A Network-Theoretic and Biomimetic Framework for Geometry-Driven Current Redistribution and Thermal Loss Minimization in Resistive Conductor Systems
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2026
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| _version_ | 1866901278011949056 |
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| author | Mokhdum Azam Mashrafi, Mokhdum Azam Mashrafi |
| author_facet | Mokhdum Azam Mashrafi, Mokhdum Azam Mashrafi |
| contents | <p><span>This research provides a rigorous theoretical reconstruction and validation of the proposed circular (garland-shaped) and leaf-inspired conductor geometries as strategies for enhancing electrical performance. Rather than treating these geometries as unconventional mechanisms for “current recycling,” the present work reinterprets them within the established and universally accepted framework of classical electromagnetism and circuit theory.</span></p> <p><span>Specifically, the reformulation is grounded in:</span></p> <ul> <li><span>Charge conservation principles</span></li> <li><span>Kirchhoff’s Current and Voltage Laws</span></li> <li><span>Resistive network and equivalent resistance theory</span></li> <li><span>Joule heating and electromagnetic energy dissipation laws</span></li> </ul> <p><span>Within this physically consistent framework, the proposed geometries are understood not as sources of additional current or energy, but as structured resistive networks that redistribute current density across multiple conductive pathways.</span></p> <p><span>Closed-loop (garland) configurations are represented as symmetric ring networks, where parallel path formation reduces effective resistance through standard equivalent circuit reduction. Leaf-inspired geometries are represented as hierarchical branched resistive graphs in which current division at junction nodes follows conductance-weighted partitioning. In both cases, effective resistance, node voltages, branch currents, and power dissipation are derived using conventional circuit analysis methods.</span></p> <p><span>The reconstruction establishes that:</span></p> <ul> <li><span>Ohm’s law remains strictly valid in its canonical form</span></li> </ul> <p><span>I=V/Req</span></p> <ul> <li><span>Energy conservation holds under all configurations.</span></li> <li><span>Any increase in delivered current is exclusively the result of reduced effective resistance.</span></li> <li><span>Performance improvements arise from spatial redistribution of Joule heating, not from energy generation or amplification.</span></li> </ul> <p><span>Accordingly, the contribution of this work does not lie in modifying fundamental electrical laws. Instead, it provides a physically rigorous and mathematically consistent interpretation of geometry-dependent current redistribution within established electromagnetic theory.</span></p> <p><span> </span></p> <p><span>We demonstrate that the proposed geometries do not violate Ohm’s law or energy conservation, but instead operate by <span>redistributing current density through closed-loop resistive networks</span>, thereby reducing localized Joule heating and voltage gradients. Using <span>Kirchhoff’s Current and Voltage Laws</span>, <span>equivalent resistance modeling</span>, and <span>graph-theoretic circuit representations</span>, we derive quantitative expressions for current distribution, effective resistance, and power loss in circular and biomimetic conductor networks.</span></p> <p><span>Analytical results show that multi-loop geometries introduce <span>parallel current pathways</span>, leading to lower effective resistance and more uniform current density compared to linear conductors of equal material volume. Finite-element-style approximations reveal that curvature and branching analogous to natural leaf venation reduce peak current density and thermal stress by distributing charge flow across redundant conductive paths.</span></p> <p><span>This study establishes mathematical framework for evaluating <span>geometry-dependent electrical efficiency</span>. The results suggest that biomimetic and closed-loop conductor designs can offer practical advantages in high-current systems, flexible electronics, power buses, and thermal-limited electrical architectures.</span></p> <p>Please check the attachment for details</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18663737 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | A Network-Theoretic and Biomimetic Framework for Geometry-Driven Current Redistribution and Thermal Loss Minimization in Resistive Conductor Systems Mokhdum Azam Mashrafi, Mokhdum Azam Mashrafi <p><span>This research provides a rigorous theoretical reconstruction and validation of the proposed circular (garland-shaped) and leaf-inspired conductor geometries as strategies for enhancing electrical performance. Rather than treating these geometries as unconventional mechanisms for “current recycling,” the present work reinterprets them within the established and universally accepted framework of classical electromagnetism and circuit theory.</span></p> <p><span>Specifically, the reformulation is grounded in:</span></p> <ul> <li><span>Charge conservation principles</span></li> <li><span>Kirchhoff’s Current and Voltage Laws</span></li> <li><span>Resistive network and equivalent resistance theory</span></li> <li><span>Joule heating and electromagnetic energy dissipation laws</span></li> </ul> <p><span>Within this physically consistent framework, the proposed geometries are understood not as sources of additional current or energy, but as structured resistive networks that redistribute current density across multiple conductive pathways.</span></p> <p><span>Closed-loop (garland) configurations are represented as symmetric ring networks, where parallel path formation reduces effective resistance through standard equivalent circuit reduction. Leaf-inspired geometries are represented as hierarchical branched resistive graphs in which current division at junction nodes follows conductance-weighted partitioning. In both cases, effective resistance, node voltages, branch currents, and power dissipation are derived using conventional circuit analysis methods.</span></p> <p><span>The reconstruction establishes that:</span></p> <ul> <li><span>Ohm’s law remains strictly valid in its canonical form</span></li> </ul> <p><span>I=V/Req</span></p> <ul> <li><span>Energy conservation holds under all configurations.</span></li> <li><span>Any increase in delivered current is exclusively the result of reduced effective resistance.</span></li> <li><span>Performance improvements arise from spatial redistribution of Joule heating, not from energy generation or amplification.</span></li> </ul> <p><span>Accordingly, the contribution of this work does not lie in modifying fundamental electrical laws. Instead, it provides a physically rigorous and mathematically consistent interpretation of geometry-dependent current redistribution within established electromagnetic theory.</span></p> <p><span> </span></p> <p><span>We demonstrate that the proposed geometries do not violate Ohm’s law or energy conservation, but instead operate by <span>redistributing current density through closed-loop resistive networks</span>, thereby reducing localized Joule heating and voltage gradients. Using <span>Kirchhoff’s Current and Voltage Laws</span>, <span>equivalent resistance modeling</span>, and <span>graph-theoretic circuit representations</span>, we derive quantitative expressions for current distribution, effective resistance, and power loss in circular and biomimetic conductor networks.</span></p> <p><span>Analytical results show that multi-loop geometries introduce <span>parallel current pathways</span>, leading to lower effective resistance and more uniform current density compared to linear conductors of equal material volume. Finite-element-style approximations reveal that curvature and branching analogous to natural leaf venation reduce peak current density and thermal stress by distributing charge flow across redundant conductive paths.</span></p> <p><span>This study establishes mathematical framework for evaluating <span>geometry-dependent electrical efficiency</span>. The results suggest that biomimetic and closed-loop conductor designs can offer practical advantages in high-current systems, flexible electronics, power buses, and thermal-limited electrical architectures.</span></p> <p>Please check the attachment for details</p> |
| title | A Network-Theoretic and Biomimetic Framework for Geometry-Driven Current Redistribution and Thermal Loss Minimization in Resistive Conductor Systems |
| url | https://doi.org/10.5281/zenodo.18663737 |