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We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (cm.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The cm. velocity autocorrelation function (cm. VAF) exhibits a slow power law relaxation in the time range between the monomer time t1 and the Rouse relaxation time tN. We obtain an analytical expression for the cm. VAF in terms of molecular parameters. In particular, the cm. VAF scales as -- N-1t5/4 (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted --t5/4 dependence of the cm. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper]. [ABSTRACT FROM AUTHOR]

A mode-coupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the density-based MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the center-of-mass velocity autocorrelation function (cm. VAF). We show that in most cases the VHI mechanism is domiijant; for long chains and prediffusive times it yields a negative tail ∝--N-1/2t-3/2 for the cm. VAF. The case of non-momentum-conserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first --N-15/4t-5/4 (as in the dMCT approach), then --N-1/2t-3/2. Both the amplitude and the duration of the first t-5/4 stage crucially depend on the Langevin friction parameter y. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the cm. VAF, thus account for the anomalous subdiffusive regime of the cm. mean square displacement widely observed in numerical and experimental works. [ABSTRACT FROM AUTHOR]

Contrary to common belief, hydrodynamic interactions in polymer melts are not screened beyond the monomer length and are important in transient regimes. We show that viscoelastic hydrodynamic interactions (VHIs) lead to anomalous dynamics of a tagged chain in an unentangled melt at t < tN, the Rouse time. The center-of-mass (c.m.) mean-square displacement is enhanced by a large factor increasing with chain length. We develop a theory of VHI-controlled chain dynamics yielding a negative c.m. velocity autocorrelation function which agrees with our molecular dynamics simulations without any fitting parameter. It is also shown that Langevin friction strongly affects the short-t c.m. dynamics, also captured by our theory. The transient VHI effects thus provide the dominant contribution to the subdiffusive c.m. motion universally observed in simulations and experiments. [ABSTRACT FROM AUTHOR]

We introduce a theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed. [ABSTRACT FROM AUTHOR]

The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89,042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early a process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early a regime where they systematically underestimate the MSD from the MD. [ABSTRACT FROM AUTHOR]

Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Fc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forward-backward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jump-length and waiting-time distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (F) dependence of these time scales. For instance, the average waiting time changes from an Arrhenius-type to a Vogel-Fulcher-type T dependence. We discuss this observation in the context of the bifurcation of the a process and (Johari) ß process found in many glass-forming materials to occur near Fc. Our analysis lays the foundation for a study of the jump-length and waiting-time distributions, their temperature and chain-length dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014)]. [ABSTRACT FROM AUTHOR]

Taking advantage of the competition between elasticity and capillarity has proven to be an efficient way to design structures by folding, bending, or assembling elastic objects in contact with liquid interfaces. Elastocapillary effects often occur at scales where gravity does not play an important role, such as in microfabrication processes. However, the influence of gravity can become significant at the desktop scale, which is relevant for numerous situations including model experiments used to provide a fundamental physics understanding, working at easily accessible scales. We focus here on the case of elastic ribbons placed in two-dimensional bubble columns: by introducing an elastic ribbon inside the central soap films of a staircase bubble structure in a square cross-section column, the deviation from Plateau's laws (capillarity-dominated case dictating the shape of usual foams) can be quantified as a function of the rigidity of the ribbon. For long ribbons, gravity cannot be neglected. We provide a detailed theoretical analysis of the ribbon profile, taking into account capillarity, elasticity, and gravity. We compute the total energy of the system and perform energy minimization under constraints, using Lagrangian mechanics. The model is then validated via a comparison with experiments with three different ribbon thicknesses.

Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability, and mechanical stresses of minimal surfaces spanning specific geometric boundaries. The "catenoid" is the best-known example where an analytical solution is known which describes the form and stability of a minimal surface held between two parallel, concentric circular frames. Here we extend this problem to nonaxisymmetric, parallel frame shapes of different orientations by developing a perturbation approach around the known catenoid solution. We show that the predictions of the perturbation theory are in good agreement with experiments on soap films and finite element simulations (Surface Evolver). Combining theory, experiment, and simulation, we analyze in depth how the shapes, stability, and mechanical properties of the minimal surfaces depend on the type and orientation of elliptic and three-leaf clover shaped frames. In the limit of perfectly aligned nonaxisymmetric frames, our predictions show excellent agreement with a recent theory established by Alimov et al. [Phys. Fluids 33, 052104 (2021)1070-663110.1063/5.0047461]. Moreover, we put in evidence the intriguing capacity of minimal surfaces between nonaxisymmetric frames to transmit a mechanical torque despite being completely liquid. These forces could be interesting to exploit for mechanical self-assembly of soft matter systems or as highly sensitive force captors.

A magnetic stirrer, an omnipresent device in the laboratory, generates a spinning magnetic dipolelike field that drives in a contactless manner the rotation of a ferromagnetic bead on top of it. We investigate here the surprisingly complex dynamics displayed by the spinning magnetic bead emerging from its dissipatively driven, coupled translation and rotation. A particularly stunning and counterintuitive phenomenon is the sudden inversion of the bead's rotational direction, from corotation to counterrotation, acting seemingly against the driving field, when the stirrer's frequency surpasses a critical value. The bead counterrotation effect, experimentally described by Chau et al. [J. Magn. Magn. Mater. 476, 376 (2019)JMMMDC0304-885310.1016/j.jmmm.2018.12.073], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.

This paper is a generalization of the models considered in J. Stat. Phys. 128, 1365 (2007). Using an analogy with free fermions, we compute exactly the large deviation function (LDF) of the energy injected up to time t in a one-dimensional dissipative system of classical spins, where a drift is allowed. The dynamics are T=0 asymmetric Glauber dynamics driven out of rest by an injection mechanism, namely, a Poissonian flipping of one spin. The drift induces anisotropy in the system, making the model more comparable to experimental systems with dissipative structures. We discuss the physical content of the results, specifically the influence of the rate of the Poisson injection process and the magnitude of the drift on the properties of the LDF. We also compare the results of this spin model to simple phenomenological models of energy injection (Poisson or Bernoulli processes of domain wall injection). We show that many qualitative results of the spin model can be understood within this simplified framework.