Perturbative analysis of wave interactions in nonlinear systems

This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solutions. Instead of including the whole obstacle in the NF, only its resonant part is included, and the remainder is assigned to the homological equation. This leaves the NF intergable and its solutons retain the character of the solutions of the unperturbed equation. We exploit the freedom in the expansion to construct canonical obstacles which are confined to te interaction region of the waves. Fo soliton solutions, e.g., in the KdV equation, the interaction region is a finite domain around the origin; the canonical obstacles then do not generate secular terms in the homological equation. When the interaction region is infifnite, or semi-infinite, e.g., in wave-front solutions of the Burgers equation, the obstacles may contain resonant terms. The obstacles generate waves of a new type, which cannot be written as functionals of the solutions of the NF. When an obstacle contributes a resonant term to the NF, this leads to a non-standard update of th wave velocity.Comment: 13 pages, including 6 figure

On the validity of mean-field amplitude equations for counterpropagating wavetrains

We rigorously establish the validity of the equations describing the evolution of one-dimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic model equation, namely the sine-Gordon equation. We consider both periodic amplitude functions and localized wavepackets. For the localized case, the wavetrains are completely decoupled at leading order, while in the periodic case the amplitude equations take the form of mean-field (nonlocal) Schr\"odinger equations rather than locally coupled partial differential equations. The origin of this weakened coupling is traced to a hidden translation symmetry in the linear problem, which is related to the existence of a characteristic frame traveling at the group velocity of each wavetrain. It is proved that solutions to the amplitude equations dominate the dynamics of the governing equations on asymptotically long time scales. While the details of the discussion are restricted to the class of model equations having a leading cubic nonlinearity, the results strongly indicate that mean-field evolution equations are generic for bimodal disturbances in dispersive systems with \O(1) group velocity.Comment: 16 pages, uuencoded, tar-compressed Postscript fil

Development of oxygen sensor for pyrochemical reactors of spent nuclear fuel reprocessing

The problem of closing the nuclear fuel cycle is not only related to the development of new types of nuclear fuel and the operation of fast neutron reactors, but also to the complex schemes for the pyrochemical reprocessing of spent nuclear fuel (SNF), which, in turn, require adherence to strict process parameters. In particular, this concerns the operation of the reduction of oxidized SNF mainly by metallic lithium. The paper presents the basic scientific principles and the results of experimental verification of the operation of an electrochemical sensor for measuring oxygen in molten salts in pyrochemical reactors for the reprocessing of spent nuclear fuel. The sensor design consists of two combined electrochemical cells based on the solid electrolyte ZrO2-Y2O3 with a common reference electrode. The sensor allows continuous measurement of the oxygen activity in the oxide-chloride melt and the partial pressure of oxygen in the gas atmosphere above the melt directly during the process of pyrochemical processing. Experimental verification of the sensor performance was performed in a reactor with LiCl-Li2O melts at a temperature of 650 ° C. The resource of continuous sensor operation exceeded 500 hours, and the number of thermal cycles without destruction was at least 20. The sensor readings were found to depend on the specified Li2O content in the LiCl melt. © Published under licence by IOP Publishing Ltd

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Justification of an asymptotic expansion at infinity

A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.Comment: 8 page

The future distribution of wetland birds breeding in Europe validated against observed changes in distribution

Wetland bird species have been declining in population size worldwide as climate warming and land-use change affect their suitable habitats. We used species distribution models (SDMs) to predict changes in range dynamics for 64 non-passerine wetland birds breeding in Europe, including range size, position of centroid, and margins. We fitted the SDMs with data collected for the first European Breeding Bird Atlas and climate and land-use data to predict distributional changes over a century (the 1970s-2070s). The predicted annual changes were then compared to observed annual changes in range size and range centroid over a time period of 30 years using data from the second European Breeding Bird Atlas. Our models successfully predicted ca. 75% of the 64 bird species to contract their breeding range in the future, while the remaining species (mostly southerly breeding species) were predicted to expand their breeding ranges northward. The northern margins of southerly species and southern margins of northerly species, both, predicted to shift northward. Predicted changes in range size and shifts in range centroids were broadly positively associated with the observed changes, although some species deviated markedly from the predictions. The predicted average shift in core distributions was ca. 5 km yr(-1) towards the north (5% northeast, 45% north, and 40% northwest), compared to a slower observed average shift of ca. 3.9 km yr(-1). Predicted changes in range centroids were generally larger than observed changes, which suggests that bird distribution changes may lag behind environmental changes leading to 'climate debt'. We suggest that predictions of SDMs should be viewed as qualitative rather than quantitative outcomes, indicating that care should be taken concerning single species. Still, our results highlight the urgent need for management actions such as wetland creation and restoration to improve wetland birds' resilience to the expected environmental changes in the future

AXISYMMETRIC PROBLEM ON PROPAGATION OF PHASE TRANSFORMATION FRONT IN HETEROGENEOUS SOLID POROUS MEDIUM IN TERMS OF BOUNDARY HEAT TRANSFER AND PRESENCE OF CENTRAL HEATPROOF RING LAYER

An axisymmetric problem on propagation of the phase transformation front in the solid porous medium in conditions of the boundary heat transfer in the presence of heatproof layer is considered. The parametric analysis that permits to determine the influence of the heat flow rate on the boundary, and the thermophysical properties of the insulating layer on the parameters of the phase transformation wave is made