A strategy for choosing Gegenbauer reconstruction parameters for numerical stability

The Gegenbauer reconstruction method was first proposed in 1992, but in early studies no attempts were made to optimize the relevant parameters of this method. These parameters were allowed to grow proportionally with the number of nodes which, in many cases, resulted in exponential convergence for a selected range of the proportionality constants. Early studies also made clear that very large error bounds could be expected if these key parameters were not chosen carefully. Subsequent studies then pointed out that, although unrelated to the method’s analytically predictable domains of poor accuracy, round-off errors could also sabotage the method’s accuracy. The challenge of successfully implementing a Gegenbauer reconstruction then rests on understanding the performance trade-offs we can expect when choosing the key parameters in accordance with different objectives.In this study, we propose a new strategy for choosing optimal parameters in the Chebyshev-Gegenbauer reconstruction method, specifically to achieve numerical stability. This strategy is based on asymptotic analysis as well as minimization problems in one and two dimensions. The effectiveness of our approach, which could also be applied to a wider selection of polynomials is then illustrated with results from numerical experiments.     

Velocity renormalization and carrier lifetime in graphene from the electron-phonon interaction

We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear band structure of graphene and deviates substantially from the usual metallic behavior. The effective band velocity of the Dirac fermions is found to be reduced by 4%-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.     

Kondo effect in magnetic tunnel junctions

Tunneling magnetoresistance was found to be suppressed with decreasing temperature for magnetic tunnel junctions (MTJs) oxidized under high plasma power. A strong temperature dependence of the junction resistance was observed, along with zero-bias anomalies of dynamic resistance at low temperatures. Resistance shows a logarithmic dependence on temperature, and resistance versus temperature exhibits a scaling behavior. Our experimental data can be explained in a consistent way by the Kondo effect in the MTJs with the Kondo temperature TK=20-30 K.     

Semiconductor Emitters in Entropy Sources for Quantum Random Number Generation

Random number generation (RNG) is needed for a myriad of applications ranging from secure communication encryption to numerical simulations to sports and games. However, generating truly random numbers can be elusive. Pseudorandom bit generation using computer algorithms provides a high random bit generation rate. Nevertheless, the reliance on predefined algorithms makes it deterministic and predictable once initial conditions are known. Relying on physical phenomena (such as measuring electrical noise or even rolling dice) can achieve a less predictable sequence of bits. Furthermore, if the physical phenomena originate from quantum effects, they can be truly random and completely unpredictable due to quantum indeterminacy. Traditionally, physical RNG is significantly slower than pseudorandom techniques. To meet the demand for high-speed RNG with perfect unpredictability, semiconductor light sources are adopted as parts of the sources of randomness, i.e., entropy sources, in quantum RNG (QRNG) systems. The high speed of their noise, the high efficiency, and the small scale of these devices make them ideal for chip-scale QRNG. Here, the applications and recent advances of QRNG are reviewed using semiconductor emitters. Finally, the performance of these emitters is compared and discuss their potential in future technologies.     

Oscillatory behavior of supersonic impinging jet flows

Oscillatory flows of a choked underexpanded supersonic impinging jet issuing from a convergent nozzle have been computed using the axisymmetric unsteady Navier--Stokes system. This paper focuses on the oscillatory flow features associated with the variation of the nozzle-to-plate distance and nozzle pressure ratio. Frequencies of the surface pressure oscillation and flow structural changes from computational results have been analyzed. Staging behavior of the oscillation frequency has been observed for both cases of nozzle-to-plate distance variation and pressure ratio variation. However, the staging behavior for each case exhibits different features. These two distinct staging behaviors of the oscillation frequency are found to correlate well if the frequency and the distance are normalized by the length of the shock cell. It is further found that the staging behavior is strongly correlated with the change of the pressure wave pattern in the jet shear layer, but not with the shock cell structure. Communicated by K. Takayama PACS 02.60.Cb; 47.40.−x; 47.40.Nm; 47.35.+I; 47.15.−x     

Stability of an Initially, Stably Stratified Fluid Subjected to a Step Change in Temperature

The onset of convective instability in an initially quiescent, stably stratified fluid layer between two horizontal plates is analyzed with linear theory. The bottom boundary is heated suddenly from below, subjected to a step change in surface temperature. The critical time t _c to mark the onset of Rayleigh-Bénard convection is predicted by propagation theory. This theory uses the length scaled by , where α denotes thermal diffusivity. Under the normal mode analysis the dimensionless disturbance equations are obtained as a function of τ(=αt/d ²) and ζ(=Z/), where d is the fluid layer depth and Z is the vertical distance. The resulting equations are transformed to self-similar ones by using scaling and finally fixing τ as τ_c under the frame of coordinates τ and ζ. For a given γ, Pr and τ_c, the minimum value of Ra is obtained from the marginal stability curve. Here γ denotes the temperature ratio to represent the degree of stabilizing effect, Pr is the Prandtl number and Ra is the Rayleigh number. With γ=0, the minimum Ra value approaches the well-known value of 1708 as τ_c increases. However, it is inversely proportional to τ_c ^3/2 as τ_c decreases. With increasing γ, the system becomes more stable. It is interesting that in the present system, propagation theory produces the stability criteria to bound the available experimental data over the whole domain of time. Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 RID="*" ID="*" This work has been supported by both SK Chemicals Co. Ltd. and LG Chemical Ltd., Seoul under the Brain Korea 21 Project of the Ministry of Education. Communicated by H.J.S. Fernando     

Three-dimensional viscoelastic simulation of coextrusion process: comparison with experimental data

 Three-dimensional numerical simulation of viscoelastic coextrusion process has been performed and numerical results were compared with the experimental data of Karagiannis et al. (1990). By varying the magnitude of the second normal stress difference and its ratio of Fluid I and Fluid II, we were able to control the interface profile and the degree of encapsulation along the downstream direction. By increasing the parameter α (α_Fluid I=α_Fluid II) from 0.1 to 0.4 in the Giesekus model and increasing the α ratio (α_Fluid Iα_Fluid II) between Fluid I and Fluid II from 2.0 to 4.0 in the permissible range of realistic polymeric systems, the interface profile and the degree of encapsulation along the downstream direction were fitted with the experimental results. There was little difference between the numerical results and the experimental data in the interface profile and the degree of encapsulation along the downstream direction when the α ratio was set to 3.0 (0.3:0.1). Fluid I with larger magnitude of the second normal stress difference protrudes into Fluid II with smaller magnitude of the second normal stress difference around the symmetric plane, while Fluid II wraps around Fluid I near the side walls. As the ξ ₁ ratio (ξ _{1 ,Fluid I}ξ _{1 ,Fluid II}) increases from 1.0 to 3.0 for the two-mode Phan-Thien and Tanner model, it was found that the curvature of the interface profile increased, and the difference between the numerical results and the experimental data in the interface profile and the degree of encapsulation along the downstream direction was almost negligible when the ξ ₁ ratio was set to 3.0 (0.54:0.18). Although the parameters of viscoelastic models were fitted by using the shear viscosity data only, quantitative agreements between the numerical results and the experimental coextrusion data were quite satisfactory. Received: 24 April 2001 Accepted: 5 June 2001     

Macroscopic and microscopic characteristics of a fuel spray impinged on the wall

An experimental study was performed to investigate the macroscopic behavior and atomization characteristics of a high-speed diesel spray impinged on the wall at various injection and impinging conditions. The development processes of sprays impinged on the wall were visualized using the spray visualization system composed of a Nd:YAG laser and an intensified charge-coupled device (ICCD) camera. The atomization characteristics of the impinged spray on the wall were also explored in terms of mean droplet diameter and velocity distributions by using a phase Doppler particle analyzer (PDPA) system. The results provide the effects of injection parameters, wall conditions, and the other various experimental conditions on the macroscopic behavior and atomization characteristics of the impinged sprays on the wall.     

Formation of a Syndiotactic Organic Polymer Inside a MOF by a [2+2] Photo‐Polymerization Reaction

Getting suitable crystals for single‐crystal X‐ray crystallographic analysis still remains an art. Obtaining single crystals of metal–organic frameworks (MOFs) containing organic polymers poses even greater challenges. Here we demonstrate the formation of a syndiotactic organic polymer ligand inside a MOF by quantitative [2+2] photopolymerization reaction in a single‐crystal‐to‐single‐crystal manner. The spacer ligands with trans,trans,trans‐conformation in the pillared‐layer MOF with guest water molecules in the channels, undergo pedal motion to trans,cis,trans‐conformation prior to [2+2] photo‐cycloaddition reaction and yield single crystals of MOF containing two‐dimensional coordination polymers fused with the organic polymer ligands. We also show that the organic polymer in the single crystals can be depolymerized reversibly by cleaving the cyclobutane rings upon heating. These MOFs also show interesting photoluminescent properties and sensing of small organic molecules.     

Chemoselective Silylative Reduction of Conjugated Nitriles under Metal‐Free Catalytic Conditions: β‐Silyl Amines and Enamines

The B(C₆F₅)₃‐catalyzed silylative reduction of conjugated nitriles has been developed to afford synthetically valuable β‐silyl amines. The reaction is chemoselective and proceeds under mild conditions. Mechanistic elucidation indicates that it proceeds by rapid double hydrosilylation of the conjugated nitrile to an enamine intermediate which is subsequently reduced to the β‐silyl amine, thus forming a new C(sp³)? Si bond. Based on this mechanistic understanding, a preparative route to enamines was also established using bulky silanes.