Causal Inference: A Bridge Between Simulation Models and Observed Phenomena
Project overview presentation
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Project overview presentation
The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics (QED) is analysed. A formal solution to the general quantum problem of the electromagnetic field interacting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics (CSED) is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenberg operators. All relations of QED connecting quantum field to quantum current lack Planck’s constant, and thus coincide with their counterparts in CSED. In Feynman’s terms, one encounters complete disentanglement of the potential and current operators in response picture. Based on this parallelism between QED and CSED, it is natural to expect validity of the Lorentz condition and Maxwell’s equations for the time-normal averages of the potential and current. Things however turn out to be more complicated. Maxwell’s equations under the time-normal ordering can only be demonstrated subject to cancellation of the so-called Schwinger terms by gauge-invariant regularisations. We presume this pattern to be general, formulating this as “commutativity conjecture”. Consistency of the latter with the Heisenberg uncertainty principle is discussed. -- Highlights: •The general structure of interaction in quantum electrodynamics (QED) is analysed. •A detailed parallelism between QED and classical stochastic electrodynamics is shown. •Validity of Maxwell’s equations for fluctuations of the field is discussed. •This validity turns out to be in essence a renormalisation postulate.
During laser powder bed fusion additive manufacturing, laser power absorption is governed by a pro -tean pool of molten metal that can present as a highly reflective surface, a deeply absorbing cavity, or some amalgamation thereof. These melt pool dynamics have been linked to defect creation, porosity, and surface finish quality. Although these are therefore critical for determining final part quality, their in-stantaneous influence on laser absorption have only been explored through simulation. To date, direct real-time observations have been elusive due to the locally extreme environment. In this work, we fo-cus a laser on Ti-6Al-4V powder and bare plate while quantifying the time-dependent, absolute energy absorption by monitoring omnidirectional backscattered laser intensity. We also simultaneously record the projective melt pool geometries with high-speed synchrotron x-ray imaging. We find that laser ab-sorption strongly reflects the stability of the vapor depression over a wide range of applied laser powers, oxygen content in the processing atmosphere, and with the presence of powder. During laser scanning of a powder bed surface, we find a significant absorption reduction after 400 mu s due to a dramatic change in the vapor depression aspect ratio-an event known to create porosity. Furthermore, as several industrial scan strate-gies necessitate thousands of these events during a build, their identification and control is of significant practical importance. Lastly, a normalized enthalpy model is demonstrated to be effective in quantifying the relationship between the laser absorption and cavity depth, even under transient conditions. In addi-tion to providing vital quantitative data for simulation calibration, the correlation of melt pool geometry with laser absorption during realistic processing conditions suggests the use of a total backscattered light detection system for real-time process control.
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In this article, we present a state-of-the-art algorithm for solving the relativistic viscous hydrodynamics equation with the QCD equation of state. The numerical method is based on the second-order Godunov method and has less numerical dissipation, which is crucial in describing of quark–gluon plasma in high-energy heavy-ion collisions. We apply the algorithm to several numerical test problems such as sound wave propagation, shock tube and blast wave problems. In sound wave propagation, the intrinsic numerical viscosity is measured and its explicit expression is shown, which is the second-order of spatial resolution both in the presence and absence of physical viscosity. The expression of the numerical viscosity can be used to determine the maximum cell size in order to accurately measure the effect of physical viscosity in the numerical simulation.
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On 2015 October 2, MMS spacecraft observed an electron micro-injection event near the southern hemispheric high-altitude cusp, coinciding with intense wave activity across several frequency bands. Here, we investigated the MMS magnetic field and plasma during this event to explore cross-scale coupling among the wave modes. Employing the Hilbert-Huang transform, we perform an empirical mode decomposition to extract frequencies and amplitudes of the intrinsic mode functions (IMFs). In this analysis, we establish both linear and nonlinear relationships and examine the information transfer between the IMFs. Notably, the transfer entropy suggests that high frequency ion cyclotron waves may be driven by the mirror mode structures. Our case study effectively demonstrates the utility of the information theory based tools for studying cross-scale wave coupling phenomena.