Hugo A. Martin

Modeling Financial Speculation in an Agent-Based/Stock-Flow Consistent (SFC) Model

I am working on a new Stock-Flow Consistent (SFC) model based on feedback loops that we have identified as crucial for representing systemic contagion risks, with a particular focus on the finance/speculation/energy aspect. Using these feedback loops, I have developed the CRISIS model, a hybrid Agent-Based (AB)/SFC model, where classical macroeconomic sectors (industry, households, banks, etc.) are disaggregated into networks of economic agents making decisions based on behavior rules specified by the modeler. This approach allows us to model a financial sector capable of taking speculative positions on energy assets, influencing their prices, and thereby affecting the solvency of industrial agents using them.

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Coupling of a Macroeconomic and a Climate Model

Designing effective climate change policies necessitates considering the intricate feedback loops between mitigation and adaptation. Increased mitigation efforts today can lead to lower adaptation costs in the future. Carbon taxes are often viewed as promising tools in this regard, but concerns exist about potentially burdening the private sector financially and depriving it of crucial economic resources. Conventional Integrated Assessment Models (IAMs) have limitations in analyzing the financial feasibility of mitigation-adaptation policies as they do not simultaneously incorporate economic growth, emissions, and damages. In response to this, we introduce the Integrated Dynamic Environment-Economic (IDEE) model, which couples an Earth Model of Intermediate Complexity with a non-linear macroeconomic model in continuous time. We then examine the simultaneous effects of carbon taxes and public spending on both climate and the global economy. Our analysis reveals that beyond a warming threshold of approximately +2.3°C, damages significantly increase the demand for additional investments in productive capital—an essential aspect of adaptation. This may potentially lead private firms into a scenario of debt overhang and trigger a worldwide cascade of defaults. Our findings suggest that the motivation behind the Paris Agreement target should not only be driven by climatic non-linearities and tipping points beyond the +2°C threshold but also by the emergence of tipping points. Additionally, we demonstrate that, with sufficiently high public subsidies, a tax of USD 300 per ton of CO2 equivalent by 2030 could enable achieving net-zero emissions by 2050. This approach helps prevent firms from experiencing global bankruptcy, emphasizing the importance of well-designed policy interventions.

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Convex Optimization Contact Dynamics (COCD) and Simulations on Erodible Beds

Erosion processes and the corresponding static/flowing transition in granular flows remain poorly understood, despite their critical role in natural hazards like landslides and debris flows. Continuum models currently struggle to adequately capture observed phenomena such as the increased runout distance of granular flows on erodible beds or the development of waves at the bed/flow interface. Discrete Element Methods (DEM), which simulate individual grain motion and complex interactions, offer a unique numerical tool to investigate these processes. Convex Methods (CM), derived from convexification of Contact Dynamics methods, present a robust theoretical framework ensuring numerical solution convergence at each time iteration. They also exhibit intrinsic stability superior to classical Molecular Dynamics methods. While implemented in engineering fields, CMs have not yet been tested for flows on erodible beds. This study introduces a Convex Optimization Contact Dynamics (COCD) method, demonstrating its ability to generate a numerical solution adhering to Coulomb’s law at each contact and iteration. Following calibration and validation against experiments and another widely used Contact Dynamics method, our simulations accurately replicate qualitative and numerous quantitative features of experimental granular flows on erodible beds. These include the runout distance increase with erodible bed thickness, spatiotemporal changes in the static/flowing interface, and the presence of erosion waves behind the flow front. Beyond erosion processes, our findings endorse CMs as potentially accurate tools for exploring complex granular mechanisms.

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Comparison Between Discrete Element, Navier-Stokes, and Thin-Layer Models

Granular flows manifest in diverse contexts, encompassing laboratory experiments, industrial processes, and natural geophysical phenomena. Various physically based models have been developed to explore their dynamics, distinguished by the length scale at which dynamic processes are described. Discrete models operate at a microscopic scale, modeling individual grains; Navier-Stokes models use a mesoscopic scale, considering elementary volumes of grains; and thin-layer models employ a macroscopic scale to capture the dynamics of elementary columns of fluids. While the derivation of associated equations is well-established for each, limited attention has been given to the coherence of results among these modeling approaches. In this study, we compared simulations of a granular dam break on horizontal or inclined planes using the discrete model Convex Optimization Contact Dynamics (COCD), the Navier-Stokes model Basilisk, and the thin-layer depth-averaged model SHALTOP. Our findings reveal that, although all three models reproduce the temporal evolution of the free surface in the horizontal case (except for SHALTOP at initiation), the modeled flow dynamics differ significantly, especially during the stopping phase. While stresses at the flow’s bottom, reflecting flow dynamics, show relatively good agreement, the COCD model introduces notable variations due to complex and rapidly changing granular lattices. Similar conclusions arise when using the same rheological parameters to model a granular dam break on an inclined plane. This comparative analysis is crucial for evaluating the limitations and uncertainties inherent in granular flow modeling.

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Modeling Ultrasound in Dense Granular Flows

Understanding the mechanisms behind the remote and local triggering of landslides and earthquakes by seismic waves at micro-strain amplitude is essential for quantifying seismic hazards. Granular materials, existing in an out-of-equilibrium and metastable state, offer a relevant model system to explore landslides and fault dynamics within the unjamming transition framework, transitioning from solid to liquid states. Recent laboratory experiments have indicated that ultrasound-induced interfacial sliding or granular avalanches may be linked to a reduction in interparticle friction through shear acoustic lubrication of contacts. However, investigating crack growth or slip at the scale of grain contacts within an optically opaque granular medium remains a challenging issue. To address this challenge, we propose a multiscale numerical modeling approach that examines dense granular flows triggered by acoustic waves in 2D granular layers excited by the inclined basal plane. We perform numerical simulations of ultrasonic vibrations in the millisecond range and the onset of flows in the second range, respectively. Our primary focus is on correlating local rearrangements at the grain scale with the onset of continuous flows at the macroscopic scale. This onset results from the decrease in the interparticle friction coefficient induced by shear acoustic lubrication. A key finding is that ultrasound primarily propagates through the strong-force chains, while the decrease in interparticle friction induced by ultrasound occurs in the weak contact forces perpendicular to the strong-force chains. This decrease in interparticle friction initiates local rearrangements, eventually leading to a continuous flow through a percolation process with a delay depending on the proximity to failure. In comparison to gravity-driven flow, ultrasound-induced flow appears much more uniform in space, indicating the role of an effective temperature due to ultrasonic vibration. We also validate these simulations by comparing them with experimental observations of granular flows triggered by ultrasound below avalanche angles, demonstrating the validity of our numerical method.

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