Avalanche Model Research Articles

Improved Model for Granular Avalanches

A well-posed multilayer model involving a dilatancy law is developed and systematically compared to three different experimental scenarios.

A well-posed multilayer model for granular avalanches: Comparisons with laboratory experiments

Granular avalanches are dangerous phenomena characterized by the rapid gravity-driven motion of granular solids. The complex dynamics of these flows can be effectively modeled by a multilayer approach, which, however, requires particular attention to the derivation of the model equations in order to allow stable solutions. In this work, we use a well-posed multilayer model, in which the μ(I)-rheology is employed and a dilatancy law, depending on the inertial number I, is also taken into account, and systematically compare it with various laboratory experiments. The model, whose well-posedness is guaranteed by a physically based viscous regularization, describes the evolution of a preset number of superimposed granular layers. As the sidewall friction is relevant under most experimental conditions, the model is fitted here with suitable resistance terms. Moreover, non-trivial closures for the mass exchanges are introduced to avoid any unrealistic partitioning of the flow domain during the avalanche evolution, and, hence, guarantee a regular spatial discretization along the normal to flow direction. The velocity fields are compared with different experiments in unsteady state, and comparisons of both velocity and volume fraction profiles are provided with steady uniform flow experiments. The results confirm the good capabilities of the multilayer model and the underlying μ(I)-rheology in capturing the granular flow dynamics. The experimental volume fraction profiles are qualitatively well reproduced by the proposed dilatancy law, while an overestimation is observed only in the upper, more dilute flow region with a thickness of a few grain diameters.

Avalanche Modeling in Mextram 505 and Implications on Circuit Simulations

This paper presents several recent advances in compact modeling of avalanche multiplication in Mextram 505, an industry standard transistor model, including both new model features and improved model implementations. Implications of these improvements on circuit simulation are illustrated using RF SiGe HBTs.Feature wise, Mextram 505 adds a new physics-based model of the avalanche multiplication factor that accounts for the complex evolution of the epi-layer electric field at high current density, which can be activated with swavl=3. At a given collector-base bias VCB, the avalanche factor Gem is constant at low collector current density JC, starts to decrease when mobile electron density becomes comparable to epi-layer doping density due to charge compensation, and ultimately increases again when the base pushes out, and the electrical CB junction shifts to the epi-layer/buried layer interface. A parameter exavl can be used to turn on/off the rise of Gem at very high JC. An example of fitting IB versus IE for a common-base RF SiGe HBT at a fixed VCB=3V is given in Fig. 1. The measured base current is calculated from the difference of measured IE and IC, and hence shows some measurement noise. At low IE, Gem is constant, IB is linearly proportional to IE, with exavl=0, only the decrease of Gem with increasing JC is modeled, the IB bends upward at 0.05 A. With exavl=1, the rise of Gem at high JC is modeled, allowing the fitting of the downward bending of IB above 0.1 A. We will also discuss implications of such complex Gem behavior for RF linearity, particularly on the modeling of linearity sweet spots, i.e. biasing currents and voltages at which linearity peaks.Implementation wise, Mextram 505 uses the main current In as the initiating current in calculating the avalanche current Iavl, i.e. Iavl = In*Gem, as opposed to using the epi-layer current Ic1c2, i.e. Iavl = Ic1c2*Gem in Mextram 504. While for DC I-V, one can always use slightly different Gem model parameters to achieve the same degree of fitting, we found that the Mextram 504 approach can lead to unphysically high avalanche noise in voltage-controlled oscillator (VCO) circuits in some cases. Users should inspect the waveforms of Iavl as well as In to determine if this problem exists. The root problem is that the epi-layer current Ic1c2 also includes the CB junction capacitive charge current, which should not experience avalanche as the corresponding electron motion occurs outside the space charge region. While the Iavl error introduced has a small absolute value, the noise it introduces is often significant, and significantly increases oscillator phase noise.At the device level, this unphysical avalanche of capacitive charge current comes into play during modeling of the CB depletion capacitance, CCB, which is often extracted from off state y-parameter. Fig. 2 compares the CCB vs VCB simulated using In (505) and Ic1c2 (504) as avalanche initiating current, together with the CCB from measurement. The Gem value is shown on the right y-axis. When Gem approaches 1, the simulated CCB using Iavl = Ic1c2*Gem increases sharply, and becomes negative when Gem>1, a unphysical result users of Mextram 504 need to be aware of for high Gem biases. Using Iavl = In*Gem, as is in Mextram 505, the simulated CCB remains physical when Gem is high. An analytical model of such discrepancy has been developed using small signal frequency domain analysis and will be presented.In Mextram 504 and earlier versions of Mextram 505, Gem is limited to be less than 1 and then further limited through elegant considerations that ensure the collector current increases monotonically with the external VBE. Such limiting, however, cannot possibly work for the dynamic charge current which is the issue in the off-state CCB example as well as the VCO example above, due to how model equations are implemented in circuit simulators. One side effect of this Gem limiting is that avalanche induced runaway cannot be modeled for investigating safe operating area (SOA). A switch swgemlim is introduced in Mextram 505.3 to allow the users to turn off Gem limiting for such modeling, as shown in Fig. 3. The new avalanche model in Mextram 505 also enhances its ability to accurately predict the SOA boundary due to electrothermal runaway from the combined effects of avalanche and self-heating. Figure 1

Avalanche Modeling in Mextram 505 and Implications on Circuit Simulations

This paper presents recent advances in compact modeling of avalanche multiplication in Mextram 505, an industry-standard transistor model, including new model features, improved model implementations, and implications for SiGe HBT RF circuit simulation and device modeling.

Implementation of an early warning for snowfall-triggered avalanche to road safety in the Tianshan Mountains

Avalanches are very active and are seriously threatening road safety in the Tianshan mountains. The snowfall-triggered avalanches have caused many serious casualties and paralyzed the transport system. A warning system of snowfall-triggered avalanches can improve the level of road management and reduce avalanche risk. However, an applicable warning model for snowfall-triggered avalanches has still not been developed for the Tianshan Mountains. This study developed a snowfall-triggered avalanche warning model (SFAW), which was tested on the 218 National Highway located in the central Tianshan Mountains - an area that was seriously affected by avalanches. Snowpack, terrain, and meteorology data were collected at the sites during the winter period from 2011 to 2019 and applied to parameterize the SFAW. The SFAW calculated the probability of regional avalanche release driven by snowfall and snow depth from automatic observation, and the simulated results were compared with the observed avalanche data. The results showed that SFAW had an overall accuracy of 80.5%, the probabilities of detection for the regional avalanche events (POD) of 75.0%, and the false alarm ratio of avalanche events (FAR) of 52.0%. SFAW can serve as an important reference for snowfall-triggered avalanche warning, help to protect local transportation, and reduce the damage caused by avalanches in the Tianshan Mountains.

Study of the dielectric breakdown strength of CO2–O2 mixtures by considering ion kinetics in a spatial–temporal growth avalanche model

The gas mixture CO2–O2 has been considered as an insulation and arc-quenching medium in gas-insulated switchgears. In this paper, the dielectric breakdown properties of CO2–O2 mixtures at different O2 concentrations and gas pressures were studied theoretically by considering ion kinetics in a spatial–temporal growth avalanche model. A kinetic scheme that includes all the main reactions likely to occur in CO2–O2 mixtures is presented. An improved method to calculate the dielectric strength of the gas mixture is developed, based on an avalanche model that considers both spatial growth and temporal processes. Next, the reaction rates of ionization, attachment, detachment and ion conversion, the effective ionization Townsend coefficient αeff/N, and reduced critical electric field strength (E/N)cr in CO2–O2 mixtures at different mixing ratios and gas pressures are analyzed in detail. Finally, a pulsed Townsend experiment is performed to verify the validity and accuracy of the calculation method. Based on this, one detachment reaction rate is modified to yield more accurate results. Better consistency between the results and the experimental values supports the validity of the kinetic system, reaction rates, and the improved calculation method.

Forecasting Solar Flares by Data Assimilation in Sandpile Models

The prediction of solar flares is still a significant challenge in space weather research, with no techniques currently capable of producing reliable forecasts performing significantly above climatology. In this paper, we present a flare forecasting technique using data assimilation coupled with computationally inexpensive cellular automata called sandpile models. Our data assimilation algorithm uses the simulated annealing method to find an optimal initial condition that reproduces well an energy-release time series. We present and empirically analyze the predictive capabilities of three sandpile models, namely the Lu and Hamilton model (LH) and two deterministically-driven models (D). Despite their stochastic elements, we show that deterministically-driven models display temporal correlations between simulated events, a needed condition for data assimilation. We present our new data assimilation algorithm and demonstrate its success in assimilating synthetic observations produced by the avalanche models themselves. We then apply our method to GOES X-Ray time series for 11 active regions having generated multiple X-class flares in the course of their lifetime. We demonstrate that for such large flares, our data assimilation scheme substantially increases the success of ``All-Clear'' forecasts, as compared to model climatology.

Do Cellular Automaton Avalanche Models Simulate the Quasi-periodic Pulsations of Solar Flares?

Quasi-periodic pulsations (QPPs) with various periods that originate in the underlying magnetohydrodynamic processes of flaring structures are detected repeatedly in solar flare emissions. We apply a 2D cellular automaton (CA) avalanche model to simulate QPPs as a result of a repetitive load/unload mechanism. We show that the frequent occurrence of magnetic reconnections in a flaring loop could induce quasi-periodic patterns in the detected emissions. We find that among 21,070 simulated flares, 813 events last over 50 s, scaled with the temporal resolution of the Yohkoh Hard X-ray Telescope, and about 70% of these rather long-lasting events exhibit QPPs. We also illustrate that the applied CA model provides a wide range of periodicities for QPPs. Furthermore, we observe the presence of multiple periods in nearly 50% of the cases by applying the Lomb–Scargle periodogram. A lognormal distribution is fitted to the unimodal distribution of the periods as a manifestation of an underlying multiplicative mechanism that typifies the effect of the system’s independently varying parameters. The global maximum of the periods’ lognormal distribution is located at 29.29 ± 0.67 s. We compare statistics of the simulated QPPs with parameters of the host flares and discuss the impacts of flare properties on the periods of QPPs. Considering the intrinsic characteristic of CA models, namely the repetitive load/unload mechanism, and the obtained pieces of evidence, we suggest that CA models may generate QPPs. We also examine the applicability of autoregressive integrated moving average models to describe the simulated and observed QPPs.

The impact of terrain model source and resolution on snow avalanche modeling

Abstract. Natural hazard models need accurate digital elevation models (DEMs) to simulate mass movements on real-world terrain. A variety of platforms (terrestrial, drones, aerial, satellite) and sensor technologies (photogrammetry, lidar, interferometric synthetic aperture radar) are used to generate DEMs at a range of spatial resolutions with varying accuracy. As the availability of high-resolution DEMs continues to increase and the cost to produce DEMs continues to fall, hazard modelers must often choose which DEM to use for their modeling. We use satellite photogrammetry and topographic lidar to generate high-resolution DEMs and test the sensitivity of the Rapid Mass Movement Simulation (RAMMS) software to the DEM source and spatial resolution when simulating a large and complex snow avalanche along Milford Road in Aotearoa/New Zealand. Holding the RAMMS parameters constant while adjusting the source and spatial resolution of the DEM reveals how differences in terrain representation between the satellite photogrammetry and topographic lidar DEMs (2 m spatial resolution) affect the reliability of the simulation estimates (e.g., maximum core velocity, powder pressure, runout length, final debris pattern). At the same time, coarser representations of the terrain (5 and 15 m spatial resolution) simulate avalanches that run too far and produce a powder cloud that is too large, though with lower maximum impact pressures, compared to the actual event. The complex nature of the alpine terrain in the avalanche path (steep, rough, rock faces, treeless) makes it a suitable location to specifically test the model sensitivity to digital surface models (DSMs) where both ground and above-ground features on the topography are included in the elevation model. Considering the nature of the snowpack in the path (warm, deep with a steep elevation gradient) lying on a bedrock surface and plunging over a cliff, RAMMS performed well in the challenging conditions when using the high-resolution 2 m lidar DSM, with 99 % of the simulated debris volume located in the documented debris area.

GIS-Based Spatial Modeling of Snow Avalanches Using Analytic Hierarchy Process. A Case Study of the Šar Mountains, Serbia

Snow avalanches are one of the most devastating natural hazards in the highlands that often cause human casualties and economic losses. The complex process of modeling terrain susceptibility requires the application of modern methods and software. The prediction of avalanches in this study is based on the use of geographic information systems (GIS), remote sensing, and multicriteria analysis—analytic hierarchy process (AHP) on the territory of the Šar Mountains (Serbia). Five indicators (lithological, geomorphological, hydrological, vegetation, and climatic) were processed, where 14 criteria were analyzed. The results showed that approximately 20% of the investigated area is highly susceptible to avalanches and that 24% of the area has a medium susceptibility. Based on the results, settlements where avalanche protection measures should be applied have been singled out. The obtained data can will help local self-governments, emergency management services, and mountaineering services to mitigate human and material losses from the snow avalanches. This is the first research in the Republic of Serbia that deals with GIS-AHP spatial modeling of snow avalanches, and methodology and criteria used in this study can be tested in other high mountainous regions.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ СНЕЖНЫХ ЛАВИН С ИСПОЛЬЗОВАНИЕМ КЛЕТОЧНЫХ АВТОМАТОВ

A description of the developed three-dimensional model of avalanche motion based on cellular automata is given. Preliminary results of avalanche modeling in relation to the real terrain of an avalanche-prone area on the territory of the Elbrus ski resort are presented.

Applicability of numerical two-layer depth-averaged models for pyroclastic density currents to powder snow avalanches: Toward developing a unified model for powder snow avalanches and pyroclastic density currents

Applicability of numerical two-layer depth-averaged models for pyroclastic density currents to powder snow avalanches: Toward developing a unified model for powder snow avalanches and pyroclastic density currents

Gap uniformity study of a resistive Micromegas for the Multi-purpose Time Projection Chamber (MTPC) at Back-n white neutron source

A Multi-purpose Time Projection Chamber prototype based on a resistive Micromegas technique has been proposed, designed and fabricated at China Spallation Neutron Source to measure the cross sections of neutron-induced light-charged particle emission reactions and fission reactions at the Back-n white neutron source. For the requirements of working stability with high voltage and high granularity of readout, the prototype is fabricated by applying a resistive Micromegas with high-density pixelated anode plane. In order to fully understand the process of charge spreading and signal induction on the anode plane covered by a resistive layer, a simulation method is developed and the energy correction function is then obtained, which can be used in the further energy correction in the experimental data analysis. Measured with a 55Fe X-ray source, the uniformity of gain and avalanche gap are specially analyzed by combining the simulated gas avalanche parameters with fitting of experimental data in which the parallel plate avalanche model is adopted.

Service Limits for Metal Oxide Varistors Having Cylindrical Symmetry as Function of the Ambient Temperature

This article presents an original experimental method applied to assess the stability limits of a given Metal Oxide Varistor (MOV), with cylindrical symmetry (cylinder or disk shape), as a direct relation between the ambient temperature and the service rated voltage, in the permanent operational regime. As the crossing current of a certain varistor is heavily influenced by its physical temperature, we must find an empirical relationship between these two parameters for a symmetrical configuration. Each ambient temperature can increase the temperature reference and any higher voltage will also produce an increased current, causing a uncontrolled runaway heating process, in an avalanche model. We tried to eliminate any references to technical dimensions or device values, focusing on material parameters. In the case of a symmetric MOV, we will consider the load coefficient, which is the ratio between the service DC voltage and the nominal DC opening voltage. By using experimental measurements and a simple mathematical model, we will establish the relation between the critical load coefficient and the ambient temperature in the case of symmetrical MOVs. This procedure could be applied to the design of more performant and safe surge arrester devices using existing MOVs, for all voltage levels and symmetrical configurations.

Different erosion and entrainment mechanisms in snow avalanches

Erosion significantly affects the dynamics of gravity-driven mass flows. In snow avalanches, the snow cover can be substantially eroded but only partially entrained, however, there are very limited investigations to substantiate this difference. Here, we study various erosion and entrainment behaviors in snow avalanches using the material point method (MPM), finite strain elastoplasticity and critical state soil mechanics. With varied snow properties, distinct erosion patterns are obtained and analyzed with the mass change rate. When there is significant eroded and entrained mass, properties of released snow and erodible bed snow have clear correlations with the eroded mass, but not with the entrained mass, disclosing the difference in erosion and entrainment. Both enhanced and inhibited avalanche mobilities due to erosion and entrainment are captured under different conditions of snow properties and lengths of release and erodible zones. These new insights may stimulate the development of advanced erosion and entrainment models for large-scale avalanches.

Flow-Py v1.0: a customizable, open-source simulation tool to estimate runout and intensity of gravitational mass flows

Abstract. Models and simulation tools for gravitational mass flows (GMFs) such as snow avalanches, rockfall, landslides, and debris flows are important for research, education, and practice. In addition to basic simulations and classic applications (e.g., hazard zone mapping), the importance and adaptability of GMF simulation tools for new and advanced applications (e.g., automatic classification of terrain susceptible for GMF initiation or identification of forests with a protective function) are currently driving model developments. In principle, two types of modeling approaches exist: process-based physically motivated and data-based empirically motivated models. The choice for one or the other modeling approach depends on the addressed question, the availability of input data, the required accuracy of the simulation output, and the applied spatial scale. Here we present the computationally inexpensive open-source GMF simulation tool Flow-Py. Flow-Py's model equations are implemented via the Python computer language and based on geometrical relations motivated by the classical data-based runout angle concepts and path routing in three-dimensional terrain. That is, Flow-Py employs a data-based modeling approach to identify process areas and corresponding intensities of GMFs by combining models for routing and stopping, which depend on local terrain and prior movement. The only required input data are a digital elevation model, the positions of starting zones, and a minimum of four model parameters. In addition to the major advantage that the open-source code is freely available for further model development, we illustrate and discuss Flow-Py's key advancements and simulation performance by means of three computational experiments. Implementation and validation. We provide a well-organized and easily adaptable solver and present its application to GMFs on generic topographies. Performance. Flow-Py's performance and low computation time are demonstrated by applying the simulation tool to a case study of snow avalanche modeling on a regional scale. Modularity and expandability. The modular and adaptive Flow-Py development environment allows access to spatial information easily and consistently, which enables, e.g., back-tracking of GMF paths that interact with obstacles to their starting zones. The aim of this contribution is to enable the reader to reproduce and understand the basic concepts of GMF modeling at the level of (1) derivation of model equations and (2) their implementation in the Flow-Py code. Therefore, Flow-Py is an educational, innovative GMF simulation tool that can be applied for basic simulations but also for more sophisticated and custom applications such as identifying forests with a protective function or quantifying effects of forests on snow avalanches, rockfall, landslides, and debris flows.

Theoretical Framework in Student Debt Research: Linking Economic, Finance and Education Theories to Student Debt Literature

There has been a growing interest in student debt research in recent years among researchers and graduate students. Student loan has become a popular means of financing the increasing cost of higher education among millennia, thus spurring the rising interest of researchers in this area. However, the availability of established theories related to the student debt topic is limited. The purpose of this study is to add to the limited literature of theories in student debt scholarship. This study links two economic theories, four finance theories, and two education theories to student debt literature. The economic theories (human capital theory and life cycle Model) emphasize the role of student loans in fostering investment in human capital and its impact on future consumption. This study also examines four debt repayment models (the debt snowball model, the balance-matching model, the debt avalanche model, and the debt consolidation model) suggested by various financial advisors on debt repayments, which postulate four distinct strategies on how debtors can settle their loans. The education theories (Tinto student departure model and John Bean’s explanatory theory of student retention model) highlight the importance of student retention at colleges to ensure college completion, which in turn increases the chances of getting a job; thus, guaranteeing loan repayment. These theories will serve as a theoretical framework guide to researchers, especially graduate students who are working on their thesis or dissertation on the student loan debt topic.

ERUPCIONES SOLARES: ESTUDIO DE SU DISTRIBUCIÓN TEMPORAL USANDO UN AUTÓMATA CELULAR

For almost 30 years the Lu & Hamilton avalanche model (LH91) has been the paramount tool to study the intermittent nature of solar flares via avalanche models. In this work, we used the two-dimensional model of Lu & Hamilton to assess the statistics of the waiting time between avalanches and the possibility of forecasting synthetic solar flares. We worked with three different definitions of waiting time between∆T,∆Tiiand∆TP. For the case of the usual definition of the waiting time between avalanches (∆T) we found that the statistics can be described statistically through an exponential function. For the other definitions, they present power-law statistics with exponents that compare well with solar observations.

TCAD simulations of non-irradiated and irradiated low-gain avalanche diodes and comparison with measurements

In this work, the results of Technology-CAD (TCAD) device-level simulations of non-irradiated and irradiated Low-Gain Avalanche Diode (LGAD) detectors and their validation against experimental data will be presented. Thanks to the intrinsic multiplication of the charge within these silicon sensors, it is possible to improve the signal to noise ratio thus limiting its drastic reduction with fluence, as it happens instead for standard silicon detectors. Therefore, special attention has been devoted to the choice of the avalanche model, which allows the simulation findings to better fit with experimental data. Moreover, a radiation damage model (called “New University of Perugia TCAD model”) has been fully implemented within the simulation environment, to have a predictive insight into the electrical behavior and the charge collection properties of the LGAD detectors, up to the highest particle fluences expected in the future High Energy Physics (HEP) experiments. This numerical model allows to consider the comprehensive bulk and surface damage effects induced by radiation on silicon sensors. By coupling the “New University of Perugia TCAD model” with an analytical model that describes the mechanism of acceptor removal in the multiplication layer, it has been possible to reproduce experimental data with high accuracy, demonstrating the reliability of the simulation framework.

Subcritical and supercritical granular flow around an obstacle on a rough inclined plane

A blunt obstacle in the path of a rapid granular avalanche generates a bow shock (a jump in the avalanche thickness and velocity), a region of static grains upstream of the obstacle, and a grain-free region downstream. Here, it is shown that this interaction is qualitatively altered if the incline on which the avalanche is flowing is changed from smooth to rough. On a rough incline, the friction between the grains and the incline depends on the flow thickness and speed, which allows both rapid (supercritical) and slow (subcritical) steady uniform avalanches. For supercritical experimental flows, the material is diverted around a blunt obstacle by the formation of a bow shock and a static dead zone upstream of the obstacle. Downslope, a grain-free vacuum region forms, but, in contrast to flows on smooth beds, static levees form at the boundary between the vacuum region and the flow. In slower, subcritical, flows the flow is diverted smoothly around the dead zone and the obstacle without forming a bow shock. After the avalanche stops, signatures of the dead zone, levees and (in subcritical flows) a deeper region upslope of the obstacle are frozen into the deposit. To capture this behaviour, numerical simulations are performed with a depth-averaged avalanche model that includes frictional hysteresis and depth-averaged viscous terms, which are needed to accurately model the flowing and deposited regions. These results may be directly relevant to geophysical mass flows and snow avalanches, which flow over rough terrain and may impact barriers or other infrastructure.