A Brinkman penalization method for compressible flows in complex geometries

To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations. Its main idea is to model solid obstacles as porous media with porosity, ϕ, and viscous permeability approaching zero. It has the pronounced advantages of mathematical proof of error bound, strong convergence, and ease of numerical implementation with the volume penalization technique. In this paper, it is extended to compressible flows. The straightforward extension of penalizing momentum and energy equations using Brinkman penalization with respective normalized viscous, η, and thermal, η_T, permeabilities produces unsatisfactory results, mostly due to nonphysical wave transmissions into obstacles, resulting in considerable energy and mass losses in reflected waves. The objective of this paper is to extend the Brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media. In addition to penalizing momentum and energy equations, the continuity equation for porous media is considered inside obstacles. In this model, the penalized porous region acts as a high impedance medium, resulting in negligible wave transmissions. The asymptotic analysis reveals that the proposed Brinkman penalization technique results in the amplitude and phase errors of order O((ηϕ)^1/2) and O((η/η_T)^1/4ϕ^3/4), when the boundary layer within the porous media is respectively resolved or unresolved. The proposed method is tested using 1- and 2-D benchmark problems. The results of direct numerical simulation are in excellent agreement with the analytical solutions. The numerical simulations verify the accuracy and convergence rates.     

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.     

Peculiarities of electron field emission from ZnO nanocrystals and nanostructured films

ZnO microcrystals and nanocrystals were grown on silicon substrates by condensation from vapour phase. Nanostructured ZnO films were deposited by plasma enhanced metal organic chemical vapour deposition (PEMOCVD). The parameters of field emission, namely form-factor β and work function , were calculated for ZnO structures by the help of the Fowler–Nordheim equation. The work functions from ZnO nanostructured films were evaluated by a comparison method. The density of emission current from ZnO nanostructures reaches 0.6 mA/cm² at electric force F=2.110⁵ V/cm. During repeatable measurements β changes from 5.810⁴ to 2.310⁶ cm⁻¹, indicating improvement of field emission. Obtained values of work functions were 3.7±0.37 eV and 2.9–3.2 eV for ZnO nanostructures and ZnO films respectively.     

Quantum transport in a mesoscopic ring: Evidence of an OR gate

We explore the OR gate response in a mesoscopic ring threaded by a magnetic flux . The ring is symmetrically attached to two semi-infinite one-dimensional metallic electrodes, and two gate voltages, V_a and V_b, are applied in one arm of the ring; these are treated as the two inputs of the OR gate. All the calculations are based on the tight-binding model and the Green’s function method, which numerically compute the conductance–energy and current–voltage characteristics as functions of the gate voltages, ring-to-electrode coupling strengths and magnetic flux. Our theoretical study shows that, for =₀/2 (₀=ch/e, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if one or both the inputs to the gate are high (1), while if neither input is high (1), a low output current (0) appears. It clearly demonstrates the OR gate behavior, and this aspect may be utilized in designing an electronic logic gate.     

Suppressed transmission in aperiodically modulated multilayered dielectric structures

We investigate the transmission of electromagnetic plane waves through 1D binary dielectric multilayered structures that exhibit aperiodic incommensurated sequences of refractive indices. The aperiodicity is introduced by considering the sequence of refractive indices to follow a sinusoidal function whose phase varies as a power-law of the layer index, ∝i^ν. For ν>1, the resulting sequence is effectively uncorrelated leading to the Anderson localization of most of the electromagnetic modes, except at the Bragg resonances. The crossover from a uniform structure at ν=0 to a quasi-periodic structure at ν=1 is signaled by a minimum at the spectrally averaged transmission. We perform a spectral analysis of the refractive index sequence to show its close connection to the main features exhibited by the averaged optical transmittance. Our results suggest that aperiodically modulated dielectric structures can potentially be used in the development of wide-band filters.     

Quasi-periodic solutions of nonlinear wave equations with quasi-periodic forcing

This work focuses on one-dimensional (1D) quasi-periodically forced nonlinear wave equations. This means studying with Dirichlet boundary conditions, where ε is a small positive parameter, (t) is a real analytic quasi-periodic function in t with frequency vector ω=(ω₁,ω₂…,ω_m) and the nonlinearity h is a real analytic odd function of the form It is shown that, under a suitable hypothesis on (t) and h, there are many quasi-periodic solutions for the above equation via KAM theory.     

NOR gate response in a double quantum ring: An exact result

NOR gate response in a double quantum ring, where each ring is threaded by a magnetic flux , is investigated. The double quantum ring is sandwiched symmetrically between two semi-infinite one-dimensional metallic electrodes, and two gate voltages, namely, V_a and V_b, are applied, respectively, in lower arms of the two rings those are treated as the two inputs of the NOR gate. A simple tight-binding model is used to describe the system, and all the calculations are done through the Green’s function formalism. Here we calculate exactly the conductance–energy and current–voltage characteristics as functions of the ring-to-electrode coupling strengths, magnetic flux and gate voltages. Our numerical study predicts that, for a typical value of the magnetic flux =₀/2 (₀=ch/e, the elementary flux-quantum), a high output current (1) (in the logical sense) appears if both the inputs to the gate are low (0), while if one or both are high (1), a low output current (0) results. It clearly demonstrates the NOR gate behavior, and this aspect may be utilized in designing an electronic logic gate.     

Constraining new physics in with reparametrization invariance and QCD factorization

Usually, B⁰→π⁺π⁻ decays are expressed in terms of weak amplitudes explicitly dependent on the CKM weak phase α or γ. In this Letter, we show that the weak amplitudes can be rewritten such that a manifest dependence on β emerges instead. Based on this, we constrain new-physics contributions to the CP-violating phase _d in mixing. Further, we apply reparametrization invariance and use QCD factorization predictions to investigate the bounds on an additional new-physics amplitude in B⁰→π⁺π⁻.     

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.     

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.