Condensed Matter

Self-consistent theory for concentrated electrolytes is developed. Oscillatory decay of the charge-charge correlation function with the decay length that shows perfect agreement with the experimentally discovered and so far unexplained scaling is obtained. For the density-density correlations, monotonic asymptotic decay with the decay length comparable with the decay length of the charge correlations is found. We show that the correlation lengths in concentrated electrolytes depend crucially on the local variance of the charge density.

Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultra-low-density fractal networks.

The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip type of behavior. We establish that there is a clear correlation between the slider dynamics and the response of the force network that spontaneously develop in the granular system. This correlation is established by application of the persistence homology that allows for formulation of objective measures for quantification of time-dependent force networks. We find that correlation between the slider dynamics and the force network properties is particularly strong in the dynamical regime characterized by well-defined stick-slip type of dynamics.

We consider the link between fragility and elasticity that follows from analysis of the data for a set of soft-colloid materials consisting of deformable spheres reported by Mattsson et. al., in Nature vol 462, 83 (2009). Fragility index for a soft-colloid is obtained from the density dependence of the long time relaxation near a so-called glass transition point. In addition, we fit data for the high frequency shear modulus for the respective soft-colloid to a corresponding theoretical expression for the same modulus. This expression for the elastic constant is in terms of the corresponding pair correlation function for the liquid treated as of uniform density. The pair correlation function is adjusted through a proper choice of the parameters for the two body interaction potential for the respective soft-colloid material. The nature of correlation between the fragility and Poisson ratio observed for the soft colloids is qualitatively different, as compared to the same for molecular glasses. The observed link between fragility of a metastable liquid and its elastic coefficients is a manifestation of the effects of structure of the fluid on its dynamics.

Polymers are among the most important materials in the modern society being found almost in every activity of our daily life. Understanding their chemical and physical properties lead to improvements of their usage. The correlation functions are one of most important quantities to understand a physical system. The characteristic way it behaves describe how the system fluctuates, and much of the progress achieved to understand complex systems has been due to their study. Of particular interest in polymer science are the space correlations which describe its mechanical behavior. In this work I study the stiffness of a polymer immersed in a magnetic medium and trapped in an optical tweezers. Using Monte Carlo simulations the correlation function along the chain and the force in the tweezers are obtained as a function of temperature and density of magnetic particles. The results show that the correlation decay has two regimes: an initial very fast decay of order the monomer-monomer spacing and a power law in the long distance regime. The power law exponent has a minimum at a temperature T min for any non zero density of magnetic particles indicating that the system is more correlated in this region. Using a formula for the persistence length derived from the WLC theory one observed that it has a maximum at the same temperature. These results suggest that the correlations in the system may be a combination of exponential and power law.

We present examples of body wave and surface wave propagation in deformed solids where the slowest and the fastest waves do not travel along the directions of least and greatest stretch, respectively. These results run counter to commonly accepted theory, practice, and implementation of the principles of acousto-elasticity in initially isotropic solids. For instance we find that in nickel and steel, the fastest waves are along the direction of greatest compression, not greatest extension (and vice-versa for the slowest waves), as soon as those solids are deformed. Further, we find that when some materials are subject to a small-but-finite deformations, other extrema of wave speeds appear in non-principal directions. Examples include nickel, steel, polystyrene, and a certain hydrogel. The existence of these ``oblique'', non-principal extremal waves complicates the protocols for the non-destructive determination of the directions of extreme strains.

By using long-range interacting polygons, we experimentally probe the coupling between particle shape and long-range interaction. For two typical space-filling polygons, square and triangle, we find two types of coupling modes that predominantly control the structure formation. Specifically, the rotational ordering of squares brings a lattice deformation that produces a hexagonal-to-rhombic transition in the high-density regime, whereas the alignment of triangles introduces a large geometric frustration that causes an order-to-disorder transition. Moreover, the two coupling modes lead to small and large "internal roughness" of the two systems, and thus predominantly control their structure relaxations. Our study thus provides a physical picture to the coupling between long-range interaction effect and short-range shape effect in the high-density regime unexplored before.

We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulation. An external pressure restricts local motions of a single molecule within its cage and triggers the slowing down of cooperative mobility. While the ECNLE theory and simulation generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulation indicates a decrease of fragility as pressure above 1000 bar. The structural relaxation time is found to be linearly coupled with the inverse diffusion constant. Remarkably, this coupling is independent of compression. Theoretical calculations agree quantitatively well with simulations and are also consistent with prior works.

In the last decade many research efforts have been focused on understanding the rheology of disordered materials, and several theoretical predictions have been put forward regarding their yielding behavior. Nevertheless, not many experiments nor molecular dynamics simulations were dedicated to testing those theoretical predictions. Here we use computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics, and self-propelled, dense active systems. In the active systems a yielding transition is observed as expected, when the self-propulsion is increased. However, the range of self-propulsions in which a pure liquid regime exist appears to vanish upon approaching the so-called "jamming point" at which solidity of soft-sphere packings is lost. Such an "active yielding" transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existent of different universality classes for the yielding transition under different driving conditions. In addition, we present direct measurements of length and time scales for both driving scenarios. A comparison with theoretical predictions from recent literature reveals poor agreement with our numerical results.

Crystallization in a dense suspension of anisotropic spherical colloidal particles with a Yukawa potential is numerically investigated in a two-dimensional plane. It is found that a strong anisotropy can hinder the particles from crystallizing, while a weak anisotropy but super-strong coupling facilitates colloids to freeze into a hexagonal crystal. Different criterions are employed to describe the phase transition, one can find that a competition between anisotropic degree and coupling strength shall widened the transition region in the phase diagram, where the heterogeneous structures coexist, which render as a quasi-platform stretched across the probability distribution curve of the local order parameter. Our study maybe helpful for the experiments relating to the crystallizing behavior in statistical physics, materials science and biophysical systems.