Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry

We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the origin, especially under the self-consistent gravitational field for gaseous stars. A fundamental unsolved problem is whether the density of the global solution forms concentration to become a delta measure at the origin. To solve this problem, we develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated free boundary problem for the compressible Navier-Stokes-Poisson equations with a carefully adapted class of degenerate density-dependent viscosity terms, so that a rigorous convergence proof of the approximate solutions to the corresponding global solution of the compressible Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at certain time, it is proved that no concentration (delta measure) is formed in the vanishing viscosity limit for the finite-energy solutions of the compressible Euler-Poisson equations for both gaseous stars and plasmas in the physical regimes under consideration.Comment: 58 page

Global Solutions of the Compressible Euler-Poisson Equations for Plasma with Doping Profile for Large Initial Data of Spherical Symmetry

We establish the global-in-time existence of solutions of finite relative-energy for the multidimensional compressible Euler-Poisson equations for plasma with doping profile for large initial data of spherical symmetry. Both the total initial energy and the initial mass are allowed to be {\it unbounded}, and the doping profile is allowed to be of large variation. This is achieved by adapting a class of degenerate density-dependent viscosity terms, so that a rigorous proof of the inviscid limit of global weak solutions of the Navier-Stokes-Poisson equations with the density-dependent viscosity terms to the corresponding global solutions of the Euler-Poisson equations for plasma with doping profile can be established. New difficulties arise when tackling the non-zero varied doping profile, which have been overcome by establishing some novel estimates for the electric field terms so that the neutrality assumption on the initial data is avoided. In particular, we prove that no concentration is formed in the inviscid limit for the finite relative-energy solutions of the compressible Euler-Poisson equations with large doping profiles in plasma physics.Comment: 42 page

Bifurcations and chaos of rolling bearing system with fault in outer ring

Piecewise non-smooth model of three-degree-of-freedom rolling bearing system with fault in outer Ring is established by the method of the nonlinear theory. The bifurcations and chaos of bearing system is first studied in this paper. The switching matrixes of system are obtained at the switching boundaries, and the period-doubling bifurcation and Neimark-Sacker bifurcation of non-smooth bearing system is analyzed by combining the switching matrixes with the Floquet theory for smooth systems. The numerical method is used to further reveal the bifurcations and chaos of bearing system through establishing the Poincaré mapping on the collision plane. When the rotating frequency is increased to reach the critical bifurcation point, a pair of complex conjugate Floquet multipliers is on the unit circle and others into a unit circle, and the Neimark-Sacker bifurcation appears. When the rotating frequency is decreased to another critical bifurcation point, one of Floquet multipliers of the system equals to -1 and others into a unit circle, and the period-doubling bifurcation appears. With the variation of rotating frequency, the system also experiences the complex dynamical behaviors of Nermark-Sacker bifurcation of period 3 solution and chaos. The study of bifurcation and chaos of the fault bearing system provides reliable basis for the design and fault diagnosis and provides theoretical guidance and technical support for the actual design in the safe and stable operation of large high-speed rotating machinery

Higher atmospheric CO2 levels favour C3 plants over C4 plants in utilizing ammonium as a nitrogen source

Photosynthesis of wheat and maize declined when grown with NH4+ as a nitrogen (N) source at ambient CO2 concentration compared to those grown with a mixture of NO3– and NH4+, or NO3– as the sole N source. Interestingly, these N nutritional physiological responses changed when the atmospheric CO2 concentration increases. We studied the photosynthetic responses of wheat and maize growing with various N forms at three levels of growth CO2 levels. Hydroponic experiments were carried out using a C3 plant (wheat, Triticum aestivum L. cv. Chuanmai 58) and a C4 plant (maize, Zea mays L. cv. Zhongdan 808) given three types of N nutrition: sole NO3– (NN), sole NH4+ (AN) and a mixture of both NO3– and NH4+ (Mix-N). The test plants were grown using custom-built chambers where a continuous and desired atmospheric CO2 (Ca) concentration could be maintained: 280 μmol mol–1 (representing the pre-Industrial Revolution CO2 concentration of the 18th century), 400 μmol mol–1 (present level) and 550 μmol mol–1 (representing the anticipated futuristic concentration in 2050). Under AN, the decrease in net photosynthetic rate (Pn) was attributed to a reduction in the maximum RuBP-regeneration rate, which then caused reductions in the maximum Rubisco-carboxylation rates for both species. Decreases in electron transport rate, reduction of electron flux to the photosynthetic carbon [Je(PCR)] and electron flux for photorespiratory carbon oxidation [Je(PCO)] were also observed under AN for both species. However, the intercellular (Ci) and chloroplast (Cc) CO2 concentration increased with increasing atmospheric CO2 in C3 wheat but not in C4 maize, leading to a higher Je(PCR)/ Je(PCO) ratio. Interestingly, the reduction of Pn under AN was relieved in wheat through higher CO2 levels, but that was not the case in maize. In conclusion, elevating atmospheric CO2 concentration increased Ci and Cc in wheat, but not in maize, with enhanced electron fluxes towards photosynthesis, rather than photorespiration, thereby relieving the inhibition of photosynthesis under AN. Our results contributed to a better understanding of NH4+ involvement in N nutrition of crops growing under different levels of CO2

catena-Poly[[[[N′-(4-cyano­benzyl­idene)nicotinohydrazide]silver(I)]-μ-[N′-4-cyano­benzyl­idene)nicotinohydrazide]] hexa­fluoridoarsenate]

In the title compound, {[Ag(C14H10N4O)2]AsF6}n, the AgI ion is coordinated by two N atoms from two different pyridyl rings and one N atom from one carbonitrile group of three different N′-(4-cyano­benzyl­idene)nicotinohydrazide ligands in a distorted T-shaped geometry. The Ag—Ncarbonitrile bond distance is significant longer than those of Ag—Npyrid­yl. The bond angles around the AgI atom are also not in line with those in an ideal T-shaped geometry. One type of ligand acts as the bridge that connects AgI atoms into chains along [01]. These chains are linked to each other via N—H⋯O hydrogen bonds and Ag⋯O inter­actions with an Ag⋯O separation of 2.869 (2) Å. In addition, the [AsF6]− counter-anions are linked to the hydrazone groups through N—H⋯F hydrogen bonds. Four of the F atoms of the [AsF6]− anion are disordered over two sets of sites with occupancies of 0.732 (9) and 0.268 (9)