Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations.The use of temporal fractional transport equations means that the order of the partial derivative with respect to time is a fraction. In this case, the Caputo fractional derivative relative to time is utilized, because it preserves the form of the initial conditions. A numerical calculation reveals that the fractional order of the temporal derivative α(α ∈(0, 1), sub-diffusive regime) controls the diffusion rate. The temporal fractional derivative is related to the fact that the evolution of a physical quantity is affected by its past history, depending on what are termed memory effects. The magnitude of α is a measure of such memory effects. When α decreases, so does the rate of particle diffusion due to memory effects. As a result,if a system initially has a density profile without a source, then the smaller the α is, the more slowly the density profile approaches zero. When a source is added, due to the balance of the diffusion and fueling processes, the system reaches a steady state and the density profile does not evolve. As α decreases, the time required for the system to reach a steady state increases. In magnetically confined plasmas, the temporal fractional transport model can be applied to off-axis heating processes. Moreover, it is found that the memory effects reduce the rate of energy conduction and hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.

Turbulence and Anomalous Transport

Turbulence is a thermodynamic system composed of a lot of vorticons rather than disturbance to random moving particles. The transport coefficients derived from the definition on turbulence show that the anomalous transport is a natural result of present turbulence in Tokamak plasma and provides an important theoretical reference for the design and operation of Tokamak.

Analysis of anomalous transport based on radial fractional diffusion equation

Anomalous transport in magnetically confined plasmas is investigated by radial fractional transport equations.It is shown that for fractional transport models,hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients(FDCs)are radially dependent or not.When a radially dependent FDC<D_(α)(r)1 is imposed,compared with the case under=D_(α)(r)1.0,it is observed that the position of the peak of the density profile is closer to the core.Further,it is found that when FDCs at the positions of source injections increase,the peak values of density profiles decrease.The non-local effect becomes significant as the order of fractional derivative a 1 and causes the uphill transport.However,as a 2,the fractional diffusion model returns to the standard model governed by Fick’s law.

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple onedimensional, symmetric periodic potentials under the influence of both a time periodic and a static biasing force. The physical system employed contains a friction coefficient that is speed-dependent. Within the tailored parameter regime, the absolute negative mobility, in which a particle can travel in the direction opposite to a constant applied force, is observed.This behavior is robust and can be maximized at two regimes upon variation of the characteristic factor of friction coefficient. Further analysis reveals that this uphill motion is subdiffusion in terms of localization（diffusion coefficient with the form D（t） -t-（-1） at long times）. We also have observed the non-trivially anomalous subdiffusion which is significantly deviated from the localization; whereas most of the downhill motion evolves chaotically, with the normal diffusion.

The Response of Anomalous Vertically Integrated Moisture Flux Patterns Related to Drought and Flood in Southern China to Sea Surface Temperature Anomaly

With the extreme drought(flood)event in southern China from July to August in 2022(1999)as the research object,based on the comprehensive diagnosis and composite analysis on the anomalous drought and flood years from July to August in 1961-2022,it is found that there are significant differences in the characteristics of the vertically integrated moisture flux(VIMF)anomaly circulation pattern and the VIMF convergence(VIMFC)anomaly in southern China in drought and flood years,and the VIMFC,a physical quantity,can be regarded as an indicative physical factor for the"strong signal"of drought and flood in southern China.Specifically,in drought years,the VIMF anomaly in southern China is an anticyclonic circulation pattern and the divergence characteristics of the VIMFC are prominent,while those are opposite in flood years.Based on the SST anomaly in the typical draught year of 2022 in southern China and the SST deviation distribution characteristics of abnormal draught and flood years from 1961 to 2022,five SST high impact areas(i.e.,the North Pacific Ocean,Northwest Pacific Ocean,Southwest Pacific Ocean,Indian Ocean,and East Pacific Ocean)are selected via the correlation analysis of VIMFC and the global SST in the preceding months(May and June)and in the study period(July and August)in 1961-2022,and their contributions to drought and flood in southern China are quantified.Our study reveals not only the persistent anomalous variation of SST in the Pacific and the Indian Ocean but also its impact on the pattern of moisture transport.Furthermore,it can be discovered from the positive and negative phase fitting of SST that the SST composite flow field in high impact areas can exhibit two types of anomalous moisture transport structures that are opposite to each other,namely an anticyclonic(cyclonic)circulation pattern anomaly in southern China and the coastal areas of east China.These two types of opposite anomalous moisture transport structures can not only drive the formation of drought(flood)in southern China but also exert its influence on the persistent development of the extreme weather.

Experimental Studies of Electrostatic Fluctuations and Turbulent Transport in the Boundary of J-TEXT Tokamak Using Reciprocating Probe

As the basic of a deeper investigation on the turbulent transport, the fluctuation property in the boundary of the newly-reconstructed Joint Texas Experimental Tokamak （J- TEXT） is studied experimentally using the reciprocating Langmuir four-tip probe, which has been built and operated as the primary diagnostic tool in the boundary of J-TEXT tokamak. In this paper, spatial profiles of the plasma-edge parameters are obtained, such as electron temperature, plasma density, plasma potential, poloidal electric field and their fluctuations. The results indicate the existence of a Er ×BT shear layer at the vicinity of last closed flux surface （LCFS）, with the fluctuations suppressed in varying degrees. The turbulence-induced particle and energy fluxes can be calculated by the local plasma parameters above. Convection dominates the cross-field turbulent transport in boundary plasma. Electrostatic fluctuations properties are also studied in detail with the help of numerical analysis. Statistical analysis on density fluctuation shows that, the intermittency can affect the turbulence in the scrape-off layer （SOL）.

Anisotropic transport of microalgae Chlorella vulgaris in microfluidic channel

In this work, we study the regional dependence of transport behavior of microalgae Chlorella vulgaris inside microflu- idic channel on applied fluid flow rate. The microalgae are treated as spherical naturally buoyant particles. Deviation from the normal diffusion or Brownian transport is characterized based on the scaling behavior of the mean square displacement （MSD） of the particle trajectories by resolving the displacements in the streamwise （flow） and perpendicular directions. The channel is divided into three different flow regions, namely center region of the channel and two near-wall boundaries and the particle motions are analyzed at different flow rates. We use the scaled Brownian motion to model the transitional characteristics in the scaling behavior of the MSDs. We find that there exist anisotropic anomalous transports in all the three flow regions with mixed sub-diffusive, normal and super-diffusive behavior in both longitudinal and transverse directions.

Contaminant transport in heterogeneous aquifers: A critical review of mechanisms and numerical methods of non-Fickian dispersion

Natural aquifers usually exhibit complex physical and chemical heterogeneities,which are key factors complicating kinetic processes,such as contaminant transport and transformation,posing a great challenge in the remediation of contaminated groundwater.Aquifer heterogeneity usually leads to a distinct feature,the so-called“anomalous transport”in groundwater,which deviates from the phenomenon described by the classical advection-dispersion equation(ADE)based on Fick’s Law.Anomalous transport,also known as non-Fickian dispersion or“anomalous dispersion”in a broad sense,can explain the hydrogeological mechanism that leads to the temporally continuous deterioration of water quality and rapid spatial expansion of pollutant plumes.Contaminants enter and then are retained in the low-permeability matrix from the high-permeability zone via molecular diffusion,chemical adsorption,and other mass exchange effects.This process can be reversed when the concentration of pollutants in high-permeability zones is relatively low.The contaminants slowly return to the high-permeability zones through reverse molecular diffusion,resulting in sub-dispersive anomalous transport leading to the chronic gradual deterioration of water quality.Meanwhile,some contaminants are rapidly transported along the interconnected preferential flow paths,resulting in super-dispersive anomalous transport,which leads to the rapid spread of contaminants.Aquifer heterogeneity is also an important factor that constrains the efficacy of groundwater remediation,while the development,application,and evaluation of groundwater remediation technologies are usually based on the Fickian dispersion process predicted by the ADE equation.Comprehensive studies of the impacts of non-Fickian dispersion on contaminant transport and remediation are still needed.This article reviews the non-Fickian dispersion phenomenon caused by the heterogeneity of geological media,summarizes the processes and current understanding of contaminant migration and transformation in highly heterogeneous aquifers,and evaluates mathematical methods describing the main non-Fickian dispersion features.This critical review also discusses the limitations of existing research and outlines potential future research areas to advance the understanding of mechanisms and modeling of non-Fickian dispersion in heterogeneous media.

Supersonic Flows with Nontraditional Transport Described by Kinetic Methods

A new class of supersonic nonequilibrium flows is studied on the basis of solving the Boltzmann andmodel kinetic equations with the aim to consider new nonlinear structures in open systems and to study anomalous transfer properties in relaxation zones.The Unified Flow Solver is applied for numerical simulations.Simple gases and gases with inner degrees of freedom are considered.The experimental data related to the influence of the so-called optical lattices on the supersonic molecular beams are considered and numerical analysis of the nonequilibrium states obtained on this basis is made.The nonuniform relaxation problem with these distributions is simulated numerically and anomalous transport is confirmed.The conditions for strong changes of the temperature in the anomalous transfer zones are discussed and are realized in computations.