Trajectory solution to the reflected blast wave problem
Bibliographic record
Abstract
With an unprecedented rise in explosions occurring in urban regions, it has become imperative to revisit the classical reflected blast wave problem, characterizing its backwards propagation into disturbed medium after impinging on surfaces, such as buildings. When encountering obstacles in its path, blast waves reflect backwards and become defined by more intricate decay characteristics than its unobstructed counterpart and can only be obtained via complex numerical simulation. Attempts to produce an analytical solution to post-reflection blast waves have been limited in scope and unapplicable to broader ranges of explosion scenarios. Here, we introduce a numerical data-driven, closed-form solution, R(t,θ,Z), to map the three-dimensional trajectory and decay behavior of reflected blast waves. We demonstrate the solution's accuracy within, and beyond, scaled blast strengths of 0.5≤Z≤4.0 m/kg1/3 and its adaption to arbitrary explosion sizes through Cranz–Hopkinson blast scaling law. In addition, a closed-form solution on directional post-reflected overpressure is formulated. We discuss how the developed models advance fields of blast wave collision theory, urban blast pattern formation, and real-time identification of repeated blast exposure to personnel in urban blast events. Our work provides a foundation for understanding asymmetric collisions of blast wave and pioneers a generalized fast-running solution for post-reflection explosions, enhancing military operational safety and first aid in blast trauma scenarios previously unachievable.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".