Anomalous Diffusivity Research Articles

A new parameter-free soft-core potential for silica and its application to simulation of silica anomalies.

A core-softening of the effective interaction between oxygen atoms in water and silica systems and its role in developing anomalous thermodynamic, transport, and structural properties have been extensively debated. For silica, the progress with addressing these issues has been hampered by a lack of effective interaction models with explicit core-softening. In this work, we present an extension of a two-body soft-core interatomic force field for silica recently reported by us [S. Izvekov and B. M. Rice, J. Chem. Phys. 136(13), 134508 (2012)] to include three-body forces. Similar to two-body interaction terms, the three-body terms are derived using parameter-free force-matching of the interactions from ab initio MD simulations of liquid silica. The derived shape of the O-Si-O three-body potential term affirms the existence of repulsion softening between oxygen atoms at short separations. The new model shows a good performance in simulating liquid, amorphous, and crystalline silica. By comparing the soft-core model and a similar model with the soft-core suppressed, we demonstrate that the topology reorganization within the local tetrahedral network and the O-O core-softening are two competitive mechanisms responsible for anomalous thermodynamic and kinetic behaviors observed in liquid and amorphous silica. The studied anomalies include the temperature of density maximum locus and anomalous diffusivity in liquid silica, and irreversible densification of amorphous silica. We show that the O-O core-softened interaction enhances the observed anomalies primarily through two mechanisms: facilitating the defect driven structural rearrangements of the silica tetrahedral network and modifying the tetrahedral ordering induced interactions toward multiple characteristic scales, the feature which underlies the thermodynamic anomalies.

Spontaneous reconnection at a separator current layer: 2. Nature of the waves and flows

AbstractSudden destabilizations of the magnetic field, such as those caused by spontaneous reconnection, will produce waves and/or flows. Here we investigate the nature of the plasma motions resulting from spontaneous reconnection at a 3‐D separator. In order to clearly see these perturbations, we start from a magnetohydrostatic equilibrium containing two oppositely signed null points joined by a generic separator along which lies a twisted current layer. The nature of the magnetic reconnection initiated in this equilibrium as a result of an anomalous diffusivity is discussed in detail in Stevenson and Parnell (2015). The resulting sudden loss of force balance inevitably generates waves that propagate away from the diffusion region carrying the dissipated current. In their wake a twisting stagnation flow, in planes perpendicular to the separator, feeds flux back into the original diffusion site (the separator) in order to try to regain equilibrium. This flow drives a phase of slow weak impulsive bursty reconnection that follows on after the initial fast‐reconnection phase.

Convection in a colloidal suspension in a closed horizontal cell

The experimentally detected [1] oscillatory regimes of convection in a colloidal suspension of nanoparticles with a large anomalous thermal diffusivity in a closed horizontal cell heated from below have been simulated numerically. The concentration inhomogeneity near the vertical cavity boundaries arising from the interaction of thermal-diffusion separation and convective mixing has been proven to serve as a source of oscillatory regimes (traveling waves). The dependence of the Rayleigh number at the boundary of existence of the traveling-wave regime on the aspect ratio of the closed cavity has been established. The spatial characteristics of the emerging traveling waves have been determined.

Compounding effects of fluid confinement and surface strain on the wet–dry transition, thermodynamic response, and dynamics of water–graphene systems

We studied the link between the water-mediated (tensile or compressive) strain-driven hydration free energy changes in the association process involving finite-size graphene surfaces, the resulting water–graphene interfacial behaviour, and the combined effect of surface strain and fluid confinement on the thermodynamic response functions and the dynamics of water. We found that either small surface corrugation (compressive strain) or surface stretching (tensile strain) is able to enhance significantly the water–graphene hydrophobicity relative to that of the unstrained surface, an effect that exacerbates the confinement impact on the isothermal compressibility and isobaric thermal expansivity of confined water, as well as on the slowdown of its dynamics that gives rise to anomalous diffusivity.

Phase equilibria, fluid structure, and diffusivity of a discotic liquid crystal

Molecular Dynamics simulations were performed for the Gay-Berne discotic fluid parameterized by GB(0.345, 0.2, 1.0, 2.0). The volumetric phase diagram exhibits isotropic (IL), nematic (ND), and two columnar phases characterized by radial distribution functions: the transversal fluid structure varies between a hexagonal columnar (CD) phase (at higher temperatures and pressures) and a rectangular columnar (CO) phase (at lower temperatures and pressures). The slab-wise analysis of fluid dynamics suggests the formation of grain-boundary defects in the CO phase. Longitudinal fluid structure is highly periodic with narrow peaks for the CO phase, suggestive of a near-crystalline (yet diffusive) system, but is only short-ranged for the CD phase. The IL phase does not exhibit anisotropic diffusion. Transversal diffusion is more favorable in the ND phase at all times, but only favorable at short times for the columnar phases. In the columnar phases, a crossover occurs where longitudinal diffusion is favored over transversal diffusion at intermediate-to-long timescales. The anomalous diffusivity is pronounced in both columnar phases, with three identifiable contributions: (a) the rattling of discogens within a transient "interdigitation" cage, (b) the hopping of discogens across columns, and (c) the drifting motion of discogens along the orientation of the director.

High-order jamming crossovers and density anomalies.

We demonstrate that particles interacting via core-softened potentials exhibit a series of successive density anomalies upon isothermal compression, leading to oscillations in the diffusivity and thermal expansion coefficient, with the latter reaching negative values. These finite-temperature density anomalies are then shown to correspond to zero-temperature high-order jamming crossovers. These occur when particles are forced to come into contact with neighbours in successive coordination shells upon increasing the density. The crossovers induce anomalous behavior of the bulk modulus, which oscillates with density. We rationalize the dependence of these crossovers on the softness of the interaction potential, and relate the jamming crossovers and the anomalous diffusivity via the properties of the vibrational spectrum.

2P277 Competitive reaction between enzymes with normal and anomalous diffusivity(24. Mathematical biology,Poster)

2P277 Competitive reaction between enzymes with normal and anomalous diffusivity(24. Mathematical biology,Poster)

Indirect Competitive Reaction between Enzymes with Different Diffusivity

Diffusion process of molecules within heterogeneous medium shows a peculiar behavior termed anomalous diffusion. Here the motions of molecules are hindered by the obstacles, which constitute the heterogeneity of the environment. Accordingly, compared to homogeneous medium, the area that a molecule moves for a given time is smaller for heterogeneous medium. This affects the reaction process deeply (especially for diffusion limited reactions) and the classical formulation based on mass action law fails to describe the process and a formulation based on the Fractal reaction theory is necessary [Kopelman, Science 1988].In this study we analyzed the indirect competitive reaction between enzymes with different sizes. We assume that for larger enzymes obstruction due to molecular crowding makes the environment heterogeneous to it. On the other hand for smaller enzymes the environment is assume to be homogeneous due to smaller obstruction effects from the molecular crowding. Accordingly there is a difference in the diffusivity, one with normal diffusivity and the other with anomalous diffusivity. We would like to discuss the physiological implications of this effect using Lattice Monte Carlo simulation and theoretical analysis based on the Fractal reaction theory.

Dynamics and diffusion mechanism in network forming liquid under high pressure: A new approach

The static and dynamic properties of liquid silica (SiO2) are investigated by molecular dynamics simulation at temperature of 3200 K and in the 0–25 GPa pressure range. To clarify diffusion mechanism and the anomalous diffusivity under compression, we have traced the time evolution of breakage and formation of the Si–O bond in the basic structural units SiOx (x = 4, 5, 6). The investigation reveals that atomic diffusion is realized through the transition Si[n] ↔ Si[n+1] (Si[n] means that Si atom has n coordinated oxygens) and the instability of units SiO5 is the cause of the anomalous diffusivity. Moreover, the transitions Si[n] ↔ Si[n+1] are not uniformly distributed but strongly localized in the space. The distribution of coordination units SiOx in network structure is not uniform but tends to form clusters of SiO4, SiO5 and SiO6 and this is the origin of localization of transitions resulted in the spatially heterogeneous dynamics in liquid SiO2.

Anomalous diffusivity in ionic liquids: A molecular dynamics study

Anomalous diffusivity in ionic liquids: A molecular dynamics study

Solution of inverse coefficient problem for fractional anomalous diffusion equation

An inverse coefficient problem is considered for time-fractional anomalous diffusion equations with the Riemann-Liouville and Caputo fractional derivatives. A numerical algorithm is proposed for identification of anomalous diffusivity which is considered as a function of concentration. The algorithm is based on transformation of inverse coefficient problem to extremum problem for the residual functional. The steepest descent method is used for numerical solving of this extremum problem. Necessary expressions for calculating gradient of residual functional are presented. The efficiency of the proposed algorithm is illustrated by several test examples.

Heuristic drift-based model of the power scrape-off width in low-gas-puff H-mode tokamaks

A heuristic model for the plasma scrape-off width in low-gas-puff tokamak H-mode plasmas is introduced. Grad B and curv B drifts into the scrape-off layer (SOL) are balanced against near-sonic parallel flows out of the SOL, to the divertor plates. The overall particle flow pattern posited is a modification for open field lines of Pfirsch–Schlüter flows to include order-unity sinks to the divertors. These assumptions result in an estimated SOL width of ∼2aρp/R. They also result in a first-principles calculation of the particle confinement time of H-mode plasmas, qualitatively consistent with experimental observations. It is next assumed that anomalous perpendicular electron thermal diffusivity is the dominant source of heat flux across the separatrix, investing the SOL width, derived above, with heat from the main plasma. The separatrix temperature is calculated based on a two-point model balancing power input to the SOL with Spitzer–Härm parallel thermal conduction losses to the divertor. This results in a heuristic closed-form prediction for the power scrape-off width that is in reasonable quantitative agreement both in absolute magnitude and in scaling with recent experimental data. Further work should include full numerical calculations, including all magnetic and electric drifts, as well as more thorough comparison with experimental data.

Study of electric field pulsation in helical plasmas

A model for the experimental results of the periodic oscillation of the electric field, so-called the electric field pulsation, observed in the Compact Helical Device (Fujisawa et al 1998 Phys. Rev. Lett. 81 2256) and the Large Helical Device (Shimizu et al 2010 Plasma Fusion Res. 5 S1015) is presented. A self-generated oscillation of the radial electric field is shown as the simulation result in helical plasmas. The reduction of the anomalous transport diffusivity in the core region is observed due to the strong shear of the radial electric field when the positive electric field is shown in the core region in the periodic oscillation of Er. Two different time scales are found in the self-generated oscillation, which are the transport time scale and the fast time scale at the transition of the radial electric field. This oscillation because of the hysteresis characteristic is attributed to the electric field pulsation observed in helical plasmas. The parameter region of the condition for the self-generated oscillation is derived. It is shown that the multiple solutions of the radial electric field for the ambipolar condition are necessary but not sufficient for obtaining the self-generated oscillation.

Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT++ code

A minimum set of equations based on the peeling–ballooning (P–B) model with nonideal physics effects (diamagnetic drift, E × B drift, resistivity and anomalous electron viscosity) is found to simulate pedestal collapse when using the BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Linear simulations of P–B modes find good agreement in growth rate and mode structure with ELITE calculations. The influence of the E × B drift, diamagnetic drift, resistivity, anomalous electron viscosity, ion viscosity and parallel thermal diffusivity on P–B modes is being studied; we find that (1) the diamagnetic drift and E × B drift stabilize the P–B mode in a manner consistent with theoretical expectations; (2) resistivity destabilizes the P–B mode, leading to resistive P–B mode; (3) anomalous electron and parallel ion viscosities destabilize the P–B mode, leading to a viscous P–B mode; (4) perpendicular ion viscosity and parallel thermal diffusivity stabilize the P–B mode. With addition of the anomalous electron viscosity under the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron perpendicular thermal diffusivity, or the Prandtl number is close to unity, it is found from nonlinear simulations using a realistic high Lundquist number that the pedestal collapse is limited to the edge region and the ELM size is about 5–10% of the pedestal stored energy. This is consistent with many observations of large ELMs. The estimated island size is consistent with the size of fast pedestal pressure collapse. In the stable α-zones of ideal P–B modes, nonlinear simulations of viscous ballooning modes or current-diffusive ballooning mode (CDBM) for ITER H-mode scenarios are presented.

Simulation of edge localized modes using BOUT++

The BOUT++ code is used to simulate edge localized modes (ELMs) in a shifted circle equilibrium. Reduced ideal MHD simulations are first benchmarked against the linear ideal MHD code ELITE, showing good agreement. Diamagnetic drift effects are included finding the expected suppression of high toroidal mode-number modes. Nonlinear simulations are performed, making the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron thermal diffusivity. This allows simulations with realistically high Lundquist numbers (S = 108), finding ELM sizes of 5–10% of the pedestal stored thermal energy. Scans show a strong dependence of the ELM size on resistivity at low Lundquist numbers, with higher resistivity leading to more violent eruptions. At high Lundquist numbers relevant to high-performance discharges, ELM size is independent of resistivity as hyper-resistivity becomes the dominant dissipative effect.

Levitation Effect: Role of Symmetry and Dependence of Diffusivity on the Bond Length of Homonuclear and Heteronuclear Diatomic Species

Molecular dynamics investigation of model diatomic species confined to the α-cages of zeolite NaY is reported. The dependence of self-diffusivity on the bond length of the diatomic species has been investigated. Three different sets of runs have been carried out. In the first set, the two atoms of the diatomic molecule interact with the zeolite atoms with equal strength (example, O(2), the symmetric case). In the second and third sets which correspond to asymmetric cases, the two atoms of the diatomic molecule interact with unequal strengths (example, CO). The result for the symmetric case exhibits a well-defined maximum in self-diffusivity for an intermediate bond length. In contrast to this, the intermediate asymmetry leads to a less pronounced maximum. For the large asymmetric case, the maximum is completely absent. These findings are analyzed by computing a number of related properties. These results provide a direct confirmation at the microscopic level of the suggestion by Derouane that the supermobility observed experimentally by Kemball has its origin in the mutual cancellation of forces. The maximum in diffusivity from molecular dynamics is seen at the value predicted by the levitation effect. Further, these findings suggest a role for symmetry in the existence of a diffusivity maximum as a function of diameter of the diffusant often referred to as the levitation effect. The nature of the required symmetry for the existence of anomalous diffusivity is interaction symmetry which is different from that normally encountered in crystallography.

Nonlinear Simulations of Peeling-Ballooning Modes with Anomalous Electron Viscosity and their Role in Edge Localized Mode Crashes

A minimum set of equations based on the peeling-ballooning (P-B) model with nonideal physics effects (diamagnetic drift, E×B drift, resistivity, and anomalous electron viscosity) is found to simulate pedestal collapse when using the new BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Nonlinear simulations of P-B modes demonstrate that the P-B modes trigger magnetic reconnection, which leads to the pedestal collapse. With the addition of a model of the anomalous electron viscosity under the assumption that the electron viscosity is comparable to the anomalous electron thermal diffusivity, it is found from simulations using a realistic high-Lundquist number that the pedestal collapse is limited to the edge region and the edge localized mode (ELM) size is about 5%-10% of the pedestal stored energy. This is consistent with many observations of large ELMs.

Jet launching and field advection in quasi-Keplerian discs

AbstractThe fact that self-confined jets are observed around black holes, neutron stars and young forming stars points to a jet launching mechanism independent of the nature of the central object, namely the surrounding accretion disc. The properties of Jet Emitting Discs (JEDs) are briefly reviewed. It is argued that, within an alpha prescription for the turbulence (anomalous viscosity and diffusivity), the steady-state problem has been solved. Conditions for launching jets are very stringent and require a large scale magnetic field Bz close to equipartition with the total (gas and radiation) pressure. The total power feeding the jets decreases with the disc thickness: fat ADAF-like structures with h ~ r cannot drive super-Alfvénic jets. However, there exist also hot, optically thin JED solutions that would be observationally very similar to ADAFs.Finally, it is argued that variations in the large scale magnetic Bz field is the second parameter required to explain hysteresis cycles seen in LMXBs (the first one would be Ṁa).

ETG turbulence effects on the evolution of an NTM

We study the effect of a background of microturbulence generated by unstable short scale length electron temperature gradient (ETG) modes on the excitation and nonlinear evolution of neoclassical tearing modes (NTMs) in a tokamak. A self-consistent model calculation is carried out in which low frequency stresses generated by the ETG modes act on the NTM and which in turn acts back on the ETG evolution by modulating the turbulence profile. The principal physical consequences of the ETG turbulence are to create an anomalous current diffusivity and an anomalous resistivity contribution. These turbulent transport contributions are incorporated in the evolution equations of a single helicity NTM to obtain a generalized Rutherford equation, and their impact on the instability threshold and growth rate is discussed.

Equations of anomalous absorption onto swelling porous media

Absorption is a very common process which takes place on various types of materials ranging from porous media to new nano-materials and biological tissues. The majority of studies reported on absorption to date are concentrated on “rigid” porous media, which contradict the properties of real porous media which undergo swelling and shrinking changes. Here we present new absorption equations derived from a fractional diffusion-wave equation (fDWE) for absorption onto swelling porous media in a material coordinate. We show that the cumulative anomalous absorption is I( t) = St β/2 and the absorption rate i ( t ) = 1 2 β S t β / 2 − 1 , where S is the anomalous sorptivity and β the order of fractional derivative in fDWE. Using published data on cumulative absorption against time, the two adsorption parameters are determined: β = 1.2448 and S = 2.7775 cm 2/h. The value of β = 1.2448 implies that absorption onto this swelling porous media belong to the category of super-diffusion, which is a phenomenon unknown to us before. In comparison, the traditional absorption equations do not have such features. When S is determined, the anomalous diffusivity, D m , is calculated using its relation with S. We expect that the proposed new absorption equations will be valuable for explaining new phenomena and processes encountered in broader disciplines of science and engineering applications.