We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, th...

the determination of soil wetting front which caused by emitters is one of the important issues in designing trickle irrigation system. in this study, a mathematical model introduced in order to study the position of soil wetting front during irrigation by point emitters in homegenious soil in unsteady condition. the model solves governing differential equation of unsaturated flow in cylindrica...

Modelling techniques valid for ordinary hydrological conditions are often inadequate for catastrophic runoff conditions, as the majority of the parameters included in the modelling schemes are not necessarily applicable to flood conditions. To overcome this problem, using a stochastic self-training procedure (SSTP) is proposed. The procedure is based on the real water balance equation and the s...

We prove that every Markov solution to the three dimensional Navier-Stokes equation with periodic boundary conditions driven by additive Gaussian noise is uniquely ergodic. The convergence to the (unique) invariant measure is exponentially fast. Moreover, we give a well-posedness criterion for the equations in terms of invariant measures. We also analyse the energy balance and identify the term...

We discuss notions of Gauss curvature and mean curvature for polyhedral surfaces. The discretizations are guided by the principle of preserving integral relations for curvatures, like the Gauss–Bonnet theorem and the mean-curvature force balance equation.

A balance is described with Langmuir binding of weights to each side. This simple physical system, when coupled with a previously derived equation for the equivalent displacement of weight that perturbs the equilibrium of a balance, models twostate, receptor systems in pharmacology for receptor activation. Surprisingly, this system also shows desensitization similar to many drug-receptor system...

For centuries the concept of energy balance has provided the bedrock for research into the mechanisms controlling body weight. However, in recent years there has been growing interest in the regulation of the individual macronutrients that combine to determine the energy status of an individual. Thus the classical energy balance equation can be more accurately represented as the integrated sum ...

We study exchange of stability in the dynamics of solitary wave solutions under changes in the nonlinear balance in a 1+1 evolutionary partial differential equation related both to shallow water waves and to turbulence. We find that solutions of the equation mt + umx + b uxm = ν mxx with m = u − α2uxx for fluid velocity u(x, t) change their behavior at the special values b = 0,±1,±2,±3. PACS nu...

We consider a shallow water equation of Camassa-Holm type, containing nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous solutions of a scalar conservation law...

We study stochastic interacting particle systems that model chemical reaction networks on the microscopic scale, converging to the macroscopic Reaction Rate Equation. One abstraction level higher, we also study the ensemble of such particle systems, converging to the corresponding Liouville transport equation. For both systems, we calculate the corresponding large deviations and show that under...