Spontaneous emission of a moving atom in a waveguide of rectangular cross section

We study the spontaneous emission(SE) of an excited nonrelativistic two-level system(TLS) interacting with the vacuum in a waveguide of rectangular cross section. All TLS’s transitions and the center-of-mass motion of the TLS are taken into account. The SE rate and the carried frequency of the emitted photon for the TLS initially being at rest are obtained, it is found that in the first order of the mass M, the frequency of the emitted photon is smaller than the transition frequency of the TLS and the SE rate is smaller than the SE rate Γfof the TLS fixed in the same waveguide. The SE rate for the TLS initially being moving is obtained in the second order of the mass M. The SE rate is smaller than Γfbut it is dependent not only on the atomic mass but also on the initial momentum. The carried frequency of the emitted photon is decreased when it travels along the direction of the initial momentum, whereas it is increased when it travels in the opposite direction of the initial momentum.

Influence of Axial Feeding on Hydroforming of Aluminum Alloy Tubular Part with Rectangular Section

The hydroforming experiment of aluminum tubular part with rectangular section was carried out to investigate influence of axial feeding on thickness distribution and calibration pressure of the corner.Thickness distribution and relation between corner radius and internal pressure were analyzed.The influence of lubricant was discussed.Microstructure and hardness of different region were observed.It is shown that thickness reduction in the transition region between the corner and center region is the biggest.Friction condition has influence both on the thickness distribution and calibration pressure of the corner.As the increase of the axial feeding,the calibration pressure is decreased.There is only little change for the microstructure,but the hardness is increased by 23.3% for the transition region.

Three-dimensional detonation cellular structures in rectangular ducts using an improved CESE scheme

The three-dimensional premixed H2-O2 detonation propagation in rectangular ducts is simulated using an in-house parallel detonation code based on the second-order space-time conservation element and solution element（CE/SE） scheme.The simulation reproduces three typical cellular structures by setting appropriate cross-sectional size and initial perturbation in square tubes.As the cross-sectional size decreases,critical cellular structures transforming the rectangular or diagonal mode into the spinning mode are obtained and discussed in the perspective of phase variation as well as decreasing of triple point lines.Furthermore,multiple cellular structures are observed through examples with typical aspect ratios.Utilizing the visualization of detailed three-dimensional structures,their formation mechanism is further analyzed.

ANALYTICAL SOLUTION OF RESTRAINED TORSIONAL STRESSES AND DISPLACEMENT FOR RECTANGULAR- SECTION BOX BAR WITH HONTYCOMB CORE

Differential equation of restrained torsion for rectangular-section box bar with honeycomb core was established and solved by using the method of undetermined function.Non-dimension normal stress, shear stress acting in the faceplate and shear stress acting in the honeycomb-core and warping displacement were deduced. Numerical analysis shows the normal stress attenuates quickly along x-axis. Normal stress acting on the cross section at a distance of 20 h from the fixed end is only one per cent of that acting on the fixed end.

Rectangular Section Control Technology for Silicon Steel Rolling

Rectangular section control technology （RSCT） was introduced to achieve high-precision profile control during silicon steel rolling. The RSCT principle and method were designed, and the whole RSCT control strategy was developed. Specifically, RSCT included roll contour design, roiling technology optimization, and control strategy development, aiming at both hot strip mills （HSMs） and cold strip mills （CSMs）. Firstly, through the high-performance variable crown （HVC） work roll optimization design in the upper-stream stands and the limited shifting technology for schedule-free rolling in the downstream stands of HSMs, a hot strip with a stable crown and limited wedge, ：local spot, and single wave was obtained, which was suitable for cold rolling. Secondly, an approximately rectangular section was obtained by edge varying contact （EVC） work roll contour design, edge-drop setting control, and. closed loop control in the upper-stream, stands of CSMs. Moreover, complex-mode flatness control was realized by coordinating multiple shape-control methods in the downstream stands of CSMs. In addition, the RSCT approach was applied in several silicon-steel production plants, where an outsicanding performance and remarkable economic benefits were observed.

Research and application of approximate rectangular section control technology in hot strip mills

Profile requirements of silicon steel strip are extremely high and the thickness difference of cold-rolled products is usually less than 7μm,and the profile quality of hot-rolled strip is the key to ensure the thickness difference of cold-rolled products.In order to produce the silicon steel strip with high-precision shape,the concept of quasi-rectangular rolling during hot continuous rolling was put forward;the equipment configuration and technical method of approximate rectangular section control were studied.Through the roughing multi-target load distribution technology and the roll configuration technology for uniform wear of a 4-high rolling mill,the strip crown of transfer bar was reduced and the profile control stability was guaranteed.Configuring variable contact back-up roll technology on all stands in the finishing rolling process,equipped with symmetry variable taper work roll and long-stroke intelligent shifting strategy in the downstream stands,and using side rolling lubrication technology can make the roll wear more uniform,reduce the edge drop of silicon steel strip,improve the profile quality,and make the strip section of finishing exit"quasi-rectangular".In addition,induction furnace and side heater were also equipped to guarantee the temperature uniformity of the strip,so as to improve the stability of profile control.The whole control technology is based on the 1580-mm hot continuous rolling production line,designed,and developed according to the characteristics of equipment and products,and has been successfully applied,which can obtain the approximate rectangular strip section satisfying the flatness quality,and improve the strip section precision of silicon steel and other products.

Limit Analysis for Reinforced Concrete Rectangular Members Under Bending, Shear and Torsion

The ultimate strength of reinforced concrete(RC) rectangular members subjected to combined bending,shear and torsion is obtained from the limit analysis proposed in the present paper. Based on a warped failure surface determined by external loads, and a reasonable assumed stress distribution balancing external loads but not violating the yield condition, the bending-shear-torsion interaction can be derived from equilibrium conditions.According to the definition of lower-bound theorem in limit analysis, the calculated ultimate loads will be carried safely by the structure. The present method is a simple approach to obtain carrying capacities for RC elements under complex external loads. After comparing with the test results, a good agreement has been observed. The present method can be extended to explain the failure mechanism of RC members subjected to axial loads, and it is possible to develop a simple unified theory of RC members for engineering.

Development of component stiffness equations for thread-fixed one-side bolt connections to an enclosed rectangular hollow section column under tension

The derivation and validation of analytical equations for predicting the tensile initial stiffness of threadfixed one-side bolts(TOBs),connected to enclosed rectangular hollow section(RHS)columns,is presented in this paper.Two unknown stiffness components are considered:the TOBs connection and the enclosed RHS face.First,the trapezoidal thread of TOB,as an equivalent cantilevered beam subjected to uniformly distributed loads,is analyzed to determine the associated deformations.Based on the findings,the thread-shank serial-parallel stiffness model of TOB connection is proposed.For analysis of the tensile stiffness of the enclosed RHS face due to two bolt forces,the four sidewalls are treated as rotation constraints,thus reducing the problem to a two-dimensional plate analysis.According to the load superposition method,the deflection of the face plate is resolved into three components under various boundary and load conditions.Referring to the plate deflection theory of Timoshenko,the analytical solutions for the three deflections are derived in terms of the variables of bolt spacing,RHS thickness,height to width ratio,etc.Finally,the validity of the above stiffness equations is verified by a series of finite element(FE)models of T-stub substructures.The proposed component stiffness equations are an effective supplement to the component-based method.