ~pi(t) = mi~ci(t). These two equations turn out to be the so-called SLLOD equations =-=[68]-=-. Note that in our constant γ̇ study these equations are strictly equivalent to the Newton’s equations. This equivalence is broken only when γ̇ is non-stationary which is where the possible debate on ... |

257 |
Brownian motion in a field of force and the diffusion model of chemical reactions
- Kramers
(Show Context)
Citation Context ...vated jumps. This immediately leads to ∂P (γ) ∂γ = −1 γ̇ R(γ)P (γ) (7.4) which has the solution P (γ; γ0) = exp [ −1 γ̇ ∫ γ γ0 dγ′R(γ′) ] (7.5) To estimate R(γ) we use the standard Kramers expression =-=[83]-=-, R(γ) = ω exp (−∆ET ), with the assumption ∆E/T 1 – we will have to check the validity of this assumption a posteriori. Using expressions (7.1) and (7.2) we obtain: R(γ) = ν(γc − γ)1/4 exp ( −B T (... |

205 |
editors. Handbook of Mathematical Functions
- Abramowitz, Stegun
- 1964
(Show Context)
Citation Context ...] = exp [ −ν γ̇ ( 2 3 )( T B )5/6{ Γ ( 5 6 , B T δγ3/2 ) − Γ ( 5 6 , B T δγ 3/2 0 )}] (7.7) Γ (s, x) = ∫∞ x t s−1e−tdt is the upper incomplete gamma function and has the following asymptotic behavior =-=[84]-=- i.e. Γ (s, x) ∼ xs−1e−x for x ≡ 1/ = ∆E T 1 with, the small parameter of the Kramers expression. We thus arrive at P (γ; γ0) = exp [ −ν γ̇ ( 2 3 )( T B )5/6{ Q(δγ) −Q(δγ0) }] (7.8) where Q(δγ) ∼... |

143 | The Physics of Amorphous Solids - Zallen - 1983 |

139 |
Colloidal dispersions
- Russel, Saville, et al.
- 1989
(Show Context)
Citation Context ... electrostatic repulsion due to the presence of charged particles, steric repulsion caused by adsorbed polymers, viscous forces due to the relative motion between particles and suspending liquid etc. =-=[10]-=-. Modern techniques such as video microscopy [11], confocal microscopy [12, 13] make it now possible to track the motions of particles in a colloidal suspension accurately over time. This type of meas... |

100 |
The statistical mechanical theory of transport processes
- Kirkwood
- 1946
(Show Context)
Citation Context ...scussion and analysis of these results will be presented in Part II. 4.1 Macroscopic stress The total stress generated by an instantaneous particle configuration, as formulated by Irving and Kirkwood =-=[76]-=-, reads: σαβ = 1 L2 N∑ i=1 [ 1 2 N∑ j=1;j 6=i fijαrijβ −miviαviβ ] (4.1) where α, β represent the Cartesian coordinates, ~rij = ~rj − ~ri, ~fij ≡ ~fj→i, that is the force that particle j exerts on par... |

85 |
Weak ergodicity breaking and aging in disordered systems
- Bouchaud
- 1992
(Show Context)
Citation Context ...temperature range. Soft glassy rheology (SGR) A related mean field theory has been formulated by Sollich and coworkers [45, 46] on the basis of a model of glassy relaxation proposed by Bouchaud et al =-=[47]-=- as an attempt to represent the hopping process in the PEL. The internal state of a “mesoscopic element” is characterized by a local strain variable (l); the bias due to external loading is introduced... |

83 |
On the temperature dependence of cooperative relaxation properties in glass-forming liquids
- Adam, Gibbs
- 1965
(Show Context)
Citation Context ...s transition is that it is not associated with any significant change in structure. These issues have spurred tremendous amount of work with the development of free-volume theory [22], entropy theory =-=[23]-=-, mode-coupling theory [24], random first-order transition theory [25], shoving model [26] to understand from a common ground the underlying phenomenology of the glass transition of both hard and soft... |

68 |
Theory of Elasticity. Butterworth-Heineman
- Landau, Pitaevskii, et al.
- 1986
(Show Context)
Citation Context ... due to a set of two dipoles of forces with F = 2aµ∆0. ~u E(~r) = 4∑ i=1 ~~Q(~r − ~ri). ~Fi (D.1) where ~~Q is the Green’s tensor corresponding to the response to a point force located at the origin =-=[87]-=-: ~~Q = 1 4piµ ( − ln r~~I + 1 r2 ~r~r ) (D.2) where µ is the shear modulus and ~~I is the unit tensor. An expansion in a/r yields at lowest order: ~u E = aF 2piµ xy r4 ~r (D.3) 103 104 Comparing the ... |

54 |
Dynamics of viscoplastic deformation in amorphous solids
- Falk, Langer
- 1998
(Show Context)
Citation Context ...bble raft should also be relevant to deformation in drastically different systems such as metallic glasses. More recently the validity of this idea has been confirmed by several numerical simulations =-=[41, 42, 4, 43, 3]-=- and one experiment on a colloidal suspension using confocal microscopy [13]. 1.3.1 Mean field models of plasticity Mean field theories assume shear transformations to occur independently. This assump... |

53 |
Spatially heterogeneous dynamics in supercooled liquids
- Ediger
- 1320
(Show Context)
Citation Context ... others are essentially vibrating around their original positions. The particles of higher mobilities often appear to form spatially heterogeneous clusters in 1.3 Theories of deformation 7 the system =-=[32]-=-. Huge efforts have been made both experimentally and numerically to understand the origin of these dynamical heterogeneities [33, 34, 35], and also to define the relevant observable(s), which can cha... |

45 |
Formation of glasses from liquids and biopolymers
- Angell
- 1995
(Show Context)
Citation Context ...id permitting us to bypass the formation of the crystal. Below the freezing point the liquid thus reaches the metastable “supercooled” liquid state (see Fig. 1.1(a)). Good glass formers are materials =-=[14, 15]-=- for which the crystallization can be prevented at reasonably low cooling rates: this is the case of silica which requires cooling rates of the order of 10−2K/s to be compared with ∼ 104K/s needed for... |

45 |
Relaxation processes in supercooled liquids
- Gotze, Sjogren
- 1992
(Show Context)
Citation Context ...not associated with any significant change in structure. These issues have spurred tremendous amount of work with the development of free-volume theory [22], entropy theory [23], mode-coupling theory =-=[24]-=-, random first-order transition theory [25], shoving model [26] to understand from a common ground the underlying phenomenology of the glass transition of both hard and soft glasses. We here only disc... |

41 |
Rheological constitutive equation for a model of soft glassy materials
- Sollich
- 1998
(Show Context)
Citation Context ...ntroduced to account for the fact that shear transformations do occur in the low temperature range. Soft glassy rheology (SGR) A related mean field theory has been formulated by Sollich and coworkers =-=[45, 46]-=- on the basis of a model of glassy relaxation proposed by Bouchaud et al [47] as an attempt to represent the hopping process in the PEL. The internal state of a “mesoscopic element” is characterized b... |

39 |
A topographic view of supercooled liquids and glass formation
- Stillinger
- 1995
(Show Context)
Citation Context ...lass transition of both hard and soft glasses. We here only discuss a few paradigms which are important for our deformation study. Perhaps the most important idea, which has emerged from the works of =-=[27, 28]-=-, is that a glass lives in a complex potential energy landscape (PEL), which can be envisaged as a mountain range seen upside down: broadly distributed, mountain peaks correspond to the local energy m... |

39 |
Plastic deformation in metallic glasses
- Argon
- 1979
(Show Context)
Citation Context ...city evolved from the pioneering work by Argon in the late 70’s, when he proposed that the plastic deformation of a metallic glass is the net result of the accumulation of local shear transformations =-=[39]-=-, defined as rearrangements (or flips) of small volume elements (zones) consisting of relatively few particles (a few tens of atoms). This idea was inspired by a “bubble-raft experiment” [40], where s... |

38 |
Relaxation in glassforming liquids and amorphous solids
- Angell, Ngai, et al.
- 1999
(Show Context)
Citation Context ...ollowing Maxwell’s relation a typical value of relaxation time τα ∼ η/G∞ can be estimated approximately, where G∞ is the high frequency shear modulus. Usually this value is of the order of 102 − 103s =-=[17]-=-. Crystal Glass Supercooled Liquid Tg2 TmTg 1 (a) T V (b) Fragile 13 1 Strong T /Tg ηlog Figure 1.1: (a) Schematic volume-temperature diagram: the curves indicate different possible histories of a sys... |

35 |
Supercooled liquids and glasses
- Ediger
- 1996
(Show Context)
Citation Context ...With further cooling these systems eventually fall out-of-equilibrium as they can no longer attain the supercooled liquid states at these low temperatures: they become an “amorphous solid” or “glass” =-=[16]-=-. This change of behavior shows up as a change in slope in the temperature dependence of some thermodynamic parameters (see Fig. 1.1(a)). The glass transition is not a bona fide thermodynamic phase tr... |

35 | Rheology of soft glassy materials - SoIlich, Lequeux, et al. - 1997 |

34 |
Supercooled liquids and the glass transition
- Debenedetti, Stillinger
(Show Context)
Citation Context ...perature Tg/T . For strong glass formers viscosity increases logarithmically with Tg/T , that is, they exhibit the Arrhenius behavior compared to the super-Arrhenius behavior of fragile glass formers =-=[18]-=-. 1.2.1 Glass transition in colloids and granular systems Soft glasses are also out-of-equilibrium systems but their fabrication does not usually proceed via changing temperature. Instead, e.g in coll... |

24 |
Viscous liquids and the glass transition: A potential energy barrier picture
- Goldstein
- 1969
(Show Context)
Citation Context ...lass transition of both hard and soft glasses. We here only discuss a few paradigms which are important for our deformation study. Perhaps the most important idea, which has emerged from the works of =-=[27, 28]-=-, is that a glass lives in a complex potential energy landscape (PEL), which can be envisaged as a mountain range seen upside down: broadly distributed, mountain peaks correspond to the local energy m... |

23 |
A universal criterion for plastic yielding of metallic glasses with a (T/Tg)2/3 temperature dependence
- Johnson, Samwer
- 1955
(Show Context)
Citation Context ...structure of metallic glasses rather dense. Corresponding to their crystalline alloys metallic glasses have: (i) higher yield strengths and hardness, and (ii) smaller Young’s modulus (∼ 30 to 200 GPa =-=[8]-=-) and shear modulus (∼ 10 to 60 GPa [8], reduced by roughly 15%) [9]. Their high mechanical strengths, large elastic limits, soft magnetic properties (iron-based and cobalt-based metallic glasses), hi... |

23 |
Nonlinear dynamics: Jamming is not just cool any more
- Liu, Nagel
- 1998
(Show Context)
Citation Context ...on of the parameters. We see significant stress drops with T for all γ̇. of the shear-stress we further plot (Fig. 4.6(b)) σ(γ̇, T ) as a function of T for all our strain rates as previously shown in =-=[78, 57]-=-. We see that at low γ̇, σ decreases significantly with increasing temperature. To explain the decrease of average shear-stress with increasing temperature in the domain well below of the glass transi... |

18 |
Colloquium: The glass transition and elastic models of glassforming liquids
- Dyre
- 2006
(Show Context)
Citation Context ...which can characterize them. But there are still many open questions in particular how they relate to hopping in a PEL. A theoretical approach which is especially appealing to us is the shoving model =-=[26, 36, 37]-=- as it connects with our study of deformation. Near Tg, glass forming liquids are considered as “solids which flow” [38] as the particles are most of the time vibrating around a given energy minimum d... |

18 |
Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid," 1
- Berthier, Barrat
- 2002
(Show Context)
Citation Context ...e simulations The many questions posed by the construction of theories of deformation in amorphous solids have motivated a large number of numerical simulations, in particular molecular dynamics (MD) =-=[54, 55, 42, 29, 56, 57, 58, 59, 60, 2, 61, 4, 43, 5, 62, 6, 3, 63, 64, 65]-=-. The key information has come in particular from studies focusing on the low temperature (T ) range: indeed, studies of glassy relaxation have shown that as soon as T is sufficiently well below the g... |

17 |
Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion
- Yamamoto, Onuki
- 1998
(Show Context)
Citation Context ...e simulations The many questions posed by the construction of theories of deformation in amorphous solids have motivated a large number of numerical simulations, in particular molecular dynamics (MD) =-=[54, 55, 42, 29, 56, 57, 58, 59, 60, 2, 61, 4, 43, 5, 62, 6, 3, 63, 64, 65]-=-. The key information has come in particular from studies focusing on the low temperature (T ) range: indeed, studies of glassy relaxation have shown that as soon as T is sufficiently well below the g... |

15 |
Theory of structural glasses and supercooled liquids
- Lubchenko, Wolynes
(Show Context)
Citation Context ...in structure. These issues have spurred tremendous amount of work with the development of free-volume theory [22], entropy theory [23], mode-coupling theory [24], random first-order transition theory =-=[25]-=-, shoving model [26] to understand from a common ground the underlying phenomenology of the glass transition of both hard and soft glasses. We here only discuss a few paradigms which are important for... |

14 |
Amorphous systems in athermal, quasistatic shear,” Phys
- Maloney, Lemaı̂tre
- 2006
(Show Context)
Citation Context ...ehavior and to formulate predictive equations. In recent years many works have thus progressively shown the importance of long range elastic fields [1], stress fluctuations [2, 3], avalanche behavior =-=[2, 4, 5, 6, 3]-=- in the elementary mechanisms relevant to large deformations. In this PhD work we perform numerical simulations in view of understanding specifically how at low temperatures, that is, well below the g... |

14 |
On the free-volume model of the liquid–glass transition
- Turnbull, Cohen
- 1970
(Show Context)
Citation Context ...of the liquid to glass transition is that it is not associated with any significant change in structure. These issues have spurred tremendous amount of work with the development of free-volume theory =-=[22]-=-, entropy theory [23], mode-coupling theory [24], random first-order transition theory [25], shoving model [26] to understand from a common ground the underlying phenomenology of the glass transition ... |

12 | Structural rearrangements that govern flow in colloidal glasses
- Schall, Weitz, et al.
- 2007
(Show Context)
Citation Context ...epulsion caused by adsorbed polymers, viscous forces due to the relative motion between particles and suspending liquid etc. [10]. Modern techniques such as video microscopy [11], confocal microscopy =-=[12, 13]-=- make it now possible to track the motions of particles in a colloidal suspension accurately over time. This type of measurements are of course inaccessible in molecular or atomic glasses (e.g. oxide-... |

12 | Diverging length scale and upper critical dimension in the mode-coupling theory of the glass transition
- Biroli, Bouchaud
(Show Context)
Citation Context ...ly heterogeneous clusters in 1.3 Theories of deformation 7 the system [32]. Huge efforts have been made both experimentally and numerically to understand the origin of these dynamical heterogeneities =-=[33, 34, 35]-=-, and also to define the relevant observable(s), which can characterize them. But there are still many open questions in particular how they relate to hopping in a PEL. A theoretical approach which is... |

12 |
Shearing a glassy material: numerical tests of nonequilibrium mode-coupling approaches and experimental proposals. Phys
- Berthier, Barrat
(Show Context)
Citation Context ...e simulations The many questions posed by the construction of theories of deformation in amorphous solids have motivated a large number of numerical simulations, in particular molecular dynamics (MD) =-=[54, 55, 42, 29, 56, 57, 58, 59, 60, 2, 61, 4, 43, 5, 62, 6, 3, 63, 64, 65]-=-. The key information has come in particular from studies focusing on the low temperature (T ) range: indeed, studies of glassy relaxation have shown that as soon as T is sufficiently well below the g... |

12 |
Continuum limit of amorphous elastic bodies: A finite-size study of lowfrequency harmonic vibrations
- Tangui, Wittmer, et al.
(Show Context)
Citation Context ...his potential differs from the most commonly used [ 1r̃12 − 1r̃6 ] form of the Lennard-Jones potential [67] which presents a minimum at 21/6 and vanishes at 1. A potential similar to ours was used in =-=[70, 43]-=-. The number ratio of large to small particles in our simulations is NL/NS = 1+ √ 5 4 [42, 62, 6]. We show in the following sections that with this number ratio our system remains amorphous irrespecti... |

12 | C.: On the microscopic foundations of elasticity
- Goldhirsch, Goldenberg
- 2002
(Show Context)
Citation Context ... they do not grant direct access to the avalanche size. It is then useful to complement our data set with information regarding the stress and strain fields. For this study we follow Goldhirsch et al =-=[80]-=-, who proposed a systematic way to define coarse-grained fields via the consideration of mass and momentum conservation equations. In the first section we provide a detailed derivation of coarse-grain... |

11 |
Nature of the divergence in low shear viscosity of colloidal hard-sphere dispersions
- Cheng, Zhu, et al.
- 2002
(Show Context)
Citation Context ....56, that traps the particles and brings the system into the colloidal glassy phase, where 1.2 The glass transition 6 a dramatic slow down of the relaxation timescale with volume fraction is observed =-=[20]-=-. This type of transitions can be seen experimentally in suspensions of monodisperse colloidal particles [21]. Dense colloidal suspensions can thus be considered as glasses in a very low temperature r... |

11 |
Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations
- Berthier, Biroli, et al.
- 2007
(Show Context)
Citation Context ...ly heterogeneous clusters in 1.3 Theories of deformation 7 the system [32]. Huge efforts have been made both experimentally and numerically to understand the origin of these dynamical heterogeneities =-=[33, 34, 35]-=-, and also to define the relevant observable(s), which can characterize them. But there are still many open questions in particular how they relate to hopping in a PEL. A theoretical approach which is... |

10 |
Growing length and time scales in glass-forming liquids
- Karmakar, Dasgupta, et al.
(Show Context)
Citation Context ...ly heterogeneous clusters in 1.3 Theories of deformation 7 the system [32]. Huge efforts have been made both experimentally and numerically to understand the origin of these dynamical heterogeneities =-=[33, 34, 35]-=-, and also to define the relevant observable(s), which can characterize them. But there are still many open questions in particular how they relate to hopping in a PEL. A theoretical approach which is... |

10 |
HA study of the static yield stress in a binary Lennard-Jones glass
- Vamik, Bocquet, et al.
- 2004
(Show Context)
Citation Context |

9 |
Subextensive scaling in the athermal, quasistatic limit of amorphous matter in plastic shear
- Maloney, Lemâıtre
- 1600
(Show Context)
Citation Context ...phenomenology of material behavior and to formulate predictive equations. In recent years many works have thus progressively shown the importance of long range elastic fields [1], stress fluctuations =-=[2, 3]-=-, avalanche behavior [2, 4, 5, 6, 3] in the elementary mechanisms relevant to large deformations. In this PhD work we perform numerical simulations in view of understanding specifically how at low tem... |

9 |
Plastic Flow in a Disordered Bubble Raft (an Analog of a Metallic Glass
- Argon, Kuo
- 1979
(Show Context)
Citation Context ...rmations [39], defined as rearrangements (or flips) of small volume elements (zones) consisting of relatively few particles (a few tens of atoms). This idea was inspired by a “bubble-raft experiment” =-=[40]-=-, where soap-bubbles of two different diameters (∼ few mm) with roughly equal numbers were placed randomly on the water surface to form a raft. When sheared in a Couette cell few zones in the raft wer... |

9 |
Universal breakdown of elasticity at the onset of material failure
- Maloney, Lemâıtre
(Show Context)
Citation Context |

9 |
Stability and structure of a supercooled liquid mixture in two dimensions
- Perera, Harrowell
- 1999
(Show Context)
Citation Context ...tegration time step. At this temperature the system equilibrates extremely fast. We then lower the temperature stepwise and ensuring that the system has enough time to equilibrate at each temperature =-=[71, 72]-=-. 3.2 Glassy relaxation 29 3.2.1 Static properties Pair distribution function We denote the local instantaneous particle density at a point ~r and time t as ρ(~r) = N∑ i=1 δ(~r − ~ri) (3.2) where ~ri ... |

9 |
Molecular-level mechanical instabilities and enhanced self-diffusion in flowing liquids
- Malandro, Lacks
- 1998
(Show Context)
Citation Context ...he zone is supposed to present a mechanical instability threshold at γ = γc corresponding to the saddle-node bifurcation. Near γc a single eigenvalue of the Hessian matrix vanishes as λ ∝ (γc − γ)1/2 =-=[81, 29, 61, 4, 64]-=-; the eigenfrequency thus obeys the form: ω ≈ ν(γc − γ)1/4 (7.1) 7.1 Analytical framework 75 while the free energy barrier height (∆E) gradually vanishes as [82] ∆E ≈ B(γc − γ)3/2 (7.2) where ν and B ... |

8 |
Spectroscopy simulation and scattering, and the medium range order problem in glass
- Angell
- 1985
(Show Context)
Citation Context ...id permitting us to bypass the formation of the crystal. Below the freezing point the liquid thus reaches the metastable “supercooled” liquid state (see Fig. 1.1(a)). Good glass formers are materials =-=[14, 15]-=- for which the crystallization can be prevented at reasonably low cooling rates: this is the case of silica which requires cooling rates of the order of 10−2K/s to be compared with ∼ 104K/s needed for... |

8 |
Metastability and crystallization in suspensions of mixtures of hard spheres
- Henderson, Megen
- 1998
(Show Context)
Citation Context ...sition 6 a dramatic slow down of the relaxation timescale with volume fraction is observed [20]. This type of transitions can be seen experimentally in suspensions of monodisperse colloidal particles =-=[21]-=-. Dense colloidal suspensions can thus be considered as glasses in a very low temperature range where an effective temperature scale is set by the Brownian fluctuations to the typical scale of interac... |

8 |
Plastic response of a 2d lennard-jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain rate,” Eur
- Tanguy, Leonforte, et al.
- 2006
(Show Context)
Citation Context ...e volume ou des zones comprenant de quelques dizaines d’atomes. Transformations de cisaillement (flips) ont été observés dans de nombreux modèles informatiques différents des matériaux amorphes =-=[41, 42, 4, 43, 3]-=- et dans une expérience sur une suspension collöıdale [13]. À partir d’études de simulation numérique dans le athermique (T = 0) des conditions [2, 5, 62, 6, 3], nous savons que d’autres zones fl... |

8 |
Shear localization in a model glass
- Varnik, Bocquet, et al.
(Show Context)
Citation Context |

7 |
Conventional optical microscopy of colloidal suspensions
- Elliot, Poon
(Show Context)
Citation Context ...harged particles, steric repulsion caused by adsorbed polymers, viscous forces due to the relative motion between particles and suspending liquid etc. [10]. Modern techniques such as video microscopy =-=[11]-=-, confocal microscopy [12, 13] make it now possible to track the motions of particles in a colloidal suspension accurately over time. This type of measurements are of course inaccessible in molecular ... |

7 |
Extremal model for amorphous media plasticity
- Baret, Vandembroucq, et al.
(Show Context)
Citation Context ...ght enhance the number of flip events and leads to macroscopic strain localization [1]. This idea is currently receiving considerable attention and generalized in many so called elasto-plastic models =-=[52, 50, 53]-=-. The notion that zone rearrangements may interact via long range elastic fields is of course entirely absent from the previously mentioned mean field theories. This questions their relevance to accou... |

7 |
Evolution of displacements and strains in sheared amorphous solids
- Maloney, Robbins
(Show Context)
Citation Context ...strain rate simulations: T ≈ 0 conditions are enforced by introducing interparticle dissipative forces which allow the system to release the energy introduced by homogeneous shearing at a constant γ̇ =-=[66, 6]-=-. One major difficulty arising in finite γ̇ simulations is that avalanches have a finite duration and hence, they no longer show up as discontinuous 1.4 Studies of plastic deformation via discrete sim... |

7 |
Relaxation dynamics and their spatial distribution in a two-dimensional glass-forming mixture
- Perera, Harrowell
- 1999
(Show Context)
Citation Context ...tegration time step. At this temperature the system equilibrates extremely fast. We then lower the temperature stepwise and ensuring that the system has enough time to equilibrate at each temperature =-=[71, 72]-=-. 3.2 Glassy relaxation 29 3.2.1 Static properties Pair distribution function We denote the local instantaneous particle density at a point ~r and time t as ρ(~r) = N∑ i=1 δ(~r − ~ri) (3.2) where ~ri ... |

6 |
Avalanche size scaling in sheared three-dimensional amorphous solid
- Bailey, Schiøtz, et al.
(Show Context)
Citation Context ... shear transformations which can be defined as rearrangements or flips of small volume elements or zones consisting of a few tens of atoms. Moreover, at athermal conditions a few discrete simulations =-=[2, 5, 62, 6, 3]-=- showed that a flip modifies the surrounding stress field via the Eshelby mechanism and thus may trigger secondary events. This results to an avalanche process, that is, a series of flips is correlate... |

6 |
Three-dimensional imaging of submicrometer colloidal particles in concentrated suspensions using confocal scanning laser microscopy
- Blaaderen, Imhof, et al.
- 1992
(Show Context)
Citation Context ...epulsion caused by adsorbed polymers, viscous forces due to the relative motion between particles and suspending liquid etc. [10]. Modern techniques such as video microscopy [11], confocal microscopy =-=[12, 13]-=- make it now possible to track the motions of particles in a colloidal suspension accurately over time. This type of measurements are of course inaccessible in molecular or atomic glasses (e.g. oxide-... |

6 |
Local elastic expansion model for viscous-flow activation energies of glass-forming molecular liquids
- Dyre, Olsen, et al.
- 1996
(Show Context)
Citation Context ...issues have spurred tremendous amount of work with the development of free-volume theory [22], entropy theory [23], mode-coupling theory [24], random first-order transition theory [25], shoving model =-=[26]-=- to understand from a common ground the underlying phenomenology of the glass transition of both hard and soft glasses. We here only discuss a few paradigms which are important for our deformation stu... |

5 |
Relationships of shear-induced changes in the potential energy landscape to the mechanical properties of ductile glasses
- Malandro, Lacks
- 1999
(Show Context)
Citation Context ...pe (PEL), which can be envisaged as a mountain range seen upside down: broadly distributed, mountain peaks correspond to the local energy minima, while mountain passes correspond to the saddle points =-=[28, 29, 30]-=-. Either in glassy regimes or in supercooled liquid states, systems most of the time vibrate around typical local minima [27] called “inherent states” [28] and rarely undergo local relaxation events v... |

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Volume dependence of potential energy landscapes in glasses
- Malandro, Lacks
- 1997
(Show Context)
Citation Context ...system hops from one minimum to the next [30]. The differences between supercooled liquids and glasses seem to be that in the former high vibrations allow more frequent relaxation events than glasses =-=[31]-=-. The relaxation slowdown is associated with the emergence of dynamical heterogeneities near the glass transition: within a certain large time window of the order of τα few particles manage to cover a... |

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Source of non-arrhenius average relaxation time in glass-forming liquids
- Dyre
- 1998
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Citation Context ...which can characterize them. But there are still many open questions in particular how they relate to hopping in a PEL. A theoretical approach which is especially appealing to us is the shoving model =-=[26, 36, 37]-=- as it connects with our study of deformation. Near Tg, glass forming liquids are considered as “solids which flow” [38] as the particles are most of the time vibrating around a given energy minimum d... |

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A stochastic-model for continuum elastoplastic behavior .3. plasticity in ordered versus disordered solids
- Bulatov, Argon
- 1994
(Show Context)
Citation Context ...uch needed to identify a phenomenology of material behavior and to formulate predictive equations. In recent years many works have thus progressively shown the importance of long range elastic fields =-=[1]-=-, stress fluctuations [2, 3], avalanche behavior [2, 4, 5, 6, 3] in the elementary mechanisms relevant to large deformations. In this PhD work we perform numerical simulations in view of understanding... |

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Hopping in a supercooled Lennard-Jones liquid: Metabasins, waiting time distribution, and diffusion
- Doliwa, Heuer
(Show Context)
Citation Context ...pe (PEL), which can be envisaged as a mountain range seen upside down: broadly distributed, mountain peaks correspond to the local energy minima, while mountain passes correspond to the saddle points =-=[28, 29, 30]-=-. Either in glassy regimes or in supercooled liquid states, systems most of the time vibrate around typical local minima [27] called “inherent states” [28] and rarely undergo local relaxation events v... |

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Nonlinear rheology of a highly supercooled liquid
- Yamamoto, Onuki
- 1997
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Yield stress discontinuity in a simple glass
- Vamik, Henrich
- 2006
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4 | Statistical physics of elastoplastic steady states in amorphous solids: Finite temperatures and strain rates - Karmakar, Lerner, et al. |

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Quantitative test of the modecoupling theory of the ideal glass transition for a binary Lennard-Jones system
- Nauroth, Kob
- 1997
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Citation Context ...on in a scattering experiment and can be ignored [73]. On both panels we find that the positions of the first maxima have very weak dependence on T as found earlier in the case of other binary models =-=[75, 71]-=-. The first maxima of SSS and SLL for all these temperatures occur at around k ≈ 12.46 and k ≈ 8.4 respectively. 3.2 Glassy relaxation 32 3.2.2 Dynamic properties Incoherent scattering functions We ne... |

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Anisotropic cooperative structural rearrangements in sheared supercooled liquids
- Furukawa, Kim, et al.
- 2009
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Citation Context ...4 0.00037 0.04 0.5 0.00194 0.2 Table 4.3: The values of γ̇∗σ and τ−1α for temperatures in the supercooled liquid state. We find that γ̇∗σ(T ) is much smaller than τ−1α (T ) as found by Furukawa et al =-=[77]-=-. We would expect that the crossover takes place at a time when a few percent strain matches the relaxation time, that is, γ̇∗σ(T ) would be a couple of orders of magnitude smaller than τ−1α (T ). Fig... |

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and Itamar Procaccia. Locality and nonlocality in elastoplastic responses of amorphous solids
- Lerner
(Show Context)
Citation Context ...e volume ou des zones comprenant de quelques dizaines d’atomes. Transformations de cisaillement (flips) ont été observés dans de nombreux modèles informatiques différents des matériaux amorphes =-=[41, 42, 4, 43, 3]-=- et dans une expérience sur une suspension collöıdale [13]. À partir d’études de simulation numérique dans le athermique (T = 0) des conditions [2, 5, 62, 6, 3], nous savons que d’autres zones fl... |

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Engineering Physics
- Marikani
- 2009
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Citation Context ...rystalline alloys metallic glasses have: (i) higher yield strengths and hardness, and (ii) smaller Young’s modulus (∼ 30 to 200 GPa [8]) and shear modulus (∼ 10 to 60 GPa [8], reduced by roughly 15%) =-=[9]-=-. Their high mechanical strengths, large elastic limits, soft magnetic properties (iron-based and cobalt-based metallic glasses), high corrosion resistance motivate a large interest in view of potenti... |

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Plasticdeformation in glassy-polymers by atomistic and mesoscopic simulations
- Argon, Bulatov, et al.
- 1995
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Citation Context ...bble raft should also be relevant to deformation in drastically different systems such as metallic glasses. More recently the validity of this idea has been confirmed by several numerical simulations =-=[41, 42, 4, 43, 3]-=- and one experiment on a colloidal suspension using confocal microscopy [13]. 1.3.1 Mean field models of plasticity Mean field theories assume shear transformations to occur independently. This assump... |

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François Lequeux, and Lydéric Bocquet. Elastic consequences of a single plastic event : A step towards the microscopic modeling of the flow of yield stress fluids
- Picard, Ajdari
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Citation Context ... (left) The Eshelby model for an ellipsoidal inclusion. (right) The perturbation due to a localized plastic event corresponds to the perturbation due to a set of two dipoles of forces with F = 2aµ∆0 =-=[50]-=-. showed that uEi (~r) is linear inside the inclusion and therefore strain and stress are constants. He was also able to calculate the displacement field at a distant point from the inclusion by takin... |

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Blanter and Mikhail Solomonovich Blanter. Internal friction in metallic materials: a handbook
- Mikhail
- 2007
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Citation Context ... field Eshelby solution by considering the elastic response in an infinite, isotropic, homogeneous and elastic medium to a four point forces with zero mean force and zero torque – an “elastic dipole” =-=[51]-=- as depicted in Fig. 1.2(right). The resulting stress field obtained by the derivation of the elastic displacement is of the form (see Appendix D for the derivation): σExy(r, θ) = 2µa2∆0 pi cos(4θ) r... |

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Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity
- Talamali, Petäjä, et al.
- 2011
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Citation Context ...ght enhance the number of flip events and leads to macroscopic strain localization [1]. This idea is currently receiving considerable attention and generalized in many so called elasto-plastic models =-=[52, 50, 53]-=-. The notion that zone rearrangements may interact via long range elastic fields is of course entirely absent from the previously mentioned mean field theories. This questions their relevance to accou... |

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Plastic response of a twodimensional amorphous solid to quasistatic shear:transverse particle diffusion and phenomenology of dissipative events
- Lemâıtre, Caroli
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Anael Lemâıtre, Edan Lerner, and Itamar Procaccia. Predicting plastic flow events in athermal shear-strained amorphous solids
- Karmakar
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Itamar Procaccia. Size of plastic events in strained amorphous solids at finite temperatures
- Hentschel, Karmakar, et al.
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Anaël Lemâıtre. Universal additive effect of temperature on the rheology of amorphous solids
- Chattoraj, Caroli
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Citation Context ...ficantly with increasing temperature. To explain the decrease of average shear-stress with increasing temperature in the domain well below of the glass transition we have proposed a theoretical model =-=[79]-=-. This is discussed in detail in Chapter 7. 4.2 Particle diffusion 43 4.2 Particle diffusion In section 1.4.2 we have already raised the issue that the diffusion coefficient is sensitive to the possib... |

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Itamar Procaccia. Do athermal amorphous solids exist? Phys
- Hentschel, Karmakar, et al.
(Show Context)
Citation Context ...ind the linear behavior of the stress for T . 0.2. We recall that, in the thermodynamic (L → ∞) limit, a continuous density of low lying modes builds up, as evidenced via anomalous elastic properties =-=[85]-=-. The predicted T 2/3 behavior of the flow stress, however, firmly supports that saddle node bifurcations (i.e. the vanishing of single eigenvalues) control the energy barrier heights. These observati... |

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Anaël Lemâıtre. Robustness of avalanche dynamics in sheared amorphous solids as probed by transverse diffusion
- Chattoraj, Caroli
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Citation Context ... to T ∼ 0.75Tg ; (iii) a lack of collapse in the γ̇ < γ̇c(L) range for the highest temperatures of our study, should arise from activation processes which start to intermingle with avalanche dynamics =-=[86]-=-. To explain the significant decrease of stress, yet, the existence of avalanche behavior at finite temperatures we propose that thermal fluctuations trigger flips “prematurely” by activation over the... |

2 | Elastic models for the non-arrhenius viscosity of glass-forming liquids
- Dyre, Christensen, et al.
(Show Context)
Citation Context ...tical approach which is especially appealing to us is the shoving model [26, 36, 37] as it connects with our study of deformation. Near Tg, glass forming liquids are considered as “solids which flow” =-=[38]-=- as the particles are most of the time vibrating around a given energy minimum due to extremely large viscosity. Relaxation proceeds via “rare and localized” rearrangements of particles which are very... |

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Energy barrier scalings in driven systems
- Maloney, Lacks
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Citation Context ...shes as λ ∝ (γc − γ)1/2 [81, 29, 61, 4, 64]; the eigenfrequency thus obeys the form: ω ≈ ν(γc − γ)1/4 (7.1) 7.1 Analytical framework 75 while the free energy barrier height (∆E) gradually vanishes as =-=[82]-=- ∆E ≈ B(γc − γ)3/2 (7.2) where ν and B are the proportionality constant. As a zone is experiencing the influence of continuous shear driving and thermal fluctuations it also receives mechanical noise ... |