We explore the connections between the constraints on the precision of quantum logical operations that arise from a conservation law, and those arising from quantum field fluctuations. We show that the conservation-law based constraints apply in a number of situations of experimental interest, such as Raman excitations, and atoms in free space interacting with the multimode vacuum. We also show...

This paper contains a qualitative study of a scalar conservation law with viscosity: ut + f(u)x = uxx . We consider the problem of identifying the location of viscous shocks, thus obtaining an optimal finite dimensional description of solutions to the viscous conservation law. We introduce a nonlinear functional whose minimizers yield the viscous travelling profiles which “optimally fit” the gi...

In her famous paper [14] Emmy Noether proved that each Noether symmetry associated with a Lagrangian generates a conservation law. (Modern treatment of relationship between components of Noether conserved vector and Lie–Bäcklund operators which are Noether symmetries was adduced in [10,18]. Kara et al [12,13] constructed conservation laws of some classes of PDEs with two independent variables u...

We study a class of artificial neural networks in which a physics-like conservation law upon the activity of connected neurons is imposed at each time. We postulate that the modification of the network activities may be interpreted as a learning capability if a judicious conservation law is chosen. We illustrate our claim by modeling a rat behavior in a labyrinth: the exploration of the labyrin...

In this paper, a simulation model of a spray flash desalination system is proposed. In the spray flash desalination system, the freshwater is made from the evaporation-condensation process, i.e., evaporation of warm surface seawater in a flash chamber and condensation of the generated vapor by deep cool seawater. A simulation model of the spray flash desalination system is constructed by using ...

We study shock statistics in the scalar conservation law ∂tu+∂xf(u) = 0, x ∈ R, t > 0, with a convex flux f and random initial data. We show that a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps) is preserved by the entropy solution to the conservation law and we derive kinetic equations that describe the evolution ...

A semiclassical transport equation for electrons in a semiconductor crystal is considered. It includes a nonlinear scattering operator modelling electron-phonon interaction. A formal macroscopic limit under the assumption of a small phonon energy is carried out, leading to the so called spherical harmonics expansion (SHE-) model for an energy-dependent distribution function with a scattering op...

We prove global well-posedness for the L-critical cubic defocusing nonlinear Schrödinger equation on R with data u0 ∈ H(R) for s > 1 3 . The proof combines a priori Morawetz estimates obtained in [4] and the improved almost conservation law obtained in [6]. There are two technical difficulties. The first one is to estimate the variation of the improved almost conservation law on intervals given...

We study a scalar conservation law with a nonlinear dissipative inhomogeneity, which serves as a simplified model for nonlinear heat radiation effects in high–temperature gases. We establish global existence and uniqueness of weak entropy solutions along with L contraction and monotonicity properties of the solution semigroup. We derive explicit threshold conditions ensuring formation of shocks...

Global entropy solutions in BV for a scalar nonlocal conservation law with fading memory are constructed as limits of vanishing viscosity approximate solutions. The uniqueness and stability of entropy solutions in BV are established, which also yield the existence of entropy solutions in L∞ while the initial data is only in L∞. Moreover, if the memory kernel depends on a relaxation parameter ε ...