Multiplication for solutions of the equation

Linear first-order systems of partial differential equations (PDEs) of the form f=Mg, where M is a constant matrix, are studied on vector spaces over the fields of real and complex numbers. The Cauchy–Riemann equations belong to this class. We introduce on the solution space a bilinear *-multiplication, playing the role of a nonlinear superposition principle, that allows for algebraic construction of new solutions from known solutions. The gradient equation f=Mg is a simple special case of a large class of systems of PDEs, admitting a *-multiplication of solutions. We prove that any gradient equation has the exceptional property that the general analytic solution can be expressed as *-power series of certain simple solutions.     

A Roe Scheme for Ideal MHD Equations on 2D Adaptively Refined Triangular Grids

In this paper we present a second order finite volume method for the resolution of the bidimensional ideal MHD equations on adaptively refined triangular meshes. Our numerical flux function is based on a multidimensional extension of the Roe scheme proposed by Cargo and Gallice for the 1D MHD system. If the mesh is only composed of triangles, our scheme is proved to be weakly consistent with the condition …B=0. This property fails on a cartesian grid. The efficiency of our refinement procedure is shown on 2D MHD shock capturing simulations. Numerical results are compared in case of the interaction of a supersonic plasma with a cylinder on the adapted grid and several non-refined grids. We also present a mass loading simulation which corresponds to a 2D version of the interaction between the solar wind and a comet.     

Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schrödinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → pˆ = −i, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov–Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion.     

Asymmetric di-jet production in polarized hadronic collisions

Using the collinear QCD factorization approach, we study the single-transverse-spin dependent cross section Δσ(S) for the hadronic production of two jets of momenta P₁=P+q/2 and P₂=−P+q/2. We consider the kinematic region where the transverse components of the momentum vectors satisfy PqΛ_QCD. For the case of initial-state gluon radiation, we show that at the leading power in q/P and at the lowest non-trivial perturbative order, the dependence of Δσ(S) on q decouples from that on P, so that the cross section can be factorized into a hard part that is a function only of the single scale P, and into perturbatively generated transverse-momentum dependent (TMD) parton distributions with transverse momenta .     

Improvement of cubic silicon carbide crystals grown from solution

Cubic-silicon carbide crystals have been grown from carbon-rich silicon solutions using the travelling-zone method. To improve the growth process, we investigated the effect of controlling more tightly some of the growth parameters. Using such improved growth conditions, our best sample is a 12 mm diameter and 3 mm long 3C–SiC crystal. It is grown on a (0001) 2 off, 6H–SiC seed and has 111-orientation. The low amount of silicon inclusions results in a reduced internal stress, which is demonstrated by the consideration of μ-Raman spectra collected at room temperature on a large number of samples.     

Antiferromagnetic Mn50Fe50 wire with large magnetostriction

This work presents a study on the relation between the fiber texture and the magnetostrictive performance in an antiferromagnetic Mn₅₀Fe₅₀ alloy wire, which was prepared through the combining process of hot rolling and cold drawing. The face-centered cubic (fcc) crystal structure can be retained during the plastic deformation process. Mixed fiber textures consisting of both 1 1 0 and 1 0 0 components were formed along the drawing direction (DD) in the wire. A large magnetostriction of 750 ppm was obtained along DD under 1.2 T, which can be ascribed to the single γ phase and the formation of preferred crystal orientation.     

A rapid measurement of : The DECPMG sequence

The Driven-Equilibrium Carr–Purcell Meiboom–Gill (DECPMG) pulse sequence is a rapid method for obtaining the average ratio of longitudinal to transverse relaxation times T₁/T₂ as a function of T₂. Since this is a one-dimensional experiment, the T₁/T_2T2 ratio can be acquired, potentially, in just two scans; the second scan being a reference CPMG measurement. Conventionally, T₁/T₂ is determined from a two-dimensional T₁-T₂ relaxation correlation experiment. The method described here offers a significant reduction in experimental time without a reduction in signal-to-noise. The T₁/T₂ ratio is useful for comparing the behaviour of liquids in porous media. Here we demonstrate the application of the DECPMG sequence to the study of oil-bearing rocks by differentiating oil or water saturated rock cores, and by observing the relative strengths of surface interaction for water in two types of rock by measuring T₁/T₂ as a function of magnetic field strength.     

Surface morphology and composition of c-, a- and m-sapphire surfaces in O2 and H2 environments

This paper reports that monitoring the composition of the c(0 0 0 1), a(11–20) and m(10–10) sapphire surfaces is essential for a proper interpretation of the surface morphologies obtained after annealing at 1253 and 1473 K in ArH₂ or ArO₂ atmospheres. Our experimental investigations, which have used Auger electron spectroscopy (AES) and atomic force microscopy (AFM) on the surfaces of 99.99% pure sapphire wafers, have led to the following original conclusions: (i) Calcium segregates at the c-surface of sapphire both under ArO₂ and ArH₂. (ii) Potassium adsorption enhances the kinetics of step-bunching on the c-surface under ArO₂. (iii) The step edges on the a-surface may develop a comb-like morphology made of parallel strips along the [10–10] direction. (iv) At 1253 K, clean m-surfaces may be stable. (v) Under ArH₂, alumina surface diffusion is much slower than under ArO₂ for all surface orientations, the surface concentration of impurities is low, and the Al–O ratio of the AES signals at the surface is significantly larger.     

Dielectric/piezoelectric properties and temperature dependence of domain structure evolution in lead free single crystal

(K_0.5Na_0.5)NbO₃ (KNN) single crystals were grown using a high temperature flux method. The dielectric permittivity was measured as a function of temperature for [001]-oriented KNN single crystals. The ferroelectric phase transition temperatures, including the rhombohedral–orthorhombic T_R−O, orthorhombic–tetragonal T_O−T and tetragonal–cubic T_C were found to be located at −149  C, 205 C and 393 C, respectively. The domain structure evolution with an increasing temperature in [001]-oriented KNN single crystal was observed using polarized light microscopy (PLM), where three distinguished changes of the domain structures were found to occur at −150  C, 213 C and 400 C, corresponding to the three phase transition temperatures.     

Anomalous dimension with wrapping at four loops in SYM

In this paper we give all the details of the calculation that we presented in our previous paper [F. Fiamberti, A. Santambrogio, C. Sieg, D. Zanon, Wrapping at four loops in SYM, arXiv: 0712.3522], concerning the four-loop anomalous dimension of the Konishi descendant tr(ZZ−ZZ) in the SU(2) sector of the planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an superspace approach and Gegenbauer polynomial x-space techniques.     

Simulation of a turbulent non-premixed flame using conditional source-term estimation with trajectory generated low-dimensional manifold

Conditional source-term estimation (CSE) is a method to close the mean chemical reaction source-term in an averaged transport equation. It is used with a trajectory generated low-dimensional manifold (TGLDM) to simulate a turbulent non-premixed flame. Integral equations are inverted for two progress variables, Y_CO2|ξ and Y_H2O|ξ, by assuming spatial homogeneity in the conditional averages. Using these two progress variables, the conditional source terms of temperature and other scalars are interpolated from the TGLDM table and mapped back into the physical space to be substituted into the transport equations. Solving a transport equation using a source-term interpolated from the TGLDM is found to improve the prediction of NO over simply interpolating the mass fraction of NO directly from the TGLDM. This method has been applied in a large eddy simulation (LES) of a turbulent non-premixed flame. Both GRI-Mech 3.0 and GRI-Mech 2.11 are found to be able to predict the temperature and major species well. However, only GRI-Mech 2.11 gives an acceptable prediction of NO. It is found that major species can be interpolated from the TGLDM table which can significantly reduce the computational cost.     

Experimental and numerical investigation of the hetero-/homogeneous combustion of lean propane/air mixtures over platinum

The pure heterogeneous and the coupled hetero-/homogeneous combustion of fuel-lean propane/air mixtures over platinum have been investigated at pressures 1 bar  p  7 bar, fuel-to-air equivalence ratios 0.23  φ  0.43, and catalytic wall temperatures 723 K  T_w  1286 K. Experiments were performed in an optically accessible catalytic channel-flow reactor and involved 1-D Raman measurements of major gas-phase species concentrations across the reactor boundary layer for the assessment of catalytic fuel conversion and planar laser induced fluorescence (LIF) of the OH radical for the determination of homogeneous ignition. Numerical predictions were carried out with a 2-D elliptic CFD code that included a one-step catalytic reaction for the total oxidation of propane on Pt, an elementary C₃ gas-phase chemical reaction mechanism, and detailed transport. A global catalytic reaction step valid over the entire pressure–temperature-equivalence ratio parameter range has been established, which revealed a p^0.75 dependence of the catalytic reactivity on pressure. The aforementioned global catalytic step was further coupled to a detailed gas-phase reaction mechanism in order to simulate homogeneous ignition characteristics in the channel-flow reactor. The predictions reproduced within 10% the measured homogeneous ignition distances at pressures p  5 bar, while at p = 7 bar the simulations overpredicted the measurements by 19%. The overall model performance suggests that the employed hetero-/homogeneous chemical reaction schemes are suitable for the design of propane-fueled catalytic microreactors.     

The extraction of total cross section from

We report on the first measurement of the differential cross section of -meson photoproduction for the d(γ,pK⁺K⁻)n exclusive reaction channel. The experiment was performed using a tagged-photon beam and the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. A combined analysis using data from the d(γ,pK⁺K⁻)n channel and those from a previous publication on coherent production on the deuteron has been carried out to extract the −N total cross section, σ_N. The extracted −N total cross section favors a value above 20 mb. This value is larger than the value extracted using vector-meson dominance models for photoproduction on the proton.     

Dynamics of the collective excitations of the quantum Hall system

Using the non linear optical technique of 3-pulse 4-wave mixing, we study the dynamics of the collective excitations of the quantum Hall system. We excite the system with 100 fs pulses propagating in directions k₁ and k₃ and then probe its time evolution with a delayed pulse k₂. We measure the non-linear optical response from the lowest Landau level along the direction k₁+k₂−k₃. As function of the time delay of pulse k₂, this signal shows striking beats for short time delays (500 fs), followed by a rise (20 ps) and then a decay (100 ps). We identify the microscopic origin of this dynamics by extending the standard theory of ultra fast nonlinear optics to include the effects of the correlations.     

Velocity of electroweak bubble walls

We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, 0.1v_w0.6. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermions which are strongly coupled to the Higgs boson may provide a strongly first-order phase transition and small velocities, 10⁻²v_w10⁻¹, as required by electroweak baryogenesis.     

Simulation of kinetically limited growth of electrodeposited polycrystalline Ni films

A kinetic Monte Carlo (KMC) technique was adopted to simulate the growth dynamics of electrodeposited polycrystalline Ni thin films under kinetically limited conditions with a two-dimensional triangle lattice mapping the cross-section of the film. Effects of surface diffusion and surface-energy anisotropy on the microstructures of the plated film such as shape and size of grains, density, surface roughness, and textures were examined. This work focuses on the microstructure evolutions for different deposition parameters (for example, deposition rate and electrolyte temperature). We obtained the growth exponent β=0.46, which characterizes the scaling behavior of this growth. Preferential orientation of 1 1 1 and 1 0 0 have been observed at elevated temperature and at elevated deposition rate, respectively. To simulate the evolution of texture, the influence of hydrogen absorption on the surface energy of six main surfaces of nickel was investigated.     

Enhancement of surface morphology and optical properties of nanocolumnar ZnO films

Nanocolumnar ZnO films were prepared by electrodeposition (ED) on a glass substrate covered with a conductive layer of thin oxide doped with fluorine (FTO). After deposition the samples were annealed in oxidizing or reducing atmosphere, at temperatures between 100 to 500 C, in order to follow the evolution of optical properties and morphology. The optical properties of these films were studied by means of photoluminescence spectroscopy (PL) and the morphology by scanning electron microscopy (SEM). Films annealed at 300 C exhibit a higher ultraviolet emission peak, originating from exciton transitions. A green band related to deep-level emission centered at 500 nm, shows a drastic increase at 500 C. These results are independent of the annealing atmosphere. An increase of coalescence is also observed after annealing at 500 C. These results are explained taking into account the contribution of different point defects.     

Concavity for nuclear bindings, thermodynamical functions and density functionals

Sequences of experimental ground-state energies for both odd and even A are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential Ω(β,μ) for a mixture of nuclei at low or moderate temperatures T=β⁻¹ and at many chemical potentials μ. The average nucleon number A(β,μ) then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to the drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of A. Concavity, which always occurs for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.     

Morphological and electro-optical responses of dichroic polymer dispersed liquid crystal films

Dichroic polymer dispersed liquid crystal (DPDLC) films containing different concentration of dichroic dye have been prepared by polymerization induced phase separation technique using nematic liquid crystal material in UV curable polymer NOA 65 and anthraquinone dichroic dye. The effects of applied voltage and temperature on the LC droplet morphology and its optical characteristics were studied in detail. Liquid crystal droplets containing low concentration of dye (0.25%) in polymer matrix exhibit bipolar configuration at lower applied voltage (10 V) whereas at relatively higher voltage (15 V) maltese type liquid crystal droplets were seen. In addition, low concentration DPDLC film shows better optical transmission and higher contrast ratio.     

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. , in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as  = _r + i_i and μ = μ_r + iμ_i. The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability _i > 0 and μ_i > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability _i < 0 and μ_i < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters _r, μ_r, _i, and μ_i, in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re{Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously  < 0 and μ < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for _r < 0, μ_r > 0, _i > 0, and μ_i > 0, the refractive index is negative n < 0 provided μ_i/_i > μ_r/_r.