E-018 — descent profile |M|/|R0| on z=x+iy0, y0 in {1,0.3,0.1}

08-18-2026 · 1944 rows · script research/numerics/scripts/E-018-descent-profile.py

Metadata

Validation checks

C1_W_offaxis_vs_mp	PASS
C2_F_complex_vs_acb	PASS

Key values

C1_worst	`0.000000000000006910665131911271`
C2_worst	`0.0000000005272337420798375`
report	{'4.0_pi_y1.0': {'median': 0.0058782721256475925, 'mean': 0.008291178962858501, 'p90': 0.019481733636454057, 'max': 0.03396554015684706}, '4.0_pi_y0.3': {'median': 0.006564175181002058, 'mean': 0.010435809591546516, 'p90': 0.022551552466665042, 'max': 0.07278660391646481}, '4.0_pi_y0.1': {'median': 0.006707751880242824, 'mean': 0.012108924528906726, 'p90': 0.0228730299200152, 'max': 0.14810301480988547}, '4.0_zero_y1.0': {'median': 0.004555296424658213, 'mean': 0.00664953683969302, 'p90': 0.015072268250518295, 'max': 0.03396554015684706}, '4.0_zero_y0.3': {'median': 0.005025643749280622, 'mean': 0.009101172413255655, 'p90': 0.016734980735750398, 'max': 0.11312570363787529}, '4.0_zero_y0.1': {'median': 0.0050887171054875445, 'mean': 0.012271728907487723, 'p90': 0.022571197533653917, 'max': 0.32130537611362625}, '6.0_pi_y1.0': {'median': 0.005941393135128255, 'mean': 0.008489600378158872, 'p90': 0.019841105716330586, 'max': 0.03790590678226328}, '6.0_pi_y0.3': {'median': 0.006536290457633615, 'mean': 0.010806263351104477, 'p90': 0.022677423020264244, 'max': 0.07232104437585961}, '6.0_pi_y0.1': {'median': 0.006724513347452873, 'mean': 0.011478890149315125, 'p90': 0.023648740968485068, 'max': 0.09142267471562603}, '6.0_zero_y1.0': {'median': 0.005124172727938264, 'mean': 0.00746876580462103, 'p90': 0.017026245677604794, 'max': 0.03790590678226328}, '6.0_zero_y0.3': {'median': 0.005650623829821188, 'mean': 0.01021180418503125, 'p90': 0.018928933792391946, 'max': 0.12699513605911442}, '6.0_zero_y0.1': {'median': 0.005579365441718518, 'mean': 0.014022393997392265, 'p90': 0.02552089348096885, 'max': 0.3808913219434005}, '8.0_pi_y1.0': {'median': 0.005995466672509657, 'mean': 0.008644983185117708, 'p90': 0.020036607368895728, 'max': 0.03989553973139515}, '8.0_pi_y0.3': {'median': 0.00680712183885795, 'mean': 0.011120526604333894, 'p90': 0.022652043996305035, 'max': 0.09017250858015384}, '8.0_pi_y0.1': {'median': 0.006712953176200126, 'mean': 0.011681318246964178, 'p90': 0.02287777460583436, 'max': 0.07957427900229018}, '8.0_zero_y1.0': {'median': 0.005392890424355264, 'mean': 0.007844722503562416, 'p90': 0.017950018792760015, 'max': 0.03989553973139515}, '8.0_zero_y0.3': {'median': 0.005944031943257411, 'mean': 0.010734555526343437, 'p90': 0.019952286436256017, 'max': 0.13369578063199172}, '8.0_zero_y0.1': {'median': 0.005893840548583633, 'mean': 0.014735232502103948, 'p90': 0.02689214879887816, 'max': 0.40147689610052184}, '10.0_pi_y1.0': {'median': 0.006039113063356135, 'mean': 0.008720513184988234, 'p90': 0.02015010481452299, 'max': 0.041077396588368544}, '10.0_pi_y0.3': {'median': 0.006834329345532207, 'mean': 0.011358219449539573, 'p90': 0.02269955693499299, 'max': 0.10221282132184713}, '10.0_pi_y0.1': {'median': 0.006785856028914855, 'mean': 0.012429028565700174, 'p90': 0.026315834945999973, 'max': 0.10947969136140419}, '10.0_zero_y1.0': {'median': 0.005552510043266734, 'mean': 0.008080195039525702, 'p90': 0.018485879275465477, 'max': 0.041077396588368544}, '10.0_zero_y0.3': {'median': 0.006112777419801557, 'mean': 0.011042350086136783, 'p90': 0.02054129578864212, 'max': 0.13759688657079275}, '10.0_zero_y0.1': {'median': 0.006202458156384956, 'mean': 0.015145435561662934, 'p90': 0.0276428672378227, 'max': 0.4131908062703263}}

Parameters

a_sweep	`[4.0, 6.0, 8.0, 10.0]`
thetas	`['pi', 'zero']`
h	`0.01`
lambda	`-1.0`
x_grid	`[-20.0, 20.0, 81]`
y0_list	`[1.0, 0.3, 0.1]`

Chart

Data preview (1944 rows total)

a	theta	y0	x	M_re	M_im	R0_re	R0_im	ratio_M_R0
4.0	pi	1.0	-20.000	-6.2218464948e+00	-7.0596715238e+00	-2.9487030423e+03	4.3762507026e+02	3.156698e-03
4.0	pi	1.0	-19.500	-4.6640374944e+00	7.2950774731e+00	1.6247579006e+03	2.5009313210e+03	2.903268e-03
4.0	pi	1.0	-19.000	7.7093395870e+00	1.7666974189e+00	1.5964273213e+03	-2.5191343855e+03	2.651965e-03
4.0	pi	1.0	-18.500	-1.1289923184e+00	-7.1525593009e+00	-2.9534542597e+03	-4.0427171021e+02	2.429093e-03
4.0	pi	1.0	-18.000	-5.6031904344e+00	3.5728578205e+00	8.6171397280e+02	2.8556071722e+03	2.227906e-03
4.0	pi	1.0	-17.500	5.1379890735e+00	3.2370408395e+00	2.2362551721e+03	-1.9724320720e+03	2.036558e-03
4.0	pi	1.0	-17.000	4.5568522002e-01	-5.4932323103e+00	-2.7229350040e+03	-1.2139644380e+03	1.848898e-03
4.0	pi	1.0	-16.500	-4.4776678689e+00	2.2383586170e+00	3.0026403947e+01	2.9828069931e+03	1.678191e-03
4.0	pi	1.0	-16.000	4.2731866190e+00	2.0893427410e+00	2.6979442179e+03	-1.2686069504e+03	1.595476e-03
4.0	pi	1.0	-15.500	-1.4854762974e+00	-5.1578375388e+00	-2.2755083069e+03	-1.9269534546e+03	1.800088e-03
4.0	pi	1.0	-15.000	-4.6466918929e+00	5.9630531607e+00	-8.0405305103e+02	2.8723981191e+03	2.534435e-03
4.0	pi	1.0	-14.500	1.0735082706e+01	2.9324413017e+00	2.9447165741e+03	-4.6372532648e+02	3.733101e-03
4.0	pi	1.0	-14.000	3.6900648622e-01	-1.4907701631e+01	-1.6468159226e+03	-2.4864424638e+03	5.000177e-03
4.0	pi	1.0	-13.500	-1.7242369391e+01	2.5428497899e+00	-1.5740821009e+03	2.5331756576e+03	5.843905e-03
4.0	pi	1.0	-13.000	6.1822053986e+00	1.6783302577e+01	2.9569144962e+03	3.7809639113e+02	5.999926e-03
4.0	pi	1.0	-12.500	1.4148478767e+01	-1.0356783078e+01	-8.8693912612e+02	-2.8478628918e+03	5.878418e-03
4.0	pi	1.0	-12.000	-1.4034757597e+01	-9.7738648158e+00	-2.2187206731e+03	1.9921618755e+03	5.735605e-03
4.0	pi	1.0	-11.500	-4.1390287875e+00	1.6294104455e+01	2.7335663047e+03	1.1897991670e+03	5.639057e-03
4.0	pi	1.0	-11.000	1.6566805917e+01	-2.1575822395e+00	-5.6409267295e+01	-2.9824241945e+03	5.600720e-03
4.0	pi	1.0	-10.500	-8.3042417302e+00	-1.4534824537e+01	-2.6866172284e+03	1.2924536206e+03	5.614877e-03
4.0	pi	1.0	-10.000	-1.0325604367e+01	1.3410787852e+01	2.2924637885e+03	1.9067232233e+03	5.676265e-03
4.0	pi	1.0	-9.500	1.6691320614e+01	4.3493771033e+00	7.7861412142e+02	-2.8794072957e+03	5.782675e-03
4.0	pi	1.0	-9.000	-2.6205775060e+00	-1.7486034563e+01	-2.9404993956e+03	4.8978925113e+02	5.931313e-03
4.0	pi	1.0	-8.500	-1.5532714376e+01	9.6042531105e+00	1.6687449212e+03	2.4717588008e+03	6.123454e-03
4.0	pi	1.0	-8.000	1.5552542694e+01	1.0867617592e+01	1.5516135556e+03	-2.5470184624e+03	6.361726e-03