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Register a new userUniversal non-exponential relaxation and memory effects in a fluid with non-linear drag
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We analyse the dynamical evolution of a fluid with non-linear drag, for which binary collisions are elastic, at the kinetic level of description. When quenched to low temperatures, the system displays a really complex behaviour. The glassy response of the system is controlled by a long-lived non-equilibrium state, and includes non-exponential, algebraic, relaxation and strong memory effects in the time evolution of its kinetic temperature. Moreover, the observed behaviour is universal, in the sense that the time evolution of the temperature -- for both relaxation and memory effects -- falls onto a master curve, regardless of the details of the experiment. Our theoretical predictions are checked against simulations of the kinetic equation, and an excellent agreement is found.
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We study the effect of rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $exp(-2r/sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in steady state, while the temporal auto-correlation function follows $exp(-(t/tau_L)^{1/2})$, where $t$ is the time and $tau_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $mathcal{L}(t_w) sim t_w^{1/2}$ and $mathcal{R}(t_w) sim t_w^{1/4}$; the spatial correlation function decays as $exp(-r/ mathcal{R}(t_w))$. Interestingly, the stretched exponential form of the auto-correlation function of a single typical sample in steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power law decay at large times.
Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A exp [-(t/tau)^{beta}]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corte et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $beta$ that depends on the strain amplitude: $0.25 < beta < 1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.
We study a granular gas of viscoelastic particles (kinetic energy loss upon collision is a function of the particles relative velocities at impact) subject to a stochastic thermostat. We show that the system displays anomalous cooling and heating rates during thermal relaxation processes, this causing the emergence of thermal memory. In particular, a significant textit{Mpemba effect} is present; i.e., an initially hotter/cooler granular gas can cool down/heat up faster than an in comparison cooler/hotter granular gas. Moreover, a textit{Kovacs effect} is also observed; i.e., a non-monotonic relaxation of the granular temperature --if the gas undergoes certain sudden temperature changes before fixing its value. Our results show that both memory effects have distinct features, very different and eventually opposed to those reported in theory for granular fluids under simpler collisional models. We study our system via three independent methods: approximate solution of the kinetic equation time evolution and computer simulations (both molecular dynamics simulations and Direct Simulation Monte Carlo method), finding good agreement between them.
The nano-particle systems under theoretically and experimentally investigation because of the potential applications in the nano-technology such as drug delivery, ferrofluids mechanics, magnetic data storage, sensors, magnetic resonance imaging, and cancer therapy. Recently, it is reported that interacting nano-particles behave as spin-glasses and experimentally show that the relaxation of these systems obeys stretched exponential i.e., KWW relaxation. Therefore, in this study, considering the interacting nano-particle systems we model the relaxation and investigate frequency and temperature behaviour depends on slow relaxation by using a simple operator formalism. We show that relaxation deviates from Debye and obeys to KWW in the presence of the memory effects in the system. Furthermore, we obtain the frequency and temperature behaviour depend on KWW relaxation. We conclude that the obtained results are consistent with experimental results and the simple model, presented here, is very useful and pedagogical to discuss the slow relaxation of the interacting nano-particles.
Materials undergoing both phase separation and chemical reactions (defined here as all processes that change particle type or number) form an important class of non-equilibrium systems. Examples range from suspensions of self-propelled bacteria with birth-death dynamics, to bio-molecular condensates, or membraneless organelles, within cells. In contrast to their passive counterparts, such systems have conserved and non-conserved dynamics that do not, in general, derive from a shared free energy. This mismatch breaks time-reversal symmetry and leads to new types of dynamical competition that are absent in or near equilibrium. We construct a canonical scalar field theory to describe such systems, with conserved and non-conserved dynamics obeying Model B and Model A respectively (in the Hohenberg-Halperin classification), chosen such that the two free energies involved are incompatible. The resulting minimal model is shown to capture the various phenomenologies reported previously for more complicated models with the same physical ingredients, including microphase separation, limit cycles and droplet splitting. We find a low-dimensional subspace of parameters for which time-reversal symmetry is accidentally recovered, and show that here the dynamics of the order parameter field (but not its conserved current) is exactly the same as an equilibrium system in which microphase separation is caused by long-range attractive interactions.
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