Physics Commons^™

Depinning And Plasticity Of Driven Disordered Lattices, M. Cristina Marchetti

Physics - All Scholarship

We review in these notes the dynamics of extended condensed matter systesm, such as vortex lattices in type-II superconductors and charge density waves in anisotropic metals, driven over quenched disorder. We focus in particular on the case of strong disorder, where topological defects are generated in the driven lattice. In this case the repsonse is plastic and the depinning transition may become discontinuous and hysteretic.

Mean Field Theory Of Collective Transport With Phase Slips, Karl Saunders, J. M. Schwarz, M. Cristina Marchetti, Alan Middleton

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The driven transport of plastic systems in various disordered backgrounds is studied within mean field theory. Plasticity is modeled using non-convex interparticle potentials that allow for phase slips. This theory most naturally describes sliding charge density waves; other applications include flow of colloidal particles or driven magnetic flux vortices in disordered backgrounds. The phase diagrams exhibit generic phases and phase boundaries, though the shapes of the phase boundaries depend on the shape of the disorder potential. The phases are distinguished by their velocity and coherence: the moving phase generically has finite coherence, while pinned states can be coherent or incoherent. …

Driven Depinning Of Strongly Disordered Media And Anisotropic Mean-Field Limits, M. Cristina Marchetti, Alan Middleton, Karl Saunders, J. M. Schwarz

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Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the driving force and that slip along at least one of the directions transverse to the motion. A realization of such a model is a collection of elastic channels with transverse viscous couplings. In the infinite range limit this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special …

Models Of Plastic Depinning Of Driven Disordered Systems, M. Cristina Marchetti

Physics - All Scholarship

Two classes of models of driven disordered systems that exhibit history-dependent dynamics are discussed. The first class incorporates local inertia in the dynamics via nonmonotonic stress transfer between adjacent degrees of freedom. The second class allows for proliferation of topological defects due to the interplay of strong disorder and drive. In mean field theory both models exhibit a tricritical point as a function of disorder strength. At weak disorder depinning is continuous and the sliding state is unique. At strong disorder depinning is discontinuous and hysteretic.

Nematic And Polar Order In Active Filament Solutions, A. Ahmadi, Tanniemola B. Liverpool, M. Cristina Marchetti

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Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in determining the organization of the filaments in homogeneous isotropic, polarized and nematic states, while motor-induced bundling yields spatially inhomogeneous structures.

Hydrodynamics Of Polar Liquid Crystals, William Kung, M. Cristina Marchetti, Karl Saunders

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Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local

C1v-symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D1h) in that it contains terms violating the n −n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poissonbracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence …

Geometric Precipices In String Cosmology, Scott Watson, Nemanja Kaloper

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We consider the effects of graviton multiplet fields on transitions between string gas phases. Focusing on the dilaton field, we show that it may obstruct transitions between different thermodynamic phases of the string gas, because the sign of its dimensionally reduced, T-duality invariant, part is conserved when the energy density of the universe is positive. Thus, many interesting solutions for which this sign is positive end up in a future curvature singularity. Because of this, some of the thermodynamic phases of the usual gravitating string gases behave like superselection sectors. For example, a past-regular Hagedorn phase and an expanding FRW …

Depinning In A Two-Layer Model Of Plastic Flow, Pierre Le Doussal, M. Cristina Marchetti, Kay Jorg Wiese

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We study a model of two layers, each consisting of a d-dimensional elastic object driven over a random substrate, and mutually interacting through a viscous coupling. For this model, the mean-field theory (i.e. a fully connected model) predicts a transition from elastic depinning to hysteretic plastic depinning as disorder or viscous coupling is increased. A functional RG analysis shows that any small inter-layer viscous coupling destablizes the standard (decoupled) elastic depinning FRG fixed point for d4 most aspects of the mean-field theory are recovered. A one-loop study at non-zero velocity indicates, for d

Glassy Motion Of Elastic Manifolds, Valerii M. Vinokur, M. Cristina Marchetti, Lee-Wen Chen

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We discuss the low-temperature dynamics of an elastic manifold driven through a random medium. For driving forces well below the

T = 0 depinning force, the medium advances via thermally activated hops over the energy barriers separating favorable metastable states. We show that the distribution of waiting times for these hopping processes scales as a power-law. This power-law distribution naturally yields a nonlinear glassy response for the driven medium, v exp(−const x F−μ).

Hydrodynamics Of Self-Propelled Hard Rods, Aparna Baskaran, M. Cristina Marchetti

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Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via excluded volume and their dynamics is overdamped by the interaction with the substrate. Starting from a microscopic model with non-thermal noise sources, a continuum description of the system is derived. The hydrodynamic equations are then used to characterize the possible steady states of the systems and their stability as a function of the particles packing fraction and the speed of self propulsion.

Dynamical Transition In Sliding Charge-Density Waves With Quenched Disorder, Lee-Wen Chen, Leon Balents, Matthew P. A. Fisher, M. Cristina Marchetti

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We have studied numerically the dynamics of sliding charge-density waves (CDWs) in the presence of impurities in d=1,2. The model considered exhibits a first order dynamical transition at a critical driving force

Fc between “rough” (disorder dominated) (F < Fc) and “flat” (F > Fc) sliding phases where disorder is washed out by the external drive. The effective model for the sliding CDWs in the presence of impurities can be mapped onto that of a magnetic flux line pinned by columnar defects and tilted by an applied field. The dynamical transition of sliding CDWs corresponds to the transverse Meissner effect of the tilted flux line.

Patterned Geometries And Hydrodynamics At The Vortex Bose Glass Transition, M. Cristina Marchetti, David R. Nelson

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Patterned irradiation of cuprate superconductors with columnar defects allows a new generation of experiments which can probe the properties of vortex liquids by confining them to controlled geometries. Here we show that an analysis of such experiments that combines an inhomogeneous Bose glass scaling theory with the hydrodynamic description of viscous flow of vortex liquids can be used to infer the critical behavior near the Bose glass transition. The shear viscosity is predicted to diverge as

|T − TBG|−z at the Bose glass transition, with z ≃

6 the dynamical critical exponent.

Viscoelasticity From A Microscopic Model Of Dislocation Dynamics, M. Cristina Marchetti, Karl Saunders

Physics - All Scholarship

It is shown that the dynamics of a two-dimensional crystal with a finite concentration of dislocations, as well as vacancy and interstitial defects, is governed by the hydrodynamic equations of a viscoelastic medium. At the longest length scales the viscoelasticity is described by the simplest Maxwell model, whose shear and compressional relaxation times are obtained in terms of microscopic quantities, including the density of free dislocations. At short length scales, bond orientational order effects become important and lead to wavevector dependent corrections to the relaxation times.

Nonequilibrium Steady States Of Driven Periodic Media, Leon Balents, M. Cristina Marchetti, Leo Radzihovsky

Physics - All Scholarship

We study a periodic medium driven over a random or periodic substrate, characterizing the nonequilibrium phases which occur by dynamic order parameters and their correlations. Starting with a microscopic lattice Hamiltonian, we perform a careful coarse-graining procedure to derive continuum hydrodynamic equations of motion in the laboratory frame. This procedure induces nonequilibrium effects (e.g. convective terms, KPZ nonlinearities, and non-conservative forces) which cannot be derived by a naive Galileian boost. Rather than attempting a general analysis of these equations of motion, we argue that in the random case instabilities will always destroy the LRO of the lattice. We suggest that …

Vortex Dynamics And Defects In Simulated Flux Flow, Michael Chance Faleski, M. Cristina Marchetti, Alan Middleton

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We present the results of molecular dynamic simulations of a two-dimensional vortex array driven by a uniform current through random pinning centers at zero temperature. We identify two types of flow of the driven array near the depinning threshold. For weak disorder the flux array contains few dislocation and moves via correlated displacements of patches of vortices in a {\it crinkle} motion. As the disorder strength increases, we observe a crossover to a spatially inhomogeneous regime of {\it plastic} flow, with a very defective vortex array and a channel-like structure of the flowing regions. The two regimes are characterized by …

Interstitials, Vacancies And Dislocations In Flux-Line Lattices: A Theory Of Vortex Crystals, Supersolids And Liquids, M. Cristina Marchetti, Leo Radzihovsky

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We study a three dimensional Abrikosov vortex lattice in the presence of an equilibrium concentration of vacancy, interstitial and dislocation loops. Vacancies and interstitials renormalize the long-wavelength bulk and tilt elastic moduli. Dislocation loops lead to the vanishing of the long-wavelength shear modulus. The coupling to vacancies and interstitials - which are always present in the liquid state - allows dislocations to relax stresses by climbing out of their glide plane. Surprisingly, this mechanism does not yield any further independent renormalization of the tilt and compressional moduli at long wavelengths. The long wavelength properties of the resulting state are formally …

Vortex Physics In Confined Geometries, M. Cristina Marchetti, David R. Nelson

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Patterned irradiation of cuprate superconductors with columnar defects allows a new generation of experiments which can probe the properties of vortex liquids by forcing them to flow in confined geometries. Such experiments can be used to distinguish experimentally between continuous disorder-driven glass transitions of vortex matter, such as the vortex glass or the Bose glass transition, and nonequilibrium polymer-like glass transitions driven by interaction and entanglement. For continuous glass transitions, an analysis of such experiments that combines an inhomogeneous scaling theory with the hydrodynamic description of viscous flow of vortex liquids can be used to infer the critical behavior. After …

A Hydrodynamic Approach To The Bose-Glass Transition, Panayotis Benetatos, M. Cristina Marchetti

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Nonlinear hydrodynamics is used to evaluate disorder-induced corrections to the vortex liquid tilt modulus for finite screening length and arbitrary disorder geometry. Explicit results for aligned columnar defects yield a criterion for locating the Bose glass transition line at all fields.

Hydrodynamics Of Liquids Of Arbitrarily Curved Flux-Lines And Vortex Loops, Panayotis Benetatos, M. Cristina Marchetti

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We derive a hydrodynamic model for a liquid of arbitrarily curved flux-lines and vortex loops using the mapping of the vortex liquid onto a liquid of relativistic charged quantum bosons in 2+1 dimensions recently suggested by Tesanovic and by Sudbo and collaborators. The loops in the flux-line system correspond to particle-antiparticle fluctuations in the bosons. We explicitly incorporate the externally applied magnetic field which in the boson model corresponds to a chemical potential associated with the conserved charge density of the bosons. We propose this model as a convenient and physically appealing starting point for studying the properties of the …

Organization And Instabilities Of Entangled Active Polar Filaments, Tanniemola B. Liverpool, M. Cristina Marchetti

Physics - All Scholarship

We study the dynamics of an entangled, isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and entanglement. At low filament density the system develops a density instability, while at high filament density entanglement effects drive the instability of orientational fluctuations.

Toroidal Crystals, Mark Bowick, Luca Giomi

Physics - All Scholarship

Crystalline assemblages of identical sub-units packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled monolayers and carbon nanomaterials. In this Letter we analyze the structural properties of toroidal crystals and we provide a unified description based on the elastic theory of defects in curved geometries. We find ground states characterized by the presence of 5-fold disclinations on the exterior of the torus and 7-fold disclinations in the interior. The number of excess disclinations is controlled primarily …

Note On A Sigma Model Connection With Instanton Dynamics, Joseph Schechter, Amir H. Fariborz, Renata Jora

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It is well known that the instanton approach to QCD generates an effective term which looks like a three flavor determinant of quark bilinears. This has the right behavior to explain the unusual mass and mixing of the $\eta(958)$ meson, as is often simply illustrated with the aid of a linear SU(3) sigma model. It is less well known that the instanton analysis generates another term which has the same transformation property but does not have a simple interpretation in terms of this usual linear sigma model. Here we point out that this term has an interpretation in a generalized …

Rheology Of Active Filament Solutions, Tanniemola B. Liverpool, M. Cristina Marchetti

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We study the viscoelasticity of an active solution of polar biofilaments and motor proteins. Using a molecular model, we derive the constitutive equations for the stress tensor in the isotropic phase and in phases with liquid crystalline order. The stress relaxation in the various phases is discussed. Contractile activity is responsible for a spectacular difference in the viscoelastic properties on opposite sides of the order-disorder transition.

Energy-Dependent Ps-He Momentum-Transfer Cross Section At Low Energies, J. J. Engbrecht, M. J. Erickson, C. P. Johnson, A. J. Kolan, A. E. Legard, S. P. Lund, M. J. Nyflot, J. D. Paulsen

Physics - All Scholarship

Positronium (Ps)-He scattering presents one of the few opportunities for both theory and experiment to tackle the fundamental interactions of Ps with ordinary matter. Below the dissociation energy of 6.8 eV, experimental and theoretical work has struggled to find agreement on the strength of this interaction as measured by the momentum-transfer cross section (Ïm). Here, we present work utilizing the Doppler broadening technique with an age-momentum correlation apparatus. This work demonstrates a strong energy dependence for this cross section at energies below 1 eV and is consistent with previous experimental results.

Isotropic-Cholesteric Transition Of A Weakly Chiral Elastomer Cylinder, Xiangjun Xing, Aparna Baskaran

Physics - All Scholarship

When a chiral isotropic elastomer is brought to low temperature cholesteric phase, the nematic degree of freedom tends to order and form a helix. Due to the nemato-elastic coupling, this also leads to elastic deformation of the polymer network that is locally coaxial with the nematic order. However, the helical structure of nematic order is incompatible with the energetically preferred elastic deformation. The system is therefore frustrated and appropriate compromise has to be achieved between the nematic ordering and the elastic deformation. For a strongly chiral elastomer whose pitch is much smaller than the system size, this problem has been …

Exact Lattice Supersymmetry: The Two-Dimensional N = 2 Wess-Zumino Model, Simon Catterall, Sergey Karamov

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We study the two-dimensional Wess-Zumino model with extended N = 2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving exactly a single supersymmetric invariance at finite lattice spacing a. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to O(ga2) where g is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the …

Picovoltmeter For Probing Vortex Dynamics In A Single Weak-Pinning Corbino Channel, T. W. Heitmann, Kang Yu, C. Song, M P. Defeo, B.L.T. Plourde

Physics - All Scholarship

We have developed a picovoltmeter using a Nb dc Superconducting QUantum Interference Device (SQUID) for measuring the flux-flow voltage from a small number of vortices moving through a submicron weak-pinning superconducting channel. We have applied this picovoltmeter to measure the vortex response in a single channel arranged in a circle on a Corbino disk geometry. The circular channel allows the vortices to follow closed orbits without encountering any sample edges, thus eliminating the influence of entry barriers.