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oai:figshare.com:article/34035786 2026-09-30T17:40:32Z category_1 category_4 category_146 category_915 category_12 category_15 category_21 category_873 category_734 category_64 category_132 portal_5 item_type_1 month_year_09_2026

<p>Per-mode power decomposition across the broadband sweep.</p> Muna Elsadig (25145379) Muhammad Safdar (1474231) Hala H. Taha (22838328) Muhammad Afzal (83943) Biophysics Biochemistry Space Science Physical Sciences not elsewhere classified Cell Biology Neuroscience Biotechnology Chemical Sciences not elsewhere classified Biological Sciences not elsewhere classified Cancer Infectious Diseases whose projection yields wavepacket &# 8211 wall cosine modes truncation convergence study transient treatment follows precomputed wavenumber grid form coupling matrix every matching plane cavity hybrid resonances block linear system power fluxes entering absorbed power fraction weighted matrix product broadband acoustic pulse membrane &# 8211 dependent acoustic scattering incident power vector product pulse energy dependent propagation dependent field xlink "> wise reconstruction velocity continuity single gaussian reflection regimes porous segments porous model porous filler porous core maximum absorption lossless limit fourier approach field splits dissipative decay dissipation audit computational framework centre line <p>Per-mode reflected and transmitted power fractions for <i>n</i> = 0 (solid), <i>n</i> = 1 (dashed) and <i>n</i> = 2 (dotted), across the broadband sweep Hz at <i>a</i> = 0.05 m, <i>L</i> = 0.10 m, <i>T</i> = 350.0 N/m, <i>N</i> = 24 transverse modes, <i>M</i> = 32 Galerkin modes. The vertical grey dotted lines mark the cut-on frequencies <i>f</i>₁ = <i>c</i>/(4<i>a</i>) and <i>f</i>₂ = <i>c</i>/(2<i>a</i>). Physical interpretation: below <i>f</i>₁ only the plane-wave channel carries energy. The <i>n</i> = 1 curves stay identically zero across the whole sweep because the parity selection rule of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0358579#pone.0358579.e057" target="_blank">Eq (14)</a> ( only when <i>m</i> + <i>n</i> is odd) prevents the <i>y</i>-symmetric structure from coupling the plane-wave incidence into odd transverse modes. The first higher mode that activates is <i>n</i> = 2, above <i>f</i>₂, marking the onset of multi-mode propagation.</p> 2026-09-30T17:40:25Z Image Figure 10.1371/journal.pone.0358579.g004 https://figshare.com/articles/figure/_p_Per-mode_power_decomposition_across_the_broadband_sweep_p_/34035786 CC BY 4.0