Non-local Transport Effects Research Articles

Space-time dependent non-local thermal transport effects on laser ablation dynamics in inertial confinement fusion

In inertial confinement fusion (ICF), electron thermal transport plays a key role in laser ablation and the subsequent implosion processes, which always exhibits intractable non-local effects. Simple modifications of the local Spitzer–Härm model with either an artificially-assumed constant flux limiter or a purely time-dependent one are applied to explain some experimental data, but fail to simultaneously reproduce the space-time evolution of the whole laser ablation process. Here, by carrying out a series of one-dimensional and two-dimensional radiation hydrodynamic simulations where the space-time-dependent non-local thermal transport model proposed by Schurt, Nicolaï and Busquet (the SNB model) are self-consistently included, we systematically study the non-local effects on the whole laser ablation dynamics including those occurring at the critical surface, the conduction zone and the ablation front. Different from those obtained previously, our results show that due to the non-local heat flow redistribution and redirection, at the critical surface the thermal flux is more inhibited, in the conduction zone the lateral thermal transport is suppressed, and ahead of the ablation front the plasma is preheated. When combined together they eventually result in significant improvement of the laser absorption efficiency, extension of the conduction zone, increase of both the mass ablation rate and shock velocity. Furthermore, the dependence of these laser ablation dynamics on different drive laser intensities is investigated, which provides beneficial enlightenments on potential laser pulse shaping and/or ignition scheme optimization in ICF.

A unified nonlocal method for capturing discontinuous and multi‐physical behaviors of quasi‐brittle materials

AbstractA unified nonlocal method (UNM) is developed to simulate discontinuous and multi‐physical coupling dynamic behaviors for quasi‐brittle materials. In the proposed method, unified nonlocal momentum equations and constitutive laws are proposed to capture the nonlocal fluid transport effect and loading‐rate effect of quasi‐brittle materials. A general multiscale framework, which couples the proposed nonlocal method and the finite element method (FEM), is presented to accelerate the computational efficiency. The effectiveness and accuracy of this method are verified by comparing its results with experimental observations. Numerical examples show that the proposed model can well simulate the discontinuous and multi‐physical behaviors of quasi‐brittle materials, which can serve an effective numerical method for the simulation of engineering problems such as failure of concrete structures.

Effect of non-local transport of hot electrons on the laser-target ablation

The non-local heat transport of hot electrons during high-intensity laser interaction with plasmas can preheat the fuel and limit the heat flow in inertial confinement fusion. It increases the entropy of the fuel and decreases the final compression. In this paper, the non-local electron transport model that is based on the improved Schurtz–Nicolaï–Busquet (SNB) algorithm has been embedded into the radiation hydrodynamic code and is benchmarked with two classical non-local transport cases. Then, we studied a 2ω laser ablating a CH target by using the non-local module. It is found that the non-local effect becomes significant when the laser intensity is above 1×1014W/cm2. The mass ablation rate from the SNB model is increased compared to that of the flux-limited model due to the lower coronal plasma temperature. This non-local model has a better agreement with the experimental results compared to that of the flux-limited model. The non-local transport is strongly dependent on the laser frequency, and the thresholds that the non-local transport should be considered are obtained for lasers of different frequencies. The appropriate flux-limiters that should be employed in the flux-limited model for different lasers are also presented. The results here should have a good reference for the laser-target ablation applications.

Non-local transport effects in semiconductors under low-field conditions

Macroscopically non-local effects arise in semiconductor devices whenever the mean free path and/or the deBroglie wavelength are not small compared to geometry/flow length scales. In such cases standard diffusion-drift (DD) theory becomes inaccurate and in need of revision, with the best known example being density-gradient (DG) theory. Here we consider a similarly motivated gradient correction to the electron-lattice interaction that accounts for non-locality in the transport physics. Versions of DD and DG theory with this correction are discussed and the DD-based approach is illustrated by applying it to the analysis of long-channel field-effect transistors where it provides a new physics-based approach for treating surface scattering.

Mitigation of the ablative Rayleigh–Taylor instability by nonlocal electron heat transport

The effects of electron nonlocal heat transport (NLHT) on the two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) up to the highly nonlinear phase are reported for the first time through numerical simulations with a multigroup diffusion model. It is found that as well as its role in the linear stabilization of ARTI growth, NLHT can also mitigate ARTI bubble nonlinear growth after the first saturation to the classical terminal velocity, compared with what is predicted by the local Spitzer–Härm model. The key factor affecting the reduction in the linear growth rate is the enhancement of the ablation velocity Va by preheating. It is found that NLHT mitigates nonlinear bubble growth through a mechanism involving reduction of vorticity generation. NLHT enhances ablation near the spike tip and slows down the spike, leading to weaker vortex generation as the pump of bubble reacceleration in the nonlinear stage. NLHT more effectively reduces the nonlinear growth of shorter-wavelength ARTI modes seeded by the laser imprinting phase in direct-drive laser fusion.

A unified non-local fluid transport model for heterogeneous saturated porous media

A unified non-local fluid transport model is proposed for heterogeneous saturated porous media. First, a non-local governing equation of fluid transport is presented based on the Non-ordinary State-based Peridynamics (NOSB-PD), and a novel flux vector state and a non-local Darcy’s law is proposed to illustrate non-local fluid transport effects in heterogeneous saturated porous media. The proposed flux state vector ensures the non-local governing equation of fluid transport model in heterogeneous saturated porous media degenerates into the local one when the horizon of each material point approaches to zero. A non-local pressure gradient at each material point can be obtained by averaging all the flux state vectors in its horizon, which unifies the weak and strong discontinuities of pressure in heterogeneous saturated porous media in a consistent way. Second, a variational formulation of the unified non-local fluid transport model is developed. This variational formulation enables the proposed model to deal with complex boundary conditions, which is difficult or even impossible for current fluid transport models based on Bond-based Peridynamics (BB-PD) and Ordinary State-based Peridynamics (OSB-PD). Third, a fully implicit algorithm combined with the Newton–Raphson method is introduced to solve the general non-linear problems in the heterogeneous saturated porous media. The penalty function method is employed to eliminate the zero-energy mode oscillation in NOSB-PD. Further, numerical examples demonstrate that the proposed model is accurate and can well capture the weak and strong discontinuities of pressure at the material interfaces and crack surfaces in the heterogeneous saturated porous media. Numerical examples also indicate that the model can effectively eliminate the zero-energy mode oscillation inherently rooted in the NOSB-PD, and thus reaches a stable numerical solution.

Continuum simulation of non-local effects in a granular silo discharge flow using a regularized μ(I) rheology model

The effect of non-local momentum transport on a silo discharge process is numerically investigated using a continuum simulation with the μ(I) rheology model in which the gradient expansion model is adopted to account for the non-local effects due to the non-uniform field of inertial number I [Bouzid et al., Phys. Rev. Lett. 111, 238301 (2013)]. The singularity for I = 0 is handled with a regularization scheme [Lin and Yang, J. Comput. Phys. 420, 109708 (2020)]. Compared to the discharge dynamics predicted with the local μ(I) rheology model, the non-local effect enhances the velocity field to increase the volume discharge flow rate Q, especially when the silo orifice L is narrower. Both the local and non-local flow simulations conform to the Beverloo relation Q=Cρg(L−kd)3/2, where d is the intrinsic grain diameter but the non-local effects appear to lessen the orifice reduction effect coefficient k. The difference between the local and the non-local flow rates ΔQ¯, made dimensionless by ρgd3/2, grew monotonically with decreasing L/d with a slight enhancement if the silo height-to-width aspect ratio deviates from unity. Finally, we evaluated the ratio of the shear strain rate to the instantaneous maximum value to define a high-shear zone when the ratio is above a threshold and studied its evolution from the onset to the end of the discharge process. Interestingly, non-local momentum transport helped to reduce the size of the high-shear zone to give a more uniformly fluidized central zone above the orifice.

The Knudsen Paradox in Micro-Channel Poiseuille Flows with a Symmetric Particle

The Knudsen paradox—the non-monotonous variation of mass-flow rate with the Knudsen number—is a unique and well-established signature of micro-channel rarefied flows. A particle which is not of insignificant size in relation to the duct geometry can significantly alter the flow behavior when introduced in such a system. In this work, we investigate the effects of a stationary particle on a micro-channel Poiseuille flow, from continuum to free-molecular conditions, using the direct simulation Monte-Carlo (DSMC) method. We establish a hydrodynamic basis for such an investigation by evaluating the flow around the particle and study the blockage effect on the Knudsen paradox. Our results show that with the presence of a particle this paradoxical behavior is altered. The effect is more significant as the particle becomes large and results from a shift towards relatively more ballistic molecular motion at shorter geometrical distances. The need to account for combinations of local and non-local transport effects in modeling reactive gas–solid flows in confined geometries at the nano-scale and in nanofabrication of model pore systems is discussed in relation to these results.

On the Relationship between the TKE Dissipation Rate and the Temperature Structure Function Parameter in the Convective Boundary Layer

Abstract Under stably stratified conditions, the dissipation rate ε of turbulence kinetic energy (TKE) is related to the structure function parameter for temperature , through the buoyancy frequency and the so-called mixing efficiency. A similar relationship does not exist for convective turbulence. In this paper, we propose an analytical expression relating ε and in the convective boundary layer (CBL), by taking into account the effects of nonlocal heat transport under convective conditions using the Deardorff countergradient model. Measurements using unmanned aerial vehicles (UAVs) equipped with high-frequency response sensors to measure velocity and temperature fluctuations obtained during the two field campaigns conducted at Shigaraki MU observatory in June 2016 and 2017 are used to test this relationship between ε and in the CBL. The selection of CBL cases for analysis was aided by auxiliary measurements from additional sensors (mainly radars), and these are described. Comparison with earlier results in the literature suggests that the proposed relationship works, if the countergradient term γ D in the Deardorff model, which is proportional to the ratio of the variances of potential temperature θ and vertical velocity w, is evaluated from in situ (airplane and UAV) observational data, but fails if evaluated from large-eddy simulation (LES) results. This appears to be caused by the tendency of the variance of θ in the upper part of the CBL and at the bottom of the entrainment zone to be underestimated by LES relative to in situ measurements from UAVs and aircraft. We discuss this anomaly and explore reasons for it.

Quantum aspects of hydrodynamic transport from weak electron-impurity scattering

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed non-local transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has largely been motivated by a phenomenological analogy to classical fluids. This is due to difficulty in incorporating strong correlations in quantum mechanical calculation of transport, which has been the primary angle for interpreting the apparently hydrodynamic transport. Here we demonstrate that even free fermion systems, in the presence of (inevitable) disorder, exhibit non-local conductivity effects such as those observed in experiment because of the fermionic system's long-range entangled nature. On the basis of explicit calculations of the conductivity at finite wavevector, $\sigma({\bf q})$, for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering.

Modeling stratified suspension concentration distribution in turbulent flow using fractional advection–diffusion equation

The distribution of suspended sediment particles in a steady, uniform and stratified turbulent flow through open-channels is investigated in this study using fractional advection–diffusion equation (FADE). Unlike previous studies on FADE, the FADE is employed with the effects of stratification due to the presence of the sediment particles. Analogous to the approach of stratified flow, the effect of stratification is connected with the damping of the sediment diffusivity. A general model of sediment diffusion coefficient in stratified flow is proposed which changes along vertical direction as well as with the order of the fractional derivative. Finally the model of sediment distribution is derived incorporating the effects of non-local transport of particles, stratification, hindered settling velocity and damping of mixing length. The model is solved numerically using the fractional Adams–Bashforth–Moulton method and solutions are validated with the experimental data. The validation results are satisfactory. The variation of the depth average sediment diffusion coefficient and the proposed model of sediment diffusion coefficient with the fractional order $$\alpha$$ are investigated. The results show that with the decrease of fractional order $$\alpha$$, the value of depth average sediment diffusion coefficient increases and the depth variable sediment diffusion coefficient shows a overall increases throughout the flow depth. The rationality of the dependence of $$\alpha$$ on both types of sediment diffusion coefficients have been justified physically. It is also found that the effect of stratification results a decrease both for the suspension distribution and the sediment diffusion coefficient which is consistent with the results using traditional ADE.

The nonlocal transport and switch effect in light- and electric-controlled silicene–superconductor hybrid structure**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504084 and 11647164) and the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant Nos. 18KJB140005, 17KJD170004, and 16KJB140008).

We theoretically investigate the influence of off-resonant circularly polarized light field and perpendicular electric field on the quantum transport in a monolayer silicene-based normal/superconducting/normal junction. Owing to the tunable band structure of silicene, a pure crossed Andreev reflection process can be realized under the optical and electrical coaction. Moreover, a switch effect among the exclusive crossed Andreev reflection, the exclusive elastic cotunneling and the exclusive Andreev reflection, where the former two are the nonlocal transports and the third one is the local transport, can be obtained in our system by the modulation of the electric and light fields. In addition, the influence of the relevant parameters on the nonlocal and local transports is calculated and analyzed as well.

Thermodynamic framework for non-local transport-damage modeling of fluid driven fracture in porous media

We present a novel non-local damage transport model for hydraulic fracture in porous media. The new model is sought to provide an enhanced description for the long-range damage and transport interactions in the fracture process zone. The non-local model is derived from thermodynamic principles, where a new thermodynamic potential expression for non-local transport is introduced. The thermodynamically consistent model is reduced to a gradient non-local permeability relationship that simultaneously provides a non-local transport description and regularized damage growth via a permeability-stress relationship. The analogy of the proposed model to Darcy-Brinkman fluid flow is demonstrated and discussed. A monolithic 3-field (u−P−κ˜) mixed finite element framework is then used to discretize and solve the nonlinear coupled physics poromechanics problem. The hydraulic fracture continuum models previously presented in the literature rely on using different fluid flow laws inside and outside the fracture zone, which introduces a discontinuity in the continuum model. Our model prescribes Darcy type fluid flow all over the domain with a non-linear permeability constitutive law that allows for elevated fluid velocity in the crack zone, which preserves the continuity of all quantities within the domain. The numerical examples confirm the capability of the proposed model in capturing the essential features of hydraulic fracture simulation. The significance of the non-local transport modeling is demonstrated through modeling hydraulic fracturing in materials with pre-existing high permeability zones. The incorporation of non-local transport effects in hydraulic fracture modeling is proved to uncover possible flow paths through pre-existing high permeability zones. The proposed model can act as a platform for quantifying the fluid leak-off from hydraulic fracture and can be further used to analyze the hydraulic fracture interaction with neighboring geological material.

Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Lévy Stable Processes.

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

Topological quantum properties of chiral crystals.

Chiral crystals are materials with a lattice structure that has a well-defined handedness due to the lack of inversion, mirror or other roto-inversion symmetries. Although it has been shown that the presence of crystalline symmetries can protect topological band crossings, the topological electronic properties of chiral crystals remain largely uncharacterized. Here we show that Kramers-Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin-orbit coupling and are guaranteed by structural chirality, lattice translation and time-reversal symmetry. Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. We identify representative chiral materials in 33 of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to the low-energy physics. We determine that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin-orbit coupling carry non-trivial Chern numbers. Kramers-Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window.

Nonlocal heat transport and improved target design for x-ray heating studies at x-ray free electron lasers

The extremely high power densities and short durations of single pulses of x-ray free electron lasers (XFELs) have opened new opportunities in atomic physics, where complex excitation-relaxation chains allow for high ionization states in atomic and molecular systems, and in dense plasma physics, where XFEL heating of solid-density targets can create unique dense states of matter having temperatures on the order of the Fermi energy. We focus here on the latter phenomena, with special emphasis on the problem of optimum target design to achieve high x-ray heating into the warm dense matter (WDM) state. We report fully three-dimensional simulations of the incident x-ray pulse and the resulting multielectron relaxation cascade to model the spatial energy density deposition in multicomponent targets, with particular focus on the effects of nonlocal heat transport due to the motion of high energy photoelectrons and Auger electrons. We find that nanoscale high-Z/low-Z multicomponent targets can give much improved energy density deposition in lower-Z materials, with enhancements reaching a factor of 100. This has three important benefits. First, it greatly enlarges the thermodynamic parameter space in XFEL x-ray heating studies of lower-Z materials. Second, it allows the use of higher probe photon energies, enabling higher-information content X-ray diffraction (XRD) measurements such as in two-color XFEL operations. Third, while this is merely one step toward optimization of x-ray heating target design, the demonstration of the importance of nonlocal heat transport establishes important common ground between XFEL-based x-ray heating studies and more traditional laser plasma methods.

Momentum transport and nonlocality in heat-flux-driven magnetic reconnection in high-energy-density plasmas.

Recent theory has demonstrated a novel physics regime for magnetic reconnection in high-energy-density plasmas where the magnetic field is advected by heat flux via the Nernst effect. Here we elucidate the physics of the electron dissipation layer in this regime. Through fully kinetic simulation and a generalized Ohm's law derived from first principles, we show that momentum transport due to a nonlocal effect, the heat-flux-viscosity, provides the dissipation mechanism for magnetic reconnection. Scaling analysis, and simulations show that the reconnection process comprises a magnetic field compression stage and quasisteady reconnection stage, and the characteristic width of the current sheet in this regime is several electron mean-free paths. These results show the important interplay between nonlocal transport effects and generation of anisotropic components to the distribution function.

A comparison of non-local electron transport models for laser-plasmas relevant to inertial confinement fusion

We compare the reduced non-local electron transport model developed by Schurtz et al. [Phys. Plasmas 7, 4238 (2000)] to Vlasov-Fokker-Planck simulations. Two new test cases are considered: the propagation of a heat wave through a high density region into a lower density gas, and a one-dimensional hohlraum ablation problem. We find that the reduced model reproduces the peak heat flux well in the ablation region but significantly over-predicts the coronal preheat. The suitability of the reduced model for computing non-local transport effects other than thermal conductivity is considered by comparing the computed distribution function to the Vlasov-Fokker-Planck distribution function. It is shown that even when the reduced model reproduces the correct heat flux, the distribution function is significantly different to the Vlasov-Fokker-Planck prediction. Two simple modifications are considered which improve agreement between models in the coronal region.

Charged particle dynamics in the presence of non-Gaussian Lévy electrostatic fluctuations

Full orbit dynamics of charged particles in a 3-dimensional helical magnetic field in the presence of α-stable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous non-Gaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit non-Gaussian Lévy statistics, gyro-averaging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Buoyant Turbulent Kinetic Energy Production in Steep-Slope Katabatic Flow

We develop several critical concepts that should be considered when interpreting, modelling and designing future experiments for flows over sloping terrain. Vertical buoyancy fluxes in katabatic flows can be positive and a source of turbulent kinetic energy (TKE) despite the statically stable, thermal stratification that drives these flows. This phenomenon occurs when the ratio of along-slope to slope-normal kinematic heat fluxes is greater than the cotangent of the slope angle, suggesting a critical value of slope-angle steepness found in earlier studies. We provide field-data-based evidence that the along-slope heat flux may dominate the variables in this inequality, and therefore in generating buoyant TKE production or suppression over a steep slope. These data show the along-slope heat flux can be more variable and significantly larger in magnitude than the slope-normal component. The gradient Richardson number does not include the effects of the along-slope buoyancy; furthermore, none of the canonical stability parameters can properly reflect the TKE redistribution from turbulent transport divergence and the sink of TKE in cases of counter-gradient momentum fluxes, which we frequently observe near the peak of the katabatic jet. In such cases, canonical stability parameters inadequately represent the physical mechanisms associated with stability. These results have broad implications related to accurately modelling turbulence and surface exchanges over sloping terrain and illustrate the need to more thoroughly investigate the along-slope heat flux and its drivers, the meaning and definitions of stability, and the effects of non-local turbulent transport.