An exploration of the Hénon quadratic map

The two-dimensional mapping, introduced by Hénon in 1976, which yields a strange attractor for the parameter values a=1.4, b=0.3 has been investigated over the extended region -2≤a≤6, -1≤b≤1. Analytical solutions have been obtained for the onset of real stable cycles of periods 1 through 6. The associated bifurcations to stable cycles of twice the period (2 to 12) have also been determined. All the resulting boundary curves are displayed in the a, b parameter plane. Finally, an interesting three-dimensional generalization of the Hénon map is announced.     

Langmuir-Blodgett films of hydrophobins HFBI and HFBII

Hydrophobins are small fungal proteins, which have remarkable surface-chemical properties. They self-assemble at hydrophobic/hydrophilic interfaces and work as adhesive agents and coatings. Sixteen layer Langmuir-Blodgett films of hydrophobins HFBI and HFBII from the fungus Trichoderma reesei were prepared and studied using grazing-incidence X-ray diffraction and reflectivity techniques. Both kind of films contain hexagonally ordered crystallites on the substrate with unit cell parameters of a = b = 54 Å (HFBI) and a = b = 55 Å (HFBII). The structure is similar to the structure of monolayer Langmuir-Blodgett films.     

Optical absorption in tin monoselenide single crystal

Optical absorption in single crystals of tin monoselenide has been measured at room temperature with plane polarized light near the fundamental absorption edge. The electric field of the incident light was oriented parallel to the a- and b-crystallographic axes in the plane of cleavage. Results have been analyzed on basis of two- and three-dimensional models. Absorption near the fundamental edge was found to be due to indirect forbidden transition with two phonons involved in the process. The energy gap and phonon energies were found to be 0.948 eV and 54 and 21 meV for the a-axis and 0.902 eV and 41 and 20meV for the b-axis. The two-dimensional model gave results similar to those obtained from the three-dimensional model and could thus be used to describe the main optical properties of SnSe single crystal.     

Strain relaxation in the epitaxy of La2/3Sr1/3MnO3 grown by pulsed-laser deposition on SrTiO3(001)

With a Curie point at 370?K, the half-metal (La_0.7Sr_0.3)MnO₃ (LSMO) is one of the most interesting candidates for electronic devices based on tunnel magnetoresistance. SrTiO₃ (STO) is up to now the best substrate for the epitaxy of suitable thin films of LSMO. The pseudocubic unit cell of rhombohedral LSMO has a parameter a _LSMO such that (a _STO ? a _LSMO)/a _LSMO = +?0.83% (where a _STO is the parameter of cubic STO) and an angle of 90.26°. As strained growth is tetragonal, relaxation implies recovery of both the pseudocubic parameter and of the original angle. In the LSMO layers that we prepare by pulsed-laser deposition, we show that these two processes are quite independent. The angular distortion is partially recovered by twinning in films 25?nm thick, while recovery of the parameter never occurs in the thickness range that we explored (up to 432?nm). A relaxation, however, takes place above a thickness of 100?nm, associated with a transition from two-dimensional to three-dimensional columnar growth. It is accompanied by chemical fluctuations. Our magnetic measurements exhibit Curie temperatures and magnetic moments very close to the bulk values in those layers where the crystal parameter is strained but the angle partially relaxed.     

Preparation and structural properties of YBCO films grown on GaN/c-sapphire hexagonal substrate

Epitaxial YBCO thin films have been grown on hexagonal GaN/c-sapphire substrates using DC magnetron sputtering and pulsed laser deposition. An MgO buffer layer has been inserted between the substrate and the YBCO film as a diffusion barrier. X-ray diffraction analysis indicates a c-axis oriented growth of the YBCO films. Φ-scan shows surprisingly twelve maxima. Transmission electron microscopy analyses confirm an epitaxial growth of the YBCO blocks with a superposition of three a-b YBCO planes rotated by 120° to each other. Auger electron spectroscopy and X-ray photoelectron spectroscopy reveal no surface contamination with Ga even if a maximum substrate temperature of 700 °C is applied.     

Enhancement of L10 ordered FePt by Pt buffer layer

L₁₀-ordered FePt thin films prepared by molecular-beam epitaxy on MgO (0 0 1) substrate at 320 °C with different thickness of Pt buffer layer have been investigated. The out-of-plane coercivity increases with increasing thickness of Pt buffer. The maximum values of the long-range order parameter and uniaxial magnetic anisotropy energy are 0.72 and 1.78×10⁷ erg/cm³, respectively, for films with 12 nm thick Pt buffer layer, where the c/a ratio (0.976) shows the minimum value. The reason for the enhancement in ordering is due to the proper lattice strains Pt buffer bestows on FePt layer, these strains are equal to the contraction in lattice parameter c and the expansion in a. Studies of angular-dependent coercivity revealed that the magnetization reversal behaviour shifts from a domain-wall motion dominated case towards a near rotational mode with increasing thickness of Pt buffer layer.     

Thermal stability of organic layered systems based on lead stearate

The structural variation in multilayer Langmuir-Blodgett films of lead stearate caused by heat treatment under different conditions in the temperature range 20–100°C is investigated by X-ray reflectometry and high-resolution electron diffraction. Successive annealing of the samples is shown to not alter the initial layered structure at temperatures of 60, 80, and 100°C; partial disturbance of the layered structure occurs upon successive annealing at 80°C and 100°C. Significant disturbance of the structure is observed when the films are heated immediately to 100°C. In all these cases, the orthorhombic (pseudomonoclinic) lattice, with the lattice constants: a = 0.496, b = 0.738, c = 9.60 nm, α = β = γ = 90°, space group P2/1b, formed by transferring monolayers onto the substrate is retained in the crystalline domains of the film.     

Growth of ultrathin YBa2Cu3O7−x films on the SrTiO3 substrate

The growth of ultrathin (1.7–7.3 nm) YBa₂Cu₃O_7?x films on the SrTiO₃(100) substrate is investigated by the mean-energy ion scattering technique. It is found that the growth of islands proceeds according to the two-dimensional and three-dimensional models and depends on the growth conditions.     

On the bifurcations occuring in the parameter space of the sixteen vertex model: I. Discrete bifurcations

The 16-dimensional parameter space of homogeneous sixteen vertex models is scanned for bifurcation points, i.e. points corresponding to models which possess extra symmetries not existing in nearby points. Equivalence classes of models having the same partition function are identified by means of a characteristic “normal” model, represented by a (4 x 4)-diagonal matrix N, and a pair of (2 x 2)-matrices A and B. In this paper the matrix N is assumed to be non-degenerate and the only bifurcations found are those associated with special types of matrices A and B, i.e. matrices whose decomposition in terms of Pauli-matrices corresponds to a vector a ≡ (a₁, a₂, a₃) or b ≡ (b₁, b₂, b₃) that is invariant with respect to one or more elements of the cubic symmetry group.The various bifurcation classes of models found include: a) the families of general- and “complementary” eight vertex models, b) discrete sets of doubly- and one-sided cyclic models and c) a number of secondary bifurcation classes within the eight-vertex families, among which is Baxters symmetric eight-vertex model.     

The one-dimensional 1/4-filled Hubbard model with alternating interactions

The one-dimensional Hubbard model with different on-site interaction on the even (U_a) and odd (U_b) sites is considered within the framework of the weak coupling approach. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in the system and to the dynamical generation of a commensurability gap in the charge excitation spectrum for U_a ≠ U_b and U_a>0 or U_b>0. Depending on the relation between the bare coupling constants the system shows four different regimes of behaviour in the infrared limit corresponding to normal metal, nonmagnetic insulator, antiferromagnetic insulator and superconducting states. The extended model including interaction between particles on nearest and next-nearest neighbour sites is also considered.     

Fabrication and characterization of a Cu seed layer on a 60-nm trench-patterned SiO2 substrate by a self-assembled-monolayer (SAM) process

Continuous electroless deposition of a 10-nm thick layer of Cu was successfully performed on a SiO₂/Si substrate coated with a 3-nm Au catalytic layer. The Au catalytic layer was formed by a self-assembled monolayer (SAM) process terminated with NH₂ headgroups, upon which negatively charged Au particles were deposited via electrostatic interaction with the positively charged NH₂-SAM. The Au and NH₂-SAM layers were analyzed by X-ray photoelectron spectroscopy (XPS) and contact angle analysis. Atomic force microscopy, field emission scanning electron microscopy, and XPS revealed that the Cu layer formed by this electroless processes had good step-coverage, small grain size, and excellent adhesion to the substrate. The proposed process is a very promising method for fabrication of a conductive Cu seed layer in a 60-nm trench-pattern.     

Controlling the orientation and coverage of silica-MFI zeolite films by surface modification

The silica-MFI (Si-MFI) zeolite films are fabricated on α-Al₂O₃ supported silica-zirconia layers. The roughness and chemistry of the substrate surface are changed by surface modification with hydrogen peroxide and carboxymethyl chitosan (CMCS) solution to investigate their effects on the formation and orientation control of Si-MFI zeolite films. The AFM images reveal that the roughness of the silica-zirconia surface can be increased under the treatment of hydrogen peroxide. The Si-MFI zeolite films grown on the rough substrate surface are also b-oriented. Diffuse-reflectance FT-IR studies demonstrate that the abundance of functional groups such as -OH and -COOH can be successfully seeded onto the α-Al₂O₃ supported silica-zirconia layer through modification with CMCS solution. Continuous b-oriented Si-MFI zeolite films can be fabricated on the CMCS-modified α-Al₂O₃ supported silica-zirconia layer. It is evident that the orientation and microstructure of Si-MFI zeolite films on α-Al₂O₃ supported silica-zirconia layers are dominantly controlled by the chemical nature of the substrate surface, where the functional groups serve as the structure-directing matrix to induce the orientation and growth of the zeolite crystals with their b-axes perpendicular to the substrate surface.     

Growth of germanium thin films on the W(100) surface

The growth of Ge thin films on the surface of a textured predominantly (100)-oriented tungsten ribbon is studied by thermal desorption spectrometry at different substrate temperatures over a wide range of coverages. The mechanism of growth of the Ge films at T = 300 K is similar to a layer-by-layer mechanism. For T > 300 K, the films grow through the Stranski-Krastanov mechanism, according to which the completion of the monolayer coverage is followed by the formation of three-dimensional crystallites; as a result, the desorption kinetics changes. For small coverages (i.e., in the absence of lateral interactions), the activation energy of Ge desorption from W(100) is E = 4.9 ± 0.2 eV. In a monolayer, this activation energy decreases to E = 3.9 ± 0.2 eV due to the repulsive lateral interactions. The energy of pairwise lateral interactions is determined to be ω = 0.3 eV.     

Static properties of asymmetric vortex-like domain walls in magnetically uniaxial thick films

The structure and energy of asymmetric vortex-like Bloch and Néel walls in a magnetically uniaxial film with an easy magnetization axis lying in the film plane are investigated by numerically minimizing the total energy within the rigorous micromagnetic approach and the two-dimensional model of the magnetization distribution. The calculations are performed over wide ranges of film thicknesses b (up to b = 1 μm) and magnetic parameters of the films. It is established that the asymmetric vortex-like domain walls are the most universal wall structures in the films under consideration. In magnetically uniaxial films, unlike in magnetically multiaxial films, the asymmetric Bloch walls are always stable.     

Sequential deposition of polydisperse particles with double layer interactions: An integral-equation theory

Adsorption of charged colloidal particles to oppositely charged surfaces is usually an irreversible process. The interaction between a pair of particles can be modeled with an exponentially decaying potential originating from double layer interactions. This work explored the effect of the Debye length on monolayer structures using the integral-equation theory which was successfully developed based on a binary-mixture approximation to include the effect of particle size polydispersity. The theoretical results from the integral equations with a Percus-Yevick closure showed that upon increasing the Debye length, the radial distribution functions, g(r), as well as the structure factor, S(k), decreased, in good agreement with simulation results. When the effect of size distributions was investigated, the prominent peak of the radial distribution function increased non-linearly with the product κσ_av, which followed the same trend as was reported for the case of the jamming coverage of the monolayer film.     

Fermion mass generation via Kaluza-Klein fermions under the influence of a gauge field within a (2 + 1)-dimensional model

We considered the generation of mass on a two-dimensional brane within a three-dimensional model with four-fermion interaction, including an external gauge field A ₃. In the scope of this model, the generated mass proves to be lighter than the masses of the Kaluza-Klein modes. This indicates the possibility of solving the mass hierarchy problem in realistic four-dimensional models. As well, the dependences of the effective potential and the constant of coupling on such characteristics of the model as the radius of compactification, gauge field, and phase-shift parameter were obtained.     

Experimental study of structure functions and sum rules in charge-changing interactions of neutrinos and antineutrinos on nucleons

High-energy exclusive and inclusive cross sections are discussed in terms of their dependence on the transverse-position variables (impact parameters) of incident and outgoing particles. The objective is to clarify the points of conflict and agreement of various models with each other and with intuitive ideas based on macroscopic collisions. First the impact parameter representation of states and amplitudes is reviewed. New impact parameter conservation laws and sum rules are derived from Lorentz invariance. The generalized optical theorem of Mueller is extended to give the impact parameter distribution of produced particles. Mueller-Regge behaviour is shown to imply three-dimensional limiting fragmentation in (impact parameter, rapidity)- space and a specific linear structure of the final-state particle density in the central region of this space. The predictions of weak- and strong-coupling multiperipheral models, the φ³ ladder eikonal model and the dual resonance model are presented, with emphasis on the dependence of average multiplicity on impact parameter and the dependence of mean square impact parameter on multiplicity. Special techniques for strong-coupling multiperipheral models are used to study the breakdown of the random-walk impact-parameter structure of the weak-coupling case, and to show explicitly that the average multiplicity is a decreasing function of impact parameter in the strongly coupled ABFST model.     

Effect of growth time on the structure, Raman shift and photoluminescence of Al and Sb codoped ZnO nanorod ordered array thin films

Al and Sb codoped ZnO nanorod ordered array thin films have been deposited on glass substrate with a ZnO seed layer by hydrothermal method at different growth time. The effect of growth time on structure, Raman shift, and photoluminescence (PL) was studied. The thin films at growth time of 5 h consist of nanorods growth vertically oriented with ZnO seed layer, and the nanorods with an average diameter of 27.8 nm and a length of 1.02 μm consist of single crystalline wurtzite ZnO crystal and grow along [0 0 1] direction. Raman scattering analysis demonstrates that the thin films at the growth time of 5 h have great Raman shift of 15 cm⁻¹ to lower wavenumber and have low asymmetrical factor Г_a/Г_b of 1.17. Room temperature photoluminescence reveals that there is more donor-related PL in films with growth time of 5 h.     

Neutron scattering study of the structure and dynamics of butane adsorbed on graphite2

Inelastic and elastic neutron scattering have been used to study the dynamics and structure of monolayer films of butane (CH₃(CH₂)₂CH₃) adsorbed on a graphitized carbon powder at 77 K. In addition to the intramolecular torsional modes found in the bulk solid, the inelastic spectra of the films contain new excitations associated with coupling of the molecular motion to the substrate. Model calculations are described which show the monolayer excitation spectrum to be sensitive to the orientation of the adsorbed butane molecule and the location and strength of the bonds to the substrate. For butane we infer that the molecule is adsorbed with the plane of the carbon skeleton parallel to the graphite layers. We have also used elastic neutron diffraction to investigate the possibility of long-range order in the butane films. Although we have not found Bragg peaks indicative of an ordered two-dimensional structure in a 1.5 layer film at 81 K, a large modulation of the graphite 002 Bragg reflection is observed. The experimental approach discussed here would seem to be applicable to the study of the dynamics, molecular orientation, and bonding of other hydrogenous adsorbates as a function of film thickness and temperature. Measurements are presently being extended to propane (CH₃CH₂CH₃) and ethane (CH₃CH₃) adsorbed on graphite.     

Effects of long-range interaction on critical and multicritical behavior of compressible disordered systems

A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a. A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.