Realistic Diffusion Research Articles

Emergence of Influential Spreaders in Modified Rumor Models

The burst in the use of online social networks over the last decade has provided evidence that current rumor spreading models miss some fundamental ingredients in order to reproduce how information is disseminated. In particular, recent literature has revealed that these models fail to reproduce the fact that some nodes in a network have an influential role when it comes to spread a piece of information. In this work, we introduce two mechanisms with the aim of filling the gap between theoretical and experimental results. The first model introduces the assumption that spreaders are not always active whereas the second model considers the possibility that an ignorant is not interested in spreading the rumor. In both cases, results from numerical simulations show a higher adhesion to real data than classical rumor spreading models. Our results shed some light on the mechanisms underlying the spreading of information and ideas in large social systems and pave the way for more realistic diffusion models.

An efficient diffusion model for viscous fingering

Viscous fingering is one of the most important factors to produce realistic diffusion among two miscible fluids with differing viscosities. Diffusion-limited Aggregation (DLA) has been a popular choice for the synthesis of the viscous fingering effect. However, as DLA provides a mere description of aggregation process, it is not clear how to apply the DLA model into conventional 3D fluid simulation equations. The DLA model first generates a shape description of the viscous fingering effect. The shape description is changed to a fluid flow region by the application of dilation and erosion operators. The flow region is then filled with the directions which will guide the fluid motion in a simulation. The directions are converted into a form of external force by means of a linear feedback system. Our results show that the DLA model can generate the viscous fingering effect effectively in a single phase simulation without relying on a high resolution grid. Our method is semi-physical due to the employment of DLA and is easy to implement, as the underlying concept is simple. Computational overhead is also negligible from the conventional fluid simulation.

Ongoing Cortical Activity at Rest: Criticality, Multistability, and Ghost Attractors

The ongoing activity of the brain at rest, i.e., under no stimulation and in absence of any task, is astonishingly highly structured into spatiotemporal patterns. These spatiotemporal patterns, called resting state networks, display low-frequency characteristics (<0.1 Hz) observed typically in the BOLD-fMRI signal of human subjects. We aim here to understand the origins of resting state activity through modeling via a global spiking attractor network of the brain. This approach offers a realistic mechanistic model at the level of each single brain area based on spiking neurons and realistic AMPA, NMDA, and GABA synapses. Integrating the biologically realistic diffusion tensor imaging/diffusion spectrum imaging-based neuroanatomical connectivity into the brain model, the resultant emerging resting state functional connectivity of the brain network fits quantitatively best the experimentally observed functional connectivity in humans when the brain network operates at the edge of instability. Under these conditions, the slow fluctuating (<0.1 Hz) resting state networks emerge as structured noise fluctuations around a stable low firing activity equilibrium state in the presence of latent "ghost" multistable attractors. The multistable attractor landscape defines a functionally meaningful dynamic repertoire of the brain network that is inherently present in the neuroanatomical connectivity.

Atomistic modeling of alloy self-growth by vapor deposition: Ni and Al on NiAl(110)

ABSTRACTA multisite lattice-gas (msLG) model with realistic and precise surface diffusion kinetics is applied to provide a reliable description of the initial stages of non-equilibrium self-growth of a NiAl alloy by simultaneous stoichiometric codeposition of Ni and Al on the NiAl(110) surface. Deposition at 300 K produces intermixing but poor alloy ordering. Increasing temperature enhances alloy ordering to near perfection at 600 K, but island shapes remain un-equilibrated.

Acceleration of the growth of Cu3Sn voids in solder joints

Soldering to Cu surface finishes usually leads to the formation of a bi-layer intermetallic structure, Cu3Sn/Cu6Sn5, that provides a more robust bond than common alternatives. Occasionally, and so far unpredictably, voids may however grow within the Cu3Sn over time and allow for premature failure of microelectronics products in service. A quantitative assessment of the reliability risk of voids observed after accelerated aging requires the knowledge of the variation of void growth with temperature and time. It is argued that in the case of realistic solder joints diffusion controlled void growth kinetics are unlikely to follow simple Arrhenius and parabolic dependencies, respectively. Nevertheless, three very different sets of samples were all shown to exhibit void growth that could be well approximated by a parabolic time dependence and an effective activation energy of 0.65–0.80eV.

Implementing Realistic Geometry and Measured Diffusion Coefficients into Single Particle Electrode Modeling Based on Experiments with Single LiMn2O4 Spinel Particles

Realistic geometry and diffusion coefficients were measured from a single particle LiMn2O4 electrode and implemented into a three-dimensional multiphysics simulation of a single particle, in order to demonstrate a novel approach to electrode material study. Dispersed particles were used, and electrochemical techniques and atomic force microscopy were performed on isolated single particles. Diffusion coefficients measured from both cyclic voltammetry and the potentiostatic intermittent titration technique ranged between 3.2 × 10−12 and 1.2 × 10−11 cm2/s, which was similar to values measured from thin film LiMn2O4 electrodes. The trend of diffusivity change over potential (versus lithium counter electrode) was similar to those observed from both composite cells and thin film electrodes. The measured diffusion coefficients were then used in simulation of discharge of the irregular particle, by importing the particle morphology into a finite element simulation, in order to simulate intercalation-induced stress generation. Simulation results showed a higher maximum stress generation due to altering diffusivity around the peak current potentials and high local stress concentration on the sharply indented surface area, suggesting that particle irregularities are important in studying both electrochemical performance and local failure mechanisms in cathode materials.

Long-Time Exudation of Plasticizer from Swollen Rubber Vulcanizates: (I) Diffusivity during Swelling

This series of two papers attempt to obtain appropriate estimates of diffusivity during extensive swelling/exudation of plasticizer in vulcanized rubbers and make clearer the difference in their behaviors in terms of diffusivity and time taken to reach equilibrium. Therefore, two mutually consistent kinetic models for extensive absorption/desorption are presented first. A particular treatment of the models is an incorporation of characteristic parameters into the theoretical diffusion coefficient, based on the Flory–Rehner theory. In this first paper, using the model for swelling (or absorption), we confirm that it can provide realistic diffusion coefficients by analyzing experimental data on the swelling of several standard rubber vulcanizates immersed in plasticizer (i.e., dioctyl phthalate), taken from the literature. In the second paper, the counterpart for exudation will provide both diffusivities during extensive exudation and time periods taken to reach equilibrium using the corresponding data. The results have a great difference from those of the swelling case, with the cause being explained.

Kinetics of heterogeneous grain boundary precipitation of Ni3Al in nickel alloy

We study heterogeneous precipitation of Ni3Al in nickel alloy using Monte Carlo simulations based on a simple atomic description of the main mechanisms, which control the kinetic pathway at the grain boundary and in the bulk. A complete model of the grain boundary takes into account both the Σ5 [0 0 1](2 1 0) tilt grain boundary structure and the misorientation between the two grains. The simulation involves realistic vacancy diffusion mechanisms, with a faster diffusion of substitutional atoms at the grain boundary and slower diffusion in the bulk. The grain boundary interacts with solute atoms through local segregation energies. The system was parametrized from experimental data such as cohesive energy, solubility limit and diffusion coefficients. The segregation energies have been computed using a relaxed equilibrium Monte Carlo method based on the Metropolis et al algorithm in conjunction with the embedded atom method potentials. Owing to the complexity of this problem, we first present the Ni3Al homogeneous and heterogeneous precipitation kinetics and then we explore the impact of pair interaction energies at grain boundaries on the morphology of precipitates, as well as the impact of segregation energies on the nucleation behaviour.

Formation ofY2O3nanoclusters in nanostructured ferritic alloys during isothermal and anisothermal heat treatment: A kinetic Monte Carlo study

Kinetic Monte Carlo simulations, based on parameters obtained with density-functional theory in the local-density approximation and experimental data, are used to study bulk precipitation of ${\text{Y}}_{2}{\text{O}}_{3}$ in $\ensuremath{\alpha}$ iron. The simulation involves realistic diffusion mechanisms, with a rapid diffusion of O atoms by interstitial jumps and a slower diffusion of Fe and Y atoms by vacancy jumps, and a point defect source which drives the vacancy concentration toward its equilibrium value, during isothermal and anisothermal heat treatments. Depending on alloy and thermal history conditions, the Monte Carlo simulations predict different kinetic behavior, including transient precipitation of metastable iron oxides followed by precipitation of ${\text{Y}}_{2}{\text{O}}_{3}$ nanoclusters.

Enhancing Realism of Wet Surfaces in Temporal Bone Surgical Simulation

We present techniques to improve visual realism in an interactive surgical simulation application: a mastoidectomy simulator that offers a training environment for medical residents as a complement to using a cadaver. As well as displaying the mastoid bone through volume rendering, the simulation allows users to experience haptic feedback and appropriate sound cues while controlling a virtual bone drill and suction/irrigation device. The techniques employed to improve realism consist of a fluid simulator and a shading model. The former allows for deformable boundaries based on volumetric bone data, while the latter gives a wet look to the rendered bone to emulate more closely the appearance of the bone in a surgical environment. The fluid rendering includes bleeding effects, meniscus rendering, and refraction. We incorporate a planar computational fluid dynamics simulation into our three-dimensional rendering to effect realistic blood diffusion. Maintaining real-time performance while drilling away bone in the simulation is critical for engagement with the system.

Improvement of a mathematical model for low-pressure superheated steam drying of a biomaterial

Although there currently are a number of works reporting experimental study of low-pressure superheated steam drying (LPSSD), which has proved to be an attractive alternative to drying heat-sensitive biomaterials, there are a very few works reporting the development of a mathematical model to predict the evolutions of product moisture content and temperature during LPSSD. Moreover, the predictions of those few developed models are still not satisfactory because, most of the time, the models do not include the effect of initial steam condensation; the use of mass transfer boundary condition is, in some cases, also not quite realistic. The aim of the present study was thus to develop a more realistic liquid diffusion based model to simulate the transport of heat and mass within a product undergoing LPSSD. The effect of initial steam condensation, in terms of film condensation, was included and a more realistic mass transfer boundary condition, in terms of the vapor pressure gradient and the physical condition at the drying surface, was applied in the newly developed model. The effect of the product shrinkage was also included directly in the model. The predictability of the model was tested against the available experimental data. The model with initial steam condensation was found to be able to predict the center temperature and average moisture content of the product undergoing LPSSD very well. However, at higher temperatures and lower pressures the product core temperature was still under predicted.

Modeling Microscopic Chemical Sensors in Capillaries

Nanotechnology-based microscopic robots could provide accurate in vivo measurement of chemicals in the bloodstream for detailed biological research and as an aid to medical treatment. Quantitative performance estimates of such devices require models of how chemicals in the blood diffuse to the devices. This paper models microscopic robots and red blood cells (erythrocytes) in capillaries using realistic distorted cell shapes. The models evaluate two sensing scenarios: robots moving with the cells past a chemical source on the vessel wall, and robots attached to the wall for longer-term chemical monitoring of chemicals released into the bloodstream. Using axial symmetric geometry with realistic flow speeds and diffusion coefficients, we compare detection performance with a simpler model that does not include the cells. The average chemical absorption is quantitatively similar in both models, indicating the simpler model is an adequate design guide to sensor performance in capillaries. However, determining the variation in forces and absorption as cells move requires the full model.

Kinetics of heterogeneous grain boundary precipitation of NbC in α-iron: A Monte Carlo study

We propose Monte Carlo simulations of the NbC grain boundary (GB) precipitation kinetics in α-iron, based on an atomic description of the main mechanisms that control the kinetic pathway. The simulation involves realistic diffusion mechanisms, with a rapid diffusion of C atoms by interstitial jumps and a slower diffusion of Fe and Nb atoms by vacancy jumps; a simple model of the GB which reproduces the equilibrium segregation properties of Nb and C; and a point defect source which drives the vacancy concentration towards its equilibrium value. Depending on the precipitation conditions, Monte Carlo simulations predict different kinetic behaviours, including early segregation of C atoms at the grain boundaries, transient precipitation of metastable carbides, and homogeneous and heterogeneous NbC precipitation.

Kinetics of heterogeneous dislocation precipitation of NbC in alpha-iron

We propose Monte Carlo simulations of the precipitation kinetics of NbC on dislocations in α-iron based on an atomistic description of the main mechanisms controlling the kinetic pathway. The algorithm takes into account realistic diffusion properties, with a rapid diffusion of C atoms by interstitial jumps and a slower diffusion of Fe and Nb atoms by vacancy jumps. A simple model of dislocation includes interactions with solute atoms, through local segregation energy and long range elastic fields. The relative importance of local segregation energies and long range elastic stresses on the precipitation characteristics, such as early segregation of carbon atoms on dislocations, transient precipitation of metastable carbides, and homogeneous and heterogeneous NbC precipitation, is discussed.

Kinetics of the formation of a new phase in nanoparticles

We present Monte Carlo simulations of the formation of a new phase (e.g., hydride in metal) during uptake of atoms by a nanoparticle. The corresponding kinetics exhibit a short initial stage, which is sensitive to the specification of the subsurface layers, and a more universal long stage with the time scale proportional to L z , where L is the lattice size, and 2.3 ⩽ z ⩽ 3 is the exponent dependent on the diffusion dynamics. For realistic diffusion dynamics, the model also predicts the third late stage when the growth of a new phase becomes very slow compared to that observed during the former stages.

MARCOS, a numerical tool for the simulation of multiple time-dependent non-linear diffusive shock acceleration

We present a new code aimed at the simulation of diffusive shock acceleration (DSA), and discuss various test cases which demonstrate its ability to study DSA in its full time-dependent and non-linear developments. We present the numerical methods implemented, coupling the hydrodynamical evolution of a parallel shock (in one space dimension) and the kinetic transport of the cosmic-rays (CR) distribution function (in one momentum dimension), as first done by Falle. Following Kang and Jones and collaborators, we show how the adaptive mesh refinement technique (AMR) greatly helps accommodating the extremely demanding numerical resolution requirements of realistic (Bohm-like) CR diffusion coefficients. We also present the paral lelization of the code, which allows us to run many successive shocks at the cost of a single shock, and thus to present the first direct numerical simulations of linear and non-linear multiple DSA, a mechanism of interest in various astrophysical environments such as superbubbles, galaxy clusters and early cosmological flows.

Dependent multivariate diffusion models and related point process models of ensemble spiking neurons

The first-passage time of a diffusion process through a constant or variable boundary has been the focus of many stochastic models of neuronal membrane potential dynamics. Diffusion processes have been used extensively to model a latent process that may only be observable through consequent renewal point process events. The mathematical relationship between inter-spike intervals and the first-passage time of simple diffusion models is well-known, however this relationship becomes increasingly more complex as the diffusion models become more physiologically realistic, and when multivariate diffusion processes are no longer considered to be independent. The probability density of a diffusing particle position at a particular point in time P(x, t) as defined by the Fokker-Planck equation can be solved, under suitable conditions, using the method of images. We show how the method of images can be extended to a multivariate probability density constructed from marginal densities modeling simple individual spiking neurons using a copula construction that factors out the correlated (dependent) noise structure. This in turn provides a straightforward method for estimating multivariate spike survival and hazard functions from simultaneously recorded single unit activity and, indirectly, the ensemble neuron diffusion noise dependence. The analytical approach is supported by simulated Wiener processes with drift and applied to simultaneous single unit recordings from Heschl's gyrus in awake human subjects. Extensions of this approach to more physiologically realistic diffusion models such as the Ornstein-Uhlenbeck and Feller processes will be discussed.

A Diffusional Model with a Moisture-Dependent Diffusion Coefficient

Many investigators point out that a more realistic diffusion model is obtained when the effective diffusivity is considered with both temperature and moisture content dependent. Two mathematical models to predict the drying curves of pineapple at different temperatures have been compared. The simulation provided by model I, where the effective diffusion coefficient was considered as a function of the temperature, was unsatisfactory as indicated by the mean relative error (%E) of 19.8 ± 2.4%. The diffusion equation was modified by including both the effect of the temperature and the local moisture content on the effective diffusion coefficient in model II, being the %E of the simulation of 4.5 ± 2.0%.

A Structure-Based Simulation Approach for Electron Paramagnetic Resonance Spectra Using Molecular and Stochastic Dynamics Simulations

Electron paramagnetic resonance (EPR) spectroscopy using site-directed spin-labeling is an appropriate technique to analyze the structure and dynamics of flexible protein regions as well as protein-protein interactions under native conditions. The analysis of a set of protein mutants with consecutive spin-label positions leads to the identification of secondary and tertiary structure elements. In the first place, continuous-wave EPR spectra reflect the motional freedom of the spin-label specifically linked to a desired site within the protein. EPR spectra calculations based on molecular dynamics (MD) and stochastic dynamics simulations facilitate verification or refinement of predicted computer-aided models of local protein conformations. The presented spectra simulation algorithm implies a specialized in vacuo MD simulation at 600 K with additional restrictions to sample the entire accessible space of the bound spin-label without large temporal effort. It is shown that the distribution of spin-label orientations obtained from such MD simulations at 600 K agrees well with the extrapolated motion behavior during a long timescale MD at 300 K with explicit water. The following potential-dependent stochastic dynamics simulation combines the MD data about the site-specific orientation probabilities of the spin-label with a realistic rotational diffusion coefficient yielding a set of trajectories, each more than 700 ns long, essential to calculate the EPR spectrum. Analyses of a structural model of the loop between helices E and F of bacteriorhodopsin are illustrated to demonstrate the applicability and potentials of the reported simulation approach. Furthermore, effects on the motional freedom of bound spin-labels induced by solubilization of bacteriorhodopsin with Triton X-100 are examined.

Shear and Static Instability of Inertia–Gravity Wave Packets: Short-Term Modal and Nonmodal Growth

Abstract The problem of nonmodal instabilities of inertia–gravity waves (IGW) in the middle atmosphere is addressed, within the framework of a Boussinesq model with realistic molecular viscosity and thermal diffusion, by singular-vector analysis of horizontally homogeneous vertical profiles of wind and buoyancy obtained from IGW packets at their statically least stable or most unstable horizontal location. Nonmodal growth is always found to be significantly stronger than that of normal modes, most notably at wave amplitudes below the static instability limit where normal-mode instability is very weak, whereas the energy gain between the optimal perturbation and singular vector after one Brunt–Väisälä period can be as large as two orders of magnitude. Among a multitude of rapidly growing singular vectors for this optimization time, small-scale (wavelengths of a few 100 m) perturbations propagating in the horizontal parallel to the IGW are most prominent. These parallel optimal perturbations are amplified by a roll mechanism, while transverse perturbations (with horizontal scales of a few kilometers) are to a large part subject to an Orr mechanism, both controlled by the transverse wind shear in the IGW at its statically least stable altitude, but further enhanced by reduced static stability. The elliptic polarization of the IGW leaves its traces in an additional impact of the roll mechanism via the parallel wind shear on the leading transverse optimal perturbation.