We prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curves in the manifold. The result is an extension of Nash C Embedding Theorem. For more general metric spaces the same result is false, e.g., for Finsler non-Riemannian manifolds. However, we also show that any metric space of finite Hausdorff dimension can be embedded in some Eu...

The variation of assemblage composition in space is characterised by the decrease similarity with spatial distance. Climatic constraint and dispersal limitation are major drivers distance-decay similarity. Distance-decay usually conceptualised modelled as an isotropic pattern, that is, assuming decays same rate all directions. Because climatic gradients markedly anisotropic, they have different...

It is demonstrated that a waveguide consisting of two dielectric slabs may become an all-optical spring when guiding a superposition of two transverse evanescent modes. Both slabs are transversally trapped in stable equilibrium due to the optical forces developed. A condition for stable equilibrium on the wavenumbers of the two modes is expressed analytically. The spring constant characterizing...

Based on a nonequilibrium thermodynamic description of the coupled bioenergetic processes of ATP synthesis, I show for the first time that the entropy production depends on the physical system of coupling; completely delocalized coupling leads to minimum rate of entropy production in the steady state. Further, when nonlinear processes are considered, the free energy dissipation exhibits a minim...

Earth is a chemical battery where, over evolutionary time with a trickle-charge of photosynthesis using solar energy, billions of tons of living biomass were stored in forests and other ecosystems and in vast reserves of fossil fuels. In just the last few hundred years, humans extracted exploitable energy from these living and fossilized biomass fuels to build the modern industrial-technologica...

This contribution is concerned with the control parameters for arriving at defined, electrochemically relevant materials. The treatment is precise as far as the equilibrium situation of simple crystals is concerned, but becomes more and more qualitative if the distance from equilibrium or the (structural or compositional) complexity increases. It proves useful to distinguish between in situ par...