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An angle θ = π 2 indicates that the positive disclination is closer to the top of the bump. Open symbols represent the numerical minimization of a fixed connectivity harmonic model for which the separation of the positive or negative disclination pair representing the dislocation is fixed while varying the dimensionless radial distance | x|/ x 0 of the dislocation from the bump. 17 (including boundary corrections) is plotted as a continuous line for a Gaussian bump parameterized by α = 0.5 in the limit R ≫ x 0 ≫ a. The dislocation potential D( r, θ = ± π 2) in Eq. Such defects are important for particle diffusion and relaxation of concentration fluctuations. Other point defects such as vacancies, interstitials, or impurity atoms create shorter-range disturbances that introduce only local stretching or compression in the lattice (see Fig. Disclinations are points of local 5- and 7-fold symmetry in a triangular lattice (labeled by topological charges q = ± 2 π 6), whereas dislocations are disclination dipoles characterized by a Burger’s vector, b, defined as the amount by which a circuit drawn around the dislocation fails to close (see Fig. Disclinations and dislocations are important topological defects that induce long-range disruptions of orientational or translational order, respectively (ref. The substrate can then be assumed smooth, as would be the case for monolayers composed of di-block copolymers ( 2, 3). We suppose that the monolayer has a lattice constant of order, say, 10 nm or more. In this article, we present a theoretical and numerical study of point-like defects in a soft crystalline monolayer grown on a rigid substrate of varying Gaussian curvature. Curved crystalline order also affects the mechanical properties of biological structures like clathrin-coated pits ( 6, 7) or HIV viral capsids ( 8, 9) whose irregular shapes appear to induce a nonuniform distribution of disclinations in their shell ( 10). The physics of 2D crystals on curved substrates is emerging as an intriguing route to the engineering of self-assembled systems such as the “colloidosome,” a colloidal armor used for drug delivery ( 1), devices based on ordered arrays of block copolymers that are a promising tool for “soft lithography” ( 2, 3), and liquid–solid domains in vesicles ( 4, 5).