Session T13: Focus Session: Transport and Diffusion in Non-equilibrium Systems

Thermodiffusion (Ludwig-Soret Effect) in Geological Systems

Since its discovery more than a century and a half ago, the Ludwig-Soret effect (development of concentration gradients in response to a temperature gradient) has been documented in a large variety of inorganic and organic solutions, and exploited as an industrial tool for chemical and isotopic refinement. Theoretical treatments are numerous based on kinetic and thermodynamic principles, but none adequately explains the phenomenon operating in complex naturally occurring fluids. In the geological sciences, the Ludwig-Soret effect has received extraordinary attention as an agent for small (and large) scale chemical differentiation and a probe of fundamental fluid properties of the Earth's hydrosphere, and silicate (crust-mantle) and alloy (core) interior. In particular, silicate liquids show significant isotope fractionation by thermodiffusion at temperatures greatly exceeding those where equilibrium fractionation effects are vanishingly small, and this can persist to lower temperatures even with concomitant crystallization. We review these recent findings and present new experimental work on silicate and Fe(FeS) melts, considering the underlying causes towards reconciling observed mass-dependent isotope and mass-independent chemical effects.   

Galilean thermodynamics of a multicomponent fluid and its induced electromagnetic fields

The phenomenological theory of irreversible processes in fluid systems has been successfully applied to new research fields, for example spintronics and spincaloritronics (arXiv:1011.2323). We include the electromagnetic interaction into the thermodynamic description of a multicomponent fluid. Our analysis is performed in the Galilean limit of electromagnetism. The tensorial part of the Onsager relations accounts in particular for mutliferroic effects.   

Thresholds, memory, and self-similarity on river deltas

The bulk dynamics of river deltas and alluvial fans result from several physical processes acting on a wide range of scales. We study a series of experimental alluvial fans to sort the relevant processes and determine the way in which their interaction drives fan behavior. We find a timescale of channel movement that depends on mass conservation, as sediment fills a wedge of space determined by a separation between conditions of grain entrainment and distrainment, in a manner analogous to the separation between static and dynamic angles of repose in dry granular systems. Channel path selection behavior shows a marked tendency for flow to reoccupy abandoned paths, in a way that can be abstracted with a random walk model in a system with absorbing states, and resulting in a predictable self-similar shoreline growth pattern. Because we isolate the processes that drive the evolution of our experimental fans, we are able to translate our findings to the study of natural fans and deltas in which the same processes operate.   

Tailoring Polymer Nanocomposite Properties by Nanoparticle Assembly

Novel materials based on polymer-grafted nanoparticles (NP) are the focus of this talk. Since inorganic NPs and organic polymers typically ``dislike'' each other, these ``hairy'' particles behave like block-copolymers or amphiphiles. They can, therefore, self-assemble into a range of superstructures when placed in an organic matrix. Understanding the factors controlling this this assembly state and how it affects the properties of the resulting material are our central interests in this area. As part of this global effort, here we address three questions: (i) Can we direct NP assembly using external fields, e.g., shear, with the ultimate goal of designing membranes with directional transport properties? (ii) Can we assemble grafted NPs at interfaces with the aim of compatibilizing immiscible polymer blends? (iii) Can NP assemblies result in simultaneous improvements in the Young's modulus, the yield stress and strain-to-break of an amorphous polymer in the solid-state? As with all of our work we combine theory and experiments to understand these concepts that underpin our nascent understanding in this area.   

Thermodynamic Analysis of Nanoporous Membrane Separation Processes

We give an analysis of desalination energy requirements in order to quantify the potential for future improvements in desalination membrane technology. Our thermodynamic analysis makes it possible to draw conclusions from the vast array of equilibrium molecular dynamics simulations present in the literature as well as create a standardized comparison for measuring and reporting experimental reverse osmosis material efficiency. Commonly employed methods for estimating minimum desalination energy costs have been revised to include operations at positive input stream recovery ratios using a thermodynamic cycle analogous to the Carnot cycle. Several gaps in the statistical mechanical theory of irreversible processes have also been identified which may in the future lead to improved communication between materials engineering models and statistical mechanical simulation. Simulation results for silica surfaces and nanochannels are also presented.   

Geometric Phase Effect in Heat Transport

Nonlinear molecular heat-pumping devices, which operate via explicitly modulating at least two parameters, are crucial for energy control in low dimensional nano-scale systems. We have applied slow two-parameter modulations on such a molecular junctions and consequently uncovered an intrinsic heat flux contribution, additional to the known, usual dynamical heat flux (from hot to cold). This additional heat flux derives from a nontrivial geometric origin that relates to a non-vanishing, so termed finite Berry phase. It provides a free lunch for the pumped heat and even can direct heat flux against the temperature bias. In addition we are able to show that this so pumped energy exhibits a novel robust fractional quantization phenomenon. Interestingly, this additional geometric heat pump mechanism is also shown to cause a breakdown of the heat-flux fluctuation theorem, which holds true for the non-driving, stationary heat flux transfer. The validity of this theorem is guaranteed whenever (i) the geometric phase contribution vanishes and (ii) the cyclic protocol preserves the detailed balance symmetry.   

Contact processes in crowded environments

A nonequilibrium absorbing state phase transition with conserved particle number has been realized in a periodically sheared particle suspension. A diffusing (active) particle in the suspension collides with a stationary (inactive) particle and activates it. As the strain amplitude is increased, the fraction of active particles per shear cycle becomes nonzero only above some critical strain amplitude. To further study this system at higher densities, we construct a lattice model with active and inactive particles occupying some fraction of the lattice sites with each site being occupied by at most one particle. The active particles hop to empty neighboring sites and activate $k$ neighboring inactive particles at some rate $\lambda_k$. Also, active particles become inactive at some rate $\gamma$. We investigate this model for $\lambda_{k=1}=0$ and $\lambda_{k>1}>0$ to study the effects of multi-particle collisions which are likely to occur at higher densities, i.e. crowded environments.   

Mixing of Diffusing Particles

We study how the order of $N$ independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number $m$, defined as the number of pairs that are out of sort with respect to the initial configuration. In the steady-state, the distribution of the inversion number is Gaussian with the average $\langle m\rangle \simeq N^2/4$ and the standard deviation $\sigma\simeq N^{3/2}/6$. The survival probability, $S_m(t)$, which measures the likelihood that the inversion number remains below $m$ until time $t$, decays algebraically in the long-time limit, $S_m\sim t^{-\beta_m}$. Interestingly, there is a spectrum of $N(N-1)/2$ distinct exponents $\beta_m(N)$. We also find that the kinetics of first passage in a circular cone provides a good approximation for these exponents. When $N$ is large, the first-passage exponents are a universal function of a single scaling variable, $\beta_m(N)\to \beta(z)$ with \hbox{$z=(m-\langle m\rangle)/\sigma$}. In the cone approximation, the scaling function is a root of a transcendental equation involving the parabolic cylinder equation, $D_{2\beta}(-z)=0$, and surprisingly, numerical simulations show this prediction to be exact.   

Crossover behavior in models of depinning

We explore the behavior of models describing driven interfaces in random media. These models are useful in describing a wide range of real-world systems: disordered magnets, fluids in porous medium, pinning of flux lines in superconductors, and fluid imbibition in paper. Variations of these models have been numerically studied and classified into distinct universality classes at the depinning transition, however the exact structure of the phase space is still not known. We are investigating the crossover behavior in between various linear and nonlinear models with short-range and long-range interactions, and will report on their respective scaling functions of height-height correlation and size distributions of avalanches.   

An Information-Theoretic Order Parameter for Non-Equilibrium Systems

In non-equilibrium statistical physics, symmetry and free energy are difficult to define, preventing application of classical machinery for analysis of phase transitions. Can one define a ``universal'' order parameter that would be measurable from experimental data, would allow identification of an onset of a phase transition, and would be meaningful independently of the underlying systems dynamics? We suggest that predictive information, which is the mutual information between the sequence of the observed past states of a system and its future states, introduced by us in 2001,\footnote{W Bialek, I Nemenman, N Tishby. Neural Computation (2001),13,2409} may serve as such order parameter. We study this suggestion in the context of a model non-stationary Langevin process. We show analytically that the predictive information attains its maximum value at the phase transition, diverging logarithmically with the length of the observed past. We demonstrate that the speed of divergence is related to traditional critical exponents. Finally, we show how the onset of a phase transition can be found empirically from data, independently of its parameterization.   

Classical nucleation theory explains the critical cooling rate of cryoprotectant solutions

We have measured critical cooling rates for a range of concentrations of different solutes in aqueous solutions. Our results show that the glass formability of aqueous solutions is exponential in the concentration for all solutes tested, with a different characteristic concentration for each solute. This characteristic correlates with the Stokes radius of the solute. A simple modification of critical droplet theory relates the characteristic concentration to the critical nucleation radius in pure water, and explains the relationship between the Stokes radius and the exponential characteristic. This simple, general theory of glass formability in aqueous solutions is important at a fundamental level, and will also have broad consequences for the field of cryobiology.