Drift-Free Conservative Dynamics from Quantized Interaction Rules
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| Format: | Preprint |
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2026
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| _version_ | 1866916057398116352 |
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| author | Junhu, Park Ha, Youngsoo Kang, Myungjoo |
| author_facet | Junhu, Park Ha, Youngsoo Kang, Myungjoo |
| contents | Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissible weak solutions selected by reconstruction and Riemann solvers. Here we introduce an operator-level formulation in which conservative dynamics is realized as an exact discrete interaction rule on a quantized state space. The update is defined by an antisymmetric integer-transfer operator, which enforces conservation exactly at the arithmetic level and eliminates round-off drift from the primitive evolution. For scalar laws, monotone order-preserving transfers select admissible shock structures within the primitive update, rather than through flux reconstruction. Numerical experiments show that the interaction rule preserves high-frequency transport near the Nyquist limit and maintains sharply localized discontinuities in Burgers dynamics. The same construction extends to multidimensional problems and systems of conservation laws through oriented, vector-valued integer transfers. The results show that exact integer-transfer dynamics can suppress cumulative transport drift while preserving entropy-shock localization in nonlinear conservative evolution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_26383 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Drift-Free Conservative Dynamics from Quantized Interaction Rules Junhu, Park Ha, Youngsoo Kang, Myungjoo Numerical Analysis Computational Physics 35L65, 65M08, 65M12, 76M12 Conservation laws are conventionally discretized through floating-point flux evaluation, with invariants obtained by cancellation of approximate interface contributions and admissible weak solutions selected by reconstruction and Riemann solvers. Here we introduce an operator-level formulation in which conservative dynamics is realized as an exact discrete interaction rule on a quantized state space. The update is defined by an antisymmetric integer-transfer operator, which enforces conservation exactly at the arithmetic level and eliminates round-off drift from the primitive evolution. For scalar laws, monotone order-preserving transfers select admissible shock structures within the primitive update, rather than through flux reconstruction. Numerical experiments show that the interaction rule preserves high-frequency transport near the Nyquist limit and maintains sharply localized discontinuities in Burgers dynamics. The same construction extends to multidimensional problems and systems of conservation laws through oriented, vector-valued integer transfers. The results show that exact integer-transfer dynamics can suppress cumulative transport drift while preserving entropy-shock localization in nonlinear conservative evolution. |
| title | Drift-Free Conservative Dynamics from Quantized Interaction Rules |
| topic | Numerical Analysis Computational Physics 35L65, 65M08, 65M12, 76M12 |
| url | https://arxiv.org/abs/2604.26383 |