A family of integrable evolution equations of third order

We construct a family of integrable equations of the form v_t = f(v; v_x; v_xx; v_xxx) such that f is a transcendental function in v; v_x; v_xx. This family is related to the Krichever-Novikov equation by a differential substitution. Our construction of integrable equations and the corresponding differential substitutions involves geometry of a family of genus two curves and their Jacobians.     

Extension of the module of invertible transformations. Classification of integrable systems

We demonstrate that for the systems of equations, which are invariant under a point group or possess conservation laws of the zeroth or first order, a nontrivial extension of the module of invertible transformations is possible. That simplifies greatly a classification of the integrable systems of equations. Here we present an exhaustive list and a classification of the second order systems of the formu _t =u _xx +f(u, v, u _x v _x ), –v _t=v _xx +g(u, v, u _x ,v _x ), which possess the conservation laws of higher order. The reduction group approach allows us to define the Lax type representations for some new equations of our list.     

Generic phase diagram of “electron-doped” T′ cuprates

We investigated the generic phase diagram of the electron doped superconductor, Nd_2−xCe_xCuO₄, using films prepared by metal organic decomposition. After careful oxygen reduction treatment to remove interstitial O_ap atoms, we found that the T_c increases monotonically from 24 K to 29 K with decreasing x from 0.15 to 0.00, demonstrating a quite different phase diagram from the previous bulk one. The implication of our results is discussed on the basis of tremendous influence of O_ap “impurities” on superconductivity and also magnetism in T′ cuprates. Then we conclude that our result represents the generic phase diagram for oxygen-stoichiometric Nd_2−xCe_xCuO₄.     

Metal-insulator transition in Bi-doped,amorphous Ga:Ar mixtures: Influence of spin-orbit scattering

Doping amorphous Ga_xAr_1?x mixtures with the strong spin-orbit scatterer Bi has a dramatic effect on the metal-insulator transition (MIT) occurring in this system at a critical metal atomic concentration x_c: (i) the MIT is shifted from x′_c = 0.36 ± 0.01 (corresponding to a critical metal volume fraction v′_c = 0.19 ± 0.01) of the undoped system to a lower value of x_c = 0.25 ± 0.01 (v_c = 0.14 ± 0.01) for (Ga_0.9Bi_0.1)_xAr_1?x and (ii) the critical exponent v and g of the dc conductivity and Hall coefficient, respectively, change from v′ = 0.5 ± 0.1 and g′ = 0 for the undoped samples to v = 1.3 ± 0.3 and g = 0.5 ± 0.1 for (Ga_0.9Bi_0.1)_xAr_1?x.     

Magnetische Monopole und Quarks

We discuss the concept of Schwinger, which starts with the hypothesis of the existence of magnetical monopoles and results in a baryon model with magnetically charged constituents. Especially we analyse the mathematical consistency of such a theory. which admits a connection between some magnetically charged “quarks” and the homogeneous Maxwell-equations ?_v*F^μv(x^u) = 0, which, displaying a lack of symmetry with respect to the inhomogeneous one, ?_vF^μv(x^u) = 4?j^μ, are replaced by ?*j^μv. Here *j^μ(x^μ) means a conserved magnetic current which provides a monopole source for the magnetic field.     

57Fe Mössbauer and infrared studies of the system Co1−x Cd x Fe2O4

Mössbauer and infrared studies were made on samples of the ferrite system Co_1–xCd_xFe₂O₄ x=0.0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1. Mössbauer spectra were taken at room temperature. The spectra of the samples withx0.7 showed well defined Zeeman patterns and they have been analyzed with two components, one due to A-site Fe³⁺ ions, and the other due to B-site Fe³⁺ and Fe²⁺ ions. The pattern due to B-site appeared to be composite and an explanation is given. The spectra withx=0.9 and 1 showed only a quadrupole splitting. The effect of cadmium substitution on the various hyperfine interactions has been discussed and the cationic distribution has been deduced for all values ofx. Far infrared spectra of the ferrite samples in the range 200–700 cm^–1 were reported. Four bands were observed: the high frequency bandv ₁ is assigned to tetrahedral complexes, and the low frequency bandv ₂ to octahedral complexes, a small bandv ₃ is due to Co²⁺-O^2– complexes andv ₄ is assigned to the lattice vibration of the system. The splitting occurred in thev ₁ andv ₂ bands atx=0.9 and inv ₂ atx=1, indicating the presence of Fe²⁺ ions in octahedral sites.     

Random field effects in the three dimensional Ising magnet: Fe x Zn1−x F2

We have carried out a comprehensive neutron scattering study of random field effects in the diluted three dimensional Ising antiferromagnet Fe _x Zn_1–x F₂ withx=0.35 and 0.5. Emphasis is on the global trands from the small to the large random field regimes. It is found, as in previous experiments, that when the system is cooled in a field it evolves from the high temperature paramagnetic state to a low temperature domain wall state. The low temperature peaks are well-described by Lorentzian squared profiles although for thex=0.5 sample extinction made the measurements difficult. In both samples, the results show that in the field-cooled state the correlation length varies asH ^–v withv=2.2±0.1. In thex=0.35 sample this power law holds over a length scale varying from 2 to 1500 lattice constants. At low fields pretransitional behavior similar to that observed previously in Fe_0.6Zn_0.4F₂ is found. AtT _N (H=0) it is found that the correlation length also scales algebraically withH but withv=0.86±0.04. Pronounced history-dependent effects are observed below the phase boundary determined by the peak in the critical scattering. For example, on cooling in zero-field, raising the field and then warming, long range order survives up to the phase boundary; at this point it appears to convert abruptly into the finite correlation length field cooled state although elucidation of the explicit nature of this transition is complicated by rounding due to a concentration gradient. These results are discussed in the context of recent theories incorporating metastability effects as well as recent experiments.     

A microscopic calculation of dynamic critical exponents for displacive phase transitions

For anO(n)-isotropic lattice dynamicalQ ⁴-model describing displacive phase transitions ind dimensions, we employ a microscopic 1/n-expansion in order to show that over-damped soft-phonon behavior emerges for frequencies smaller than those of the characteristic orderv _c =O(n ^–x ). This is concluded from the fact that the displacement propagatorD(q, v) assumes the time-dependent Ginzburg-Landau (TDGL) form with a damping coefficient=O(n ^–x ), whenv becomes smaller thanv _c . The exponentx is found to bex=4–d for 2<d<3,x=(d–1)/2 for 3<d<5, andx=2 ford>5. The dynamic critical exponents forv _c (q) and forD(0,v) are derived atT=T _c 0 and toO(1/n). Their values are nontrivial for 2<d<4 and, within the TDGL-region, agree with the those appearing already for frequencies ofO(n ⁰) in TDGL-models with nonconserved order parameter andO(n ⁰)-damping coefficient. The latter case was studied by Halperin, Hohenberg, and Ma in 1972. Even in the TDGL-region, the energy conservation does not affect the dynamic exponents for largen(>2, since the specific heat is finite), but an energy diffusion singularity appears in theQ ²-response function which is related to the basic quantity of the 1/n-method, the effective interactionU _eff. By an estimate of order we find that the damping coefficients resulting from the coupling between the relaxation modes contained inU _eff and the critical modes inD are of ordern ^–w withw>x, such that the coupling between weakly damped critical modes is responsible for the crossover to the TDGL-behavior for largen. The exponentz=d/2, known to be generated by the coupling between order parameter and conservedO(n)-densities in TDGL-models, cannot be seen up to the order calculated. We also point out problems of a microscopic-expansion and comment upon differences between microscopic treatments for displacive transitions and those for the Bose condensation.     

Delta shock waves in conservation laws with impulsive moving source: some results obtained by multiplying distributions

The present paper concerns the study of a Riemann problem for the conservation law u_t + [? (u)]_x = kδ (x ? vt) where x, t, k, v and u = u(x,t) are real numbers. We consider ? an entire function taking real values on the real axis and δ stands for the Dirac measure. Within a convenient space of distributions we will explicitly see the possible emergence of waves with the shape of shock waves, delta waves and delta shock waves. For this purpose, we define a rigorous concept of a solution which extends both the classical solution concept and a weak solution concept. All this framework is developed in the setting of a distributional product that is not constructed by approximation. We include the main ideas of this product for the reader’s convenience. Recall that delta shock waves are relevant physical phenomena which may be interpreted as processes of concentration of mass or even as processes of formation of galaxies in the universe.     

CoFe-based granular alloys: the role of the metallic matrix

RF-sputtered CoFe-NM granular alloys (NM=Ag, Cu) with CoFe volume content, x_v, ranging from 0.10 to 0.45 have been studied. These two series of samples show similar features depending on the synthesis conditions and post-deposition annealing treatments, revealing the strong dependence of magnetotransport properties on microstructure. Three different regimes have been observed as x_v is increased: the classical giant magnetoresistance (GMR) regime at low ferromagnetic contents; at intermediate x_v, a domain structure appears, and GMR and anisotropic magnetoresistance (AMR) together with domain wall scattering are observed; and a third regime at x_v close but below the volume percolation threshold, where the two latter contributions still coexist, while the GMR contribution has been suppressed by strong magnetic correlations. The role of the metallic matrix is crucial to determine the crossover ferromagnetic contents between these three regimes, which depend on the relative immiscibility of CoFe either in the Ag or Cu matrices and the diffusivity of Ag and Cu. Moreover, the metallic matrix settles the degree of CoFe segregation, sample crystallisation and texture, which are responsible for the magnetotransport properties.     

Decay Properties of the Connectivity for Mixed Long Range Percolation Models on ℤ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>

In this short note we consider mixed short-long range independent bond percolation models on ℤ ^k+d . Let p _uv be the probability that the edge (u,v) will be open. Allowing a x,y-dependent length scale and using a multi-scale analysis due to Aizenman and Newman, we show that the long distance behavior of the connectivity τ _xy is governed by the probability p _xy . The result holds up to the critical point.     

Anharmonic corrections for linear triatomic molecules subject to the Rennet-Teller effect

The effects of vibrational anharmonic terms and of the g_K -correction on the energy levels of a triatomic molecule in a degenerate electronic state are considered. The electronic wavefunctions are described using the approach first suggested in the original paper of Renner. Formulae for the anharmonic corrections in a number of different situations are derived. For an electronic Π state the corrections are given in the form where i runs over the various contributions and x ₁, x ₂, … depend on the anharmonic force constants. The functions F_i can be determined numerically (see equations (4.3) and 4.7)). For the case without spin-orbit interaction the F_i s are given explicitly to first order in ∈ in table 1. Further-more, the same results apply for levels with |K|=v ₂+1 even if the spinorbit interaction is not negligible. Explicit results for levels with |K|<v ₂ including spin-orbit interaction are given in tables 2 and 3. The cases with larger values for Λ (2, 3, …) are also considered. The energy level formulae for a Δ state differ from those derived earlier by Merer and Travis. In particular, the small separation between the vibronic Φ and Π levels with v ₂=1 is now found to be 4g_K . The additional terms that arise from end-over-end rotation of the molecule are discussed in § 6.     

Grain Boundary Grooving as an Indicator of Grain Boundary Phase Transformations

The atomic force microscopy (AFM) was used to study the grain boundary (GB) groove profiles far away from the melting temperature T _m. It is shown that AFM allows one to measure the temperature dependence of the GB energy in a rather broad temperature interval (from 0.85 T _m to T _m). The GB energy and GB segregation of Bi were measured at 1123 K in the interval of the Bi bulk concentration x ^v _Bi from 5 to 140 ppm Bi. The transition from monolayer to multilayer adsorption is observed for the 19a GB at 1123 K and x ^v _Bi = 60 at. ppm Bi. At the same point (1123 K and x ^v _Bi = 60 at. ppm Bi) a discontinuity of the first derivative of the GB energy is observed. These features were explained using the model of GB prewetting phase transformation developed previously.     

A study of the nuclear-medium influence on <Emphasis Type="Italic">ρ</Emphasis><Superscript>0</Superscript> neutrinoproduction

The nuclear effects in ρ ⁰-meson neutrino production are investigated using the data obtained with the SKAT bubble chamber. The nuclear-medium influence on the ρ ⁰ total yield and inclusive distributions on z = E _ρ /v and Feynman x _F variable is found to be approximately the same as for pions. It is shown that these distributions with increasing A tend to shift toward smaller values of z and x _F, thus indicating an increasing role of secondary intranuclear interactions. The predictions of a simple model incorporating the latter are found to be in qualitative agreement with experimental data. The text was submitted by the authors in English.     

Modification of GaAs by medium-energy N<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> ions

The modification of GaAs with a 2500-eV beam containing N ₂ ⁺ and Ar⁺ ions is examined with Auger electron spectroscopy. Most implanted nitrogen atoms are found to react with the matrix, substituting arsenic atoms to produce a several-nanometer-thick layer of the single-phase GaAs_1−x N_x (x=6%) solid solution. The GaN phase is absent. Displaced arsenic atoms and nitrogen atoms unreacted with the matrix are present in the layer and on its surface. The former segregate, whereas the latter form molecules.     

First-Passage and Extreme-Value Statistics of a Particle Subject to a Constant Force Plus a Random Force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point x ₁ of a particle which starts at x ₀ with velocity v ₀. The probability that the particle has not yet arrived at x ₁ after a time t, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement m=max  _t [x(t)].     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.     

Fourier spectrometry: Rovibrational analysis of an infrared Π → Σ system of yttrium monoiodide

The infrared spectrum of yttrium monoiodide has been excited in an electrodeless microwave discharge and explored between 2500 and 12 000cm⁻¹ with a high-resolution Fourier transform spectrometer. A unique system is observed (ν₀₀ = 9905.520 cm⁻¹), which we attribute to a ¹Π → ¹Σ transition and an extensive analysis is made. Rovibrational constants are obtained for both states mainly from a simultaneous multiband fitting. This procedure is applied to the whole set of 2231 observed line wavenumbers in the 1-0, 0-0, and 0–1 bands, yielding a final weighted standard deviation of 0.0038 cm⁻¹. Furthermore, a partial analysis of the 2-0 and 3-1 bands is performed. The following equilibrium constants are derived (cm⁻¹): ω′_e=192.210 ω′_ex′_e=0.463B′_e=0.0399133 α′_e=0.0001150ω″_e=215.815 ω″_ex″_e=0.514B″_e=0.0422163 α″_e=0.0001125 High-order constants D_v and H_v are also calculated for the various vibrational levels (v′ = 0, 1, 2, 3; v″ = 0, 1).     

Orthorhombic symmetry of valence-band states in CdTe/Cd1−x MnxTe quantum wells

A study is reported of the anisotropy in magnetic-field-induced linear polarization in (001) CdTe/Cd_1−x Mn_xTe quantum wells. The observed limiting anisotropy is shown to be due to the low C _2v symmetry of the quantum well. The relations obtained for the C _2v point group are in a good agreement with experiment. Considered on the microscopic scale, the effect is associated with the heavy-hole g-factor anisotropy in the well plane. Fiz. Tverd. Tela (St. Petersburg) 41, 903–906 (May 1999)