Homoclinic Splitting without Trees

We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. When the coupling takes place through an even trigonometric polynomial in the angle variables, we extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a large neighbourhood of the real line representing time. Subsequently, we devise an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing gravity, by a shift-of-countour argument. Hence, we infer a similar upper bound for the splitting itself. In particular, the derivation of the result does not call for a tree expansion with explicit cancellation mechanisms.

Influence of site, storage and steaming on Eucalyptus nitens log-end splitting

Key message Log-end splitting is one of the single most important defects in veneer logs. We show that log-end splitting in the temperate plantation species Eucalyptus nitens varies across sites and within-tree log position and increases with time in storage. Context Log-end splitting is one of the single most important defects in veneer logs because it can substantially reduce the recovery of veneer sheets. Eucalyptus nitens can develop log-end splits, but factors affecting log-end splitting in this species are not well understood. Aims The present study aims to describe the effect of log storage and steaming on the development of log-end splitting in logs from different plantations and log positions within the tree. Methods The study was conducted on upper and lower logs from each of 41 trees from three 20–22-year-old Tasmanian E. nitens plantations. Log-end splitting was assessed immediately after felling, after transport and storage in a log-yard, and just before peeling. A pre-peeling steam treatment was applied to half the logs. Results Site had a significant effect on splitting, and upper logs split more than lower logs with storage. Splitting increased with tree diameter breast height (DBH), but this relationship varied with site. The most rapidly growing site had more splitting even after accounting for DBH. No significant effect of steaming was detected. Conclusion Log-end splitting varied across sites and within-tree log position and increased with time in storage.

Transition from radiatively inefficient to cooling dominated phase in two temperature accretion disks around black holes

We investigate the transition of a radiatively inefficient phase of a viscous two temperature accreting flow to a cooling dominated phase and vice versa around black holes. Based on a global sub-Keplerian accretion disk model in steady state, including explicit cooling processes self-consistently, we show that general advective accretion flow passes through various phases during its infall towards a black hole. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. Hence the flow governs a much lower electron temperature similar to 10(8) - 10(9.5) K compared to the hot protons of temperature similar to 10(10.2) - 10(11.8) K in the range of the accretion rate in Eddington units 0.01 less than or simiar to (M) over dot less than or similar to 100. Therefore, the solutions may potentially explain the hard X-rays and the gamma-rays emitted from AGNs and X-ray binaries. We finally compare the solutions for two different regimes of viscosity and conclude that a weakly viscous flow is expected to be cooling dominated compared to its highly viscous counterpart which is radiatively inefficient. The flow is successfully able to reproduce the observed minosities of the under-fed AGNs and quasars (e.g. Sgr A*), ultra-luminous X-ray sources (e.g. SS433), as well as the highly luminous AGNs and ultra-luminous quasars (e.g. PKS 0743-67) at different combinations of the mass accretion rate and ratio of specific heats.

Ce0.67Cr0.33O2.11: A New Low-Temperature O-2 Evolution Material and H-2 Generation Catalyst by Thermochemical Splitting of Water

Ce0.67Cr0.33O2.11 was synthesized by hydrothermal method using diethylenetriamine as complexing agent (Chem. Mater. 2008, 20, 7268). Ce0.67Cr0.33O2.11 being the only compound likes UO2+delta to have excess oxygen, it releases a large proportion of its lattice oxygen (0.167 M [O]/mole of compound) at relatively low temperature (465 degrees C) directly and it has been utilized for generation of H-2 by thermo-splitting of water. An almost stoichiometric amount of H-2 (0.152 M/Mole of compound) is generated at much lower temperature (65 degrees C). There is an almost comparable amount of oxygen release and hydrogen generation over this material at very low temperature comparedto other CeO2-MOx (Mn, Fe, Cu, and Ni) mixed-oxide solid solutions (O-2 evolution >= 1300 degrees C and H-2 generation at 1000 degrees C). The reversible nature of oxygen release and intake of this material is attributed to its fluorite Structure and coupling between the Ce4+/Ce3+ and Cr4+/6+/Cr3+ redox couples. Compound shows reversible oxygen release and intake by H2O absorption and subsequent hydrogen release to gain parent structure and hence this material can be utilized for generation of H-2 at very low temperature by thermo-chemical splitting of water.

Studies of electronic structure by x-ray Raman and emission spectroscopy: applications to MgB2 superconductors and high pressure physics

X-ray Raman scattering and x-ray emission spectroscopies were used to study the electronic properties and phase transitions in several condensed matter systems. The experimental work, carried out at the European Synchrotron Radiation Facility, was complemented by theoretical calculations of the x-ray spectra and of the electronic structure. The electronic structure of MgB2 at the Fermi level is dominated by the boron σ and π bands. The high density of states provided by these bands is the key feature of the electronic structure contributing to the high critical temperature of superconductivity in MgB2. The electronic structure of MgB2 can be modified by atomic substitutions, which introduce extra electrons or holes into the bands. X ray Raman scattering was used to probe the interesting σ and π band hole states in pure and aluminum substituted MgB2. A method for determining the final state density of electron states from experimental x-ray Raman scattering spectra was examined and applied to the experimental data on both pure MgB2 and on Mg(0.83)Al(0.17)B2. The extracted final state density of electron states for the pure and aluminum substituted samples revealed clear substitution induced changes in the σ and π bands. The experimental work was supported by theoretical calculations of the electronic structure and x-ray Raman spectra. X-ray emission at the metal Kβ line was applied to the studies of pressure and temperature induced spin state transitions in transition metal oxides. The experimental studies were complemented by cluster multiplet calculations of the electronic structure and emission spectra. In LaCoO3 evidence for the appearance of an intermediate spin state was found and the presence of a pressure induced spin transition was confirmed. Pressure induced changes in the electronic structure of transition metal monoxides were studied experimentally and were analyzed using the cluster multiplet approach. The effects of hybridization, bandwidth and crystal field splitting in stabilizing the high pressure spin state were discussed. Emission spectroscopy at the Kβ line was also applied to FeCO3 and a pressure induced iron spin state transition was discovered.

Splitting Algorithms for Fast Relay Selection: Generalizations, Analysis, and a Unified View

Relay selection for cooperative communications promises significant performance improvements, and is, therefore, attracting considerable attention. While several criteria have been proposed for selecting one or more relays, distributed mechanisms that perform the selection have received relatively less attention. In this paper, we develop a novel, yet simple, asymptotic analysis of a splitting-based multiple access selection algorithm to find the single best relay. The analysis leads to simpler and alternate expressions for the average number of slots required to find the best user. By introducing a new contention load' parameter, the analysis shows that the parameter settings used in the existing literature can be improved upon. New and simple bounds are also derived. Furthermore, we propose a new algorithm that addresses the general problem of selecting the best Q >= 1 relays, and analyze and optimize it. Even for a large number of relays, the scalable algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. We also propose a new and simple scheme for the practically relevant case of discrete metrics. Altogether, our results develop a unifying perspective about the general problem of distributed selection in cooperative systems and several other multi-node systems.

Comments on "Full-sphere simulations of circulation-dominated solar dynamo: Exploring the parity issue" - Reply

We respond to Dikpati et al.'s criticism of our recent solar dynamo model. A different treatment of the magnetic buoyancy is the most probable reason for their different results.

K -shell diagram and hypersatellite spectra of 4d transition elements

The K-shell diagram (K alpha(1,2) and K beta(1,3)) and hypersatellite (HS) (K-h alpha(1,2)) spectra of Y, Zr, Mo, and Pd have been measured with high energy-resolution using photoexcitation by 90 keV synchrotron radiation. Comparison of the measured and ab initio calculated HS spectra demonstrates the importance of quantum electrodynamical (QED) effects for the HS spectra. Phenomenological fits of the measured spectra by Voigt functions yield accurate values for the shift of the HS from the diagram lines, the splitting of the HS lines, and their intensity ratio. Good agreement with theory was found for all quantities except for the intensity ratio, which is dominated by the intermediacy of the coupling of the angular momenta. The observed deviations imply that our current understanding of the variation of the coupling scheme from LS to jj across the periodic table may require some revision.

Relaxation dominated by inertia: Solvation dynamics of a small ion in a dipolar solvent

It is shown from an analytical theory that the solvation dynamics of a small ion can be controlled largely by the inertial response of the dipolar solvent when the liquid is in the underdamped limit. It is also shown that this inertial response arises primarily from the long wavelength (with wavevector k≃0) processes which have a collective excitation-like behaviour. The long time decay is dominated by the processes occurring at molecular lengthscales. The theoretical results are in good agreement with recent computer simulation results.

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

Novel geodesic splitting on paraboloid of revolution with applications to ray-theoretic analysis

Computer simulations have shown a novel geodesic splitting on the paraboloid of revolution leading to a multiplicity of surface ray paths. Such a phenomenon would have wide ramifications for wave propagation problems in general, besides applications in target-detection problems and the computational requirements of ray-theoretic formulations such as the UTD, in computing the antenna characteristics in the high-frequency domain.

KFVS (Kinetic Flux Vector Splitting) on moving grids for unsteady aerodynamics

Accurate numerical solutions to the problems in fluid-structure (aeroelasticity) interaction are becoming increasingly important in recent years. The methods based on FCD (Fixed Computational Domain) and ALE (Alternate Lagrangian Eulerian) to solve such problems suffer from numerical instability and loss of accuracy. They are not general and can not be extended to the flowsolvers on unstructured meshes. Also, global upwind schemes can not be used in ALE formulation thus leads to the development of flow solvers on moving grids. The KFVS method has been shown to be easily amenable on moving grids required in unsteady aerodynamics. The ability of KFMG (Kinetic Flux vector splitting on Moving Grid) Euler solver in capturing shocks, expansion waves with small and very large pressure ratios and contact discontinuities has been demonstrated.

Providing quality of service via opportunistic splitting using stochastic approximation

We consider the problem of wireless channel allocation to multiple users. A slot is given to a user with a highest metric (e.g., channel gain) in that slot. The scheduler may not know the channel states of all the users at the beginning of each slot. In this scenario opportunistic splitting is an attractive solution. However this algorithm requires that the metrics of different users form independent, identically distributed (iid) sequences with same distribution and that their distribution and number be known to the scheduler. This limits the usefulness of opportunistic splitting. In this paper we develop a parametric version of this algorithm. The optimal parameters of the algorithm are learnt online through a stochastic approximation scheme. Our algorithm does not require the metrics of different users to have the same distribution. The statistics of these metrics and the number of users can be unknown and also vary with time. Each metric sequence can be Markov. We prove the convergence of the algorithm and show its utility by scheduling the channel to maximize its throughput while satisfying some fairness and/or quality of service constraints.

Opportunistic splitting for scheduling via stochastic approximation

We consider the problem of scheduling a wireless channel among multiple users. A slot is given to a user with a highest metric (e.g., channel gain) in that slot. The scheduler may not know the channel states of all the users at the beginning of each slot. In this scenario opportunistic splitting is an attractive solution. However this algorithm requires that the metrics of different users form independent, identically distributed (iid) sequences with same distribution and that their distribution and number be known to the scheduler. This limits the usefulness of opportunistic splitting. In this paper we develop a parametric version of this algorithm. The optimal parameters of the algorithm are learnt online through a stochastic approximation scheme. Our algorithm does not require the metrics of different users to have the same distribution. The statistics of these metrics and the number of users can be unknown and also vary with time. We prove the convergence of the algorithm and show its utility by scheduling the channel to maximize its throughput while satisfying some fairness and/or quality of service constraints.

Modified kinetic flux vector splitting (m-KFVS) method for compressible flows

To resolve many flow features accurately, like accurate capture of suction peak in subsonic flows and crisp shocks in flows with discontinuities, to minimise the loss in stagnation pressure in isentropic flows or even flow separation in viscous flows require an accurate and low dissipative numerical scheme. The first order kinetic flux vector splitting (KFVS) method has been found to be very robust but suffers from the problem of having much more numerical diffusion than required, resulting in inaccurate computation of the above flow features. However, numerical dissipation can be reduced by refining the grid or by using higher order kinetic schemes. In flows with strong shock waves, the higher order schemes require limiters, which reduce the local order of accuracy to first order, resulting in degradation of flow features in many cases. Further, these schemes require more points in the stencil and hence consume more computational time and memory. In this paper, we present a low dissipative modified KFVS (m-KFVS) method which leads to improved splitting of inviscid fluxes. The m-KFVS method captures the above flow features more accurately compared to first order KFVS and the results are comparable to second order accurate KFVS method, by still using the first order stencil. (C) 2011 Elsevier Ltd. All rights reserved.