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Register a new userUniversal interrelation between dynamics and thermodynamics of fluids: dynamically-driven c-transition
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Our first very wide survey of the supercritical phase diagram and its key properties reveals a universal interrelation between dynamics and thermodynamics and an unambiguous transition between liquidlike and gaslike states. This is seen in the master plot showing a collapse of the data representing the dependence of specific heat on key dynamical parameters in the system for many different paths on the phase diagram. As a result, the observed transition is path-independent. We call it a c-transition due to the c-shaped curve parameterizing the dependence of the specific heat on key dynamical parameters. The c-transition has a fixed inversion point and provides a new structure to the phase diagram, operating deep in the supercritical state (up to at least 2000 times the critical pressure and 50 times the critical temperature). The data collapse and path independence as well as the existence of a special inversion point on the phase diagram are indicative of either of a sharp crossover or a new phase transition in the deeply supercritical state.
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Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($varepsilon=1$) as well as inelastic ($varepsilon < 1$) collisions, are studied. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 le phi le 0.805$, scaling is shown to hold: $S_4(q,t)/chi_4(t)=s(qxi(t))$. Both the dynamic susceptibility, $chi_4(tau_{alpha})$, as well as the dynamic correlation length, $xi(tau_{alpha})$, evaluated at the $alpha$ relaxation time, $tau_{alpha}$, can be fitted to a power law divergence at a critical packing fraction. The measured $xi(tau_{alpha})$ widely exceeds the largest one previously observed for hard sphere 3d fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, $chi_4(tau_{alpha}) approxxi^{d-p}(tau_{alpha})$, with an exponent $d-papprox 1.6$. This scaling is remarkably independent of $varepsilon$, even though the strength of the dynamical heterogeneity increases dramatically as $varepsilon$ grows.
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.
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, epsilon, at a critical packing fraction, phi_c(epsilon), below random close packing. The divergence of timescales at the glass-transition implies a dependence on compression rate upon further increase of the density - similar to the cooling rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be non-universal with exponents depending on space dimension and degree of dissipation.
We study single crystals of Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ under magnetic field and stress applied along their [001] direction. We find that many of the features that the emergent gauge field of spin ice confers to the macroscopic magnetic properties are preserved in spite of the finite temperature. The magnetisation vs. field shows an upward convexity within a broad range of fields, while the static and dynamic susceptibilities present a peculiar peak. Following this feature for both compounds, we determine a single experimental transition curve: that for the Kasteleyn transition in three dimensions, proposed more than a decade ago. Additionally, we observe that compression up to $-0.8%$ along [001] does not significantly change the thermodynamics. However, the dynamical response of Ho$_2$Ti$_2$O$_7$ is quite sensitive to changes introduced in the ${rm Ho}^{3+}$ environment. Uniaxial compression can thus open up experimental access to equilibrium properties of spin ice at low temperatures.
Topological defects are typically quantified relative to ordered backgrounds. The importance of these defects to the understanding of physical phenomena including diverse equilibrium melting transitions from low temperature ordered to higher temperatures disordered systems (and vice versa) can hardly be overstated. Amorphous materials such as glasses seem to constitute a fundamental challenge to this paradigm. A long held dogma is that transitions into and out of an amorphous glassy state are distinctly different from typical equilibrium phase transitions and must call for radically different concepts. In this work, we critique this belief. We examine systems that may be viewed as simultaneous distribution of different ordinary equilibrium structures. In particular, we focus on the analogs of melting (or freezing) transitions in such distributed systems. The theory that we arrive at yields dynamical, structural, and thermodynamic behaviors of glasses and supercooled fluids that, for the properties tested thus far, are in qualitative and quantitative agreement with experiment. We arrive at a prediction for the viscosity and dielectric relaxations that is universally satisfied for all experimentally measured supercooled liquids and glasses over 15 decades.
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