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General Relativity receives quantum corrections relevant at cosmological distance scales from the conformal scalar degrees of freedom required by the trace anomaly of the quantum stress tensor in curved space. In the theory including the…
A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This allows us to introduce…
There has been recent interest in the question of whether four dimensional scale invariant unitary quantum field theories are actually conformally invariant. In this note we present a complete analysis of possible scale anomalies in…
Isotropic hyper-elasticity, altogether with the equilibrium equation and the usual boundary conditions, are formulated directly on the body B, a three-dimensional compact and orientable manifold with boundary equipped with a mass measure.…
A quadratic invariant is defined as a quadratic form in the elements of a tensor that remains invariant under a group of coordinate transformations. It is proved that there are 7 quadratic invariants of the 21-element elastic modulus tensor…
Given an embedded closed submanifold $\Sigma^n$ in the closed Riemannian manifold $M^{n + k}$, where $k < n + 2$, we define extrinsic global conformal invariants of $\Sigma$ by renormalizing the volume associated to the unique singular…
Functionals involving surface curvature are important across a range of scientific disciplines, and their extrema are representative of physically meaningful objects such as atomic lattices and biomembranes. Inspired in particular by the…
We find the rules of the conformal transformation for the energetic quantities such as the Einstein energy-momentum complex, the Bergmann-Thomson angular momentum complex, the superenergy tensor, and the angular supermomentum tensor of…
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map of Weingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type…
When thermal energies are weak, two dimensional lamellar structures confined on a curved substrate display complex patterns arising from the competition between layer bending and compression in the presence of geometric constraints. We…
Stacking and twisting 2D van der Waals (vdW) layers have become versatile platforms to tune electron correlation. These platforms rely on exfoliating vdW materials down to a single and few vdW layers. We calculate the intrinsic…
We analyze a model of hypercubic random surfaces with an extrinsic curvature term in the action. We find a first order phase transition at finite coupling separating a branched polymer from a stable flat phase.
Here we report the first evidence of the inverse energy cascade in a flow dominated by 3D motions. Experiments are performed in thick fluid layers where turbulence is driven electromagnetically. It is shown that if the free surface of the…
We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion…
An anisotropic surface energy is the integral of an energy density that depends on the normal at each point over the considered surface, and it is a generalization of surface area. The minimizer of such an energy among all closed surfaces…
Data available in literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (2015), Bernardini et al. (2014), Yamamoto and Tsuji (2018) and Orlandi et al. (2015) in a large range of Reynolds number…
Inverse cascades of kinetic energy and thermal variance in the subset of vertically homogeneous modes in spectral space are found to cause a slow aggregation to a pair of convective supergranules that eventually fill the whole horizontally…
Polyconvexity is one of the known conditions which guarantee existence of solutions of boundary value problems in finite elasticity. In this work we propose a framework for development of polyconvex strain energy functions for hyperelastic…
A formal correspondence is established between the curvature theory of generalized implicit hypersurfaces, electromagnetism as expressed in terms of exterior differential systems, and thermodynamics. Starting with a generalized implicit…