arXiv subjects

Annette Zippelius

Publications and source records attributed to Annette Zippelius.

At least 55 records · Page 3Linked to original sources

arXiv2012

Single-Particle Dynamics in Dense Granular Fluids under Driving

We present a mode-coupling theory for the dynamics of a tagged particle in a driven granular fluid close to the glass transition. The mean-squared displacement is shown to exhibit a plateau indicating structural arrest. In contrast to elastic hard-sphere fluids, which are solely controlled by volume fraction, the localisation length as well as the critical dynamics depend on the degree of dissipation, parametrized by the coefficient of normal restitution epsilon. Hence the resulting glassy structure as well as the critical dynamics are nonuniversal with respect to epsilon.

cond-mat.stat-mech↗

arXiv2011

Three-phase coexistence with sequence partitioning in symmetric random block copolymers

We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation λ. Upon increasing the incompatibility χ (by decreasing temperature) in the disordered state, the known ordered phases form: for λ > λ_c, two coexisting macroscopic A- and B-rich phases, for λ < λ_c, a microstructured (lamellar) phase with wave number k(λ). In addition, we find a fourth region in the λ-χ plane where these three phases coexist, with different, non-Markovian sequence distributions (fractionation). Fractionation is revealed by our analytically derived multiphase free energy, which explicitly accounts for the exchange of individual sequences between the coexisting phases. The three-phase region is reached, either, from the macroscopic phases, via a third lamellar phase that is rich in alternating sequences, or, starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases. These incipient phases emerge with zero volume fraction. The four regions of the phase diagram meet in a multicritical point (λ_c, χ_c), at which A-B segregation vanishes. The analytical method, which for the lamellar phase assumes weak segregation, thus proves reliable particularly in the vicinity of (λ_c, χ_c). For random triblock copolymers, Q=3, we find the character of this point and the critical exponents to change substantially with the number M of monomers per block. The results for Q=3 in the continuous-chain limit M -> \infty are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.

cond-mat.soft↗

arXiv2011

Slow dynamics and precursors of the glass transition in granular fluids

We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified, such as an increase of relaxation times over several orders of magnitude. As the inelasticity is increased, the glass transition is shifted to higher densities and the precursors of the transition become less and less pronounced -- in agreement with a recent mode-coupling theory. We analyze the long-time tails of the velocity autocorrelation and discuss its consequences for the nonexistence of the diffusion constant in two dimensions.

cond-mat.stat-mech↗

arXiv2011

Long-time tails and cage effect in driven granular fluids

We study the velocity autocorrelation function (VACF) of a driven granular fluid in the stationary state in 3 dimensions. As the critical volume fraction of the glass transition in the corresponding elastic system is approached, we observe pronounced cage effects in the VACF as well as a strong decrease of the diffusion constant. At moderate densities the VACF is shown to decay algebraically in time (t^{-3/2}) like in a molecular fluid, as long as the driving conserves momentum locally.

cond-mat.stat-mech↗

arXiv2011

Orientational order and glassy states in networks of semiflexible polymers

Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration and the stiffness of the polymers. A crossing angle $θ\sim 2π/M$ leads to long range $M$-fold orientational order, e.g., "hexatic" or "tetratic" for $θ=60^{\circ}$ or $90^{\circ}$, respectively. The transition is discontinuous and the critical cross-link density depends on the bending stiffness of the polymers and the cross-link geometry: the higher the stiffness and the lower $M$, the lower the critical number of cross-links. In between the sol and the long range ordered state, we always observe a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.

cond-mat.soft↗

arXiv2010

Hydrodynamic Correlation Functions of a Driven Granular Fluid in Steady State

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function, F_incoh(q,t), is seen to follow time-density superposition with a relaxation time that increases significantly as volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,omega) we compare our results to the predictions of generalized fluctuating hydrodynamics which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,omega) and the longitudinal current correlation function C_l(q,omega). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

cond-mat.stat-mech↗

arXiv2010

Soft random solids and their heterogeneous elasticity

Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their \emph{elastic properties}. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids, in terms of residual stress and Lamé-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.

cond-mat.dis-nn↗

arXiv2010

Random networks of cross-linked directed polymers

We explore the effect of random permanent cross-links on a system of directed polymers confined between two planes with their end-points free to slide on them. We treat the cross-links as quenched disorder and we use a semimicroscopic replica field theory to study the structure and elasticity of this system. Upon increasing the cross-link density, we get a continuous gelation transition signaled by the emergence of a finite in-plane localization length. The distribution of localization length turns out to depend on the height along the preferred direction of the directed polymers. The gelation transition also gives rise to a finite in-plane shear modulus which we calculate and turns out to be universal, i.e., independent of the energy and length scales of the polymers and the cross-links. Using a symmetry argument, we show that cross-links of negligible extent along the preferred axis of the directed polymers do not cause any renormalization to the tilt modulus of the uncross-linked system.

cond-mat.soft↗

arXiv2010

Glass Transition for Driven Granular Fluids

We investigate the dynamics of a driven system of dissipative hard spheres in the framework of mode-coupling theory. The dissipation is modeled by normal restitution, and driving is applied to individual particles in the bulk. In such a system, a glass transition is predicted for a finite transition density. For increasing inelasticity, the transition shifts to higher densities. Despite the strong driving at high dissipation, the transition persists up to the limit of totally inelastic normal restitution.

cond-mat.soft↗

arXiv2009

Partitioning of energy in highly polydisperse granular gases

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.

cond-mat.soft↗

arXiv2009

Dilute Wet Granulates: Nonequilibrium Dynamics and Structure Formation

We investigate a gas of wet granular particles, covered by a thin liquid film. The dynamic evolution is governed by two-particle interactions, which are mainly due to interfacial forces in contrast to dry granular gases. When two wet grains collide, a capillary bridge is formed and stays intact up to a certain distance of withdrawal when the bridge ruptures, dissipating a fixed amount of energy. A freely cooling system is shown to undergo a nonequillibrium dynamic phase transition from a state with mainly single particles and fast cooling to a state with growing aggregates, such that bridge rupture becomes a rare event and cooling is slow. In the early stage of cluster growth, aggregation is a self-similar process with a fractal dimension of the aggregates approximately equal to D_f ~ 2. At later times, a percolating cluster is observed which ultimately absorbs all the particles. The final cluster is compact on large length scales, but fractal with D_f ~ 2 on small length scales.

cond-mat.soft↗

arXiv2009

Cooling and aggregation in wet granulates

Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium transition, setting in as the granular temperature falls below the bond energy. The subsequent aggregation of particles into clusters is shown to be a self-similar growth process with a cluster size distribution that obeys scaling. In the early phase of aggregation the clusters are fractals with D_f=2, for later times we observe gelation. We use simple scaling arguments to derive the temperature decay in the early and late stages of cooling and verify our results with event-driven simulations.

cond-mat.soft↗

arXiv2008

Diffraction from the beta-sheet crystallites in spider silk

We analyze the wide angle x-ray scattering from oriented spider silk fibers in terms of a quantitative scattering model, including both structural and statistical parameters of the $β$-sheet crystallites of spider silk in the amorphous matrix. The model is based on kinematic scattering theory and allows for rather general correlations of the positional and orientational degrees of freedom, including the crystallite's size, composition and dimension of the unit cell. The model is evaluated numerically and compared to experimental scattering intensities allowing us to extract the geometric and statistical parameters. We show explicitly that for the experimentally found mosaicity (width of the orientational distribution) inter-crystallite effects are negligible and the data can be analyzed in terms of single crystallite scattering, as is usually assumed in the literature.

cond-mat.soft↗

arXiv2007

Anisotropic Random Networks of Semiflexible Polymers

Motivated by the organization of crosslinked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent crosslinks which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the crosslink density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization is accompanied by a {\em continuous} isotropic-to-nematic (IN) transition occuring at the same crosslink density. As the polymer stiffness decreases, the IN transition becomes first order, shifts to a higher crosslink density, and is preceeded by an orientational glass (statistically isotropic amorphous solid) where the average polymer orientations freeze in random directions.

cond-mat.soft↗

arXiv2007

Variational bounds for the shear viscosity of gelling melts

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $η$, which implies that it diverges algebraically with a critical exponent $k\ge 2ν-β$. Here, $ν$ and $β$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.

cond-mat.stat-mech↗

arXiv2007

Finitely coordinated models for low-temperature phases of amorphous systems

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behavior of finite dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von-Karman type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well known universal glassy low temperature anomalies when quantum effects are taken into account.

cond-mat.dis-nn↗

arXiv2006

Elastic heterogeneity of soft random solids

Spatial heterogeneity in the elastic properties of soft random solids is investigated via a two-pronged approach. First, a nonlocal phenomenological model for the elastic free energy is examined. This features a quenched random kernel, which induces randomness in the residual stress and Lame coefficients. Second, a semi-microscopic model network is explored using replica statistical mechanics. The Goldstone fluctuations of the semi-microscopic model are shown to reproduce the phenomenological model, and via this correspondence the statistical properties of the residual stress and Lame coefficients are inferred. Correlations involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.

cond-mat.dis-nn↗

arXiv2006

Microscopic dynamics of thin hard rods

Based on the collision rules for hard needles we derive a hydrodynamic equation that determines the coupled translational and rotational dynamics of a tagged thin rod in an ensemble of identical rods. Specifically, based on a Pseudo-Liouville operator for binary collisions between rods, the Mori-Zwanzig projection formalism is used to derive a continued fraction representation for the correlation function of the tagged particle's density, specifying its position and orientation. Truncation of the continued fraction gives rise to a generalised Enskog equation, which can be compared to the phenomenological Perrin equation for anisotropic diffusion. Only for sufficiently large density do we observe anisotropic diffusion, as indicated by an anisotropic mean square displacement, growing linearly with time. For lower densities, the Perrin equation is shown to be an insufficient hydrodynamic description for hard needles interacting via binary collisions. We compare our results to simulations and find excellent quantitative agreement for low densities and qualtitative agreement for higher densities.

cond-mat.soft↗