Fluctuations about simple nonequilibrium steady states

Fluctuations about hydrodynamic nonequilibrium steady states

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.

Improved Langevin methods for spin systems

Process optimization requires knowledge of equilibrium constants. From these, the mole fractions of species present at equilibrium can be determined, allowing the calculation of the maximum theoretical conversion of a given system. However, many experimental thermodynamic data are not available. This is due to experimental complexity and the high cost involved in obtaining such data. Thus, the use of computational resources for the acquisition of these data proves to be of great interest. In recent decades, quantum-mechanic methods have been used coupled with computational techniques for the prediction of thermodynamic properties. Thus, the present work provided a comparison between the values of thermodynamic quantities obtained by some methods based on Quantum Theory with data calculated from experimental energies of formation at 298.15 K. For that, the ab-initio methods Hartree-Fock (HF), Gaussian-1 (G1), Gaussian-2 (G2), Gaussian-3 (G3), Gaussian-4 (G4) and CBS-QB3, as well as the approach based on Density Functional Theory, represented by the hybrid functional B3LYP, were used. The experimental data of standard heat of formation (fH0 f) and entropy (fS0) of the chemical species in the desired temperatures were extrapolated by integrating the specific heat at constant pressure as a function of temperature. From these quantities, the Gibbs free energy for the reactions involved in the systems of steam reforming of methane and of Liquefied Petroleum Gas (LPG) was obtained, and consequently, their equilibrium constants. As previously expected, the HF method provided the largest deviations from values based on experimental quantities. The hybrid functional B3LYP showed better results compared to the HF method, although with high deviations from the extrapolated experimental data. It was noticed a remarkable improvement on the predictive capability of DFT approach when diffuse and polarized functions were added to the basis set employed. The compound method G1 proved to be unsatisfactory, since it has improved slightly compared to the DFT approach with no diffuse and polarized functions on the basis set and showed a significantly higher computational cost. Statistical analysis proved that the results provided by G2 and CBS-QB3 methodologies are equivalent, in the present context. Even with a considerable computational cost, smaller deviations between the experimental and theoretical quantities were obtained by using the G2, G3, and G4 methods.

Structure formation under non-equilibrium steady state conditions is poorly understood. A non-equilibrium steady state can be achieved in a system by maintaining a temperature gradient. A class of cross-linked microgel particles, such as poly-N-iso-propylacrylamide, is reported to increase in size due to the adsorption of water as the temperature decreases. Here, we study thermo-responsive particles with a temperature sensitive diameter in the presence of a temperature gradient, using molecular dynamics simulations with the Langevin thermostat. We find long-ranged structural order using bond order parameters in both cold and hot regions of the system beyond a certain diameter ratio of the cold and hot particles. This is due to an increase in packing and pressure in both regions. Our observations might be useful in understanding ordered structures under extreme conditions of a non-equilibrium steady state.

The school from Brussels have found that for the systems maintained far from thermodynamic equilibrium and when the kinetic laws are suitably nonlinear, the excess entropy production, δxP, becomes negative for t > to. In this case, the nonequilibrium steady state becomes unstable and sometimes, when the internal structure permits, the system executes limit cycle oscillations [1–3].

Stochastic-dissipative least-action framework for self-organizing biological systems, Part I: Variational rationale and Lyapunov-type behavior.

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical simulations, both at thermodynamic equilibrium and at a nonequilibrium steady state.

The fluctuation-dissipation theorem is a central result of statistical physics, which applies to any system at thermodynamic equilibrium. Its violation is a strong signature of nonequilibrium behavior. We show that for any system with Markovian dynamics, in a nonequilibrium steady state, a proper choice of observables restores a fluctuation-response theorem identical to a suitable version of the equilibrium fluctuation-dissipation theorem. This theorem applies to a broad class of dynamical systems. We illustrate it with linear stochastic dynamics and examples borrowed from the physics of molecular motors and Hopf bifurcations. Finally, we discuss general implications of the theorem.

Entropy production rate (EPR) is the fundamental theoretical quantity in non-equilibrium thermodynamics whereas reaction rate is the primary experimental quantity for a chemical system out-of-equilibrium. In this work, we explore a connection between the above two quantities for general reaction networks. Both cyclic and linear networks of arbitrary dimension are studied, along with a mixed variety. The systems can attain a non-equilibrium steady state (NESS) under chemiostatic condition, which becomes the state of true thermodynamic equilibrium when detailed balance holds. We show that there exists a universal functional relationship of the EPR with reaction rate close to steady states for all the networks considered. Near a NESS, the former varies linearly with the reaction rate. On the other hand, around a true equilibrium, it varies quadratically with the latter. Numerical experiments justify our analytical findings quite transparently.

We investigate the dynamical properties of monodomain nematic liquid crystals under shear flow and magnetic fields on the basis of the Ericksen-Leslie theory. Stable and unstable states appear depending on the magnetic field and the shear rate. The trajectory of the unstable state shows tumbling motion. The phase diagram of these states is plotted as a function of the three components of the magnetic field at a constant shear rate. The phase diagram changes depending on the viscous properties of different types of nematic liquid crystals. In this nonequilibrium steady state, we calculate the correlation function of director fluctuations and the response function, and discuss the nonequilibrium fluctuations and the modified fluctuation-dissipation relation in connection with nonconservative forces due to shear flow.

Relativistic transport phenomena are important from both a theoretical and practical point of view. Accordingly, hydrodynamics of relativistic gas has been extensively studied theoretically. Here we introduce a three-dimensional canonical model of hard-sphere relativistic gas which allows us to impose appropriate temperature gradient along a given direction maintaining the system in a nonequilibrium steady state. We use such a numerical laboratory to study the appropriateness of the so-called first order (Chapman-Enskog) relativistic hydrodynamics by calculating various transport coefficients. Our numerical results are consistent with predictions of such a theory for a wide range of temperatures. Our results are somewhat surprising since such linear theories are not consistent with the fundamental assumption of the special theory of relativity ($v\ensuremath{\le}c$). We therefore seek to explain such results by studying the appropriateness of diffusive transport in the relativistic gas, comparing our results with that of a classical gas. We find that the relativistic correction (constraint) in the hydrodynamic limit amounts to small negligible corrections, thus indicating the validity of the linear approximation in near equilibrium transport phenomena.

Macroscopic gas motions are widespread throughout the solar atmosphere and\nshearing motions couple to the non--ideal effects, destabilising low frequency\nfluctuations in the medium. The origin of this non-ideal magnetohydrodynamic\ninstability lies in the collisional coupling of the neutral particles to the\nmagnetized plasma in the presence of a sheared background flow. Unsurprisingly,\nthe maximum growth rate and most unstable wavenumber depend on the flow\ngradient and ambient diffusivities.\n The orientation of the magnetic field, velocity shears and perturbation wave\nvector play a crucial role in assisting the instability. When the magnetic\nfield and wave vector are both vertical, ambipolar and Ohm diffusion can be\ncombined as Pedersen diffusion and cause only damping; in this case only Hall\ndrift in tandem with shear flow drives the instability. However, for\nnon-vertical fields and oblique wave vectors, both ambipolar diffusion and Hall\ndrift are destabilizing.\n We investigate the stability of magnetic elements in the network and\ninternetwork regions. The shear scale is not yet observationally determined,\nbut assuming a typical shear flow gradient $\\sim 0.1 \\,\\mbox{s}^{-1}$ we show\nthat the magnetic diffusion shear instability grows on a time scale of one\nminute. Thus, it is plausible that network--internetwork magnetic elements are\nsubject to this fast growing, diffusive shear instability, which could play an\nimportant role in driving low frequency turbulence in the plasma in the solar\nphotosphere and chromosphere.\n

<p>Functionalities and structural properties of multiphase polymeric materials can be modified by imposing external forces to the mixture undergoing phase separation resulting in non-uniform anisotropic microstructures. Anisotropic heterogeneous polymeric materials have practical engineering applications such as anisotropic porous polymer membranes and switchable holographic polymer-dispersed liquid crystal films. Anisotropy can be generated by applying singly or in combination, an external force like shear flow, electric or magnetic field, surface effect, controlled chemical reaction, concentration gradient, or temperature gradient to a polymer solution undergoing phase separation. In this study, the self-condensation polymerization of a monomer in a monomer-solvent mixture and phase separation of the system were simultaneously modeled and simulated. The numerical Galerkin finite-element method was applied to develop the mathematical model. Short-range surface potential, long-range surface potential, and linear temperature and concentration gradients were applied singly and also simultaneously to the system undergoing the polymerization-induced phase separation (PIPS). The expected non- uniform structures were achieved. A comprehensive parametric study was carried out by investigating the effects of diffusivity, temperature gradient, concentration gradient, and surface potential parameter on the lag time, process time, morphology development, thickness of the wetting layer, and the extent of anisotropy of the system. The size analysis and structural characterization of the phase-separated system were also carried out using ImageJ 1.51j8 which is an image processing and analysis software. The numerical results are in good agreement with published experimental data.</p>

This is the Final Technical Report for University of Colorado's portion of the SciDAC project 'Center for Gyrokinetic Particle Simulation of Turbulent Transport.' This is funded as a multi-institutional SciDAC Center and W.W. Lee at the Princeton Plasma Physics Laboratory is the lead Principal Investigator. Scott Parker is the local Principal Investigator for University of Colorado and Yang Chen is a Co-Principal Investigator. This is Cooperative Agreement DE-FC02-05ER54816. Research personnel include Yang Chen (Senior Research Associate), Jianying Lang (Graduate Research Associate, Ph.D. Physics Student) and Scott Parker (Associate Professor). Research includes core microturbulence studies of NSTX, simulation of trapped electron modes, development of efficient particle-continuum hybrid methods and particle convergence studies of electron temperature gradient driven turbulence simulations. Recently, the particle-continuum method has been extended to five-dimensions in GEM. We find that actually a simple method works quite well for the Cyclone base case with either fully kinetic or adiabatic electrons. Particles are deposited on a 5D phase-space grid using nearest-grid-point interpolation. Then, the value of delta-f is reset, but not the particle's trajectory. This has the effect of occasionally averaging delta-f of nearby (in the phase space) particles. We are currently trying to estimate the dissipation (or effective collision operator). We have been using GEM to study turbulence and transport in NSTX with realistic equilibrium density and temperature profiles, including impurities, magnetic geometry and ExB shear flow. Greg Rewoldt, PPPL, has developed a TRANSP interface for GEM that specifies the equilibrium profiles and parameters needed to run realistic NSTX cases. Results were reported at the American Physical Society - Division of Plasma Physics, and we are currently running convergence studies to ensure physical results. We are also studying the effect of parallel shear flows, which can be quite strong in NSTX. Recent long-time simulations of electron temperature gradient driven turbulence, show that zonal flows slowly grow algebraically via the Rosenbluth-Hinton random walk mechanism. Eventually, the zonal flow gets to a level where it shear suppresses the turbulence. We have demonstrated this behavior with Cyclone base-case parameters, except with a 30% lower temperature gradient. We can demonstrate the same phenomena at higher gradients, but so far, have been unable to get a converged result at the higher temperature gradient. We find that electron ion collisions cause the zonal flows to grow at a slower rate and results in a higher heat flux. So, far all ETG simulations that come to a quasi-steady state show continued build up of zonal flow, see it appears to be a universal phenomena (for ETG). Linear and nonlinear simulations of Collisional and Collisionless trapped electron modes are underway. We find that zonal flow is typically important. We can, however, reproduce the Tannert and Jenko result (that zonal flow is unimportant) using their parameters with the electron temperature three times the ion temperature. For a typical weak gradient core value of density gradient and no temperature gradient, the CTEM is dominant. However, for a steeper density gradient (and still no temperature gradient), representative of the edge, higher k drift-waves are dominant. For the weaker density gradient core case, nonlinear simulations using GEM are routine. For the steeper gradient edge case, the nonlinear fluctuations are very high and a stationary state has not been obtained. This provides motivation for the particle-continuum algorithm. We also note that more physics, e.g. profile variation and equilibrium ExB shear flow should be significantly stabilizing, making such simulations feasible using standard delta-f techniques. This research is ongoing.