Diffusive Energy Transport Research Articles

Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain

Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary driving is increased, this minimal classical model recovers the main features of the "dissipative phase transition" seen experimentally. Between the transmitting and non-transmitting regimes on either side of this transition (which support ballistic and diffusive energy transport respectively), we observe additional dynamical regimes of interest. These include a regime of superdiffusive energy transport at weaker driving strengths, together with a "resonant nonlinear wave" regime at stronger driving strengths, which is characterized by emergent translation symmetry, ballistic energy transport, and coherent oscillations of a nonlinear normal mode. We propose a non-local Lyapunov exponent as an experimentally measurable diagnostic of many-body chaos in this system, and more generally in open systems that are only coupled to an environment at their boundaries.

Changes in Poleward Atmospheric Energy Transport over a Wide Range of Climates: Energetic and Diffusive Perspectives and A Priori Theories

Abstract The midlatitude poleward atmospheric energy transport increases in radiatively forced simulations of warmed climates across a range of models from comprehensive coupled general circulation models (GCMs) to idealized aquaplanet moist GCMs to diffusive moist energy balance models. These increases have been rationalized from two perspectives. The energetic (or radiative) perspective takes the atmospheric energy budget and decomposes energy flux changes (radiative forcing, feedbacks, or surface fluxes) to determine the energy transport changes required by the budget. The diffusive perspective takes the net effect of atmospheric macroturbulence to be a diffusive energy transport down-gradient, so transport changes can arise from changes in mean energy gradients or turbulent diffusivity. Here, we compare these perspectives in idealized moist, gray-radiation GCM simulations over a wide range of climates. The energetic perspective has a dominant role for radiative forcing in this GCM, with cancellation between the temperature feedback components that account for the GCM’s nonmonotonic energy transport changes in response to warming. Comprehensive CMIP5 simulations have similarities in the Northern Hemisphere to the idealized GCM, although a comprehensive GCM over several CO2 doublings has a distinctly different feedback evolution structure. The diffusive perspective requires a non-constant diffusivity to account for the idealized GCM-simulated changes, with important roles for the eddy velocity, dry static stability, and horizontal energy gradients. Beyond diagnostic analysis, GCM-independent a priori theories for components of the temperature feedback are presented that account for changes without knowledge of a perturbed climate state, suggesting that the energetic perspective is the more parsimonious one.

1D Finite Volume Scheme for Simulating Gas–Solid Reactions in Porous Spherical Particles with Application to Biomass Pyrolysis

Models for gas–solid reactions in porous particles typically consist of a set of mass and energy balances in the form of conservation equations. For spherical or close to spherical particles, these equations are formulated in 1D spherical coordinates. In the case where accumulation of gas inside the particle is significant, the balance equations contain convective terms. The present work presents a simple numerical scheme based on flux limited finite volume methods for discretizing conservation equations for convective and diffusive transport of mass and energy in radial direction in a porous sphere. The velocity is governed by Darcy’s law coupled to an equation of state. The proposed scheme is applied to a series of test problems that admit full or partial analytical solutions. For the cases where only partial analytical solutions are available, a Comsol model is adopted for comparison. It is found that the scheme is able to resolve step gradients without generating oscillations and that it properly handles changes in the sign of the convective velocity. Applying the scheme for solving a common model for biomass pyrolysis reveals the importance of convective gas transport in the pyrolysis of thermally thick biomass particles.

Unconventional picosecond strain pulses resulting from the saturation of magnetic stress within a photoexcited rare earth layer.

Optical excitation of spin-ordered rare earth metals triggers a complex response of the crystal lattice since expansive stresses from electron and phonon excitations compete with a contractive stress induced by spin disorder. Using ultrafast x-ray diffraction experiments, we study the layer specific strain response of a dysprosium film within a metallic heterostructure upon femtosecond laser-excitation. The elastic and diffusive transport of energy to an adjacent, non-excited detection layer clearly separates the contributions of strain pulses and thermal excitations in the time domain. We find that energy transfer processes to magnetic excitations significantly modify the observed conventional bipolar strain wave into a unipolar pulse. By modeling the spin system as a saturable energy reservoir that generates substantial contractive stress on ultrafast timescales, we can reproduce the observed strain response and estimate the time- and space dependent magnetic stress. The saturation of the magnetic stress contribution yields a non-monotonous total stress within the nanolayer, which leads to unconventional picosecond strain pulses.

Entanglement front generated by an impurity traveling in an isolated many-body quantum system

We investigate the effect on the entanglement dynamics of an impurity moving at constant velocity in a closed quantum system. We focus on one-dimensional strongly-correlated lattice models, both in the presence of integrable and chaotic dynamics. In the former, the slow impurity is preceded by fast quasiparticles carrying an "endogenous" entanglement front which decays in time as a power-law; on the contrary, a fast impurity drags itself an "exogenous" entanglement front which never fades. We argue that these effects are valid for generic systems whose correlations propagate inside a light-cone. To assess the fully chaotic regime, we formulate a random circuit model which supports a moving impurity and a sharp lightcone. Although the qualitative behavior is similar to the integrable case, the endogenous regime is only visible at short times due to the onset of diffusive energy transport. Our predictions are supported by numerical simulations in the different regimes.

Mixing and heat transfer in micro/nano-channel due to charged corrugated surfaces

Fluid transport and mixing analysis is performed numerically in micro/nano-channels, where the channel walls are fabricated with separated charged blocks. Two different streams of miscible fluids with different concentrations are supplied through the inlet port with an external applied electric field. The fluid is flowing under low Reynolds numbers experiences convection and diffusion effects which promote the desired mixing. In this paper theory of dynamic equations are used for the time scales with the coefficient as zero linear growth. Both Joule heating effects and pressure variation is considered for the fluid transport using a lubrication theory approximation, considering the combined formulation of the Navier-Stokes and Nernst-Planck model for electromigration. It is observed that axial pressure variation are maximum above the heterogeneous regions providing a zero gradient along the fully-developed regions. The diffusive transport of thermal energy for an unaltered wall temperature can be enhanced due to the augmentation of the local fluid temperature with the applied electric field. It is observed that wall heterogeneity creates a high convective zone in the diffuse layers resulting complex flow structures of fluids and ions. The improvement of ion transport in the species layers at different horizontal positions significantly enhance the mixing rate.

X-ray Fokker\u2013Planck equation for paraxial imaging

The Fokker–Planck equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity equation. The x-ray Fokker–Planck equation can simultaneously account for both propagation-based phase contrast, and the diffusive effects of sample-induced small-angle x-ray scattering, when forming an x-ray image of a thin sample. Two derivations are given for the Fokker–Planck equation associated with x-ray imaging, together with a Kramers–Moyal generalisation thereof. Both equations are underpinned by the concept of unresolved speckle due to unresolved sample micro-structure. These equations may be applied to the forward problem of modelling image formation in the presence of both coherent and diffusive energy transport. They may also be used to formulate associated inverse problems of retrieving the phase shifts due to a sample placed in an x-ray beam, together with the diffusive properties of the sample. The domain of applicability for the Fokker–Planck and Kramers–Moyal equations for paraxial imaging is at least as broad as that of the transport-of-intensity equation which they generalise, hence the technique is also expected to be useful for paraxial imaging using visible light, electrons and neutrons.

Role of conserved quantities in Fourier's law for diffusive mechanical systems

Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space-time scale. In these situations the Fourier law depends also from the gradient of the other conserved quantities. The rotor chain is a classical example of such systems, where energy and angular momentum are conserved. We review here some recent mathematical results about diffusive transport of energy and other conserved quantities, in particular for systems where the bulk Hamiltonian dynamics is perturbed by conservative stochastic terms. The presence of the stochastic dynamics allows to define the transport coefficients (thermal conductivity) and in some cases to prove the local equilibrium and the linear response argument necessary to obtain the diffusive equations governing the macroscopic evolution of the conserved quantities. Temperature profiles and other conserved quantities profiles in the non-equilibrium stationary states can be then understood from the non-stationary diffusive behaviour. We also review some results and open problems on the two step approach (by weak coupling or kinetic limits) to the heat equation, starting from mechanical models with only energy conserved.

Asymmetry in energy versus spin transport in certain interacting disordered systems

We study energy transport in XXZ spin chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries. We discuss the transition between diffusive and subdiffusive transport regimes in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder strengths. However, when finite magnetization is induced, both energy and spin currents decay as a function of system size with the same exponent. Based on this, we conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase-space; we suggest this is due to conservation laws present in the clean XXZ limit.

Ballistic and diffusive vibrational energy transport in molecules.

Energy transport in molecules is essential for many areas of science and technology. Strong covalent bonds of a molecular backbone can facilitate the involvement of the molecule's high-frequency modes in energy transport, which, under certain conditions, makes the transport fast and efficient. We discuss such conditions and describe various transport regimes in molecules, including ballistic, diffusive, directed diffusion, and intermediate regime cases, in light of recently developed experimental and theoretical approaches.

Tomographic imaging of non-local media based on space-fractional diffusion models

We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models

The Sachdev-Ye-Kitaev model is a (0 + 1)-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with N Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large N limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a “butterfly velocity” describing the propagation of chaos in space. We mainly present results for a (1 + 1)-dimensional example, and discuss the general case near the end.

Enhanced Thermionic-Dominated Photoresponse in Graphene Schottky Junctions.

Vertical heterostructures of van der Waals materials enable new pathways to tune charge and energy transport characteristics in nanoscale systems. We propose that graphene Schottky junctions can host a special kind of photoresponse that is characterized by strongly coupled heat and charge flows that run vertically out of the graphene plane. This regime can be accessed when vertical energy transport mediated by thermionic emission of hot carriers overwhelms electron-lattice cooling as well as lateral diffusive energy transport. As such, the power pumped into the system is efficiently extracted across the entire graphene active area via thermionic emission of hot carriers into a semiconductor material. Experimental signatures of this regime include a large and tunable internal responsivity [Formula: see text] with a nonmonotonic temperature dependence. In particular, [Formula: see text] peaks at electronic temperatures on the order of the Schottky barrier potential ϕ and has a large upper limit [Formula: see text] (e/ϕ = 10 A/W when ϕ = 100 meV). Our proposal opens up new approaches for engineering the photoresponse in optically active graphene heterostructures.

Thermal Conductivity of the One-Dimensional Fermi-Hubbard Model.

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at a finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interaction strengths. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultracold quantum-gas experiments and for transport measurements with quasi-one-dimensional materials.

Thermalization of entanglement.

We explore the dynamics of the entanglement entropy near equilibrium in highly entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with either less or more entanglement entropy than the equilibrium value, as well as the dynamics of the spontaneous fluctuations of the entanglement that occur in equilibrium. For the spin chain with a time-independent Hamiltonian and thus an extensive conserved energy, we find slow relaxation of the entanglement entropy near equilibration. Such slow relaxation is absent in a Floquet spin chain with a Hamiltonian that is periodic in time and thus has no local conservation law. Therefore, we argue that slow diffusive energy transport is responsible for the slow relaxation of the entanglement entropy in the Hamiltonian system.

Validation of turbulent flame speed models for methane–air-mixtures at high pressure gas engine conditions

To describe the premixed combustion of natural gas in internal combustion engines, the flamelet approach is often assumed to be appropriate. It postulates a thin flame front which is wrinkled by turbulence but locally spreads like a laminar flame. Numerous correlations for the macroscopic turbulent flame speed to the local laminar flame speed exist. In this study seven correlations are validated at engine conditions, i.e., at high pressure (up to 7.0MPa) and high turbulence (turbulent Reynolds number up to 4.4·104), with the help of measurements from a single cylinder research gas engine. The stoichiometry, the exhaust gas recirculation rate, and the engine speed are varied. Simulations of the detailed reaction kinetics with the diffusive species and energy transport are performed to calculate the laminar flame speed. The flame propagation is described by a zonal cylinder model on the basis of the measured in-cylinder pressure traces, to determine the turbulent flame speed with respect to the thermal expansion of the reacting gas. Additionally, Computational Fluid Dynamics (CFD) simulations of the in-cylinder charge motion are performed to describe the turbulent flow field. It is found that four flame speed correlations including a pressure-dependent term predict flame speed ratios in quantitative accordance to the measurements. This is noteworthy, as these correlations are mostly developed for lower turbulence and at considerable lower pressure. It supports the hypothesis that flamelet-like combustion is still found above the Klimov–Williams criterion.

Coexistence of energy diffusion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking.

In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit. We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently, we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.

Simulation of complete liquid–vapour phase change process inside porous evaporator using local thermal non-equilibrium model

The present article demonstrates the necessity and the usefulness of a newly proposed smoothing algorithm for the effective diffusion coefficient in order to avoid non-physical “jump” in the predicted properties during numerical simulations of the complete liquid–vapour phase change process within porous media. The formulation is based on the two-phase mixture model (TPMM) along with the assumption of local thermal non-equilibrium (LTNE) condition where the governing equations have been solved using the finite volume method. For the purpose of demonstration, one-dimensional phase change problem of water has been considered. Comparison between results obtained with the local thermal equilibrium (LTE) and LTNE models indicates that wherever applicable, particularly for lower inlet Reynolds number and higher heat input, the latter should be used. The effect of employing different models for the partitioning of wall heat flux using LTNE model has been found negligible owing to the very high convective heat transfer coefficient between the solid and the fluid phases. A representative parametric study suggests that the diffusive energy transport process in the upstream direction through the solid and the fluid phases has a strong influence on the initiation and the termination of the phase change process.

Vibrational energy transport in molecules studied by relaxation-assisted two-dimensional infrared spectroscopy.

This review presents an overview of the relaxation-assisted two-dimensional infrared (RA 2DIR) spectroscopy method for measuring structures and energy transport dynamics in molecules. The method strongly enhances the range of accessible distances compared to traditional 2DIR and offers new structural reporters, such as the energy transport time, cross-peak amplification factors, and connectivity patterns. The use of the method for assigning vibrational modes with various levels of delocalization is illustrated. RA 2DIR relies on vibrational energy transport in molecules; as such, the transport mechanism can be conveniently studied by the method. Applications to identify diffusive and ballistic energy transport are demonstrated.

Generalised scale-by-scale energy-budget equations and large-eddy simulations of anisotropic scalar turbulence at various Schmidt numbers

A necessary condition for the accurate prediction of turbulent flows using large-eddy simulation (LES) is the correct representation of energy transfer between the different scales of turbulence in the LES. For scalar turbulence, transfer of energy between turbulent length scales is described by a transport equation for the second moment of the scalar increment. For homogeneous isotropic turbulence, the underlying equation is the well-known Yaglom equation. In the present work, we study the turbulent mixing of a passive scalar with an imposed mean gradient by homogeneous isotropic turbulence. Both direct numerical simulations (DNS) and LES are performed for this configuration at various Schmidt numbers, ranging from 0.11 to 5.56. As the assumptions made in the derivation of the Yaglom equation are violated for the case considered here, a generalised Yaglom equation accounting for anisotropic effects, induced by the mean gradient, is derived in this work. This equation can be interpreted as a scale-by-scale energy-budget equation, as it relates at a certain scale r terms representing the production, turbulent transport, diffusive transport and dissipation of scalar energy. The equation is evaluated for the conducted DNS, followed by a discussion of physical effects present at different scales for various Schmidt numbers. For an analysis of the energy transfer in LES, a generalised Yaglom equation for the second moment of the filtered scalar increment is derived. In this equation, new terms appear due to the interaction between resolved and unresolved scales. In an a-priori test, this filtered energy-budget equation is evaluated by means of explicitly filtered DNS data. In addition, LES calculations of the same configuration are performed, and the energy budget as well as the different terms are thereby analysed in an a-posteriori test. It is shown that LES using an eddy viscosity model is able to fulfil the generalised filtered Yaglom equation for the present configuration. Further, the dependence of the terms appearing in the filtered energy-budget equation on varying Schmidt numbers is discussed.