Three-dimensional Stochastic Model Research Articles

Safe Range of Retaining Pressure for Three-dimensional Face of Pressurized Tunnels based on Limit Analysis and Reliability Method

Based on the existing research, the 3D active and passive failure mechanisms of a pressurized tunnel face are constructed. The nonlinear failure criterion is introduced into the limit analysis by virtue of the tangent technique. By neglecting the randomness of soil parameters, the collapse pressure of active failure and the blowout pressure of passive failure, namely the lower and upper limit of retaining pressure, are obtained along with the failure ranges. On account of the randomness of soil properties, a three-dimensional stochastic model of a pressurized tunnel face is established, and the optimal range of retaining pressure of the pressurized tunnel face is presented on the basis of the multiple correlated failure modes. Taking Changsha Metro Line 2 as an example, the good agreement of the measured data in situ with the reasonable range of retaining pressure verifies the presented method. The combination of limit analysis and reliability method can provide more scientific and reasonable support parameters for the construction of pressurized tunnels in the future.

Influence of hydration heat on stochastic thermal regime of frozen soil foundation considering spatial variability of thermal parameters

Construction method of cast-in-situ concrete is very popular for the foundation engineering in permafrost regions. But the hydration heat of concrete can lead to the melt of ice in frozen soil zone, and then the temperature variation can lower the bearing capacity of frozen soil foundation. In this study, a three-dimensional (3D) stochastic thermal model of frozen soil foundation with phase change and internal heat source is proposed, and the influences of the hydration heat on the stochastic thermal regime of frozen soil foundation are estimated. Considering the different variability of thermal conductivity, heat capacity and latent heat, a sensitivity analysis for the stochastic thermal regime is presented. The results show that the hydration heat of concrete has a great influence on the stochastic thermal regime of frozen soil foundation in the early days after the base constructed. The variability of temperature is more obvious when the distance from the footing centerline is close. Different variability of the thermal parameters has a different effect on the stochastic thermal regime. These results can improve our understanding of the influences of hydration heat on the stochastic thermal regime and provide a theoretical basis for the safety of cast-in-place construction method.

A Study of Electron Forbush Decreases with a 3D SDE Numerical Model

Abstract Because of the precise measurements of the cosmic ray electron flux by the PAMELA and AMS02, Electron Forbush decreases (Fds) have recently been observed for the first time. This serves as motivation to perform a numerical study of electron Forbush decreases with an advanced time-dependent, three-dimensional (3D) stochastic differential equation model, developed earlier to study proton Fds. The model includes a realistic interstellar electron spectrum reconstructed from Voyager observations, and diffusion and drift coefficients to reproduce the modulated spectrum observed by PAMELA in 2009. On the basis of this numerical model, electron Fd profiles for a range of rigidities are simulated. In addition, a systematic comparison between electron and proton Fds during different solar polarity epochs is performed. This approach gives insight into the rigidity dependence of the heliospheric diffusion coefficients and of drift effects over two magnetic field polarity cycles. We find that during an A > 0 epoch, the recovery time of a 1 GV proton Fd is remarkably shorter than the 1 GV electrons, whereas the electron Fd display a faster recovery during an A < 0 epoch. This model clear predicts a charge-sign dependent effect in the recovery time of Fds but less so for their magnitude.

Dynamic Clustering of Dyneins on Axonal Endosomes: Evidence from High-Speed Darkfield Imaging

One of the fundamental features that govern the cooperativity of multiple dyneins during cargo trafficking in cells is the spatial distribution of these dyneins on the cargo. Geometric considerations and recent experiments indicate that clustered distributions of dyneins are required for effective cooperation on micron-sized cargos. However, very little is known about the spatial distribution of dyneins and their cooperativity on smaller cargos, such as vesicles or endosomes <200 nm in size, which are not amenable to conventional immunostaining and optical trapping methods. In this work, we present evidence that dyneins can dynamically be clustered on endosomes in response to load. Using a darkfield imaging assay, we measured the repeated stalls and detachments of retrograde axonal endosomes under load with <10 nm localization accuracy at imaging rates up to 1 kHz for over a timescale of minutes. A three-dimensional stochastic model was used to simulate the endosome motility under load to gain insights on the mechanochemical properties and spatial distribution of dyneins on axonal endosomes. Our results indicate that 1) the distribution of dyneins on endosomes is fluid enough to support dynamic clustering under load and 2) the detachment kinetics of dynein on endosomes differs significantly from the in vitro measurements possibly due to an increase in the unitary stall force of dynein on endosomes.

Neck muscle spindle noise biases reaches in a multisensory integration task.

Reference frame transformations (RFTs) are crucial components of sensorimotor transformations in the brain. Stochasticity in RFTs has been suggested to add noise to the transformed signal due to variability in transformation parameter estimates (e.g., angle) as well as the stochastic nature of computations in spiking networks of neurons. Here, we varied the RFT angle together with the associated variability and evaluated the behavioral impact in a reaching task that required variability-dependent visual-proprioceptive multisensory integration. Crucially, reaches were performed with the head either straight or rolled 30° to either shoulder, and we also applied neck loads of 0 or 1.8 kg (left or right) in a 3 × 3 design, resulting in different combinations of estimated head roll angle magnitude and variance required in RFTs. A novel three-dimensional stochastic model of multisensory integration across reference frames was fitted to the data and captured our main behavioral findings: 1) neck load biased head angle estimation across all head roll orientations, resulting in systematic shifts in reach errors; 2) increased neck muscle tone led to increased reach variability due to signal-dependent noise; and 3) both head roll and neck load created larger angular errors in reaches to visual targets away from the body compared with reaches toward the body. These results show that noise in muscle spindles and stochasticity in general have a tangible effect on RFTs underlying reach planning. Since RFTs are omnipresent in the brain, our results could have implications for processes as diverse as motor control, decision making, posture/balance control, and perception. NEW & NOTEWORTHY We show that increasing neck muscle tone systematically biases reach movements. A novel three-dimensional multisensory integration across reference frames model captures the data well and provides evidence that the brain must have online knowledge of full-body geometry together with the associated variability to plan reach movements accurately.

Numerical analysis of the dynamics of aerosol inertial collection and aggregation on raindrops

A three-dimensional stochastic model is developed for predicting atmospheric aerosol collection and aggregation on the surface of a falling raindrop at its terminal velocity. Potential flow and vis...

Three-dimensional stochastic modeling of metallic surface roughness resulting from pure waterjet peening

We propose a new approach named FEM-Stochastic approach for predicting the surface roughness resulting from waterjet peening of a metallic surface. This approach consists three aspects. One is Coupled Eulerian Lagrangian (CEL) simulation for studying the deformation behavior of single droplet; the second is the stochastic analysis for synthesizing a deformed surface; the third is to calculate the surface roughness parameters. CEL simulation results agree well with the liquid impact theory. Four situations with a different number of droplets (1000, 5000, 10,000 and 20,000) are analyzed, for which the deformed target surfaces and corresponding roughness profiles are shown and compared. Calculated values of roughness parameters indicate that there are three stages of evolution for the arithmetic average height Ra and quadrature average Rq. Those are: roughness increase stage, roughness decrease and roughness steady-state stage, respectively. The total roughness Rt and kurtosis parameter Rku decline gradually when more and more droplets are modeled because the sharp ridges formed by fewer droplets are obliterated by the impingement of subsequent droplets. Skewness parameter Rsk values are all negative, no matter how many droplets, moreover, its absolute value becomes increasingly smaller as the number of droplet changes from 1000 to 20,000. The present spatial model of droplets, although still incomplete, is capable of synthesizing a deformed surface and calculating the relevant roughness parameters.

Stationary Distribution and Extinction of a Stochastic Viral Infection Model

We present a kind of stochastic viral infection model with or without a loss term in the free virus equation. We obtain critical condition to ensure the existence of the unique stationary distribution by constructing Lyapunov functions. We also obtain the sufficient conditions for the extinction of the virus by the comparison theorem of stochastic differential equation and law of large numbers. We give a unified method to systematically analyze such three-dimensional stochastic viral infection model. Furthermore, numerical simulations are carried out to examine the effect of white noises on model behavior. We investigate the fact that the small magnitudes of white noises can sustain the irregular recurrence of healthy target cells and virions, while the big ones may contribute to viral clearance.

3-D Spatial Modeling of Network Interference in Two-Tier Heterogeneous Networks

The multi-tier heterogeneous network (HetNet) architecture can potentially address the massive connectivity and high throughput demands of the emerging fifth generation (5G) of wireless networks. However, the inter-tier interference in HetNets is considered to be a major performance bottleneck. This paper proposes a geometry-based three-dimensional (3-D) stochastic channel model for the spatial characterization of the sum interference in a two-tier HetNet with small cells in tier-1 overlaid with massive multiple-input-multiple-output equipped macro-cell base stations in tier-2. The angular spreads of the interference and the desired signals are analyzed by using the theory of 3-D multipath shape-factors and analytical expressions are derived for their second-order fading statistics, viz: level-crossing-rate (LCR), average-fade-duration (AFD), spatial autocovariance, and the coherence distance. Further, analytical expressions to investigate the second-order fading statistics against signal-to-interference ratio are also derived. The validation of the derived analytical expressions is established through a comparison with computer-based simulations. To provide insights into the network sum interference mechanism, the LCR and AFD expressions are derived for the special case when the rate of fluctuation of the desired signal is much higher than that of the interference signal and vice versa. Furthermore, the impact of the model’s physical parameters, such as the link distance and the receiver’s direction of motion as well as the fading distribution parameters such as its intensity and shape factors on the fading statistics of the interference are evaluated. These results demonstrate that the elevation angle has a significant impact on the interference characterization in HetNet architectures such that it cannot be ignored in modeling emerging 5G communication scenarios.

Three-dimensional stochastic model of actin-myosin binding in the sarcomere lattice.

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

Geometry-Based Stochastic Channel Model for Two-Story Lobby Environment at 10 GHz

This paper presents a complete parametrization for a three-dimensional (3-D) geometry-based stochastic radio channel model (GSCM) at 10.1 GHz based on a measurement campaign. The radio channel measurements were carried out with a vector network analyzer over a 500 MHz bandwidth in a two-story lobby environment. The measurements were conducted with $9 \times 324$ dual polarized virtual antenna arrays in line-of-sight (LOS) and non-LOS propagation conditions. The recorded data was postprocessed using the estimation of signal parameters via rotation invariance algorithm. The statistical analysis was carried out to provide full 3-D parametrization for the GSCM. The parametrization was verified by radio channel simulations. Multiple-input multiple-output (MIMO) channel is reconstructed from the estimated propagation paths and equivalently the channel simulations are performed by quasi-deterministic radio channel generator using our measurements-based parameters. The channel capacity, Demmel condition number, and relative condition numbers are used as the verification metrics. The results show that the reconstructed MIMO channel matches well the simulated MIMO channel.

A Novel 3D Analytical Scattering Model for Air-to-Ground Fading Channels

A geometry-based three-dimensional (3D) novel stochastic channel model for air-to-ground (A2G) and ground-to-air (G2A) radio propagation environments is proposed. The vicinity of a ground station (GS) is modelled as surrounded by effective scattering points; whereas the elevated air station’s (AS) vicinity is modelled as a scattering-free region. Characterization of the Doppler spectrum, dispersion in the angular domain and second order fading statistics of the A2G/G2A radio communication channels is presented. Closed-form analytical expressions for joint and marginal probability density functions (PDFs) of Doppler shift, power and angle of arrival (AoA) are derived. Next, the paper presents a comprehensive analysis on the characteristics of angular spread on the basis of shape factors (SFs) for A2G/G2A radio propagation environments independently in both the azimuth and elevation planes. The analysis is further extended to second order statistics of the fading channel; where the behaviour of the level crossing rate (LCR), average fade duration (AFD), auto-covariance and coherence distance for the A2G/G2A radio propagation environment is studied. Finally, the impact of physical channel parameters, such as the mobility of AS, the height of AS, the height of GS and the delay of the longest propagation path, on the distribution characteristics of Doppler shift, angular spread and second order statistics is thoroughly studied.

A Particle Tracking Model for Sedimentation from Buoyant Jets

AbstractSediment-laden turbulent buoyant jets are commonly found in natural and engineered environments. Examples include volcanic eruptions, deep sea hydrothermal vents, discharge of partially-treated wastewater, and dredging operations. A horizontal sediment buoyant jet is characterized by a horizontal momentum jet, rising plume, and a horizontal surface gravity current. The settling of particles from a sediment buoyant jet depends on the complex interaction of particles with turbulent fluctuations and the mean flow—in particular particle re-entrainment due to the external irrotational flow induced by the jet. A three-dimensional (3D) stochastic particle tracking model is proposed to predict the sedimentation from an arbitrarily inclined sediment-laden buoyant jet in a stagnant ambient. The simple model predicts the entire 3D jet flow field via a coupling of semianalytical models for the mean flow as well as turbulent fluctuations. The mean flow for the turbulent buoyant jet and the surface gravity curr...

A numerical study of the positive cloud-to-ground flash from the forward flank of normal polarity thunderstorm

This study investigates the electrical conditions favorable to the occurrence of positive cloud-to-ground (+CG) flashes from the forward flank of normal polarity thunderstorm by building a three-dimensional stochastic lightning model and a normal polarity charge structure model. The lightning model well simulated the bilevel branched structure of lightning flash, which has been observed by previous studies. Simulation results indicate that the downshear extension of the charge layer to the forward flank would decrease the electric field of thunderstorm. When only the upper positive charge layer downshear extended to the forward flank, it could not give rise to the occurrence of +CG flashes. When both the upper positive and midlevel negative charge layers downshear extended to the forward flank, if the charge of the negative charge layer was less than the positive charge layer above it in the forward flank of the thunderstorm, that generated sufficient charge imbalance between these two charge layers, +CG flashes could originate from the forward flank; otherwise, IC flashes occur.

3D STOCHASTIC ROCK FRACTURE MODELING RELATED TO STRIKE-SLIP FAULTS

Fault zones and fault-related fracture systems control the mechanical behaviors and fluid-flow properties of the Earth's crust. Furthermore, nowadays, modeling is being increasingly used in order to understand the behavior of rock masses, and to determine their characteristics. In this work, fault zones and fracture patterns are reviewed, and also comprehensive studies are carried out on the fracture geometry and density variations. A model to describe damage zones around the strike-slip faults is developed, in which the range of damage zone styles commonly found around strike-slip fault zones are shown. A computer code, named DFN- FRAC 3D , is developed for the two- and three-dimensional stochastic modeling of rock fracture systems in fault zones. In this code, the pre-existing and fault-related fractures are modeled by their respective probability distributions, and the joint density may be varied by the distance from the fault core. This work describes the theoretical basis and the implementation of the code, and provides a case study in the rock fracture modeling to demonstrate the application of the prepared code.

Crossover from the coffee-ring effect to the uniform deposit caused by irreversible cluster-cluster aggregation.

The coffee-ring effect for particle deposition near the three-phase line after drying a pinned sessile colloidal droplet has been suppressed or attenuated in many recent studies. However, there have been few attempts to simulate the mitigation of the effect in the presence of strong particle-particle attraction forces. We develop a three-dimensional stochastic model to investigate the drying process of a pinned colloidal sessile droplet by considering the sticking between particles, which was observed in the experiments. The Monte Carlo simulation results show that by solely promoting the particle-particle attraction in the model, the final deposit shape is transformed from the coffee ring to the uniform film deposition. This phenomenon is modeled using the colloidal aggregation technique and explained by the "Tetris principle," meaning that unevenly shaped or branched particle clusters rapidly build up a sparse structure spanning throughout the entire domain in the drying process. The influence of the controlled parameters is analyzed as well. The simulation is reflected by the drying patterns of the nanofluid droplets through the surfactant control in the experiments.

An Efficient 3D Stochastic Model for Predicting the Columnar-to-Equiaxed Transition in Alloy 718

A three-dimensional (3D) stochastic model for simulating the evolution of dendritic crystals during the solidification of alloys was developed. The model includes time-dependent computations for temperature distribution, solute redistribution in the liquid and solid phases, curvature, and growth anisotropy. The 3D model can run on PCs with reasonable amount of RAM and CPU time. 3D stochastic mesoscopic simulations at the dendrite tip length scale were performed to simulate the evolution of the columnar-to-equiaxed transition in alloy 718. Comparisons between simulated microstructures and segregation patterns obtained with 2D and 3D stochastic models are also presented.

Generation and verification of three-dimensional network of fractured rock masses stochastic discontinuities based on digitalization

Accuracy of seepage simulation in rock masses is directly influenced by related geometrical parameters of DFN (discrete fracture network) models. In this paper a well-planned investigation of rock mass discontinuities was conducted on well-exposed outcrops in Beishan (Gansu province), one of the main candidate sites for the Chinese high-level radioactive waste repository using digital techniques, e.g. global positioning system, close range digital photogrammetry and geographical information system. This allows for very efficient collection of large volumes of data, over 10,000 discontinuities were obtained at the study site (Jijicao block), based on statistical parameters two homogeneities were identified, and the dominant sets were also delineated, which suggested that two sets exist in homogeneity I, while three sets in homogeneity II. In homogeneity I, The optimal fracture diameter probability distributions of both sets were lognormal. Three-dimensional stochastic DFN models were established for both homogeneities based on stochastic process as well as statistical parameters. The reliability of the model was validated by both graphical and numerical methods. Results showed that: digital techniques used in this study can overcome the problem of sample size and precision restriction posed by traditional methods, which leads to a more effective application of DFN model, and are thus suitable for tasks such as detailed mapping of rock masses in large area. It is believed that this verified DFN model is more appropriate for subsequent calculations of mechanical properties and seepage of fractured rock masses.

Particle tracking modeling of sediment-laden jets

Abstract. This paper presents a general model to predict the particulate transport and deposition from a sediment-laden horizontal momentum jet. A three-dimensional (3-D) stochastic particle tracking model is developed based on the governing equation of particle motion. The turbulent velocity fluctuations are modelled by a Lagrangian velocity autocorrelation function that captures the trapping of sediment particles in turbulent eddies, which result in the reduction of settling velocity. Using classical solutions of mean jet velocity, and turbulent fluctuation and dissipation rate profiles derived from computational fluid dynamics calculations of a pure jet, the equation of motion is solved numerically to track the particle movement in the jet flow field. The 3-D particle tracking model predictions of sediment deposition and concentration profiles are in excellent agreement with measured data. The computationally demanding Basset history force is shown to be negligible in the prediction of bottom deposition profiles.

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Tsunami generation and propagation caused by stochastic seismic fault driven by two Gaussian white noises in the x- and y-directions are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading uplift length and rise times of the three-dimensional stochastic fault source model. Tsunami waveforms within the frame of the linearized shallow-water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space). The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to the geometric spreading and also due to dispersion. The maximum amplitude amplification is proportional to the propagation length of the stochastic source model and inversely proportional to the water depth. The increase of the normalized noise intensities on the bottom topography leads to an increase in oscillations and amplitude in the free surface elevation. We derived and analyzed the mean and variance of the random tsunami waves as a function of the propagated uplift length, noise intensities, and the average depth of the ocean along the generation and propagation path.