Non-linear superposition in non-linear evolution equations

Special non-linear evolution equations are discussed and classified in integrable and non-integrable partial differential equations. Important methods of solution are sketched. An interesting task is the calculation of the so-called superposition functions permitting to construct from a few known solutions whole chains of further solutions. For integrable partial differential equations they are computed with the help of BÄcklund transformations providing a rather general superposition rule for special types of solutions. At present however a consistent treatment of non-linear evolution equations is only possible in 1 + 1 space and time dimensions. The extension to higher space dimensions brings many problems. An insight into the results and problems in the one-dimensional case is given together with an outlook indicating the conceptual difficulties for a treatment in higher space dimensions.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Temperature dependence of development of slip bands and of strain hardening in AgCl crystals

The dependence of the flow stress and the slip band density on the plastic strain has been measured at 201 K, 293 K and 363 K. The growth of deformation concentrated in an average slip band has been stated. The types of obstacles acting against the rise and development of a slip band and the temperature dependence of the strain hardening in AgCl crystals are discussed. An equation stating the dependence of the flow stress on the slip band density is presented. The hardening in AgCl crystals is classified as the stage III — hardening.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Splitting the Cartesian point

It is argued that the point structure of space and time must be constructed from the primitive extensional character of space and time. A procedure for doing this is laid down and applied to one-dimensional and two-dimensional systems of abstract extensions. Topological and metrical properties of the constructed point systems, which differ nontrivially from the usual and ² models, are examined. Briefly, constructed points are associated with directions and the Cartesian point is split. In one-dimension each point splits into a point pair compatible with the linear ordering. An application to one-dimensional particle motion is given, with the result that natural topological assumptions force the number of left point, right point transitions to remain locally finite in a continuous motion. In general, Cartesian points are seen to correspond to certain filters on a suitable Boolean algebra. Constructed points correspond to ultrafilters. Thus, point construction gives a natural refinement of the Cartesian systems.     

Optical studies of pulsed-laser fragmentation of biliary calculi

The fragmentation of gallstones and kidney stones using pulsed visible laser radiation has recently been demonstrated; however, the fragmentation mechanism is not well understood. The temporal and spectral characteristics of the bright flash of light accompanying fragmentation of gallstones were studied using 0.8 and 360-s-long, 690-nm-wavelength, dye-laser pulses. Time-resolved visible emission spectra show a broad continuum upon which line spectra are superimposed. The continuum emission is due to free-free and free-bound electron transitions indicative of a plasma and the line spectra are due to neutral and ionized calcium. Initiation of this plasma is fluence rather than intensity dependent. A model is proposed in which laser energy is coupled to the plasma, which then impulsively expands, generating intense acoustic transients which fracture the stone.     

Level structure of 68 149 Er81 and high-spin isomerism in proton-richN=81, 82, 83 nuclei

The level structure of theN=81 nucleus¹⁴⁹Er has been studied by γ-ray spectroscopy following the reaction⁹²Mo+255 MeV⁶⁰Ni. Yrast levels in¹⁴⁹Er are established up to ~3.3 MeV, including 0.61 and 4.8 μs isomeric states. Most of the observed levels are interpreted as seniority-three states arising from the coupling of s_1/2, d_3/2 and h_11/2 neutron holes with πh ₁₁ ^2/n . Isomers identified in the reaction⁹⁶Ru+255 MeV⁵⁸Ni are tentatively assigned to¹⁵¹Yb. TheB (E2) values of high-spin isomers inZ=66?70,N=81?83 nuclei are surveyed.     

Multiparticle excitations in142Nd

An (α, 2nγ) in-beam study of excited states in 142Nd revealed 27 new levels on top of the 6⁺ isomer. Nanosecond lifetimes were found for two levels. The measured excitation energies were compared with spherical shell-model predictions obtained from suitably truncated model spaces.     

Damping width of double resonances

Damping width of the double giant dipole resonance of ¹³⁶Xe excited in relativistic heavy ion collisions is calculated by diagonalizing a microscopic Hamiltonian in a basis containing one-, two- and three-phonon states. The coupling between these states is determined making use of the fermion structure of the phonons. The resulting width of the double giant dipole resonance is close to \(\left( {3_1^ + } \right)\) times the width of the single giant dipole resonance.