Integrability of a system of two nonlinear Schrödinger equations

P. P. Shirshov Institute of Oceanology, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 79, No. 2, pp. 180–184, May, 1989.     

Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Magnetic,electrical transport and electron spin resonance studies of ferromagnetic insulating manganites Nd0.85Na0.15MnO3

We have investigated the magnetic, electrical transport and electron spin resonance (ESR) properties of polycrystalline Nd_0.85Na_0.15MnO₃ prepared by sol–gel method. A ferromagnetic–paramagnetic (FM–PM) transition is observed around 110 K, which is not accompanied by a metal–insulator transition. The sample displays the complete PM state associated with the ESR spectra fitted by single Lorentzian line shape above 130 K. Below 130 K, ESR spectra become distorted and then linewidth increases rapidly, where short-range magnetic order develops and coexists with PM phase due to the inhomogeneous magnetic state. In addition, the large difference between the activation energies obtained from the resistivity and ESR parameters (peak-to-peak linewidth and line intensity) at the frame of adiabatic small polaron hopping model is pointed out for Nd_0.85Na_0.15MnO₃.     

Dielectric and conduction mechanism studies of PVA-orthophosphoric acid polymer electrolyte

Polyvinyl alcohol (PVA)-based proton conducting polymer electrolytes have been prepared by the solution cast technique. The conductivity is observed to increase from 10⁻⁹ to 10⁻⁴ S cm⁻¹ as a result of orthophosphoric acid (H₃PO₄) addition. The plot of conductivity vs temperature shows that a phase transition occurred at 343 K in the sample PVA-33 wt% H₃PO₄. The β-relaxation peak is observed at 313 K. The glass transition temperature of PVA-33 wt% H₃PO₄ is 343 K. Orthophosphoric acid seems to play a dual role, i.e., as a proton source and as a plasticizer. The ac conductivity σ _ac = Aω ^s was also calculated in the temperature range from 303 to 353 K. The conduction mechanism was inferred by plotting the graph of s vs T from which the conduction mechanism for sample PVA-17 wt% H₃PO₄ was inferred to occur by way of the overlapping large polaron tunneling (OLPT) model and the conduction mechanism for the sample PVA-33 wt% H₃PO₄ by way of the correlated barrier height (CBH) model.     

Physicochemical aspects of preservation of cellulose paper with polymers

The process of preservation of newspaper with aqueous solutions and dispersions of acrylic copolymers is considered from the instant of impregnation till removal of the polymeric preservative from paper.     

System dependence of the correlation function of IMFs in Ar + Sn at 35 MeV/u

The inclusive reduced velocity correlation functions of the intermediate mass fragments were measured in the reactions of ³⁶Ar + ^112,124Sn at 35 MeV/u. The anti-correlation is observed to be stronger in ³⁶Ar + ¹²⁴Sn system than that in ³⁶Ar + ¹¹²Sn. The difference of the correlation functions between the two reactions is mainly contributed by the particle pairs with high momenta. A three body Coulomb repulsive trajectory model is employed to calculate the emission time scale of the IMFs for the two systems. The time scale is 150 fm/c in ³⁶Ar + ¹¹²Sn and 120 fm/c in the ³⁶Ar + ¹²⁴Sn, respectively.     

Microwave synthesis of magnetic Fe3O4 nanoparticles used as a precursor of nanocomposites and ferrofluids

Methods to synthesize magnetic Fe₃O₄ nanoparticles and to modify the surface of particles are presented in the present investigation. Fe₃O₄ magnetic nanoparticles were prepared by the co-precipitation of Fe³⁺ and Fe²⁺, NH₃·H₂O was used as the precipitating agent to adjust the pH value, and the aging of Fe₃O₄ magnetic nanoparticles was accelerated by microwave (MW) irradiation. The obtained Fe₃O₄ magnetic nanoparticles were characterized by Fourier transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), X-ray powder diffraction (XRD) and vibrating sample magnetometer (VSM). The average size of Fe₃O₄ crystallites was found to be around 8–9 nm. Thereafter, the surface of Fe₃O₄ magnetic nanoparticles was modified by stearic acid. The resultant sample was characterized by FT-IR, scanning electron microscopy (SEM), XRD, lipophilic degree (LD) and sedimentation test. The FT-IR results indicated that a covalent bond was formed by chemical reaction between the hydroxyl groups on the surface of Fe₃O₄ nanoparticles and carboxyl groups of stearic acid, which changed the polarity of Fe₃O₄ nanoparticles. The dispersion of Fe₃O₄ in organic solvent was greatly improved. Effects of reaction time, reaction temperature and concentration of stearic acid on particle surface modification were investigated. In addition, Fe₃O₄/polystyrene (PS) nanocomposite was synthesized by adding surface modified Fe₃O₄ magnetic nanoparticles into styrene monomer, followed by the radical polymerization. The obtained nanocomposite was tested by thermogravimetry (TG), differential scanning calorimetry (DSC) and XRD. Results revealed that the thermal stability of PS was not significantly changed after adding Fe₃O₄ nanoparticles. The Fe₃O₄ magnetic fluid was characterized using UV–vis spectrophotometer, Gouy magnetic balance and laser particle-size analyzer. The testing results showed that the magnetic fluid had excellent stability, and had susceptibility of 4.46×10⁻⁸ and saturated magnetization of 6.56 emu/g. In addition, the mean size d (0.99) of magnetic Fe₃O₄ nanoparticles in the fluid was 36.19 nm.     

A polynomial algorithm for one problem of guillotine cutting

We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectangular pieces. A polynomial time algorithm is described to construct the convex hull of solutions to this problem.