We study a recently introduced model of one-component glass-forming liquids whose constituents interact with anisotropic potential. This system is interesting per-se and as a model of liquids like glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.The study of associated liquids like glycerol as glass formers has a long and rich history [1], but until now the role of the anisotropic hydrogen bonds, while clearly important in frustrating crystallization, has not been made explicit. Recently a model of one component liquids with anisotropic interaction potential was introduced [2], together with numerical simulations in two-dimensions that demonstrated clearly the importance of the anisotropic interaction in frustrating crystallization and allowing the formation of a glassy state of matter. This model is important in stressing the fact that even simple onecomponent liquids may not crystallize if the local symmetry of the interaction potential does not perfectly match the symmetry of the equilibrium crystal. It is worthwhile therefore to analyze further this example of glass formation and put it in the general context of the glass transition. In this Letter we present a theory of this model, constructing its statistical mechanics and providing an understanding of the phenomenology of its glass transition, including an identification of a diverging length and explaining the diverging time scales. Our analysis allows putting this interesting example of glass formation on the same footing as other classical glass formers such as binary mixtures with central potentials [3,4], stressing the generality of the approach [5,6] and of the glass transition phenomenon at the same time.Particles of mass m in this model interact viawhere r ij is the distance between the two particles i and j. The first term on the RHS of (1) is the standard isotropic Lennard-Jones potentialwhereas the anisotropic part of the potential is given byh(x) = (1 − x 2 ) 3 for |x| < 1 ; h(x) = 0 for |x| ≥ 1 .Here θ i (θ j ) is the included angle between the relative vector r ij ≡ r i − r j and a unit vector u i (u j ) (referred to below as 'spin') which represents the orientation of the axis of particle i (j). The function h((θ − θ 0 )/θ c ) (with θ 0 = 126 o and θ c = 53.1 o ) has a maximum at θ = θ 0 , and thus θ 0 is a favored value of θ i . Thus the anisotropic term in the potential favors structures of five-fold symmetry. The parameter ∆ controls the tendency of fivefold symmetry, and therefore of the frustration against crystallization. The units of mass, length, time and temperature are m, σ, τ = σ m/ǫ and ǫ/k B , respectively, with k B being Boltzmann's constant.Accordin...

We address the additive equivalence discovered by Virk and co-workers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.

The understanding of dynamic failure in amorphous materials via the propagation of free boundaries like cracks and voids must go beyond elasticity theory, since plasticity intervenes in a crucial and poorly understood manner near the moving free boundary. In this Letter we focus on failure via a cavitation instability in a radially-symmetric stressed material, set up the free boundary dynamics taking both elasticity and visco-plasticity into account, using the recently proposed athermal Shear Transformation Zone theory. We demonstrate the existence (in amorphous systems) of fast cavitation modes accompanied by extensive plastic deformations and discuss the revealed physics.The principal difficulty in describing the mechanical failure of materials using elasticity theory is that this approach does not provide a law of motion for the free boundary that naturally occurs when a crack or a void is propagating. Recently, phenomenological phase-field models [1] were proposed in order to overcome this fundamental problem. In reality the high stress concentration near the moving boundary must be associated with some form of plastic deformations that are rather poorly understood in the context of amorphous materials; the consequences of these plastic deformations are usually referred to as the "process zone" whose properties one usually does not dare to probe too closely. The aim of this Letter is to do just the opposite [2]. We set up the simplest (from the point of view of symmetries) example of free boundary dynamics, i.e. that of a circular cavity responding to radially symmetric stresses at infinity (or equivalently high pressure inside the cavity). This problem has a rather long history [3,4]; the main contribution of our study is the elucidation of the role of amorphous plasticity and the detailed interaction between elasticity and plasticity, throughout the system and in particular near the free boundary where plastic dynamics is explicitly described in terms of the athermal Shear Transformation Zone theory (STZ) [5,6]. This theory automatically includes hardening and rate-dependent effects in addition to a proper Eulerian description of the equations of motion which allows the discussion of inertial effects and of large deformations including accelerating and catastrophic cavitation instability.Consider then an infinite 2D medium with a circular hole around the origin of radius R(t), loaded by a radially symmetric stress σ ∞ at infinity. The symmetry dictates a radial velocity field v that is independent of the azimuthal angle θ, i.e. v r (r, t) = v(r, t) and v θ (r, t) = 0. This velocity field implies the components of the total rate of deformation tensorIn this Letter we restrict the elastic part of the deformation to be small, allowing us to decompose the total rate of deformation tensor into its elastic and plastic parts.Denoting the material time derivative as D t = ∂ t +v∂ r ,where the plastic part D pl ij will be discussed below. The (linear) elastic part ǫ el ij in the present symmetry is determined by th...

Reynolds number dependence of drag reduction by rodlike polymersAmarouchene, Y.; Bonn, D.; Kellay, H.; Lo, T.-S.; L'vov, V.S.; Procaccia, I. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We present experimental and theoretical results addressing the Reynolds number ͑Re͒ dependence of drag reduction by sufficiently large concentrations of rodlike polymers in turbulent wall-bounded flows. It is shown that when Re is small the drag is enhanced. On the other hand, when Re increases, the drag is reduced and eventually, the maximal drag reduction asymptote is attained. The theory is shown to be in agreement with experiments, explaining the universal and rationalizing some of the the nonuniversal aspects of drag reduction by rodlike polymers. Download date: 12 May 2018 Reynolds number dependence of drag reduction by rodlike polymers

We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they are subjected to remote, time-dependent tractions. The theory is illustrated here for the case of a circular hole in an infinite two-dimensional plate, a highly symmetric situation that allows us to solve much of the problem analytically. In spite of its special symmetry, this example contains many general features of systems in which stress is concentrated near free boundaries and deforms them irreversibly. We depart from conventional treatments of such problems in two ways. First, the STZ analysis allows us to keep track of spatially heterogeneous, internal state variables such as the effective disorder temperature, which determines plastic response to subsequent loading. Second, we subject the system to stress pulses of finite duration, and therefore are able to observe elasto-plastic response during both loading and unloading. We compute the final deformations and residual stresses produced by these stress pulses. Looking toward more general applications of these results, we examine the possibility of constructing a boundary-layer theory that might be useful in less symmetric situations.