On the numerical analtsys of generated sylvester equations

The sensivtiity of the solution of the matrix Sylvester equation AX-XB=C is considered in the context of the classical perturbation theory. Our purpose is to find the most influent parameters in the sensitivity of the solution under perturbations in the data, and to compare the theoretical error bounds with numerical evidence.     

Theory of ion reflection from amorphous surface at low glancing angles

A new theory of ion reflection from a smooth amorphous solid surface is developed. A continuous potential is introduced for describing the ion reflection from amorphous surfaces at low glancing angles. It is shown that the difference, between a true surface potential and a continuous one could be taken into account in terms of a correction factor, thus yielding a Fokker-Planck-type equation for a particle distribution in angle and transverse coordinate. Diffusion coefficients included in this equation are calculated with allowance for atom discrete positions and ion-electron collision effect. On the basis of the derived kinetic equation the angular and energy ion distributions in a reflected beam are analyzed. The presented theory, somewhat modified, can be used for describing ion reflection from a crystal surface as well.     

Laser-assisted bending of Titanium Grade-2 sheets: Experimental analysis and numerical simulation

External force laser-assisted bending of Titanium Grade-2 flat sheets to achieve sharp bending angles (>140°) with small fillet radii is herein investigated. In particular, the influence of the operational parameters, laser power, scan speed, number of passes, on bending angles and fillet radii of the metal substrates is analysed. The experimental results show that shaping of the substrates can be performed with great reliability, being springback largely minimised in broad operational ranges. Exploratory Data Analysis (EDA) allows the design of first approximation technological models and, in turn, the development of 3d processing maps. Based on the experimental findings, numerical modelling of the bending process by the Finite Element Method (FEM) through ABAQUS/Explicit software is also developed. The numerical model is found to match with great accuracy the experimental results, being it also extremely flexible and responsive to the change of the operational parameters.     

Mirror objectives with variable focal length

We consider some issues involved in constructing a mirror system with a discrete variable focal length. We propose a procedure for designing two-mirror pancratic (zoom) systems with fixed image plane. In constructing the optimal layouts, we studied a basic two-mirror system to achieve minimum spherical aberration. We present the calculated design characteristics of an objective consisting of two spherical mirrors and providing a three-fold variation in focal length. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 453–459, May–June, 2009.     

A conservative level set method for contact line dynamics

A new model for simulating contact line dynamics is proposed. We apply the idea of driving contact-line movement by enforcing the equilibrium contact angle at the boundary, to the conservative level set method for incompressible two-phase flow [E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys. 210 (2005) 225–246]. A modified reinitialization procedure provides a diffusive mechanism for contact-line movement, and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface. We are able to capture contact-line movement without loosing the conservation. Numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct.     

Improved SNR in linear reordered 2D bSSFP imaging using variable flip angles

This article presents a variable flip-angle approach for balanced steady-state free precession (bSSFP) imaging, which allows increases in signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) while keeping specific absorption rate (SAR) constant or reduces SAR for given CNR and SNR. The gain in SNR is achieved by utilizing the higher signal in the transient phase. Flip-angle variation during the echo train is realized using a trigonometric function with M steps (ramp length). Variation is combined with a linear k-space reordering such that outer parts of k-space are sampled using a lower flip angle α_min, while the central part of k-space is acquired with a higher flip angle α_max. No additional preparation or dummy cycles are applied prior to data acquisition. Several variation schemes with different starting flip angles α_min and ramp length M are considered. For example, using α_min=1° and M=96, α_max can be set to 47° without exceeding SAR limits at 3 T and gaining up to 50% in SNR, while, conventionally, α=34° is the maximal possible flip angle. Resolution seems unaffected in volunteer imaging. In all cases, no transient artifacts due to flip-angle variation were observed. This article demonstrates the use of flip-angle variations in bSSFP to increase SNR and CNR while keeping SAR constant, which is especially important at higher field strengths. Flip-angle variation can also be combined with other methods such as parallel imaging techniques for further SAR reduction.     

Numerical simulation of a 4WD–4WS tractor turning in a rice field

For the steady-state circular turning of a 4WD–4WS (4 wheel driven–4 wheel steered) tractor in a rice field, a numerical simulation was achieved. Equations of motion of this tractor were developed in a vehicle fixed x–y coordinate system. By comparing the calculated and measured results of acting forces on the tractor tires, this simulation was evaluated. Then, the characteristic parameters of the turning vehicle, which are the side slip angle and the yaw angular velocity of the vehicle center of gravity, were simulated in several combinations of the steering wheel angle and the forward speed. Also the same simulation applied to a 4WD–2WS tractor which had the same body as the 4WD–4WS tractor. The simulated results showed a clear difference of turnability between 4WS and 2WS. ©     

Departure Processes of BMAP/G/1 Queues

A unified approach is applied to analyze the departure processes of finite/infinite BMAP/G/1 queueing systems for both vacationless and vacation arrangements via characterizing the moments, the z-transform of the scaled autocovariance function of interdeparture times C _P (z), and lag n (n1) covariance of interdeparture times. From a structural point of view, knowing departure process helps one to understand the impact of service mechanisms on arrivals. Through numerical experiments, we investigate and discuss how the departure statistics are affected by service and vacation distributions as well as the system capacity. From a practical perspective, output process analysis serves to bridge the nodal performance and connectionwise performance. Our results can be then used to facilitate connection- or networkwise performance analysis in the current high-speed networks.     

High Accuracy of Karplus Equations for Relating Three‐Bond J Couplings to Protein Backbone Torsion Angles

³J_C′C′ and ³J_HNHα couplings are related to the intervening backbone torsion angle ${\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\varphi }$ , including H‐bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small. The solution NMR structure of protein GB3, newly refined by using extensive sets of residual dipolar couplings, yields 50–60 % better Karplus equation agreement between ${\varphi }$ angles and experimental ³J_C′C′ and ³J_HNHα values than does the high‐resolution X‐ray structure. In intrinsically disordered proteins, ³J_C′C′ and ³J_HNHα couplings can be measured at even higher accuracy, and the impact of factors other than the intervening torsion angle on ³J will be smaller than in folded proteins, making these couplings exceptionally valuable reporters on the ensemble of ${\varphi }$ angles sampled by each residue.     

Controlled adhesion of Salmonella Typhimurium to poly(oligoethylene glycol methacrylate) grafts

Poly(oligoethylene glycol methacrylate), POEGMA, brushes were prepared by surface‐initiated atom transfer radical polymerization (SI‐ATRP) on gold‐coated silicon wafers. Prior to ATRP, the substrates were grafted by brominated aryl initiators via the electrochemical reduction of a noncommercial parent diazonium salt of the formula BF₄^?, ⁺N₂‐C₆H₄‐CH(CH₃)Br. The diazonium‐modified gold plates (Au‐Br) served as macroinitiators for ATRP of OEGMA which resulted in hydrophilic surfaces (Au‐POEGMA) that could be used for two distinct objectives: (i) resistance to fouling by Salmonella Typhimurium; (ii) specific recognition of the same bacteria provided that the POEGMA grafts are activated by anti‐Salmonella. The Au‐POEGMA plates were characterized by XPS, polarization modulation‐infrared reflection‐absorption spectroscopy (PM‐IRRAS) and contact angle measurements. Both Beer‐Lambert equation and Tougaard's QUASES software indicated a POEGMA thickness that exceeds the critical ～10 nm value necessary for obtaining a hydrophilic polymer with effective resistance to cell adhesion. The Au‐POEGMA slides were further activated by trichlorotriazine (TCT) in order to covalently bind anti‐Salmonella antibodies (AS). The antibody‐modified Au‐POEGMA specimens were found to specifically attach Salmonella Typhimurium bacteria. This work is another example of the diazonium salt/ATRP process to provide biomedical polymer surfaces. Copyright © 2011 John Wiley & Sons, Ltd.