Anomalous Diffusivity Research Articles

Advanced diffusion-weighted MRI models for preoperative prediction of lymph node metastasis in resectable gastric cancer.

To investigate the potential of six advanced diffusion-weighted imaging (DWI) models for preoperative prediction of lymph node metastasis (LNM) in resectable gastric cancer (GC). Between Nov 2022 and Nov 2023, standard MRI scans were prospectively performed in consecutive patients with endoscopic pathology-confirmed gastric adenocarcinoma who were referred for direct radical gastrectomy. Six DWI models, including fractional order calculus (FROC), continuous-time random walk (CTRW), diffusion kurtosis imaging (DKI), intravoxel incoherent motion (IVIM), the mono-exponential model (MEM) and the stretched exponential model (SEM) were computed. Surgical pathologic diagnosis of LNM was the reference standard, and patients were classified into LNM-positive or LNM-negative groups accordingly. The morphological features and quantitative parameters of the DWI models in different LNM categories were analyzed and compared. Multivariable logistic regression was used to screen significant predictors. Receiver-operating characteristic curves and the area under the curve (AUC) were plotted to evaluate the performances, the Delong test was performed to compare the AUCs. In the LNM-positive group, tumor thickness and kurtosis (DKI_K) were significantly higher, while anomalous diffusion coefficient (CTRW_D), diffusivity (DKI_D), diffusion coefficient (FROC_D), pseudodiffusion coefficient (IVIM_D*), perfusion fraction (IVIM_f), and ADC were lower compared to the LNM-negative group. Clinical tumor staging (cT) and CTRW_D were independent predictors. Their combination demonstrated a superior AUC of 0.930, significantly higher than that of individual parameters. Tumor thickness, DKI_K, CTRW_D, DKI_D, FROC_D, IVIM_D*, IVIM_f and ADC were associated with LNM status. The combination of independent predictors of cT and CTRW_D further enhanced the performance.

Modelling of power exhaust in TCV positive and negative triangularity L-mode plasmas

L-mode negative triangularity (NT) operation is a promising alternative to the positive triangularity (PT) H-mode as a high-confinement edge localised mode-free operational regime. In this work, two TCV Ohmic L-mode core density ramps with opposite triangularity δ≃±0.3 are investigated using SOLPS-ITER modelling. This numerical study aims to investigate the power exhaust differences between NT and PT focusing, in particular, on the geometrical effect of triangularity. To disentangle the latter from differences related to cross-field transport, anomalous diffusivities for particle ( DnAN ) and energy ( χe/iAN ) transport are fixed to the same values in PT and NT. The simulation results clearly show dissimilar transport and accumulation of neutral particles in the scrape-off layer for the two configurations. This gives rise to different ionization sources in the edge and divertor regions and produces differences in the poloidal and cross-field fluxes, ultimately leading to different power and particle divertor fluxes in the two configurations. Simulations recover the experimental feature of a hotter and attached outer target ( Te,OSPNT≳5eV ) in the NT scenario compared to the PT counterpart.

Superstatistical approach of the anomalous exponent for scaled Brownian motion

Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied by the heterogeneity of the α-anomalous diffusion exponents. In this framework, we investigate a heterogeneous ensemble of tracers governed by scaled Brownian motion (sBm). The heterogeneous features are considered on anomalous diffusion exponent and diffusivity. We introduce two superstatistics of anomalous exponent, the truncated-Gaussian and truncated χ2-Gamma distributions. In this way, we show how the statistics of anomalous exponent affect the spreading of a mixture of particles governed by sBm. We also analyse the role of different temporal scales of sBm in superstatistics. Furthermore, we investigate the effects of coupling between diffusivity and anomalous exponent on superstatistics of sBm. The investigation provides a thorough analysis of simulation and analytical approach. The results imply rich classes of anomalous diffusion processes accompanied by non-Gaussian diffusion.

Hydraulic characterization and modeling of water diffusivity through direct neutron radiography measurement on unsaturated cracked sandstone

Water diffusivity in cracked rocks is of great importance in the recovery of conventional and unconventional resources and in the sequestration of carbon dioxide and nuclear wastes. However, the mechanism of water diffusivity is not clearly revealed in the unsaturated fractured sandstone due to the limitation of accurately identifying the dynamic wetting front and water content in the conventional methods. Based on a set of self-designed coupling loading device, the novel neutron radiography imaging is used to visualize the dynamic diffusivity process of forced water from a horizontal rough crack vertically imbibed into an unsaturated sandstone matrix with nonuniform boundary in real time. As a result, an anomalous diffusivity phenomenon, namely the time exponent less than 0.5 is discovered. The anomalous diffusivity may be mainly caused by the heterogeneity and anisotropy of matrix and complicated 3-D water imbibition due to nonuniform geometric boundary. The nonstandard imbibition experiment condition may be an additional important factor. The anomalous diffusivity was calculated by three methods, including the Generalized Fickian law, Lockington and Parlange (L-P) model and the developed Meyer-Warwick (M-W) model. The value of the diffusivity increases non-linearly with the increase of normalized water content θn. The diffusivity calculated by the developed M-W model increases rapidly with increasing θn from 0 to 0.2 mm3mm−3, which is almost the same as that calculated by L-P model. When θn> 0.2 mm3mm−3, the L-P model obviously overestimates the diffusivity, but the diffusivity calculated by the developed M-W model is closest to that obtained by the Generalized Fickian law. The developed M-W model provides an effective way to quantitatively describe the diffusivity of water in the sandstone matrix.

Prediction of divertor heat flux width for ITER pre-fusion power operation using BOUT++ transport code

Prediction of divertor heat flux width is performed for the first and the second pre-fusion power operation (PFPO) phases specified in the new ITER research plan using BOUT++ transport code (Li et al 2018 Comput. Phys. Commun. 228 69–82). The initial plasma profiles inside the separatrix are taken from CORSICA scenario studies. Transport coefficients in transport code are calculated by inverting the plasma profiles inside the separatrix and are assumed to be constants in the scrape-off-layer. An anomalous thermal diffusivity scan is performed with E × B and magnetic drifts. The results in two scenarios identifying two distinct regimes: a drift-dominant regime when diffusivity is smaller than the respective critical thermal diffusivity χ c and a turbulence-dominant regime when diffusivity is larger than it. The Goldston heuristic drift model and the ITPA multi-machine experimental scaling yield a lower limit of the width λ q . From transport simulations, we obtain the critical thermal diffusivity χ c = 0.5 m2 s−1 for the PFPO-1 scenario with toroidal magnetic field B = 1.77 T and plasma current I p = 5 MA, and χ c = 0.3 m2 s−1 for the PFPO-2 scenario with toroidal magnetic field B = 2.65 T and plasma current I p = 7.5 MA. Separatrix temperature and collisionality also have a significant impact on the heat flux width in the drift-dominant regime. The investigation clearly yields a scaling for critical thermal diffusivity using ITER scenarios with fixed safety factor q 95, major radius R, aspect ratio R/a, and the separatrix temperature T sep, and establishes the connection with CFETR and C-Mod discharges. This scaling implies that for a given tokamak device with q 95, R, R/a, and T sep fixed, a reduction of poloidal magnetic field by a factor of 3 leads to a 9 times higher critical value of thermal diffusivity χ c, possibly yielding a transition from turbulence- to drift-dominant regime.

Moisture diffusion by the fractional-time model in convective drying with ultrasound-ethanol pretreatment of banana slices

Innovative drying pretreatments play an essential role in preserving food and reducing drying energy consumption. The aim of this study was, therefore, to investigate the effect of drying pretreatments with ethanol (EH) and ultrasound (UA) on the drying kinetics and moisture diffusion through an anomalous solution by the fractional time, as well as to evaluate the physical, bioactive compounds and antioxidant properties of banana slices. The results indicated that Page's model analyzed the anomalous calculus approach for emerging drying techniques with the appropriate goodness of fit. The anomalous diffusivity approach described the experimental data well and provided new insights into the structure of food material. The new approach also showed that drying pretreatments promote convective drying, reduce drying time by up to 31% and save energy by 19%. Analytical results showed that banana slices pretreated with EH + UA had higher conservation of phenolic compounds and antioxidant activity, as well as an attractive color and high shrinkage. The findings could provide help in the large-scale processing of good-quality dried banana slices.

Transport Regimes of Underdamped Brownian Particles in a Tilted Washboard Potential

In this paper, a comprehensive examination of the temperature- and bias-dependent diffusion regimes of underdamped Brownian particles is presented. A temperature threshold reminiscent of a phase transition between anomalous and normal diffusive behaviors is located. In the low temperature regime, the system exhibits an apparent negative differential mobility due to persistent, long-time subdiffusion at low-bias; at high temperature (or critical bias,) the system rapidly approaches normal diffusion below an intermediate barrier height, U0 ? 6kBT. By comparison of the underdamped and overdamped response, it is demonstrated that the non-monotonic temperature dependence of the diffusivity can be traced to inertial effects. The velocity power spectra exhibit coupling between the \locked and \running states in the giant diffusion regime, with a characteristic frequency corresponding to the principal frequency of the limit cycles of a damped, driven plane pendulum near critical bias. Non-linear second harmonic generation, corresponding to oscillatory transient anomalous diffusivity, is observed with increasing bias and decreasing temperature, further emphasizing that the low-noise diffusion problem converges to noise-free dynamics, complementing analytic results for the average velocity [L. Cheng and N.K. Yip, Physica D, 2015].

Free electron to electride transition in dense liquid potassium

At high pressures, simple metals such as potassium have a rich phase diagram including an insulating electride phase in which electrons have a localized, anionic character. Measurements in the liquid phase have shown a transition between two states, but experimental challenges have prevented detailed thermodynamic measurements. Using potassium as an example, we present numerical evidence that the liquid–liquid transition is a continuous transformation from free electron to electride behaviour. We show that the transformation manifests in anomalous diffusivity, thermal expansion, speed of sound, coordination number, reflectivity and heat capacity across a wide range of pressures. The abnormalities stem from a significant change in the local electronic and ionic structure. Although primarily a pressure-induced phenomenon, there is also a thermal expansion anomaly. By establishing the electride nature of the high-pressure liquid phase, we resolve the long-standing mystery of how a liquid can be denser than a close-packed solid. Our work is relevant for high-pressure thermodynamic properties of all alkali metal liquids. Alkali metals at high pressures have a liquid–liquid transition that is difficult to study in detail. Numerical calculations now suggest that the higher-pressure state is an electride liquid, in which electrons behave like localized anions.

Diffusion, Interactions, and Disparate Kinetic Trapping of Water-Hydrocarbon Mixtures in Nanoporous Solids.

Mixed fluids confined in porous solid hosts present challenges for the accurate characterization of individual-component behavior. NMR diffusometry with chemical resolution is used to identify unexpected loading- and composition-dependent anomalous diffusion in water/cyclohexane mixtures confined to solid nanoporous glass (NPG) hosts. Diffusion NMR results indicate that data obtained on pure-component liquids in confinement cannot be extrapolated to their nonideal liquid mixtures confined in the same solid host. Loading-dependent data must be obtained on each component in the confined mixture in order to determine which of the liquid components exhibits chemical affinity for the host and, conversely, which of the components exhibits anomalous diffusivity. Most notably, NMR diffusometry revealed that cyclohexane diffusivity varied by 2 orders of magnitude in a water-rich mixture depending on the total fluid loading in the NPG host, ranging from anomalously high diffusivities that significantly exceeded that for pure cyclohexane in NPG at low fluid loadings to kinetically trapped sequestration at high fluid loadings. NMR diffusometry indicates that nonideal solution behavior in fluids confined within nanoporous hosts may have practical implications for enhanced oil recovery methods. Specifically, kinetic trapping of hydrocarbons in water-flooding regimes can result from complex liquid-vapor equilibrium that is significantly perturbed from that which exists in bulk or microporous confinement.

Possibility of realizing superionic ice VII in external electric fields of planetary bodies.

In a superionic (SI) ice phase, oxygen atoms remain crystallographically ordered while protons become fully diffusive as a result of intramolecular dissociation. Ice VII's importance as a potential candidate for a SI ice phase has been conjectured from anomalous proton diffusivity data. Theoretical studies indicate possible SI prevalence in large-planet mantles (e.g., Uranus and Neptune) and exoplanets. Here, we realize sustainable SI behavior in ice VII by means of externally applied electric fields, using state-of-the-art nonequilibrium ab initio molecular dynamics to witness at first hand the protons' fluid dance through a dipole-ordered ice VII lattice. We point out the possibility of SI ice VII on Venus, in its strong permanent electric field.

Resolving the mystery of the concentration-dependence of amphoteric dopant diffusion in III-V semiconductors

Amphoteric dopants, such as silicon, exhibit a concentration-dependent diffusivity in III-V compounds characterized by a low to negligible diffusion at low dopant concentrations, which increases by orders of magnitude at high concentrations. The reason for this anomalous and non-intuitive diffusivity has largely remained a mystery. Leading models from literature, built to explain existing experimental results, make contradictory assumptions on the nature of the diffusing species, based only on thermodynamic considerations. In this work, we perform ab initio calculations to characterize the kinetics of dopant diffusion in III-V materials revealing how the nature of the primary diffusing species changes with concentration. We use these results to derive a new analytical model which fits historical, as well as more recent, experimental data on Si diffusion in GaAs and In0.57Ga0.43As. This work provides a fundamentals-based understanding of Si diffusion in III-V alloys as well as a new predictive analysis tool while showcasing a mutiscale approach of solving diffusion problems. We hope this work will help guide the design of the next generation of III-V based electronic and photonic devices.

Prediction of divertor heat flux width for ITER using BOUT++ transport and turbulence module

Investigation of turbulent transport dynamics in scrape-off-layer (SOL) and divertor heat flux width prediction is performed for ITER. Both BOUT++ transport and BOUT++ turbulence codes are applied to capture the physics on different temporal scales. Simulations start with an ITER 15MA baseline scenario profile generated by CORSICA (Kim et al 2015 Paper ITER_D_R9T8J9 v1.1). In BOUT++ transport code, the plasma parameters (, , ) and radial electric () profiles are evolved to steady state. The initial plasma profiles inside the separatrix are taken from CORSICA scenario studies. Transport coefficients are calculated by inverting the plasma profiles inside the separatrix. SOL transport coefficients are assumed to be constants connected to the separatrix. A parametric scan for the anomalous thermal diffusivity (, ) in the SOL is performed separately with and magnetic drift included, and without any drift effects. The results show that when the diffusivity is smaller than a critical , the heat flux width remains almost unchanged, which is roughly consistent with Goldston’s heuristic drift model (Goldston 2012 Nucl. Fusion 52 013009). Otherwise, it increases as a scaling resulting in a larger . BOUT++ six-field/two-fluid turbulence code is used to study pedestal and SOL turbulence dynamics and corresponding transport. In the turbulence simulation, pedestal is found to be peeling-ballooning unstable, which results in a larger . Pedestal structure is also found to be important in determining the effective thermal diffusivity and could lead to changes in the divertor heat flux width.

A mode-coupling theory analysis of the observed diffusion anomaly in aqueous polyatomic ions

In contrast to simple monatomic alkali and halide ions, complex polyatomic ions such as nitrate, acetate, nitrite, and chlorate have not been studied in any great detail. Experiments have shown that diffusion of polyatomic ions exhibits many remarkable anomalies; notable among them is the fact that polyatomic ions with similar size show large difference in their diffusivity values. This fact has drawn relatively little interest in scientific discussions. We show here that a mode-coupling theory can provide a physically meaningful interpretation of the anomalous diffusivity of polyatomic ions in water, by including the contribution of rotational jumps on translational friction. The two systems discussed here, namely, aqueous nitrate ion and aqueous acetate ion, although have similar ionic radii, exhibit largely different diffusivity values due to the differences in the rate of their rotational jump motions. We have further verified the mode-coupling theory formalism by comparing it with experimental and simulation results that agree well with the theoretical prediction.

Up and downstream density scale asymmetries in Aditya tokamak scrape-off layer 3D simulations

In magnetically confined tokamak plasmas the width of plasma Scrape-off Layer (SOL) allows direct estimation of anomalous diffusivity in limited and diverted versions of plasma configurations. The diffusivity coupled to edge and SOL plasma fluctuations is to be a decisive factor in stability of fusion grade plasmas and can be characterized for its dependence on 3D effects in moderate size tokamaks like Aditya. For Aditya tokamak configuration, 3D effects in SOL plasma transport are studied using 3D Monte-Carlo transport code combination EMC3-EIRENE to complement the limited probe measurements during experimental operation of the device. As an important 3D effects, variation from 1D estimates of up and downstream density scale lengths are recovered to generate appropriate corrections for estimates of plasma diffusivity and other transport propertied measured in Aditya tokamak plasma.

3D MHD MODELING OF TWISTED CORONAL LOOPS

ABSTRACT We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube in the solar atmosphere extending from the high-β chromosphere to the low-β corona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ∼30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the flux tube is heated to active region temperatures (∼3 MK) after ∼2/3 hr. Upflows from the chromosphere up to ∼100 km s−1 fill the core of the flux tube to densities above 109 cm−3. More heating is released in the low corona than the high corona and is finely structured both in space and time.

Anomalous transport in the H-mode pedestal of Alcator C-Mod discharges

Anomalous transport in the H-mode pedestal region of five Alcator C-Mod discharges, representing a collisionality scan is analyzed. The understanding of anomalous transport in the pedestal region is important for the development of a comprehensive model for the H-mode pedestal slope. In this research, a possible role of the drift resistive inertial ballooning modes (Rafiq et al 2010 Phys. Plasmas 17 082511) in the edge of Alcator C-Mod discharges is analyzed. The stability analysis, carried out using the TRANSP code, indicates that the DRIBM modes are strongly unstable in Alcator C-Mod discharges with large electron collisionality. An improved interpretive analysis of H-mode pedestal experimental data is carried out utilizing the additive flux minimization technique (Pankin et al 2013 Phys. Plasmas 20 102501) together with the guiding-center neoclassical kinetic XGC0 code. The neoclassical and neutral physics are simulated in the XGC0 code and the anomalous fluxes are computed using the additive flux minimization technique. The anomalous fluxes are reconstructed and compared with each other for the collisionality scan Alcator C-Mod discharges. It is found that the electron thermal anomalous diffusivities at the pedestal top increase with the electron collisionality. This dependence can also point to the drift resistive inertial ballooning modes as the modes that drive the anomalous transport in the plasma edge of highly collisional discharges.

Anomalous properties and the liquid-liquid phase transition in gallium.

A group of materials including water and silicon exhibit many anomalous behaviors, e.g., density anomaly and diffusivity anomaly (increase upon compression). These materials are hypothesized to have a liquid-liquid phase transition (LLPT) and the critical fluctuation in the vicinity of the liquid-liquid critical point is considered as the origin of different anomalies. Liquid gallium was also reported to have a LLPT, yet whether it shows similar water-like anomalies is not yet studied. Using molecular dynamics simulations on a modified embedded-atom model, we study the thermodynamic, dynamic, and structural properties of liquid gallium as well as its LLPT. We find that, similar to water-like materials predicted to have the LLPT, gallium also shows different anomalous behaviors (e.g., density anomaly, diffusivity anomaly, and structural anomaly). We also find that its thermodynamic and structural response functions are continuous and show maxima in the supercritical region, the loci of which asymptotically approach to the other and merge to the Widom line. These phenomena are consistent with the supercritical phenomenon in a category of materials with a liquid-liquid critical point, which could be common features in most materials with a LLPT.

Effective-medium approximation for lattice random walks with long-range jumps.

We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective-medium approximation (EMA) to find the disorder-averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In the case of a power-law scaling between transition rates and distance, lattice variants of Lévy-flights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions and demonstrate very good agreement with numerical simulations.

Repulsive Interactions Induced by Specific Adsorption: Anomalous Step Diffusivity and Inadequacy of Nearest-Neighbor Ising Model (Part II Theory)

This is Part II of two closely related papers, where we show that the strong repulsive interaction caused by specifically adsorbed anions leads to a failure of the nearest-neighbor Ising model to describe structures on electrode surfaces. In this part, an analytical form of the step diffusivity is derived in terms of nearest and next-nearest neighbor interactions for steps with a mean direction along 〈110〉 (the close-packed direction). With the help of a further analytical expression for the diffusivity of steps with 〈100〉 mean orientation a simple scheme is developed whereby the nearest and next-nearest interaction energies can be extracted from the experimental values for the diffusivity along the 〈110〉- and 〈100〉-directions. The method is applicable to repulsive and attractive next-nearest neighbor interactions, both for surfaces in vacuum and in contact with an electrolyte. An example is presented in Part I, where we apply our approach to Au(100) in Br--, Cl-- and SO42—containing electrolytes.

Repulsive interactions induced by specific adsorption: Anomalous step diffusivity and inadequacy of nearest-neighbor Ising model: (part I experimental)

This is Part I of two closely related papers, where we show that the specific adsorption of anions leads to a failure of the nearest-neighbor Ising model to describe island perimeter curvatures on Au(100) electrodes in dilute KBr, HCl and H2SO4 electrolytes and the therewith derived step diffusivity vs. step orientation. This result has major consequences for theoretical studies aiming at the understanding of growth, diffusion and degradation phenomena. Part I focuses on the experimental data.As shown theoretically in detail in Part II (doi:10.1016/j.susc.2016.03.022), a set of nearest-neighbor and next-nearest-neighbor interaction energies (ϵNN, ϵNNN) can uniquely be derived from the diffusivity of steps along 〈100〉 and 〈110〉. We find strong repulsive next-nearest neighbor (NNN) interaction in KBr and HCl, whereas NNN interaction is negligibly for H2SO4. The NNN repulsive interaction energy ϵNNN therefore correlates positively with the Gibbs adsorption energy of the anions. We find furthermore that ϵNNN increases with increasing Br− and Cl− coverage.The results for ϵNNand ϵNNN are quantitatively consistent with the coverage dependence of the step line tension. We thereby establish a sound experimental base for theoretical studies on the energetics of steps in the presence of specific adsorption.