Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in Falkovich et al. [Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small scales, in an incompressible isotropic turbulent flow, have a statistical conservation law. More specifically, in a d-dimensional flow the distance R(t) between t...

Dembski’s “Law of Conservation of Information” is investigated using a more formal approach than is provided in his latest book “No Free Lunch”. It is concluded that the Law of Conservation of Information is mathematically unsubstantiated.

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating ...

Plant Genetic Resources (PGRs) are one of the most valuable natural resources of anycountry. Biotechnology through genetic engineering of plants and the creation of new plantvarieties can increase the value of these resources. Different technical and legalmechanisms such as ex situ/in situ collection of PGRs, and Intellectual Property Rights(IPRs...

We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order, in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the coupling between the orientational field deformations and the density variations for polar and quadrupolar order, we find that the respective order parameter...

(x) when u(0, x) is the cumulative distribution function of a signed measure on IR. We associate a nonlinear martingale problem with the Fokker-Planck equation obtained by spatial differentiation of the conservation law. After checking uniqueness for both the conservation law and the martingale problem, we prove existence thanks to a propagation of chaos result for systems of interacting partic...

A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are c...

In his Comment [1] to my paper [2] Rutenberg notes that " the basis of my analysis of conserved scalar phase-ordering dynamics, to apply only the global conservation constraint dxψ = N, (1) is incorrect ". Because " for physical conserved systems, which evolve by mass transport, the stronger local conservation law embodied by continuity equation " ∂ψ/∂t = −∇j. (2) This question needs clarificat...