Nonequilibrium Transport Research Articles

Thermoelectric cooling of a finite reservoir coupled to a quantum dot

We investigate nonequilibrium transport of charge and heat through an interacting quantum dot coupled to a finite electron reservoir. Both the quantum dot and the finite reservoir are coupled to conventional electric contacts, i.e., infinite electron reservoirs, between which a bias voltage can be applied. We develop a phenomenological description of the system, combining a rate equation for transport through the quantum dot with standard expressions for bulk transport between the finite and infinite reservoirs. The finite reservoir is assumed to be in a quasiequilibrium state with a time-dependent chemical potential and temperature which we solve for self-consistently. We show that the finite reservoir can have a large impact on the stationary state transport properties, including a shift and broadening of the Coulomb diamond edges. We also demonstrate that there is a region around the conductance lines where a heat current flows out of the finite reservoir. Our results reveal the dependence of the temperature that can be reached by this thermoelectric cooling on the system parameters, in particular the coupling between the finite and infinite reservoirs and additional heat currents induced by electron-phonon couplings, and can thus serve as a guide for experiments on quantum-dot-enabled thermoelectric cooling of finite electron reservoirs. Finally, we study the full dynamics of the system, with a particular focus on the timescales involved in the thermoelectric cooling. Published by the American Physical Society 2024

Modeling of non-equilibrium suspended sediment transport process in open channel flows with vegetation

A mathematical model based on advection-diffusion theory is established to study the non-equilibrium sediment transport process in vegetated channels. The effects of vegetation on velocity distribution and sediment diffusion coefficients were considered, respectively. Validation against experimental data from flume studies confirms the model's ability to accurately predict the longitudinal sediment deposition rate and the vertical distribution of suspended sediment concentration (SSC). A comparative analysis of three sediment diffusion coefficient formulations indicates that the linear-exponential formula provides a more precise estimate of εsz, and the linear-exponential formula performs well in predicting the turbulent diffusion coefficients of both rigid and flexible vegetation when gently swaying. Moreover, the distance required for SSC to regain equilibrium is influenced by the submergence level of the vegetation canopy. At lower submergence levels, the canopy shear vortices significantly affect the vertical exchange of sediment, and the sediment diffusion coefficients exhibit pronounced stratification near the vegetation canopy. An increase in vegetation density at these lower submergence levels intensifies the shear vortices, thereby extending the distance needed for SSC to reach equilibrium. At higher submergence levels, the impact of canopy shear vortices is lessened, which reduces sediment diffusion coefficient stratification characteristics, and the flow is similar to rough boundary layer flow. An increase in vegetation density increases flow resistance, which shortens the distance required for SSC to attain equilibrium. However, further efforts are required to explore turbulent characteristics with highly flexible vegetation motion and the grain size distribution of non-uniform sediments in vegetated flows.

An implicit unified gas-kinetic particle method with large time steps for gray radiation transport

For a long time, efficient algorithms for high-dimensional equations, represented by photon radiation transport, have been one important topic in the development of computational methods for particle transport processes. In this paper, we present an implicit unified gas-kinetic particle (IUGKP) method for multiscale gray radiative transfer. Based on the integral solution of the radiative transfer equation, the photon transport processes are categorized into non-equilibrium transport processes with a large photon free path and equilibrium transport processes with a small photon free path. The long-path processes are solved by an implicit Monte Carlo (IMC) method, and the short-path processes are solved by an implicit diffusion system. The closure formulation of photon distribution is derived from the local integral solution of the radiative transfer equation to couple the IMC and diffusion system. The improvement of the proposed IUGKP method over UGKP method is that particles can be tracked continuously instead of just until the first collision, making simulation with large time steps possible. The IUGKP method has the properties of asymptotic-preserving (AP) and regime-adaptive (RA). The AP property states that the IUGKP method converges to the consistent numerical methods for the asymptotic limiting equations of RTE in the limiting regimes. The RA property states that the computational accuracy of the IUGKP method adapts to the regimes. In this paper, the mathematical proof of the AP and RA properties is presented, and the multiscale numerical tests are performed to demonstrate the accuracy and efficiency of the IUGKP method.

Non-equilibrium solute transport in a fractured rock matrix system under a radial flow pattern

Non-equilibrium solute transport in a fractured rock matrix system under a radial flow pattern

Spatiotemporal Modeling of Mitochondrial Network Architecture

In many cell types, mitochondria undergo extensive fusion and fission to form dynamic, responsive network structures that contribute to a number of homeostatic, metabolic, and signaling functions. The relationship between the dynamic interactions of individual mitochondrial units and the cell-scale network architecture remains an open area of study. In this work, we use coarse-grained simulations and approximate analytic models to establish how the network morphology is governed by local mechanical and kinetic parameters. The transition between fragmented structures and extensive networks is controlled by local fusion-to-fission ratios, network density, and geometric constraints. Similar fusion rate constants are found to account for the very different structures formed by mammalian networks (poised at the percolation transition) and well-connected budding yeast networks. Over a broad parameter range, the simulated network structures can be described by effective mean-field association constants that exhibit a nonlinear dependence on the microscopic nonequilibrium fusion, fission, and transport rates. Intermediate fusion rate constants are shown to result in the highest rates of network remodeling, with mammalian mitochondrial networks situated in a regime of high turnover. This spatially resolved modeling and simulation framework helps elucidate the emergence of cellular scale network structures, and allows for the quantitative extraction of microscopic kinetic parameters from past and future experimental data. Published by the American Physical Society 2024

Interference effects in nonequilibrium quantum transport with long-range interactions

Abstract We investigate how long-range power-law hopping interaction, ∼ 1/r a , affects the characteristics of dissipative quantum transport in a nonequilibrium setting. The model under consideration is a noninteracting bosonic chain subject to thermal baths of differing temperature at its boundaries and dephasing noise which is applied uniformly to all the sites. It is shown that the steady-state current may vary nonmonotonically and has a peak for a finite a depending on the position of the cold bath. This site-specific behaviour stems back to the interference effect caused by the parity of the total sites N and the baths positions. The fractional nature of the system, along with the interplay between coherent and incoherent transport, will affect the steady state current that characterizes the transport.

Coupled Thermal and Power Transport of Optical Waveguide Arrays: Photonic Wiedemann-Franz Law and Rectification Effect.

In isolated nonlinear optical waveguide arrays, simultaneous conservation of longitudinal momentum flow ("internal energy") and optical power ("particle number") of the optical modes enables study of coupled thermal and particle transport in the negative temperature regime. Based on exact numerical simulation and rationale from Landauer formalism, we predict generic photonic version of the Wiedemann-Franz law in such systems, with the Lorenz number L∝|T|^{-2}. This is rooted in the spectral decoupling of thermal and particle current, and their different temperature dependence. In addition, in asymmetric junctions, relaxation of the system toward equilibrium shows apparent asymmetry for positive and negative biases, indicating rectification behavior. This Letter illustrates the possibility of simulate nonequilibrium transport processes using optical networks, in parameter regimes difficult to reach in natural condensed matter or atomic gas systems. It also provides new insights in manipulating power and momentum flow of optical waves in artificial waveguide arrays.

Morphodynamics of sine-generated meandering streams under variations of the width-to-depth ratio: A numerical investigation

Meandering is one of the most common planforms of rivers, however, the ecological and fluvial integrity of meandering rivers are under challenges, resulting from increased anthropogenic pressure and extreme climate events. The present study elucidates the morphodynamics of meandering streams under variations of width-to-depth ratio (B/h) by delving into the two dynamic processes underlying within the flow, i.e. cross-circulatory motion and convective redistribution of the longitudinal flow velocity. Series of numerical simulations are performed in 70° sine-generated meandering streams under increasing flow depth that necessitates a wide range of B/h, characterizing flume experiments to large scale natural rivers. The radial flow structures and the early bed deformation patterns are computed and elucidated. Among the classical cross-circulatory flow patterns, outer bank cell occurs for flows having B/h < 9. Next, the different bed deformation patterns reveal the shift of significance in the driving forces of the bed deformation regarding different B/h ratio. At B/h = 100, bed deformation is dominated by the convective redistribution of the downstream velocity that causes longitudinal adjacent erosion–deposition zones. This implies downstream migration tendency of meander loops. At B/h = 12, the intensified cross-circulatory flow deflects the sediment trajectory, causing extra laterally adjacent erosion–deposition zones that necessitate the lateral expansion tendency of the loop. Decrement of B/h ratio (from 100 on ward) critically enhances the non-equilibrium transport of sediment that can lead to active fluvial evolution of meandering rivers. Overall, the results can be used to improve river management and restoration.

Study on Vertical Distribution of Sediment Concentration in the Tidal Estuary

The vertical distribution of sediment concentration in estuaries is the core issue of suspended sediment transport. At present, there are many researches on the vertical distribution of sediment concentration in rivers, and a lot of results have been achieved, but that in estuaries is seldom studied. The Yellow River Estuary (YRE) and the Qiantang River Estuary (QRE) are typical tidal estuaries with strong erosion/deposition and high concentration in China. Under the action of alternating tidal flow, the suspended sediment transport shows significant time-varying and non-equilibrium transport characteristics. The vertical distribution of sediment concentration is quite different from that of ordinary rivers. This paper analyzes the vertical distribution of sediment concentration under the action of tidal currents based on the theory of sediment movement and diffusion. Compared with equilibrium sediment transport, the vertical distribution of sediment concentration only differs by one vertical distribution coefficient. Based on the analysis of the measured data, it is found that the vertical distribution of sediment concentration in the YRE and QRE is mostly exponential. Firstly, the multivariate relationship between the vertical distribution coefficient and the sediment saturation and suspension index is established by means of the measured water and sediment data of the QRE. The correlation coefficient &amp;lt;I&amp;gt;R&amp;lt;/I&amp;gt;&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt; was above 0.64, which has a good correlation. Finally, the established relationship was validated using measured water and sediment data from the YRE, and the results were basically consistent, indicating that the established formula for vertical distribution of sediment concentration is suitable for general tidal estuaries, and has a certain reference value for the simulation of sediment transport in the YRE and QRE.

Nonequilibrium fast-lithiation of Li4Ti5O12 thin film anode for LIBs

Li4Ti5O12 (LTO) is known for its zero-strain characteristic in electrochemical applications, making it a suitable material for fast-charging applications. Here, we systematically studied the quasi-equilibrium and non-equilibrium lithium-ion transportation kinetics in LTO thin-film electrodes, across a range of scales from the crystal lattice to the microstructured electrodes. At the crystal lattice scale, during the non-equilibrium lithiation process, lithium ions are dispersedly embedded into the 16c position, resulting in more 8a → 16c migration compared with the quasi-equilibrium lithiation, and forming numerous fast lithium diffusion channels inside the LTO lattice. At the microstructural electrode scale, optical spectrum characterizations supported the “nano-filaments” lithiation model in polycrystalline LTO thin-film electrodes during the lithiation process. Our results reveal the patterns of lithium migration and distribution within the LTO thin film electrode under the non-equilibrium and quasi-equilibrium lithiation process, offering profound insights into the potential optimization strategies for enhancing the performance of fast-charging thin film batteries.

Simulation study of phonon transport at the GaN/AlN superlattice interface: Ballistic and non-equilibrium phenomena

GaN/AlN superlattice structures have potential for high electron mobility transistors (HEMTs) applications; however, nonequilibrium phonon transport mechanisms within the superlattice have not been systematically investigated. Therefore, we investigate in detail the non-Fourier thermal conductivity of superlattice structures in the perpendicular interface direction and in the parallel interface direction around the phonon BTE numerical solution in this paper, taking the kinetic parameter based on the first principle as the input parameter of the equations and based on the DOM numerical solution scheme. The study reveals that mode temperature non-equilibrium in superlattices arises from ballistic transport within the layers and interface scattering between the layers. The thermal conductivity (TC) of superlattices can be modulated by scale effects, and in superlattices with small thicknesses, phonons exhibit quasi-ballistic transport. The interface thermal resistance predominantly originates from contributions by acoustic phonon (AP) and the first optical phonon (OP1). With increasing interface density, the combined effects of interface scattering and boundary scattering lead to strong phonon scattering, resulting in a decrease in TC parallel to the interfaces. This work provides valuable insights into the thermal transport properties of GaN/AlN superlattice semiconductors and offers useful theoretical guidance for thermal management through phonon particle properties.

Dynamic fluctuations of current and mass in nonequilibrium mass transport processes

We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of L sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, ⟨Qi2(T)⟩c and ⟨Qsub2(l,T)⟩c , of cumulative (time-integrated) currents up to time T across the ith bond and across a subsystem of size l (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large L≫1 , the second cumulant ⟨Qi2(T)⟩c of the cumulative current up to time T across the ith bond grows linearly as ⟨Qi2⟩c∼T for initial times T∼O(1) , subdiffusively as ⟨Qi2⟩c∼T1/2 for intermediate times 1≪T≪L2 , and then again linearly as ⟨Qi2⟩c∼T for long times T≫L2 . The scaled cumulant liml→∞,T→∞⟨Qsub2(l,T)⟩c/2lT of current across the subsystem of size l and up to time T converges to the density-dependent particle mobility χ(ρ) when the large subsystem-size limit is taken first, followed by the large-time limit; when the limits are reversed, it simply vanishes. Remarkably, regardless of the dynamical rules, the scaled current cumulant D⟨Qi2(T)⟩c/2χL≡W(y) as a function of scaled time y=DT/L2 can be expressed in terms of a universal scaling function W(y) , where D is the bulk-diffusion coefficient; interestingly, the intermediate-time subdiffusive and long-time diffusive growths can be connected through a single scaling function W(y) . The power spectra for current and mass are also exactly characterized by the respective scaling functions. Furthermore, we provide a microscopic derivation of equilibrium-like Green–Kubo and Einstein relations that connect the steady-state current fluctuations to an ‘operational’ mobility (i.e. the response to an external force field) and mass fluctuation, respectively.

Modeling heat conduction with dual-dissipative variables: A mechanism-data fusion method.

Many macroscopic non-Fourier heat conduction models have been developed in the past decades based on Chapman-Enskog, Hermite, or other small perturbation expansion methods. These macroscopic models have achieved great success in capturing non-Fourier thermal behaviors in solid materials, but most of them are limited by small Knudsen numbers and incapable of capturing highly nonequilibrium or ballistic thermal transport. In this paper, we provide a different strategy for constructing macroscopic non-Fourier heat conduction modeling, that is, using data-driven deep-learning methods combined with nonequilibrium thermodynamics instead of small perturbation expansion. We present the mechanism-data fusion method, an approach that seamlessly integrates the rigorous framework of conservation-dissipation formalism (CDF) with the flexibility of machine learning to model non-Fourier heat conduction. Leveraging the conservation-dissipation principle with dual-dissipative variables, we derive an interpretable series of partial differential equations, fine tuned through a training strategy informed by data from the phonon Boltzmann transport equation. Moreover, we also present the inner-step operation to narrow the gap from the discrete form to the continuous system. Through numerical tests, our model demonstrates excellent predictive capabilities across various heat conduction regimes, including diffusive, hydrodynamic, and ballistic regimes, and displays its robustness and precision even with discontinuous initial conditions.

Enhancing herbicide adsorption in low-fertility soil using sugarcane biochar: Insights from Imazapic dynamics

Biochar amendment has emerged as a potential solution for preventing, remediating, and mitigating agricultural compound pollution. This groundbreaking technique not only improves crucial soil properties like porosity, water retention capacity, cation exchange capacity, and pH, but also intricately impacts the interaction and retention mechanisms of polluting molecules. In this study, we investigate the dynamic of the herbicide Imazapic when subjected to applying pyrolyzed biochars, specifically at temperatures of 300 and 500 °C, within the context of a low-fertility soil characterized as dystrophic Yellow Ultisol (YUd) in a sugarcane cultivation area in Igarassu-PE, Brazil. The biochars were produced from sugarcane bagasse by pyrolysis process in a muffle furnace. In laboratory conditions, with saturated soil columns under steady-state, analyses of the mechanisms involved in interaction and transport and determining hydrodispersive parameters for Imazapic were performed by the two-site nonequilibrium transport model using the CXTFIT 2.0 program. Samples of YUd soil amended with biochar pyrolyzed at 300 °C presented a negligible interaction with Imazapic. However, adding biochar pyrolyzed at 500 °C (BC500) to the soil samples enhanced the adsorption coefficient and improved the interaction with Imazapic. This research points out that biochar produced from agricultural waste biomass, such as sugarcane bagasse specifically pyrolyzed at 500 °C, offers a potential means to adsorb herbicides, reducing their leaching to deeper layers of the amended soils and the risk of groundwater contamination and potential environmental negative impacts.

Recursive analytical solution for nonequilibrium multispecies transport of decaying contaminant simultaneously coupled in both the dissolved and sorbed phases

Multispecies transport analytical models that solve advection-dispersion equations (ADEs) are efficient tools for evaluating the transport of decaying contaminants and their sequential products. This study develops a novel semi-analytical model to simulate the multispecies transport of decaying contaminants, considering nonequilibrium sorption and decay in both dissolved and sorbed phases. First-order reversible kinetic sorption equations with decay processes are coupled to ADEs. Recursive analytical solutions, using the Laplace transform and generalized integral transform, are developed to address the mathematical complexity of the governing equations. The model's simulation results show excellent agreement with both numerical models and existing analytical solutions. Applied to a four-member radionuclide decay chain, the model reveals that including decay in the sorbed phase results in a lower concentration of the first member and avoids underestimating the radioactivity concentrations of daughter elements. These differences in dissolved radioactivity concentrations between models with and without sorbed phase decay may impact health risk assessments for radioactive waste disposal. Finally, this study provides a more sophisticated mathematical tool for analyzing multispecies transport in real field conditions where nonequilibrium sorption processes predominantly occur.

Non-equilibrium transport in polymer mixed ionic-electronic conductors at ultrahigh charge densities.

Conducting polymers are mixed ionic-electronic conductors that are emerging candidates for neuromorphic computing, bioelectronics and thermoelectrics. However, fundamental aspects of their many-body correlated electron-ion transport physics remain poorly understood. Here we show that in p-type organic electrochemical transistors it is possible to remove all of the electrons from the valence band and even access deeper bands without degradation. By adding a second, field-effect gate electrode, additional electrons or holes can be injected at set doping states. Under conditions where the counterions are unable to equilibrate in response to field-induced changes in the electronic carrier density, we observe surprising, non-equilibrium transport signatures that provide unique insights into the interaction-driven formation of a frozen, soft Coulomb gap in the density of states. Our work identifies new strategies for substantially enhancing the transport properties of conducting polymers by exploiting non-equilibrium states in the coupled system of electronic charges and counterions.

Analyses of nonequilibrium transport in atmospheric-pressure direct-current argon discharge under different modes

Abstract The key plasma parameters under different discharge modes, such as heavy-particle and electron temperatures, electron number density, and nonequilibrium volume of plasmas, play important roles in various applications of gas discharge plasmas. In this study, a self-consistent two-dimensional nonequilibrium fluid model coupled with an external circuit model is established to reveal the mechanisms related to the discharge modes, including the normal glow, abnormal glow, arc, and glow-to-arc transition modes, with an atmospheric-pressure direct-current (DC) argon discharge as a model plasma system. The modeling results show that, under different discharge modes, the most significant difference between the preceding four discharge modes lies in the current and energy transfer processes on the cathode side. On one hand, the current to the cathode surface is mainly delivered by the ions coming from the plasma column under the glow discharge mode due to the low temperature of the solid cathode, whereas the thermionic and secondary electrons emitted from the hot cathode surface play a very important role under the arc mode with a higher cathode surface temperature and higher ion flux toward the cathode. On the other hand, the energy transfer channel on the cathode side changes from mainly heating the solid cathode under the glow mode to simultaneously heating both the solid cathode and plasma column under the arc mode with an increase in the discharge current. Consequently, the power density in the cathode sheath (P c) was used as a key parameter for judging different discharge modes, and the range of (0.28–1.2) × 1012 W m−3 was determined as a critical window of P c corresponding to the glow-to-arc-mode transition for the atmospheric-pressure DC argon discharge, which was also verified by comparison with the experimental results in this study and the data in the previous literature.

Nonequilibrium quantum heat transport between structured environments

We apply the hierarchical equations of motion technique to analyzing nonequilibrium heat transport in a spin-boson type model, whereby heat transfer through a central spin is mediated by an intermediate pair of coupled harmonic oscillators. The coupling between each pair of oscillators is shown to introduce a localized gap into the effective spectral densities characterizing the system–oscillator–reservoir interactions. Compared to the case of a single mediating oscillator, we find the heat current to be drastically modified at weak system-bath coupling. In particular, a second-order treatment fails to capture the correct steady-state behavior in this regime, which stems from the λ 4-scaling of the energy transfer rate to lowest order in the coupling strength λ. This leads naturally to a strong suppression in the steady-state current in the asymptotically weak coupling limit. On the other hand, the current noise follows the same scaling as in the single oscillator case in accordance with the fluctuation-dissipation theorem. Additionally, we find the heat current to be consistent with Fourier’s law even at large temperature bias. Our analysis highlights a novel mechanism for controlling heat transport in nanoscale systems based on tailoring the spectral properties of thermal environments.

Hot Carrier Nanowire Transistors at the Ballistic Limit.

We demonstrate experimentally nonequilibrium transport in unipolar quasi-1D hot electron devices reaching the ballistic limit at room temperature. The devices are realized with heterostructure engineering in nanowires to obtain dopant- and dislocation-free 1D-epitaxy and flexible bandgap engineering. We show experimentally the control of hot electron injection with a graded conduction band profile and the subsequent filtering of hot and relaxed electrons with rectangular energy barriers. The number of electrons passing the barrier depends exponentially on the transport length with a mean-free path of 200-260 nm, and the electrons reach the ballistic transport regime for the shortest devices with 70% of the electrons flying freely through the base electrode and the barrier reflections limiting the transport to the collector.

Nanoscale thermal imaging of hot electrons by cryogenic terahertz scanning noise microscopy.

Nanoscale thermal imaging and temperature detection are of fundamental importance in diverse scientific and technological realms. Most nanoscale thermometry techniques focus on probing the temperature of lattice or phonons and are insensitive to nonequilibrium electrons, commonly referred to as "hot electrons." While terahertz scanning noise microscopy (SNoiM) has been demonstrated to be powerful in the thermal imaging of hot electrons, prior studies have been limited to room temperature. In this work, we report the development of a cryogenic SNoiM (Cryo-SNoiM) tailored for quantitative hot electron temperature detection at low temperatures. The microscope features a special two-chamber design where the sensitive terahertz detector, housed in a vacuum chamber, is efficiently cooled to ∼5K using a pulse tube cryocooler. In a separate chamber, the atomic force microscope and the sample can be maintained at room temperature under ambient/vacuum conditions or cooled to ∼110K via liquid nitrogen. This unique dual-chamber cooling system design enhances the efficacy of SNoiM measurements at low temperatures. It not only facilitates the pre-selection of tips at room temperature before cooling but also enables the quantitative derivation of local electron temperature without reliance on any adjustable parameters. The performance of Cryo-SNoiM is demonstrated through imaging the distribution of hot electrons in a cold, self-heated narrow metal wire. This instrumental innovation holds great promise for applications in imaging low-temperature hot electron dynamics and nonequilibrium transport phenomena across various material systems.