We introduce a notion of stable spherical variety which includes the spherical varieties under a reductive group G and their flat equivariant degenerations. Given any projective space P where G acts linearly, we construct a moduli space for stable spherical varieties over P, that is, pairs (X, f), where X is a stable spherical variety and f : X → P is a finite equivariant morphism. This space i...

Molecular dynamics simulations together with micromechanics method have been proven an effective approach to assess the elastic moduli of either partially or fully exfoliated (i.e. single-layer) effective clay (montmorillonite) cluster. In this work, similar approach was adopted to estimate the overall compressive modulus of nylon 6/montmorillonite nanocomposites. In detail, the compressive mod...

Effective anti-plane quasistatic moduli for 2D piezoelectric phononic crystals of arbitrary anisotropy are formulated analytically using the plane-wave expansion (PWE) method and the recently proposed monodromy-matrix (MM) method. The latter approach employs Fourier series in one dimension with direct numerical integration along the other direction. As a result, the MM method converges much qui...

Abstract. In this paper we study effective recursion formulae for computing intersection numbers of mixed ψ and κ classes on moduli spaces of curves. By using the celebrated WittenKontsevich theorem, we generalize Mulase-Safnuk form of Mirzakhani’s recursion and prove a recursion formula of higher Weil-Petersson volumes. We also present recursion formulae to compute intersection pairings in the...

We describe the BPS dynamics of vortices in the presence of impurities. We argue that a moduli space of solitons survives the addition of both electric and magnetic impurities. However, dynamics on the moduli space is altered. In the case of electric impurities, the metric remains unchanged but the dynamics is accompanied by a connection term, acting as an effective magnetic field over the modu...