Dynamic programming in cricket: optimizing batting order for a sticky wicket

In cricket, a rain-affected pitch can make batting more difficult than normal. Several other conditions such as poor light or an initially lively pitch, may also result in difficulties for the batsmen. In this note, we refer to all of them as ‘sticky wickets’. On sticky wickets, lower order batsmen are often sent into ‘hold the fort’ until conditions improve. In this paper, a stochastic dynamic programming model is used to examine the appropriateness of this policy. The model suggests that the tactic is often optimal when the sticky wicket persists until the end of the day's play, but not often when the sticky wicket is transitory. In some circumstances, it is worthwhile, on a normal wicket near the end of the day, to send in a lower order batsman to hold the fort (a night watchman): when the wicket is sticky, this tactic is even more worthwhile.     

ZnO:Mn as a member of II-VI:Mn family

ZnO:Mn thin films are grown by the metal organic chemical vapor deposition technique. Mn (x) varies in the 0<x<0.44 range. Vegard’s law has been verified for the lattice parameters. Electron paramagnetic resonance (EPR) measurements prove the substitutional incorporation of Mn²⁺ on zinc sites. The behavior of the EPR line width regarding temperature is discussed. All ZnO:Mn layers show antiferromagnetic interaction and a J₁/k_B=-15 K effective exchange constant. The optical band gap of ZnO:Mn increases with the manganese concentration. Raman spectroscopy reveals a Mn-related scattering band. PACS 71.55.Gs; 75.50.Pp; 61.10.Nz; 76.30.Fc; 75.30.Et; 78.40.-q     

A few points on omnidirectional band gaps in one-dimensional photonic crystals

The universal condition for the formation of omnidirectional band gaps (OBG) in photonic crystal (PC) was derived with consideration of permeability of the materials. And it was found that there are four kinds of PCs: one of them has no OBG, and one always possesses OBG. For the other two kinds of PCs, there are OBG for only TM or TE waves respectively. Moreover, in all PCs, the OBG can be broadened by decreasing the refractive index of the ambient medium or/and increasing the contrast between the wave impedances of the component materials of the PC. PACS 42.70.Qs; 71.20.Tx     

Preliminary design of high-power wave-guide/transmission system for multimegawatt CW requirements of 100 MeV proton LINAC

Development of a 100 MeV CW proton LINAC has been planned at CAT. This LINAC will be needing CW rf power in the frequency ranges of 350 MHz and 700 MHz for its RFQ and DTL/CCDTL/SFDTL structures respectively. The power to the accelerating structures will be produced by either 1 MW CW or 250 kW CW klystrons/inductive output tubes (HOM IOTs). The power needed by respective feed points in the structure is max. 250 kW which will be powered by splitting the power from 1 MW klystron/klystrode into four channels by using a wave-guide system. In case of using 250 kW tubes the power to the structures will be provided directly from each tube. Two types of wave-guide transmission system have been considered, viz, WR 2300 for 350 MHz rf needs and WR 1500 for 700 MHz rf needs. The typical wave-guide system has been designed using the 1 MW CW klystron followed by wave-guide filter, dual directional coupler, high-power circulator, three 3 dB magic TEE power dividers to split the main channel into four equal channels of 250 kW each. Each individual channel has dual directional couplers, flexible wave-guide sections and high power ceramic vacuum window. The circulator and each power divider is terminated into the isolated ports by high power CW loads. Out of the four channels three channels have phase shifters. Present paper describes the technological aspects and design specifications-considerations for these stringent requirements.     

Complex magnetism in ultra-thin films: atomic-scale spin structures and resolution by the spin-polarized scanning tunneling microscope

In this paper we present a density functional theory investigation of complex magnetic structures in ultra-thin films. The focus is on magnetically frustrated antiferromagnetic Cr and Mn monolayers deposited on a triangular lattice provided by a Ag (111) substrate. This involves non-collinear magnetic structures, which we treat by first-principles calculations on the basis of the vector spin-density formulation of the density functional theory. We find for Cr/Ag (111) a coplanar non-collinear periodic 120° Néel structure, for Mn/Ag (111) a row-wise antiferromagnetic structure, and for Fe/Ag (111) a ferromagnetic structure as magnetic ground states. The spin-polarized scanning tunneling microscope (SP–STM) operated in the constant-current mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent atoms. We discuss a recent application of this operation mode of the SP–STM on Mn/W (110), which led to the first observation of a two-dimensional antiferromagnet on a non-magnetic metal. The future potential of this approach is demonstrated by calculating SP–STM images for different magnetic structures of Cr/Ag (111). The results show that the predicted non-collinear magnetic ground state structure can clearly be discriminated from competing magnetic structures. A general discussion of the application of different operation modes of the SP–STM is presented on the basis of the model of Tersoff and Hamann. Received: 07 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002     

Vibrational Dynamics Studies by Nuclear Resonant Inelastic X-Ray Scattering

Nuclear resonant inelastic X-ray scattering of synchrotron radiation is being applied to ever widening areas ranging from geophysics to biophysics and materials science. Since its first demonstration in 1995 using the ⁵⁷Fe resonance, the technique has now been applied to materials containing ⁸³Kr, ¹⁵¹Eu, ¹¹⁹Sn, and ¹⁶¹Dy isotopes. The energy resolution has been reduced to under a millielectronvolt. This, in turn, has enabled new types of measurements like Debye velocity of sound, as well as the study of origins of non-Debye behavior in presence of other low-energy excitations. The effect of atomic disorder on phonon density of states has been studied in detail. The flux increase due to the improved X-ray sources, crystal monochromators, and time-resolved detectors has been exploited for reducing sample sizes to nano-gram levels, or using samples with dilute resonant nuclei like myoglobin, or even monolayers. Incorporation of micro-focusing optics to the existing experimental setup enables experiments under high pressure using diamond-anvil cells. In this article, we will review these developments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Magnetic anisotropy of textured CrO2 thin films investigated by X-ray magnetic circular dichroism

Highly a-axis-textured CrO₂ films have been deposited on Al₂O₃ (0001) substrates by chemical vapor deposition. CrO₂ has been found to have highly a-axis (010)-oriented columnar growth on a Cr₂O₃ (0001) initial layer. The six-fold surface symmetry of the Cr₂O₃ initial layer leads to three equivalent in-plane orientations of the a-axis-oriented CrO₂ unit cell. We report Cr L_2,3 X-ray magnetic circular dichroism data along the surface normal and at 60° off-normal sample orientation. For a 60° sample alignment, a strong increase of the projected orbital moment could be observed for unoccupied majority t_2g states using moment analysis. Therefore, the c axis is identified as the intrinsic magnetic easy axis of CrO₂. In addition, a small spin moment and a very strong magnetic dipole term T_z have been found. Received: 8 January 2002 / Accepted: 8 January 2002