Scattering of waves from nonlinear media with rough surfaces

Abstract

Reflection and scattering of waves from plane and statistically rough interfaces between nonlinear media are studied theoretically. New hysteresis-type dependences of the reflection and transmission coefficients on the amplitude of the incident wave and on the angle of incidence are predicted. Scattering diagrams for diffusely reflected and transmitted fields are calculated. It is found that when the dielectric constant is a steep function of the incident amplitude, nonlinearity suppresses the Bragg resonant scattering mechanism. Smooth roughness of the boundary is shown to enhance the penetration of evanescent waves into nonlinear media.     

Transfer matrices and the glory

Abstract

The interaction of electrons, photons or other forms of waves with disordered matter gives rise to several complex phenomena including the effect of ‘the glory’: a peak in the cross section for scattering into the time-reversed state of the incident wave. If the disorder is relatively weak this effect can be described in perturbation theory by summing the so-called ‘maximally crossed diagrams’. Transfer matrices, which constitute the major nonperturbative approach to waves in disordered systems, have so far proved incapable of describing the glory. The authors identify the terms in the transfer matrix responsible for this effect. Not only does this remove a deeply unsatisfying incompleteness in transfer matrix theory, but it also provides an economical way of computing diffraction from more complex forms of disorder.     

Influence of atomic size mismatch on binary alloy phase diagrams

Abstract

The aim of this paper is to investigate the consequences of atomic size mismatch on the thermodynamics and the topology of binary phase diagrams of face centred cubic alloys. Simple pairwise interatomic potentials with few controlling parameters are used to identify general tendencies. Thermodynamic states are computed by Monte Carlo simulations on a non-rigid lattice. A special attention has been paid to the comparison between calculations in the canonical ensemble, where composition–temperature phase diagrams are determined through van der Waals loops, and in the grand canonical ensemble, where phase diagrams are computed using an interface migration technique. It is shown that these two procedures lead essentially to the same incoherent phase diagram. In the case of phase separating systems, we argue that the introduction of a size mismatch leads to a shrinkage of the solid solution domain and that the asymmetry of the miscibility gap is essentially controlled by the anharmonicity of the heteroatomic potential. Finally, in the case of ordering systems, we show that the asymmetry of the phase diagram may be due to the anharmonicity of the pair potentials or to the differences between their curvatures, the former effect being dominant if the atomic size mismatch is large.     

Effect of dose on irradiation-induced loop density and Burgers vector in ion-irradiated ferritic/martensitic steel HT9

Samples of F/M steel HT9 were irradiated to 20?dpa at 420°C, 440°C and 470°C in a transmission electron microscope with 1?MeV Kr ions so that the microstructure evolution could be followed in situ and characterised as a function of dose. Dynamic observations of irradiation-induced defect formation and evolution were made at the different temperatures. Irradiation-induced loops were characterised in terms of their Burgers vector, size and density as a function of dose and similar observations and trends were found at the three temperatures: (i) both a/2 <111> and a <100> loops are observed; (ii) in the early stage of irradiation, the density of irradiation-induced loops increases with dose (0–4?dpa) and then decreases at higher doses (above 4?dpa), (iii) the dislocation line density shows an inverse trend to the loop density with increasing dose: in the early stages of irradiation, the pre-existing dislocation lines are lost by climb to the surfaces while at higher doses (above 4?dpa), the build-up of new dislocation networks is observed along with the loss of the radiation-induced dislocation loops to dislocation networks; (iv) at higher doses, the decrease of number of loops affects more the a/2 <111> loop population; the possible loss mechanisms of the a/2 <111> loops are discussed. Also, the ratio of a <100> to a/2 <111> loops is found to be similar to cases of bulk irradiation of the same alloy using 5?MeV Fe²⁺ ions to similar doses of 20?dpa at similar temperatures.     

Angular scattering diagrams of linearly polarized relativistic-intensity electromagnetic radiation in a plasma

Instability of the propagation of nonlinear nonmonochromatic relativistic-intensity electromagnetic waves in a cold subcritical-density plasma is analyzed in three-dimensional geometry. Angular diagrams of their scattering are presented. The calculations show that forward and backward scattering may occur. The radiation in a specific direction is a set of harmonics, propagating against a continuum background, whose frequencies depend on the angle. Radiation at a specific frequency propagates in a set of scattering cones. The azimuthal cone angles depend on frequency. Zh. éksp. Teor. Fiz. 116, 1947–1962 (December 1999)     

Role of equilibrium plasma flow on damping of slow MHD waves

In the solar corona waves and oscillatory activities are observed with modern imaging and spectral instruments. These oscillations are interpreted as slow magneto-acoustic waves excited impulsively in coronal loops. This study explores the effect of steady plasma flow on the dissipation of slow magneto-acoustic waves in the solar coronal loops permeated by uniform magnetic field. We have investigated the damping of slow waves in the coronal plasma taking into account viscosity and thermal conductivity as dissipative processes. On solving the dispersion relation it is found that the presence of plasma flow influences the characteristics of wave propagation and dissipation. We have shown that the time damping of slow waves exhibits varying behavior depending upon the physical parameters of the loop. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 10⁶ erg cm⁻² s⁻¹ which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region.     

In situ study of self-ion irradiation damage in W and W–5Re at 500 °C

In situ self-ion irradiations (150?keV?W⁺) have been carried out on W and W–5Re at 500?°C, with doses ranging from 10¹⁶ to 10¹⁸ W⁺m^?2 (～1.0?dpa). Early damage formation (10¹⁶W⁺m^?2) was observed in both materials. Black–white contrast experiments and image simulations using the TEMACI software suggested that vacancy loops were formed within individual cascades, and thus, the loop nucleation mechanism is likely to be ‘cascade collapse’. Dynamic observations showed the nucleation and growth of interstitial loops at higher doses, and that elastic loop interactions may involve changes in loop Burgers vector. Elastic interactions may also promote loop reactions such as absorption or coalescence or loop string formation. Loops in both W and W–5Re remained stable after annealing at 500?°C. One-dimensional hopping of loops (b?=?1/2 ?111>) was only seen in W. At the final dose (10¹⁸W⁺m^?2), a slightly denser damage microstructure was seen in W–5Re. Both materials had about 3–4?×?10¹⁵ loops m^?2. Detailed post-irradiation analyses were carried out for loops of size???4?nm. Both b?=?1/2 ?111? (～75%) and b?= ?100> (～25%) loops were present. Inside–outside contrast experiments were performed under safe orientations to determine the nature of loops. The interstitial-to-vacancy loop ratio turned out close to unity for 1/2 ?111? loops in W, and for both 1/2 ?111? and ?100? loops in W–5Re. However, interstitial loops were dominant for ?100? loops in W. Re seemed to restrict loop mobility, leading to a smaller average loop size and a higher number density in the W-Re alloy.     

Beyond the triangle and uniqueness relations: non-zeta counterterms at large N from positive knots

Counterterms that are not reducible to ζ n are generated by 3 F 2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 819 and (5, 3) = 10124, are found in anomalous dimensions at O(1/N ³) in the large-N limit, which we compute analytically up to terms of level 11, corresponding to 11 loops for 4-dimensional field theories and 12 loops for 2-dimensional theories. High-precision numerical results are obtained up to 24 loops and used in Pade resummations of e-expansions, which are compared with analytical results in 3 dimensions. The O(1/N ³) results entail knots generated by three dressed propagators in the master two-loop two-point diagram. At higher orders in 1/N one encounters the uniquely positive hyperbolic 11-crossing knot, associated with an irreducible triple sum. At 12 crossings, a pair of 3-braid knots is generated, corresponding to a pair of irreducible double sums with alternating signs. The hyperbolic positive knots 10139 and 10152 are not generated by such self-energy insertions.     

Scattering of a scalar wave from a two-dimensional randomly rough Neumann surface

Abstract

We present a reciprocity and unitarity preserving formulation of the scattering of a scalar plane wave from a two-dimensional, randomly rough surface on which the Neumann boundary condition is satisfied. The theory is formulated on the basis of the Rayleigh hypothesis in terms of a single-particle Green's function G(q_‖|k_‖) for the surface electromagnetic waves that exist at the surface due to its roughness, where k_‖ and q_‖ are the projections on the mean scattering plane of the wave vectors of the incident and scattered waves, respectively. The specular scattering is expressed in terms of the average of this Green's function over the ensemble of realizations of the surface profile function (G(q_‖|k_‖)). The Dyson equation satisfied by (G(q_‖|k_‖)) is presented, and the properties of the solution are discussed, with particular attention to the proper self-energy in terms of which the averaged Green's function is expressed. The diffuse scattering is expressed in terms of the ensemble average of a two-particle Green's function, which is the product of two single-particle Green's functions. The Bethe-Salpeter equation satisfied by the averaged two-particle Green's function is presented, and properties of its solution are discussed. In the small roughness limit, and with the irreducible vertex function approximated by the sum of the contribution from the maximally-crossed diagrams, which represent the coherent interference between all time-reversed scattering sequences, the solution of the Bethe-Salpeter equation predicts the presence of enhanced backscattering in the angular dependence of the intensity of the waves scattered diffusely.     

Diffraction of picosecond bulk longitudinal and shear waves in micron thick films

Investigation of thin metallic film properties by means of picosecond ultrasonics [C. Thomsen et al., Phys. Rev. Lett. 53, 989 (1984)] has been under the scope of several studies. Generation of longitudinal and shear waves [T. Pézeril et al., Phys. Rev. B 73, 132301 (2006); O. Matsuda et al., Phys. Rev. Lett. 93, 095501 (2004)] with a wave vector normal to the film free surface has been demonstrated. Such measurements cannot provide complete information about properties of anisotropic films. Extreme focusing of a laser pump beam (≈0.5 μm) on the sample surface has recently allowed us to provide evidence of picosecond acoustic diffraction in thin metallic films (≈1 μm) [C. Rossignol et al., Phys. Rev. Lett. 94, 166106 (2005)]. The resulting longitudinal and shear wavefronts propagate at group velocity through the bulk of the film. To interpret the received signals, source directivity diagrams are calculated taking into account material anisotropy, optical penetration, and laser beam width on the sample surface. It is shown that acoustic diffraction increases with optical penetration, so competing with the increasing of directivity caused by beam width. Reflection with mode conversion at the film-substrate interface is discussed.     

Orientational effect of the dynamical interaction of circular dislocation loops with a moving edge dislocation

The glide of an edge dislocation in a crystal containing circular dislocation loops is studied theoretically. An analytical expression is obtained for the drag force exerted on a dislocation by various types of dislocation loops, and it is shown that this force depends significantly on the orientation of the Burgers vector of immobile dislocation loops with respect to the gliding dislocation line. The F _‖/F _⊥ ratio of the drag force for the parallel orientation of the Burgers vectors of the loops with respect to the gliding dislocation line (F _‖) and the drag force for the perpendicular orientation (F _⊥) is equal to K(v/c)², where v is the velocity of the dislocation; c is the velocity of acoustic waves in the crystal; and K is a dimensionless coefficient, whose value is of the order of the ratio of the concentrations of dislocation loops with parallel and perpendicular orientations of the Burgers vector.     

Quark loops and spin-flip effects in pomeron exchange

On the basis of QCD at large distances with taking account of some nonperturbative properties of the theory, the possibility of spin-flip effects in high energy hadron processes at fixed momenta transfer is investigated. It is shown that the diagrams with the quark loops in QCD at large distances may lead to the spin-flip amplitude growing ass fors→∞,t-fixed. The confirmation of this result is obtained by calculations of the nonleading contributions from quark loops int-channel exchange in QED up to the end. Physical mechaisms leading to that behavour of the spin-flip amplitude is discussed. So we conclude that the pomeron has a complicated spin structure.     

Meson loops in the f0(980) and a0(980) radiative decays into ρ , ω

We calculate the radiative decay widths of the a ₀(980) and f ₀(980) scalar mesons into ργ and ωγ considering the dynamically generated nature of these scalar resonances within the realm of the chiral unitary approach. The main ingredient in the evaluation of the radiative width of the scalar mesons are the loops coming from the decay into their constituent pseudoscalar-pseudoscalar components and the subsequent radiation of the photon. The dominant diagrams with only pseudoscalar mesons in the loops are found to be convergent while the divergence of those with a vector meson in the loop are written in terms of the two-meson loop function easily regularizable. We provide results for all the possible charge channels and obtain results, with uncertainties, which differ significantly from quark loops models and some version of vector meson dominance.     

Dispersive Calculation of the Massless Multi-loop Sunrise Diagram

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.     

Determination and calculation of high-pressure ternary phase diagrams

Abstract

By the improved high-pressure DTA, we have determined the high-pressure vertical phase diagrams of the Cd-Pb-Sn ternary system up to 2.5 GPa.

A complete method of calculating high-pressure phase diagrams has been devised, in which the special attention has been paid to the effecs of high prssure on the partial molar free energy of each component in equilibrium phases. The high-pressure phase diagrams of Cd-Pb-Sn and Cd-Sn-Zn ternary systems up to 2.5 GPa were calculated successfully.

The agreement between the observed and the calculated resuts is satisfactory.     

Giant waves in weakly crossing sea states

The formation of rogue waves in sea states with two close spectral maxima near the wave vectors k ₀ ± Δk/2 in the Fourier plane is studied through numerical simulations using a completely nonlinear model for long-crested surface waves [24]. Depending on the angle θ between the vectors k ₀ and Δk, which specifies a typical orientation of the interference stripes in the physical plane, the emerging extreme waves have a different spatial structure. If θ ≲ arctan(1/√2), then typical giant waves are relatively long fragments of essentially two-dimensional ridges separated by wide valleys and composed of alternating oblique crests and troughs. For nearly perpendicular vectors k ₀ and Δk, the interference minima develop into coherent structures similar to the dark solitons of the defocusing nonlinear Schroedinger equation and a two-dimensional killer wave looks much like a one-dimensional giant wave bounded in the transverse direction by two such dark solitons.     

A thermodynamic basis for the electronic properties of molten semiconductors: the role of electronic entropy

Abstract

The thermodynamic origin of a relation between features of the phase diagrams and the electronic properties of molten semiconductors is provided. Leveraging a quantitative connection between electronic properties and entropy, a criterion is derived to establish whether a system will retain its semiconducting properties in the molten phase. It is shown that electronic entropy is critical to the thermodynamics of molten semiconductor systems, driving key features of phase diagrams including, for example, miscibility gaps.     

Magnetic contributions to the low-temperature specific heat of the ferromagnetic insulator Pr 0.8 Ca 0.2 MnO 3

The Pr _1-x Ca_xMnO₃ system exhibits a ferromagnetic insulating state for the composition range x ? 0.25. A metallic ferromagnetic state is never realized because of the low hole concentration and the very small averaged A-site cation radius. In the present study, the nature of the magnetic excitations at low temperature has been investigated by specific heat measurements on a Pr _0.8 Ca_0.2MnO₃ single crystal. The decrease of the specific heat under magnetic field is qualitatively consistent with a suppression of ferromagnetic spin waves in a magnetic field. However, at low temperature, the qualitative agreement with the ferromagnetic spin waves picture is poor. It appears that the large reduction of the specific heat due to the spin waves is compensated by a Schottky-like contribution possibly arising from a Zeeman splitting of the ground state multiplet of the Pr³⁺ ions. Received 21 May 2001 and Received in final form 14 December 2001     

Generating mechanism of the energy-stream loops for the evanescent waves in a left-handed material slab

The generating mechanism of the energy-stream loops (ESLs) for the evanescent waves around the interfaces of a left-handed material (LHM) slab has been investigated with a finite-difference time-domain (FDTD) method. The simulations have shown that these ESLs originate from standing waves, attributed to the intervention of counter-propagating evanescent waves. Large numbers of ESLs can appear because of the numerous values of wave vectors k_y. The larger ESLs die out more quickly than the smaller ones in time after the source is switched off, the ESLs shrink continuously with increasing delay, and the oscillated distributions of the evanescent waves between the surfaces can also be validated. It is greatly helpful for the further comprehension on energy fluxes of evanescent waves in the LHM slab.