Steady-state Density Profiles Research Articles

Phase-plane analysis of driven multi-lane exclusion models

We show how a fixed-point-based boundary layer analysis technique can be used to obtainthe steady-state particle density profiles of driven exclusion processes on two-lane systemswith open boundaries. We have considered two distinct two-lane systems. In the first,particles hop on the lanes in one direction obeying the exclusion principle and there is noexchange of particles between the lanes. The hopping on one lane is affected by the particleoccupancies on the other, which thereby introduces an indirect interaction among the lanes.Through a phase-plane analysis of the boundary layer equation, we show why the bulkdensity undergoes a sharp change as the interaction between the lanes is increased. Thesecond system involves one lane with a driven exclusion process and the other withbiased diffusion of particles. In contrast to the previous model, here there is adirect interaction between the lanes due to particle exchange between them. Inthis model, we have looked at two possible scenarios with constant (flat) andnon-constant bulk profiles. The fixed-point-based boundary layer method provides a newperspective on several aspects including those related to maximal/minimal currentphases, the possibilities of shocks under very restricted boundary conditions for theflat profile but over a wide range of boundary conditions for the non-constantprofile.

Phase Diagram and Density Large Deviations of a NonconservingABCModel

The effect of particle-nonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steady-state density profile of the conserving model. In this limit one can define a chemical potential and identify first order transitions via Maxwell's construction, similarly to what is done in equilibrium systems. This method may be applied to other driven models subjected to slow nonconserving dynamics.

Modeling the Effects of Molecular Length Scale Electrode Heterogeneity in Organic Solar Cells

Kinetic Monte Carlo simulations of planar heterojunction (PHJ) organic solar cells (OPVs) constructed with electronically heterogeneous electrodes are presented which correlate the extent and length scale of electrode heterogeneity with their capacity for collecting photogenerated charge carriers. The PHJ OPV is modeled as an ensemble of discrete 1 nm3 molecular sites and 1 nm2 electrode sites for which we individually assign various effective activation energies for charge hopping. Utilizing Marcus theory to describe charge transfer reactions within the energetically disordered lattice, described by a Gaussian distribution of discrete site energies, we demonstrate the sensitivity of solar cell device performance to nanometer length scale heterogeneity at the electrode-active layer contact. Such sensitivity is reflected in the steady-state charge density profiles in the vicinity of the electrode-active material interface, charge collection efficiencies, and rates of recombination at the donor–acceptor (D/...

Long-range steady-state density profiles induced by localized drive

We show that the presence of a localized drive in an otherwise diffusive system results in steady-state density and current profiles that decay algebraically to their global average value, away from the drive in two or higher dimensions. An analogy to an electrostatic problem is established, whereby the density profile induced by a driving bond maps onto the electrostatic potential due to an electric dipole located along the bond. The dipole strength is proportional to the drive, and is determined self-consistently by solving the electrostatic problem. The profile resulting from a localized configuration of more than one driving bond can be straightforwardly determined by the superposition principle of electrostatics. This picture is shown to hold even in the presence of exclusion interaction between particles.

Asymmetric exclusion process for modeling of information flow

In this paper we investigate the dynamics of totally asymmetric exclusion process (TASEPs) on a one-dimensional lattice with long-range hopping and parallel update. The model is inspired by information traffic over networks. Compared to other TASEP models, particles in our model will firstly try to hop to the last site with a probability q. The probability q may reflect network reliability or available bandwidth. A mean-field approach is developed to deal with the long-range hopping. Theoretical calculations for stationary particle currents, density profiles and a phase diagram have been obtained. There are two possible stationary phases (LD and HD) in the system, corresponding to free flow and jammed flow, respectively. Interestingly, bulk density in the LD phase tends to zero, while in the HD phase it is the same as that of the normal TASEP. The LD and HD phase regions are obtained numerically. The steady-state currents and density profiles obtained from computer simulations show a very good agreement with theoretical predictions. The model and theoretical results may provide a better understanding of information traffic flow over networks.

IONIC COMPOSITION STRUCTURE OF CORONAL MASS EJECTIONS IN AXISYMMETRIC MAGNETOHYDRODYNAMIC MODELS

We present the ionic charge state composition structure derived from axisymmetric MHD simulations of coronal mass ejections (CMEs), initiated via the flux-cancellation and magnetic breakout mechanisms. The flux-cancellation CME simulation is run on the Magnetohydrodynamics-on-A-Sphere code developed at Predictive Sciences, Inc., and the magnetic breakout CME simulation is run on ARC7 developed at NASA GSFC. Both MHD codes include field-aligned thermal conduction, radiative losses, and coronal heating terms which make the energy equations sufficient to calculate reasonable temperatures associated with the steady-state solar wind and model the eruptive flare heating during CME formation and eruption. We systematically track a grid of Lagrangian plasma parcels through the simulation data and calculate the coronal density and temperature history of the plasma in and around the CME magnetic flux ropes. The simulation data are then used to integrate the continuity equations for the ionic charge states of several heavy ion species under the assumption that they act as passive tracers in the MHD flow. We construct two-dimensional spatial distributions of commonly measured ionic charge state ratios in carbon, oxygen, silicon, and iron that are typically elevated in interplanetary coronal mass ejection (ICME) plasma. We find that the slower CME eruption has relatively enhanced ionic charge states and the faster CME eruption shows basically no enhancement in charge states—which is the opposite trend to what is seen in the in situ ICME observations. The primary cause of the difference in the ionic charge states in the two simulations is not due to the different CME initiation mechanisms per se. Rather, the difference lies in their respective implementation of the coronal heating which governs the steady-state solar wind, density and temperature profiles, the duration of the connectivity of the CME to the eruptive flare current sheet, and the contribution of the flare-heated plasma associated with the reconnection jet outflow into the ejecta. Despite the limitations inherent in the first attempt at this novel procedure, the simulation results provide strong evidence in support of the conclusion that enhanced heavy ion charge states within CMEs are a direct consequence of flare heating in the low corona. We also discuss future improvements through combining numerical CME modeling with quantitative ionic charge state calculations.

Bidirectional transport in a multispecies totally asymmetric exclusion-process model

We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one-dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies, and organelles such as mitochondria. This minimal model, a multispecies totally asymmetric exclusion process (TASEP) with directional switching, can provide a framework for understanding the interplay between the switching dynamics of individual particles and the collective movement of particles in one dimension. When switching is much faster than translocation, the steady-state density and current profiles of the particles are homogeneous in the bulk and are well described by mean-field (MF) theory, as determined by comparison to a Monte Carlo simulation. In this limit, we can map this model to the exactly solvable partially asymmetric exclusion-process (PASEP) model. Away from this fast switching regime the MF theory fails, although the average bulk density profile still remains homogeneous. We study the steady-state behavior as a function of the ratio of the translocation and net switching rates Q and find a unique first-order phase transition at a finite Q associated with a discontinuous change of the bulk density. When the switching rate is decreased further (keeping translocation rate fixed), the system approaches a jammed phase with a net current that tends to zero as J~1/Q. We numerically construct the phase diagram for finite Q.

Smoothly varying hopping rates in driven flow with exclusion

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved, in a mean-field adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open-boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.

Density profiles in open superdiffusive systems

We numerically solve a discretized model of Lévy random walks on a finite one-dimensional domain with a reflection coefficient r and in the presence of sources. At the domain boundaries, the steady-state density profile is nonanalytic. The meniscus exponent μ, introduced to characterize this singular behavior, uniquely identifies the whole profile. Numerical data suggest that μ = α/2 + r(α/2 - 1), where α is the Lévy exponent of the step-length distribution. As an application, we show that this model reproduces the temperature profiles obtained for a chain of oscillators displaying anomalous heat conduction. Remarkably, the case of free-boundary conditions in the chain corresponds to a Lévy walk with negative reflection coefficient.

A Diffusive System Driven by a Battery or by a Smoothly Varying Field

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit, the long range pair correlation functions of the system driven by a battery turn out to be very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models.

Spatial pattern formation and polarization dynamics of a nonequilibrium spinor polariton condensate

Quasiparticles in semiconductors---such as microcavity polaritons---can form condensates in which the steady-state density profile is set by the balance of pumping and decay. By taking account of the polarization degree of freedom for a polariton condensate, and considering the effects of an applied magnetic field, we theoretically discuss the interplay between polarization dynamics, and the spatial structure of the pumped decaying condensate. If spatial structure is neglected, this dynamics has attractors that are linearly polarized condensates (fixed points), and desynchronized solutions (limit cycles), with a range of bistability. Considering spatial fluctuations about the fixed point, the collective spin modes can either be diffusive, linearly dispersing, or gapped. Including spatial structure, interactions between the spin components can influence the dynamics of vortices; produce stable complexes of vortices and rarefaction pulses with both co- and counter-rotating polarizations; and increase the range of possible limit cycles for the polarization dynamics, with different attractors displaying different spatial structures.

Diffusion and binding of finite-size particles in confined geometries

Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system and find excellent agreement with our analytic results.

Planet formation around intermediate mass stars

AbstractWe present a mechanism by which gas giants form efficiently around intermediate mass stars. MRI-driven turbulence effectively drives angular momentum transport in regions of the disk with sufficiently high ionization fraction. In the inner regions of the disk, where the midplane temperature is above ∼1000K, thermal ionization effectively couples the disk to the magnetic field, providing a relatively large viscosity. A pressure maximum will develop outside of this region as the gaseous disk approaches a steady-state surface density profile, trapping migrating solid material. This rocky material will coagulate into planetesimals which grow rapidly until they reach isolation mass. Around intermediate mass stars, viscous heating will push the critical radius for thermal ionization of the midplane out to around 1 AU. This will increase the isolation mass for solid cores. Planets formed here may migrate inwards due to type II migration, but they will induce the formation of subsequent giant planets at the outer edge of the gap they have opened. In this manner, gas giants can form around intermediate mass stars at a few AU.

Impurity Transport in Alcator C-Mod Plasmas

Trace nonrecycling impurities (scandium and CaF2) have been injected into Alcator C-Mod plasmas in order to determine impurity transport coefficient profiles in a number of operating regimes. Recycling Ar has also been injected to characterize steady-state impurity density profiles. Subsequent impurity emission has been observed with spatially scanning X-ray and vacuum ultraviolet spectrometer systems, in addition to very high spatial resolution X-ray and bolometer arrays viewing the plasma edge. Measured time-resolved brightness profiles of helium-, lithium-, and beryllium-like transitions have been compared with those calculated from a transport code that includes impurity diffusion and convection, in conjunction with an atomic physics package for individual line emission. Similar modeling has been performed for the edge observations, which are unresolved in energy. The line time histories and the profile shapes put large constraints on the impurity diffusion coefficient and convection velocity profiles. In L-mode plasmas, impurity confinement times are short (~20 ms), with diffusivities in the range of 0.5 m2/s, anomalously large compared to neoclassical values. During Enhanced Dα (EDA) H-modes, the impurity confinement times are longer than in L-mode plasmas, and the modeling suggests that there exists inward convection (≤50 m/s) near the plasma edge, with greatly reduced diffusion (of order 0.1 m2/s), also in the region of the edge transport barrier. These edge values of the transport coefficients during EDA H-mode are qualitatively similar to the neoclassical values. In edge localized mode-free H-mode discharges, impurity accumulation occurs, dominated by large inward impurity convection in the pedestal region. A scaling of the impurity confinement time with H-factor reveals a very strong exponential dependence. In internal transport barrier discharges, there is significant impurity accumulation inside of the barrier foot, typically at r/a = 0.5. Steady-state impurity density profiles in L-mode plasmas have a large up-down asymmetry near the last closed flux surface. The impurity density enhancement, in the direction opposite to the ion B × ΔB drift, is consistent with modeling of neoclassical parallel impurity transport.

Driven lattice gas of dimers coupled to a bulk reservoir

We investigate the nonequilibrium steady state of a one-dimensional (1D) lattice gas of dimers. The dynamics is described by a totally asymmetric exclusion process (TASEP) supplemented by attachment and detachment processes, mimicking chemical equilibrium of the 1D driven transport with the bulk reservoir. The steady-state phase diagram and current and density profiles are calculated using both a refined mean-field theory and extensive stochastic simulations. As a consequence of the on-off kinetics, a phase coexistence region arises intervening between low and high density phases such that the discontinuous transition line of the TASEP splits into two continuous ones. The results of the mean-field theory and simulations are found to coincide. We show that the physical picture obtained in the corresponding lattice gas model with monomers is robust, in the sense that the phase diagram changes quantitatively, but the topology remains unaltered. The mechanism for phase separation is identified as generic for a wide class of driven 1D lattice gases.

Soft colloids driven and sheared by traveling wave fields

We study the dynamics of soft colloids interacting via a Gaussian pair potential in an external moving potential which is periodic in the spatial coordinate of the direction of motion. Both dynamical density functional theory and Brownian dynamics computer simulations are used to predict the steady-state density profiles. Two different situations are investigated: the first corresponds to a light wave that travels with a constant velocity v through the quiescent solvent containing the colloidal suspension. The second setup consists of two parallel repulsive walls with a periodic topographical substructure. One of the walls is at rest relative to the solvent while the other is in motion, inducing a shearing of the suspension. In the first case, we find that the amplitude of the steady-state density behaves nonmonotonically with the traveling speed v of the wave if the shape of the wave contains an edge: for increasing v , it first grows and then decreases. In the second setup we show that a strongly confined suspension induces a shear resistance which is a nonmonotonic function of the wall velocity. These effects are verifiable in real-space experiments on colloidal suspensions exposed to external laser-optical fields. In both situations, the dynamical density functional theory is in good agreement with the Brownian dynamics simulation data.

Molecular dynamics simulation of heat conduction in near-critical fluids

Using molecular dynamics simulations we study supercritical fluids near the gas-liquid critical point under heat flow in two dimensions. We calculate the steady-state temperature and density profiles. The resultant thermal conductivity exhibits critical singularity in agreement with the mode-coupling theory in two dimensions. We also calculate distributions of the momentum and heat fluxes at fixed density. They indicate that liquidlike (entropy-poor) clusters move toward the warmer boundary and gaslike (entropy-rich) regions move toward the cooler boundary in a temperature gradient. This counterflow results in critical enhancement of the thermal conductivity.

Structural response in steady-state flow of a multi-component driven system: interacting lattice gas simulation

The effects of molecular weights (MA,MB) on the self-organized segregation of immiscible constituents (A,B) driven by pressure bias (H=0.0–1.0) generated by geologic processes are examined by an interacting lattice gas Monte Carlo simulation. Constituents (A,B), released from a source at the bottom according to their lattice concentrations, can escape the lattice from top or bottom. The longitudinal steady-state density profiles (A,B) depend on their molecular weight and bias with linear, exponential, and non-monotonic decays with the height. The transverse density profiles show signatures of partial layering. The total number (N) of constituents remains nearly constant in steady state and seems to decay with the bias, N∝H-0.14 for all but extreme range of H. At MA=0.1, MB⩾0.8, number of constituents (NA,NB) show non-monotonic dependence on H with NB⪢NA but a maximum in NA and minimum in NB.

Structural response in steady-state flow of a multi-component driven system: interacting lattice gas simulation

The effects of molecular weights ( M A , M B ) on the self-organized segregation of immiscible constituents ( A , B ) driven by pressure bias ( H = 0.0 –1.0) generated by geologic processes are examined by an interacting lattice gas Monte Carlo simulation. Constituents ( A , B ) , released from a source at the bottom according to their lattice concentrations, can escape the lattice from top or bottom. The longitudinal steady-state density profiles ( A , B ) depend on their molecular weight and bias with linear, exponential, and non-monotonic decays with the height. The transverse density profiles show signatures of partial layering. The total number ( N ) of constituents remains nearly constant in steady state and seems to decay with the bias, N ∝ H - 0.14 for all but extreme range of H . At M A = 0.1 , M B ⩾ 0.8 , number of constituents ( N A , N B ) show non-monotonic dependence on H with N B ⪢ N A but a maximum in N A and minimum in N B .

Chapter 12: FT3 - An Experiment to Study Burning Plasma Physics Issues in Deuterium Plasmas

A conceptual study is presented for a substantial upgrade of the Frascati Tokamak Upgrade (FTU) up to B = 8 T, I = 6 MA, and R [approximately equal to] 1.3 m to study burning plasma (BP) issues in deuterium plasmas operating up to an equivalent DT gain close to Q = 2 in the ELMy H-mode and to Q = 5 with an internal transport barrier (ITB). The effect of alpha particles is simulated by ~1 MeV fast 3He minority heating produced by ion cyclotron resonance heating (20 MW). Thanks to the high-density values ([approximately equal to]4 × 1020 m-3), the FT3 plasmas are characterized by short electron-ion equipartition time (60 ms in the ELMy H-mode scenario) and slowing-down time (44 ms), with respect to the energy confinement time of ~340 ms, a feature characteristic of BP experiments but not always satisfied with present tokamak devices. Advanced scenarios at 5 T with fully noninductive current drive can be investigated with a steady-state current density profile achieved in <5 s. The aim of FT3 is to prepare ITER operation and to provide a test bed for the development of the ITER auxiliary system and diagnostics. Elements of the scientific program are as follows: the investigation of energetic particle collective effects, optimization of H-mode scenarios, development of improved H-mode scenarios and scenarios with ITBs, magnetohydrodynamic and transport studies in ITER-relevant conditions, and study of edge plasma dynamics. FT3 can use all the existing facilities available in Frascati and could be constructed in ~5 yr.