Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker–Planck equations

Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville equation can be decomposed via an expansion in terms of a smallness parameter , wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to O(²) for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker–Planck equation up to O(²). This approach has applications to a broad range of problems in the nanosciences.     

Critical Casimir amplitudes for n-component models with -symmetry breaking quadratic boundary terms

Euclidean n-component ⁴ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry . The boundary terms imply the Robin boundary conditions at the boundary planes at z=0 and at z=L. Particular attention is paid to the cases in which m_j of the n variables associated with plane take the special value corresponding to critical enhancement while the remaining ones are larger and hence subcritically enhanced. Under these conditions, the semi-infinite system with boundary plane has a multicritical surface–bulk point, called m_j-special, at which an O(m_j) symmetric critical surface phase coexists with the O(n) symmetric bulk phase, provided d is sufficiently large. The L-dependent part of the reduced free energy per cross-section area behaves asymptotically as Δ_C/L^d−1 as L→∞ at the bulk critical point. The Casimir amplitudes Δ_C are determined for small =4−d in the general case where m_c,c components _α are critically enhanced at both boundary planes, m_c,D+m_D,c components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining m_D,D components satisfy asymptotic Dirichlet boundary conditions at both . Whenever m_c,c>0, the corresponding small- expansions involve, besides integer powers of , also fractional powers ^k/2 with k3 modulo powers of logarithms. Results to order ^3/2 are given for general values of m_c,c, m_c,D+m_D,c, and m_D,D. These are used to estimate the Casimir amplitudes Δ_C of the three-dimensional Heisenberg systems with surface spin anisotropies for the cases with (m_c,c,m_c,D+m_D,c)=(1,0), (0,1), and (1,1).     

Multiloop Bubbles for hot QCD

In this article, we present analytical expansion results of two single mass scale four-loop vacuum integrals in d=3−2 dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we implemented in FORM to expand these in terms of nested sums.     

Plasma excitations in the superconducting state of two-band layered superconductors

We investigate the low-frequency plasma modes polarized in the c-direction in two-band layered superconductors. The dynamic dielectric function (ω,q) is derived at T=0, using the generalized random-phase-approximation which is consistent with the Hartree–Fock single-particle states. It is shown that the dielectric function has two zero-points which correspond to the longitudinal plasma modes in two-band layered superconductors.     

Scalings of elliptic flow for a fluid at finite shear viscosity

Within a parton cascade approach we investigate the scaling of the differential elliptic flow v₂(p_T) with eccentricity _x and system size and its sensitivity to finite shear viscosity. We present calculations for shear viscosity to entropy density ratio η/s in the range from 1/4π up to 1/π, finding that the v₂ saturation value varies by about a factor 2. Scaling of v₂(p_T)/_x is seen also for finite η/s which indicates that it does not prove a perfect hydrodynamical behavior, but is compatible with a plasma at finite η/s. Introducing a suitable freeze-out condition, we see a significant reduction of v₂(p_T) especially at intermediate p_T and for more peripheral collisions. This causes a breaking of the scaling for both v₂(p_T) and the p_T-averaged v₂, while keeping the scaling of v₂(p_T)/v₂. This is in better agreement with the experimental observations and shows as a first indication that the η/s should be significantly lower than the pQCD estimates. We finally point out the necessity to include the hadronization via coalescence for a definite evaluation of η/s from intermediate p_T data.     

Further observations on the variation with dielectric constant and thickness of the reflectance and phase change on reflection of films

Studies of the behaviour with ₁, ₂ and film thickness of the optical functions reflectance (R) and phase change on reflection (Φ_r) have previously been made for both very thin and very thick films. Abelès [J. Opt. Soc. Amer. 47 (1957) 473] has formulated equations for very thin films where functions of ₁ and ₂ are the coefficients of a power series of the optical thickness, x(2πd/λ) up to x², whilst in the case of very thick films (solids) the relationships between ₁ and ₂ can be represented in polar coordinates L and α by ₁=L cos α, ₂=L sin α where L_R=2y²₀W²(1+cos α−1/W²) [W=(1+R)/(1−R)] and L_Φr=2(y₀/ tan Φ_r)²(1−cos α+tan ² Φ_r) [Ward, Opt. and Laser Tech. 27 (1995) 125]. The present study is concerned with films of intermediate optical thicknesses (1.0<2πd/λ<solid) and has revealed that the polar-type relationships previously noted for solid materials are augmented by secondary structures of maxima and minima whose position and amplitude can be predicted by adapting the exact equations for R and Φ_r.     

Contours of constant Δ and Ψ in the 2–4 plane for the ellipsometric functions

Contour graphs of ₂ vs ₄ for different film thicknesses and a range of angles of incidence have been plotted for the ellipsometric functions Δ and Ψ in both the reflection and transmission modes. In the case of reflection ellipsometry, when the plots for Δ_R and Ψ_R are superimposed, the two sets of contours cross nearly at right angles over a large part of the field, this being indicative of the high accuracy obtainable in using this technique to determine ₄ and ₂ and hence the optical constants, n and k, for the film material. The reflection ellipsometric technique is accurate over angles of incidence between 30° and 75° and for a range of film thicknesses between λ/30 and 5λ. Transmission ellipsometry is less useful, due to anomalies in both X_s and X_p where sudden phase changes of ±π occur in regions of interest. There is also the possibility of multiple solutions, although the use of a multiangle technique would enable the “correct” values to be more easily determined.     

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.     

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 .     

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.     

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.     

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.     

1.3 μm range effectively cylindrical In0.53Ga0.47As/In0.52Al0.48As quantum wires grown on (2 2 1)A InP substrates by molecular beam epitaxy

Vertically coupled quantum wires (QWRs) have been made by alternately stacking nominally 3.6 nm thick In_0.53Ga_0.47As self-organized QWR layers and 1 nm thick In_0.52Al_0.48As barrier layers on (2 2 1)A-oriented InP substrates by molecular beam epitaxy. The surface of In_0.53Ga_0.47As QWR layers was corrugated at an amplitude of 1.1 nm and period of 27 nm, and lateral confinement potential is induced by their thickness modulation. The wavelength of photoluminescence (PL) from the stacked QWRs at 15 K becomes longer from 1220 to 1327 nm with increasing total number of stacked QWR layers, N_SL, from 1 to 9, while PL full-width at half-maximum is reduced from 22 to 8.6 meV. The PL intensity with the polarization parallel to the wire direction, I, is 1.30 times larger than that with the normal polarization, I, when N_SL=1. The PL intensity ratio, I/I, reaches as large as 4 when N_SL=9, indicating successful control of relative strength between vertical confinement and lateral confinement of carriers. The value of I/I obtained for the stacked QWRs with N_SL=9 is the same value as cylindrical QWRs have. The results indicate that effectively cylindrical QWRs with the best uniformity and 1.3 μm range emission were realized by stacking of self-organized QWR layers.     

Structure and properties of the one-dimensional cobalt oxide CaCo2O4

We have studied crystal structure and transport properties of the quasi one-dimensional cobalt oxide CaCo₂O₄. The CaCo₂O₄ phase crystallizes in calcium-ferrite type structure, which consists of a corner- and edge-shared CoO₆ octahedron network including one-dimensional double chains. Large thermoelectric power (S  150 μV/K at 390 K) with metallic temperature dependence of S, moderate resistivity (ρ  2.9 × 10⁻¹ Ω cm at 390 K) with carrier localization at low temperature, and normal thermal conductivity (κ  6.3 W/Km at 390 K) were observed. The phonon mean-free path was calculated from the observed data, as a function of temperature. The long phonon mean-free path (l  24 Å at 300 K) implies that the thermal conductivity could be suppressed by impurity scattering of phonons with partial element substitution.     

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.     

Modified Kolmogorov wave turbulence in QCD matched onto “Bottom-up” thermalization

We investigate modification of Kolmogorov wave turbulence in QCD calculating gluon spectra as functions of time in the presence of a low energy source which feeds in energy density in the infrared region at a time-dependent rate. Then considering the picture of saturation constraints as has been constructed in the “bottom-up” thermalization approach we revisit that picture for RHIC center-mass energy, W=130 GeV, and also extend it to LHC center-mass energy, W=5500 GeV, thus for two cases having an opportunity to calculate the equilibration time, τ_eq|therm, of the gluon system produced in a central heavy ion collision at mid-rapidity region. Thereby, at RHIC and LHC energies we can match the equilibration time, obtained from the late stage gluon spectrum of the modified Kolmogorov wave turbulence, onto that of the “bottom-up” thermalization and other evolutional approaches as well. In addition, from the revised “bottom-up” approach we find the gluon liberation coefficient to be on the average, ε0.81–1.06 at RHIC and ε0.50–0.56 at LHC. We also present other phenomenological estimates of τ_therm which, at QCD realistic couplings, yield 0.45–0.65 fmτ_therm0.97–2.72 fm at RHIC and 0.31–0.40 fmτ_therm0.86–2.04 fm at LHC. We show that the second upper-bounds of τ_therm in both cases are due to the late stage gluon spectrum of the original Kolmogorov wave turbulence in QCD, previously deduced with a low energy source which feeds in energy density at a constant rate. On the other hand, the lower-bounds and first upper-bounds of τ_therm are due to the late stage gluon spectrum of the modified QCD wave turbulence, deduced here at the specific time-dependent rate. In the latter case, at certain conditions, taking also into account both very small and realistic couplings we give estimates: 0.65 fmτ_therm1.29 fm at RHIC and 0.52 fmτ_therm1.16 fm at LHC, as well as at realistic couplings we find 0.53<τ_therm<0.7 fm at RHIC and 0.41<τ_therm<0.65 fm at LHC.     

Wavelength and temperature dependence properties of human blood-serum

For biological importance and general scientific interest, the present paper studies the physical properties dependent on wavelength and temperature, for six different samples of human blood-serum, at two different laser wavelengths (514.5 and 632.8 nm). The properties are described in terms of scalar quantities, viz. refractive index or optical permittivity, optical and dielectric dispersion. A modified and high accurate laser Mach–Zehnder interferometric technique is used for measurement of the refractive index (n) and its gradient with temperature (dn/dT). The values of n and dn/dT are applied to calculate the optical permittivity () and its gradient with temperature d/dT. The refractive properties such as the variation of n, , −dn/dT and, −d/dT as a functions of wavelengths are determined. On the other hand, the optical properties such as reflectance, transmittance and absorptance as a function of light incident angle, temperature and wavelength are studied. Additionally the following dielectric parameters are calculated: specific refractivity, specific dispersivity, polarizability per unit volume, wave impedance, volume expansion coefficient and the electric susceptibility.     

Far-field properties and beam quality of vectorial Hermite–Laguerre–Gaussian beams beyond the paraxial approximation

The far-field properties and beam quality of vectorial nonparaxial Hermite–Laguerre–Gaussian (HLG) beams are studied in detail, where, instead of the second-order-moments-based M² factor, the extended power in the bucket (PIB) and βparameter are used to characterize the beam quality in the far field and the intensity in the formulae is replaced by the z component of the time-averaged Poynting vector S_z. It is found that the S_z PIB and βparameter of vectorial nonparaxial HLG beams depend on the mode indices n, m, αparameter and waist-width-to-wavelength ratio w₀/λ and the PIB and βparameter are additionally dependent on the bucket's size taken.     

Electron drag in intermediate magnetic fields with low electron density

Electron drag between two two-dimensional electron systems has been measured in intermediate magnetic fields (/τ<ω_ck_BT) with a relatively low electron density. We explore, in this sample, the unusual increase of drag in intermediate magnetic fields which was well characterized by a nearly temperature independent B³ dependence. The anomalous behavior of electron drag observed in higher density samples is found to persist for low sample density.     

Transport properties of single crystal

Transport properties of BaNi₂P₂ single crystals prepared by high-pressure synthesis method have been investigated. The temperature dependence of the resistivity is that of a typical metal with the anisotropy ratio ρ/ρ of 6.3 and suggests that electron–phonon interaction dominates the scattering mechanism. We have also found that the Hall effect and the magnetoresistance can be explained by a two-carrier model which is consistent with a multiple-band structure with both hole and electron characters.