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Abstract Building a representative model of a complex dynamical system from empirical evidence remains a highly challenging problem. Classically, these models are described by systems of differential equations that depend on parameters that need to be optimized by comparison with data. In this tutorial, we introduce the most common multi-parameter estimation techniques, highlighting their successes and limitations. We demonstrate how to use the adjoint method, which allows efficient handling of large systems with many unknown parameters, and present prototypical examples across several fields of physics. Our primary objective is to provide a practical introduction to adjoint optimization, catering for a broad audience of scientists and engineers.

We derive a bound for entropy production in terms of the mean of normalizable path-antisymmetric observables. The optimal observable for this bound is shown to be the signum of entropy production, which is often easier determined or estimated than entropy production itself. It can be preserved under coarse graining by the use of a simple path grouping algorithm. We demonstrate this relation and its properties using a driven network on a ring, for which the bound saturates for short times for any driving strength. This work can open a way to systematic coarse graining of entropy production.

Resonances are ubiquitous in physics and hold important functionalities in engineering wave propagation and interference effects. This work proposes an approach for computing sensitivities, i.e., partial derivatives, of complex eigenfrequencies in any resonance problem, which here is applied to efficiently optimize nanophotonic resonators and to obtain an improved quality factor.

C6H4BrNO2, orthorhombic, Pna21 (no. 33), a = 21.3992(17) Å, b = 5.9311(4) Å, c = 5.2923(4) Å, V = 671.70(9) Å3, Z = 4, R gt(F) = 0.0284, wR ref(F 2) = 0.0708, T = 200(2) K.

C8H14O5S, monoclinic, P21 (no. 4), a = 6.3783(4) Å, b = 8.2630(5) Å, c = 10.5891(7) Å, β = 90.877(2)°, V = 558.02(6) Å3, Z = 2, Rgt(F) = 0.0254, wRref(F2) = 0.0715, T = 200 K.

C17H30N2, tetragonal, P4‾$P‾{4}$21m (no. 113), a = 8.6755(3) Å, c = 11.1611(4) Å, V = 840.03(7) Å3, Z = 2, Rgt(F) = 0.0488, wRref(F2) = 0.1417, T = 200 K.

C13H8O3S, monoclinic, C2/c (no. 15), a = 9.7499(3) Å, b = 12.9758(4) Å, c = 8.2681(3) Å, β = 103.784(2)°, V = 1015.90(6) Å3, Z = 4, Rgt(F) = 0.0318, wRref(F2) = 0.0927, T = 200 K.

C6H10Cl2N2O, triclinic, P1‾$‾{1}$ (no. 2), a = 4.8274(4) Å, b = 8.0556(7) Å, c = 12.0648(10) Å, α = 71.237(4)°, β = 78.739(4)°, γ = 72.950(4)°, V = 422.06(6) Å3, Z = 2, Rgt(F) = 0.0225, wRref(F2) = 0.0614, T = 190 K.

C12H9NS, monoclinic, P21/n (no. 14), a = 5.0743(5) Å, b = 14.0545(13) Å, c = 13.3319(17) Å, β = 91.102(5)°, V = 950.61(18) Å3, Z = 4, Rgt(F) = 0.0322, wRref(F2) = 0.0908, T = 200 K.

C8H18ClNO2, monoclinic, P21/c (no. 14), a = 6.8110(5) Å, b = 8.8779(7) Å, c = 17.2774(16) Å, β = 97.582(4)°, V = 1035.59(15) Å3, Z = 4, Rgt(F) = 0.0484, wRref(F2) = 0.0922, T = 200 K.

C6H8N2O6, monoclinic, P21/c (no. 14), a = 7.4709(4) Å, b = 14.2051(9) Å, c = 7.3198(4) Å, β$\beta $ = 97.096(4)°, V = 770.86(8) Å3, Z = 4, Rgt(F) = 0.0346, wRref(F2) = 0.0946, T = 200 K.

C21H18O2, triclinic, P1‾$‾{1}$ (no. 2), a = 9.8213(6) Å, b = 9.9212(6) Å, c = 10.0400(6) Å, α = 65.510(2)°, β = 63.539(2)°, γ = 84.842(2)°, V = 791.59(8) Å3, Z = 2, Rgt(F) = 0.0463, wRref(F2) = 0.1101, T = 200 K.

C7H9N, orthorhombic, Pna21 (no. 33), a = 8.9239(5) Å, b = 5.9550(3) Å, c = 23.1168(11) Å, V = 1228.47(11) Å3, Z = 8, Rgt(F) = 0.0367, wRref(F2) = 0.1019, T = 200 K.

C32H30N8O5, orthorhombic, P212121 (no. 19), a = 9.1258(4) Å, b = 10.6225(5) Å, c = 30.1870(14) Å, V = 2926.3(2) Å3, Z = 4, Rgt(F) = 0.0367, wRref(F2) = 0.0837, T = 200 K.

C4H11Cl2N, monoclinic, I2/a (no. 15), a = 13.2374(12) Å, b = 8.2108(6) Å, c = 14.0114(14) Å, β = 93.294(8)°, V = 1520.4(2) Å3, Z = 8, Rgt(F) = 0.0398, wRref(F2) = 0.1174, T = 200 K.

C14H14F6N2O, orthorhombic, Pbcn (no. 60), a = 17.7552(12) Å, b = 10.7574(9) Å, c = 8.0207(7) Å, V = 1532.0(2) Å3, Z = 4, Rgt(F) = 0.0415, wRref(F2) = 0.1154, T = 200 K.

C9H24N2O7, monoclinic, P21/n (no. 14), a = 11.1646(7) Å, b = 6.3264(4) Å, c = 18.6926(9) Å, β = 97.5994(18)°, V = 1308.69(13) Å3, Z = 4, Rgt(F) = 0.0385, wRref(F2) = 0.1057, T = 200 K.

C6H13Cl2N, orthorhombic, P212121 (no. 19), a = 6.0087(3) Å, b = 10.1176(6) Å, c = 14.3532(7) Å, V = 872.58(8) Å3, Z = 4, Rgt(F) = 0.0304, wRref(F2) = 0.0632, T = 200 K.

C18H28BrNO2, orthorhombic, P212121 (no. 19), a = 7.0417(4) Å, b = 9.1635(5) Å, c = 27.3371(15) Å, V = 1763.97(17) Å3, Z = 4, Rgt(F) = 0.0275, wRref(F2) = 0.0596, T = 200 K.

C12H12Cl4NSb, monoclinic, P21/n (no. 14), a = 5.6693(2) Å, b = 20.2385(7) Å, c = 14.3908(5) Å, β = 100.3830(10)°, V = 1624.14(10) Å3, Z = 4, Rgt(F) = 0.0192, wRref(F2) = 0.0430, T = 200 K.

C6H4Br2FN, monoclinic, P21/c (no. 14), a = 17.0332(5) Å, b = 4.34070(10) Å, c = 21.9732(5) Å, β = 109.6910(10)°, V = 1529.61(7) Å3, Z = 8, Rgt(F) = 0.0256, wRref(F2) = 0.0518, T = 200 K.

C6H15Cl2N, triclinic, P1‾$‾{1}$ (no. 2), a = 6.9579(4) Å, b = 8.1852(5) Å, c = 8.7912(5) Å, α = 66.606(2)°, β = 86.105(3)°, γ = 89.834(2)°, V = 458.30(5) Å3, Z = 2, Rgt(F) = 0.0226, wRref(F2) = 0.0599, T = 200 K.

C15H14O4, monoclinic, C2/c (no. 15), a = 27.1122(8) Å, b = 6.4295(2) Å, c = 14.7495(4) Å, β = 91.7070(10)°, V = 2569.96(13) Å3, Z = 8, Rgt(F) = 0.0387, wRref(F2) = 0.1091, T = 200 K.

C12H10O3Se2, triclinic, P1‾$‾{1}$ (no. 2), a = 9.1794(3) Å, b = 11.5706(5) Å, c = 12.3976(5) Å, α = 85.291(2)°, β = 72.198(2)°, γ = 74.084(2)°, V = 1205.65(8) Å3, Z = 4, Rgt(F) = 0.0275, wRref(F2) = 0.0698, T = 200 K.

C7H6BrNO2, orthorhombic, P212121 (no. 19), a = 4.7019(6) Å, b = 6.4700(9) Å, c = 25.283(4) Å, V = 769.14(19) Å3, Z = 4, Rgt(F) = 0.0294, wRref(F2) = 0.0671, T = 200 K.

C19H14ClNO2, monoclinic, P21/c (no. 14), a = 19.328(4) Å, b = 7.1086(12) Å, c = 11.627(2) Å, β = 99.417(9)°, V = 1576.0(5) Å3, Z = 4, Rgt(F) = 0.0582, wRref(F2) = 0.1615, T = 200 K.

C7H5BrO, monoclinic, P21/c (no. 14), a = 27.3992(18) Å, b = 3.9369(2) Å, c = 12.8006(8) Å, β = 103.504(2) Å, V = 1342.60(14) Å3, Z = 8, Rgt(F) = 0.0469, wRref(F2) = 0.1103, T = 200(2) K.

C5H10N2O, monoclinic, Ia (no. 9), a = 4.7212(4) Å, b = 11.1424(8) Å, c = 12.8211(9) Å, β = 94.349(3)°, V = 672.52(9) Å3, Z = 4, Rgt(F) = 0.0280, wRref(F2) = 0.0821, T = 200 K.

C8H8O2, tetragonal, P43212 (no. 96), a = 10.9521(5) Å, c = 23.3014(17) Å, V = 2795.0(3) Å3, Z = 16, Rgt(F) = 0.0317, wRref(F2) = 0.0883, T = 200 K.

C8H8O3, monoclinic, P21/c (no. 14), a = 6.3037(3) Å, b = 33.102(2) Å, c = 7.0471(4) Å, β = 102.105(3)°, V = 1437.79(14) Å3, Z = 8, Rgt(F) = 0.0433, wRref(F2) = 0.1087, T = 200 K.

C8H11ClN2S, orthorhombic, Pbca (no. 61), a = 11.3126(6) Å, b = 8.3567(4) Å, c = 20.4130(11) Å, V = 1929.76(17) Å3, Z = 8, Rgt(F) = 0.0240, wRref(F2) = 0.0680, T = 200 K.

C6H6ClN, monoclinic, P21/c (no. 14), a = 6.5211(2) Å, b = 10.2467(3) Å, c = 9.1436(3) Å, β = 94.1771(11)°, V = 609.35(3) Å3, Z = 4, Rgt(F) = 0.0260, wRref(F2) = 0.0680, T = 200 K.

C8H9NO2S, triclinic, P1¯$\overline{1}$ (no. 2), a = 6.6909(5) Å, b = 7.9787(6) Å, c = 8.5551(6) Å, α = 80.065(3)°, β = 68.175(3)°, γ = 77.676(4)°, V = 412.01(5) Å3, Z = 2, Rgt(F) = 0.0263, wRref(F2) = 0.0784, T = 200(2) K.

C17H10O, orthorhombic, P212121 (no. 19), a = 5.0604(12) Å, b = 14.672(3) Å, c = 14.846(3) Å, V = 1102.2(4) Å3, Z = 4, Rgt(F) = 0.0432, wRref(F2) = 0.1022, T = 200(2) K.

C14H15AsClNOS, monoclinic, P21 (no. 4), a = 5.2852(2) Å, b = 13.3035(6) Å, c = 10.7522(5) Å, β = 90.130(2) Å, V = 756.00(6) Å3, Z = 2, Rgt(F) = 0.0200, wRref(F2) = 0.0503, T = 200(2) K.

C14H13AsClNO2, triclinic, P1¯$\overline{1}$ (no. 2), a = 7.7180(7) Å, b = 8.2190(7) Å, c = 11.9620(10) Å, α = 87.438(4)°, β = 73.450(4)°, γ = 72.167(4)°, V = 691.66(10) Å3, Z = 2, Rgt(F) = 0.0203, wRref(F2) = 0.0541, T = 200 K.

C19H15N3O2, monoclinic, P21/c (no. 14), a = 18.4336(13) Å, b = 6.0321(4) Å, c = 15.0585(10) Å, β = 112.171(3)°, V = 1550.60(18) Å3, Z = 4, Rgt(F) = 0.0535, wRref(F2) = 0.1298, T = 200 K.

C9H13NO${\text{C}}_{9}{\text{H}}_{13}\text{NO}$, orthorhombic, Pbcn (no. 60), a = 29.554(4) Å, b = 7.4930(11) Å, c = 8.2800(10) Å, V = 1833.6(4) Å3, Z = 8, Rgt${R}_{gt}$(F) = 0.0737, wRref$w{R}_{ref}$(F2${F}^{2}$) = 0.1646, T = 200 K.

C3H5ClO2, monoclinic, P21/c (no. 14), a = 5.2011(4) Å, b = 7.4362(4) Å, c = 24.1175(15) Å, β = 94.594(3)°, V = 929.78(10) Å3, Z = 8, Rgt(F) = 0.0333, wRref(F2) = 0.0795, T = 200 K.

C14H16FeO, orthorhombic, P212121 (no. 19), a = 5.6954(3) Å, b = 10.0307(6) Å, c = 20.4422(14) Å, V = 1167.84(12) Å3, Z = 4, Rgt(F) = 0.0267, wRref(F2) = 0.0559, T = 200 K.

C9H10O3, orthorhombic, Pbca (no. 61), a = 14.2570(6) Å, b = 7.9250(4) Å, c = 29.8796(13) Å, V = 3376.0(3) Å3, Z = 16, Rgt(F) = 0.0404, wRref(F2) = 0.1050, T = 200 K.

C6H6O3S, orthorhombic, Pca21 (no. 29), a = 15.3524(8) Å, b = 5.7180(3) Å, c = 15.3395(9) Å, V = 1346.58(13) Å3, Z = 8, Rgt(F) = 0.0253, wRref (F2) = 0.0663, T = 200(2) K.

C10H18O2, monoclinic, C2/c (no. 15), a = 10.0025(5) Å, b = 18.8285(9) Å, c = 11.2384(6) Å, β = 115.327(2)°, V = 1913.11(17) Å3, Z = 8, Rgt(F) = 0.0596, wRref(F2) = 0.1606, T = 200 K.

C6H10N2, triclinic, P1‾$‾{1}$ (no. 2), a = 7.4423(5) Å, b = 7.9420(5) Å, c = 11.6711(8) Å, α = 96.667(3)°, β = 95.650(3)°, γ = 100.999(3)°, V = 667.42(8) Å3, Z = 4, Rgt(F) = 0.0620, wRref(F2) = 0.1681, T = 200 K.

C45H35LaO7, trigonal, R3 (no. 146), a = 22.3832(11) Å, c = 6.4522(3) Å, V = 2799.5(3) Å3, Z = 3, Rgt(F) = 0.0192, wRref(F2) = 0.0462, T = 200 K.

C13H11NO, orthorhombic, Pca21 (no. 29), a = 23.801(4) Å, b = 6.0510(13) Å, c = 7.2677(14) Å, V = 1046.7(3) Å3, Z = 4, Rgt(F) = 0.0335, wRref (F2) = 0.0896, T = 200 K.

C8H9NO3, monoclinic, P21/n (no. 14), a = 6.9121(4) Å, b = 26.9700(15) Å, c = 8.7204(5) Å, β = 106.152(3)°, V = 1561.48(16) Å3, Z = 8, Rgt(F) = 0.0486, wRref(F2) = 0.1399, T = 200 K.

Our aim was to compare friction and traction forces between two burying beetle species of the genus Nicrophorus exhibiting different attachment abilities during climbing. Specifically, the interaction of adhesive hairs and claws during attachment with respect to various surface properties was investigated by using a 2 × 3 experimental design. Traction force was measured for two different surface energies (hydrophilic vs hydrophobic) varying in roughness from smooth to micro-rough to rough. Nanotribometric tests on single legs were also performed. The external morphology of the attachment devices investigated by scanning electron microscopy suggested higher intra-specific (intersexual) than inter-specific differences. Whereas differences between the two species in traction force were high on smooth surfaces, no differences could be detected between males and females within each species. With claws intact, both species showed the highest forces on rough surfaces, although N. nepalensis with clipped claws performed best on a smooth surface. However, N. nepalensis beetles outperformed N. vespilloides, which showed no differences between smooth and rough surfaces with clipped claws. Both species demonstrated poor traction forces on micro-rough surfaces. Results concerning the impact of surface polarity were inconclusive, whereas roughness more strongly affected the attachment performance in both species. Nanotribometric analyses of the fore tarsi performed on micro-rough and rough surfaces revealed higher friction in the proximal (pull) direction compared with the distal (push) direction. In these experiments, we detected neither differences in friction performance between the two species, nor clear trends concerning the influence of surface polarity. We conclude that the investigated morphological traits are not critical for the observed interspecific difference in attachment ability on smooth surfaces. Furthermore, interspecific differences in performance are only clear on smooth surfaces and vanish on micro-rough and rough surfaces. Our results suggest that even subtle differences in the adhesion-mediating secretion in closely related species might result in qualitative performance shifts.

We study the effect of coupled resonances and quasibound states in the continuum (quasi-BICs) on the Purcell factor in dielectric resonant nanoantennas. We analyze numerically interfering resonances in a nanodisk with and without a substrate when the modes are coupled to an emitter localized inside the nanodisk, and we quantify the modal contributions to the Purcell factor also reconstructing the radiation patterns of the resonant system. It is revealed that the Purcell effect can be boosted substantially for a strong coupling of resonances in the quasi-BIC regime.

C7H3Cl3O, monoclinic, P21/c (no. 14), a = 12.0518(15) Å, b = 9.7403(11) Å, c = 6.9562(9) Å, β = 99.047(4)°, V = 806.42(17) Å3, Z = 4, Rgt(F) = 0.0316, wRref(F2) = 0.0793, T = 200 K.