Self-organization without conservation: true or just apparent scale-invariance?

The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, as forest-fires or earthquake automata, is scrutinized in this paper. By using three different levels of description - (i) a simple mean field, (ii) a more detailed mean-field description in terms of a (self-organized) branching processes, and (iii) a full stochastic representation in terms of a Langevin equation-, it is shown on general grounds that non-conserving dynamics does not lead to bona fide criticality. Contrarily to conserving systems, a parameter, which we term "re-charging" rate (e.g. the tree-growth rate in forest-fire models), needs to be fine-tuned in non-conserving systems to obtain criticality. In the infinite size limit, such a fine-tuning of the loading rate is easy to achieve, as it emerges by imposing a second separation of time-scales but, for any finite size, a precise tuning is required to achieve criticality and a coherent finite-size scaling picture. Using the approaches above, we shed light on the common mechanisms by which "apparent criticality" is observed in non-conserving systems, and explain in detail (both qualitatively and quantitatively) the difference with respect to true criticality obtained in conserving systems. We propose to call this self-organized quasi-criticality (SOqC). Some of the reported results are already known and some of them are new. We hope the unified framework presented here helps to elucidate the confusing and contradictory literature in this field. In a second accompanying paper, we shall discuss the implications of the general results obtained here for models of neural avalanches in Neuroscience for which self-organized scale-invariance in the absence of conservation has been claimed.Comment: 40 pages, 7 figures

Debris flow interaction with open rigid barriers A DEM-LBM approach for trapping efficiency and impact force analysis

Debris flow is a dangerous landslide phenomenon occurring after intense rainfall in mountainous regions. It can be defined as a very rapid flow of heterogeneous material of different grain sizes with high water content. Due to its multi-phase nature, in which solid, fluid and air continuously interact, debris flow is a complex phenomenon, difficult both to analyze and to simulate. Because of its rapidity and unpredictability, it can cause loss of lives and extended damages to environment and structures. Thus, efficient mitigation measures are often desirable. Due to the complexity of the phenomenon, the design of barriers is still a challenging problem. Since a proper regulation does not exist, several of them have been designed only by imitating previously built barriers that have exhibited the proper functions during past events. Moreover, different types exist. The present thesis focuses on structural mitigation measures, with particular reference to open rigid barriers. Several Authors suggested that these barriers have to lower the kinetic energy of the flowing mass and to retain coarse sediments, allowing water and fine particles to pass. The main aspects to consider in the design of such barriers are: (1) the filter size problem, i.e. the size of the outlets, (2) the forces exerted on the barrier by the flowing mass during and after its impact. Thus, the present thesis addresses such two problems through a novel numerical method. An existing DEM-LBM code (Leonardi et al., 2015) has been enhanced with a complete friction model, which allows the creation of stable structures among grains. The result, a 3D continuum- discrete two-phase code, is able to consider the three-dimensional behaviour of the granular mass, the influence of the fluid phase, and their effects when they impact on the barrier. The new code has been validated and adopted to study the clogging mechanisms and the outlet geometry that promotes a retention of coarse grains. First, a monosized dry granular mass has been released under the effect of gravity in an inclined channel, at end of which the barrier is set. A complete parametric study on a single outlet barrier has been performed to provide the bases for furthersimulations on multiple-outlets barriers. The influence of the impact angle, of the channel slope, and of the normalized outlet width on both the trapping efficiency and the impact force has been evaluated and critically discussed. Then, progressively weakening the assumption of dry monosized mass, more realistic configurations have been analyzed. On one hand, bidisized dry granular simulations have been performed accounting for the presence of fine particles. On the other hand, a fluid phase, representing water and fine particles, has been added to the monosized dry granular mass. Interesting outcomes have been obtained on both trapping efficiency and impact forces. Starting from the dry monosized material and a single outlet barrier, a geometrical setting which provides a complete clogging of the barrier has been found. For opening width lower than 5 times the mean particle radius, the trapping efficiency is almost 100%. This result can be extended to the multiple-outlets barrier case if the width of the barrier piles is at least 6 times the mean particle radius. Moreover, introducing a bidispersion in grain size, the efficiency of the retaining function of the barrier is preserved up to a 70% in volume of small particles. The addition of a fluid phase, for solid volume fraction greater than 5%, does not affect the results. Considering the impact forces, high stresses are localized in the outlet neighbourhood, and their intensity increases by increasing the outlet width. The presence of bidispersion lowers the global impact forces, almost independently from the fraction of fine particles. Comparing the dry cases with those in which the fluid is added, it is noted that, in the first seconds after the impact, the presence of the fluid slightly lowers the impact forces due to the solid phase. Then, the fluid phase mainly transfers its momentum to the clogged solid phase, rather than directly to the barrier

2012 program of study : coherent structures

The 2012 GFD Program theme was Coherent structures with Professors Jeffrey Weiss of the University of Colorado at Boulder and Edgar Knobloch of the University of California at Berkeley serving as principal lecturers. Together they introduced the audience in the cottage and on the porch to a fascinating mixture of models, mathematics and applications. Deep insights snaked through the whole summer, as the principal lecturers stayed on to participate in the traditional debates and contributed stoutly to the supervision of the fellows. The first ten chapters of this volume document these lectures, each prepared by pairs of the summer's GFD fellows. Following the principal lecture notes are the written reports of the fellows' own research projects. In 2012, the Sears Public Lecture was delivered by Professor Howard Bluestein, of the University of Oklahoma on the topic of "Probing tornadoes with mobile doppler radars". The topic was particularly suitable for the summer's theme: a tornado is a special examples of a vortex, perhaps the mother of all coherent structures in fluid dynamics. Howie "Cb" showed how modern and innovative measurement techniques can yield valuable information about the formation and evolution of tornadoes, as well as truly amazing images.Funding was provided by the Office of Naval Research under Grant No. N00014-09-10844 and the National Science Foundation under Contract No. OCE-0824636

Towards realistic interactive sand : a GPU-based framework

Includes bibliographical references (leaves 147-160).Many real-time computer games contain virtual worlds built upon terrestrial landscapes, in particular, "sandy" terrains, such as deserts and beaches. These terrains often contain large quantities of granular material, including sand, soil, rubble, and gravel. Allowing other environmental elements, such as trees or bodies of water, as well as players, to interact naturally and realistically with sand, is an important milestone for achieving realism in games. In the past, game developers have resorted to approximating sand with flat. textured surfaces that are static, non-granular, and do not behave like the physical material they model. A reasonable expectation is that sand be granular in its composition and governed by the laws of physics in its behaviour. However, for a single PC user, physics-based models are too computationally expensive to simulate and animate in real-time. An alternative is to use computer clusters to handle numerically intensive simulation, but at the loss of single-user affordability and real-time interactivity. Instead, we propose a GPU-based simulation framework that exploits the massive computational parallelism of a modern GPU to achieve interactive frame rates, on a single PC. We base our method on a discrete elements approach that represents each sand granule as a rigid arrangement of particles. Our model shows highly dynamic phenomena, such as splashing and avalanching, as well as static dune formation. Moreover, by utilising standard metrics taken from granular material science, we show that the simulated sand behaves in accordance with previous numerical and experimental research. We also support general rigid bodies in the simulation by automated particle-based sampling of their surfaces. This allows sand to interact naturally with its environment without extensive modification to underlying physics engine. The generality of our physics framework also allows for real-time physically-based rigid body simulation sans sand, as demonstrated in our testing. Finally, we describe an accelerated real-time method for lighting sand that supports both self-shadowing and environmental shadowing effects

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more