The number of compact structures of a single condensed polymer (SCP), with similar free energies, grows exponentially with the degree of polymerization. In analogy with structural glasses (SGs), we expect that at low temperatures chain relaxation sho
uld occur by activated transitions between the compact metastable states. By evolving the states of the SCP that is linearly coupled to a reference state, we show that, below a dynamical transition temperature ($T_d$), the SCP is trapped in a metastable state leading to slow dynamics. At a lower temperature, $T_K e 0$, the configurational entropy vanishes, resulting in a thermodynamic random first order ideal glass transition. The relaxation time obeys the Vogel-Fulcher-Tamman law, diverging at $T=T_0 approx T_K$. These findings, accord well with the random first order transition theory, establishing that SCP and SG exhibit similar universal characteristics.
Colloidal particles, which are ubiquitous, have become ideal testing grounds for the structural glass transition (SGT) theories. In these systems glassy behavior is manifested as the density of the particles is increased. Thus, soft colloidal particl
es with varying degree of softness capture diverse glass forming properties, observed normally in molecular glasses. By performing Brownian dynamics simulations for a binary mixture of micron-sized charged colloidal suspensions, known to form Wigner glasses, we show that by tuning the softness of the potential, achievable by changing the monovalent salt concentration, there is a continuous transition between fragile to strong behavior. Remarkably, this is found in a system where the well characterized potential between the colloidal particles is isotropic. We also show that the predictions of the random first order transition (RFOT) theory quantitatively describes the universal features such as the growing correlation length, $xisim (phi_K/phi - 1)^{- u}$ with $ u = 2/3$ where $phi_K$, the analogue of the Kauzmann temperature, depends on the salt concentration. As anticipated by the RFOT predictions, we establish a causal relationship between the growing correlation length and a steep increase in the relaxation time and dynamic heterogeneity. The broad range of fragility observed in Wigner glasses is used to draw analogies with molecular glasses. The large variations in the fragility is found only when the temperature dependence of the viscosity is examined for a large class of diverse glass forming materials. In sharp contrast, this is vividly illustrated in a single system that can be experimentally probed. Our work also shows that the RFOT predictions are accurate in describing the dynamics over the entire density range, regardless of the fragility of the glasses, implying that the physics describing the SGT is universal.
A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term co
mes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.
In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gr
adient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find that in shear nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that currently available computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin and do not probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes. Even more importantly, we find that in actual experimental conditions, shear-induced pressure enhancements are caused by viscous heating and not by thermal velocity fluctuations. Hence, isothermal computer simulations are irrelevant for the interpretation of experimental shear-induced pressure enhancements.
In stationary nonequilibrium states a coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir forces or pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a
velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancement in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequiibrium Casimir pressures induced by a temperature gradient, kinetic theory shows that nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin. The idea that such computer simulations probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes is erroneous.
We develop a theory to probe the effect of non-equilibrium fluctuation-induced forces on the size of a polymer confined between two horizontal thermally conductive plates subject to a constant temperature gradient, $ abla T$. We assume that (a) the s
olvent is good and (b) the distance between the plates is large so that in the absence of a thermal gradient the polymer is a coil whose size scales with the number of monomers as $N^{ u}$, with $ u approx 0.6$. We predict that above a critical temperature gradient, $ abla T_c sim N^{-frac{5}{4}}$, favorable attractive monomer-monomer interaction due to Giant Casimir Force (GCF) overcomes the chain conformational entropy, resulting in a coil-globule transition. The long-ranged GCF-induced interactions between monomers, arising from thermal fluctuations in non-equilibrium steady state, depend on the thermodynamic properties of the fluid. Our predictions can be verified using light-scattering experiments with polymers, such as polystyrene or polyisoprene in organic solvents (neopentane) in which GCF is attractive.
In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature g
radient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.
The 1970 paper, Decay of the Velocity Correlation Function [Phys. Rev. A1, 18 (1970), see also Phys. Rev. Lett. 18, 988 (1967)] by Berni Alder and Tom Wainwright, demonstrated, by means of computer simulations, that the velocity autocorrelation funct
ion for a particle in a gas of hard disks decays algebraically in time as $t^{-1},$ and as $t^{-3/2}$ for a gas of hard spheres. These decays appear in non-equilibrium fluids and have no counterpart in fluids in thermodynamic equilibrium. The work of Alder and Wainwright stimulated theorists to find explanations for these long time tails using kinetic theory or a mesoscopic mode-coupling theory. This paper has had a profound influence on our understanding of the non-equilibrium properties of fluid systems. Here we discuss the kinetic origins of the long time tails, the microscopic foundations of mode-coupling theory, and the implications of these results for the physics of fluids. We also mention applications of the long time tails and mode-coupling theory to other, seemingly unrelated, fields of physics. We are honored to dedicate this short review to Berni Alder on the occasion of his 90th birthday!
Long-range thermal fluctuations appear in fluids in nonequilibrium states leading to fluctuation-induced Casimir-like forces. Two distinct mechanisms have been identified for the origin of the long-range nonequilibrium fluctuations in fluids subjecte
d to a temperature or concentration gradient. One is a coupling between the heat or mass-diffusion mode with a viscous mode in fluids subjected to a temperature or concentration gradient. Another one is the spatial inhomogeneity of thermal noise in the presence of a gradient. We show that in fluids fluctuation-induced forces arising from mode coupling are several orders of magnitude larger than those from inhomogeneous noise.
