Porous Colloidal Nanoparticles as Injectable Multimodal Contrast Agents for Enhanced Geophysical Sensing.

Injecting fluids into underground geologic structures is crucial for the development of long-term strategies for managing captured carbon and facilitating sustainable energy extraction operations. We have previously reported that the injection of metal-organic frameworks (MOFs) into the subsurface can enhance seismic monitoring tools to track fluids and map complex structures, reduce risk, and verify containment in carbon storage reservoirs because of their absorption capacity of low-frequency seismic waves. Here, we demonstrate that water-based Cr/Zn/Zr MOF colloidal suspensions (nanofluids) are multimodal geophysical contrast agents that enhance near-wellbore logging tools. Based on experimental fluid-only measurements, MIL-101(Cr), ZIF-8, and UiO-66 nanofluids have distinct complex conductivity and/or low-field nuclear magnetic resonance (NMR) signatures that are relevant to field-deployed technologies, implying the potential to enhance near-wellbore monitoring of CO2 injection and associated processes with downhole logging tools. Small- and wide-angle X-ray scattering characterization of ∼0.5 wt % MIL-101(Cr) suspensions confirmed phase stability and provided insight into the fractal nature of colloidal nanoparticles. Finally, low-field (2 MHz) NMR measurements of MIL-101(Cr) nanofluid injection into a prototypical Berea sandstone demonstrate how paramagnetic high-surface area MOFs may dominate the relaxation times of hydrogen-bearing fluids in porous geologic matrices, enhancing the mapping of near-surface and near-wellbore transport pathways and advancing sustainable subsurface energy technologies.

Robust risk aggregation with neural networks.

We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g., the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice, the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: First, we derive a dual representation of the considered problem and prove that strong duality holds. Second, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real-world instance.

Theoretical and empirical analysis of trading activity.

Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades N, the traded volume V, the asset price P, the squared volatility σ 2 , the bid-ask spread S and the cost of trading C. Different reasonings result in simple proportionality relations ("scaling laws") between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., N ∼ σ 2 . More sophisticated relations are the so called 3/2-law N 3 / 2 ∼ σ P V / C and the intriguing scaling N ∼ ( σ P / S ) 2 . We prove that these "scaling laws" are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility σ , which turns out to be more subtle than one might naively expect.