Trajectory Generation for Stair Ascent Walking using Rayleigh Oscillator

This paper describes a trajectory generation technique for stair-ascent walking. The knee, hip and ankle joint trajectory during stair ascent are generated using mutually coupled, nonlinear oscillators. The parameters of the oscillators are tuned using the harmonic balance method, which converts the nonlinear differential equations to a set of algebraic equations. Fourier analysis of data generated by stair-ascent walking is performed to extract the amplitude and the phase of the dominant frequency components for each joint trajectory. The solution for the oscillator is assumed to be a sinusoidal wave and then by harmonic balance method the parameters of the oscillator are found. Each oscillator is responsible for generating a single frequency component with a specific phase and amplitude. The complete trajectory is obtained by summing the output of the oscillators that are relevant to one joint and the coupling maintains the phase relationship between the oscillators

Suitability of carbon nanotubes grown by chemical vapor deposition for electrical devices

Using carbon nanotubes (CNTs) produced by chemical vapor deposition, we have explored different strategies for the preparation of carbon nanotube devices suited for electrical and mechanical measurements. Though the target device is a single small diameter CNT, there is compelling evidence for bundling, both for CNTs grown over structured slits and on rigid supports. Whereas the bundling is substantial in the former case, individual single-wall CNTs (SWNTs) can be found in the latter. Our evidence stems from mechanical and electrical measurements on contacted tubes. Furthermore, we report on the fabrication of low-ohmic contacts to SWNTs. We compare Au, Ti and Pd contacts and find that Pd yields the best results.Comment: pdf including figures, see: http://www.unibas.ch/phys-meso/Research/Papers/2004/Suitability-CVD-tubes.pd

Little evidence for entropy and energy excess beyond r500r_{500} - An end to ICM preheating?

Non-gravitational feedback affects the nature of the intra-cluster medium (ICM). X-ray cooling of the ICM and in situ energy feedback from AGN's and SNe as well as {\it preheating} of the gas at epochs preceding the formation of clusters are proposed mechanisms for such feedback. While cooling and AGN feedbacks are dominant in cluster cores, the signatures of a preheated ICM are expected to be present even at large radii. To estimate the degree of preheating, with minimum confusion from AGN feedback/cooling, we study the excess entropy and non-gravitational energy profiles upto $r_{200}$ for a sample of 17 galaxy clusters using joint data sets of {\it Planck} SZ pressure and {\it ROSAT/PSPC} gas density profiles. The canonical value of preheating entropy floor of $\gtrsim 300$ keV cm$^2$, needed in order to match cluster scalings, is ruled out at $\approx 3\sigma$. We also show that the feedback energy of 1 keV/particle is ruled out at 5.2$\sigma$ beyond $r_{500}$. Our analysis takes both non-thermal pressure and clumping into account which can be important in outer regions. Our results based on the direct probe of the ICM in the outermost regions do not support any significant preheating.Comment: 6 pages, 4 figures, 1 table, Accepted in MNRAS Letter

Excess entropy and energy feedback from within cluster cores up to r200_{200}

We estimate the "non-gravitational" entropy-injection profiles, $\Delta K$, and the resultant energy feedback profiles, $\Delta E$, of the intracluster medium for 17 clusters using their Planck SZ and ROSAT X-Ray observations, spanning a large radial range from $0.2r_{500}$ up to $r_{200}$. The feedback profiles are estimated by comparing the observed entropy, at fixed gas mass shells, with theoretical entropy profiles predicted from non-radiative hydrodynamic simulations. We include non-thermal pressure and gas clumping in our analysis. The inclusion of non-thermal pressure and clumping results in changing the estimates for $r_{500}$ and $r_{200}$ by 10\%-20\%. When clumpiness is not considered it leads to an under-estimation of $\Delta K\approx300$ keV cm$^2$ at $r_{500}$ and $\Delta K\approx1100$ keV cm$^2$ at $r_{200}$. On the other hand, neglecting non-thermal pressure results in an over-estimation of $\Delta K\approx 100$ keV cm$^2$ at $r_{500}$ and under-estimation of $\Delta K\approx450$ keV cm$^2$ at $r_{200}$. For the estimated feedback energy, we find that ignoring clumping leads to an under-estimation of energy per particle $\Delta E\approx1$ keV at $r_{500}$ and $\Delta E\approx1.5$ keV at $r_{200}$. Similarly, neglect of the non-thermal pressure results in an over-estimation of $\Delta E\approx0.5$ keV at $r_{500}$ and under-estimation of $\Delta E\approx0.25$ keV at $r_{200}$. We find entropy floor of $\Delta K\approx300$ keV cm$^2$ is ruled out at $\approx3\sigma$ throughout the entire radial range and $\Delta E\approx1$ keV at more than 3$\sigma$ beyond $r_{500}$, strongly constraining ICM pre-heating scenarios. We also demonstrate robustness of results w.r.t sample selection, X-Ray analysis procedures, entropy modeling etc.Comment: 17 pages, 15 figures, 5 tables, Accepted in MNRA

Spatial variability of climate and past atmospheric circulation patterns from central West Antarctic glaciochemistry

Atmospheric circulation patterns and the spatial variability of atmospheric chemistry and moisture transport in central West Antarctica are investigated using new 40 year long (1954–1994 A.D.) glaciochemical and accumulation rate records developed from four firn cores from this region. The core sites lie on a 200 km traverse from 82° 22′ S, 119° 17′ W to 81° 22′ S, 107° 17′ W. The glaciochemical records represent the major ionic species present in Antarctic snow: Na+, K+, Mg2+, Ca2+, Cl−, NO3−, and SO42−. High spatial variability appears in comparisons of full record averages and poor intersite linear correlation results. Accumulation rates show 50–100% changes over distances of 50–100 km and sea‐salt concentrations drop by 50% between the middle two sites. One likely contributor to the high variability seen at this spatial scale is variability in synoptic‐ and finer‐scale meteorology. Empirical orthogonal function (EOF) analysis shows that 80% or more of the variance in site chemistry can be attributed to two types of air masses: winter season air (50–70% of site variance) with a strong marine signature (heavy loading of sea‐salt species) and summer season air (21% of the variance), marked by marine biogenic non‐sea‐salt SO4 plus NO3. This pattern of winter and summer regimes appears at other West Antarctic sites suggesting it may apply to the entire region. We show that a general picture of the patterns of variability in West Antarctica can best be drawn by using an analysis technique that fully exploits high resolution, multiparameter, multisite data sets

Wall-crossing, free fermions and crystal melting

We describe wall-crossing for local, toric Calabi-Yau manifolds without compact four-cycles, in terms of free fermions, vertex operators, and crystal melting. Firstly, to each such manifold we associate two states in the free fermion Hilbert space. The overlap of these states reproduces the BPS partition function corresponding to the non-commutative Donaldson-Thomas invariants, given by the modulus square of the topological string partition function. Secondly, we introduce the wall-crossing operators which represent crossing the walls of marginal stability associated to changes of the B-field through each two-cycle in the manifold. BPS partition functions in non-trivial chambers are given by the expectation values of these operators. Thirdly, we discuss crystal interpretation of such correlators for this whole class of manifolds. We describe evolution of these crystals upon a change of the moduli, and find crystal interpretation of the flop transition and the DT/PT transition. The crystals which we find generalize and unify various other Calabi-Yau crystal models which appeared in literature in recent years.Comment: 61 pages, 14 figures, published versio

AGN feedback with the Square Kilometer Array (SKA) and implications for cluster physics and cosmology

AGN feedback is regarded as an important non-gravitational process in galaxy clusters, providing useful constraints on large-scale structure formation. It modifies the structure and energetics of the intra-cluster medium (ICM) and hence its understanding is crucially needed in order to use clusters as high precision cosmological probes. In this context, particularly keeping in mind the upcoming high quality radio data expected from radio surveys like SKA with its higher sensitivity, high spatial and spectral resolutions, we review our current understanding of AGN feedback, its cosmological implications and the impact that SKA can have in revolutionizing our understanding of AGN feedback in large-scale structures. Recent developments regarding the AGN outbursts and its possible contribution to excess entropy in the hot atmospheres of groups and clusters, its correlation with the feedback energy in ICM, quenching of cooling flows and the possible connection between cool core clusters and radio mini-halos, are discussed. We describe current major issues regarding modeling of AGN feedback and its impact on the surrounding medium. With regard to the future of AGN feedback studies, we examine the possible breakthroughs that can be expected from SKA observations. In the context of cluster cosmology, for example, we point out the importance of SKA observations for cluster mass calibration by noting that most of $z>1$ clusters discovered by eROSITA X-ray mission can be expected to be followed up through a 1000 hour SKA-1 mid programme. Moreover, approximately $1000$ radio mini halos and $\sim 2500$ radio halos at $z<0.6$ can be potentially detected by SKA1 and SKA2 and used as tracers of galaxy clusters and determination of cluster selection function.Comment: 14 pages, 10 figures, Review article accepted in Journal of Astrophysics and Astronomy (JOAA

Oxidation = group theory

Dimensional reduction of theories involving (super-)gravity gives rise to sigma models on coset spaces of the form G/H, with G a non-compact group, and H its maximal compact subgroup. The reverse process, called oxidation, is the reconstruction of the possible higher dimensional theories, given the lower dimensional theory. In 3 dimensions, all degrees of freedom can be dualized to scalars. Given the group G for a 3 dimensional sigma model on the coset G/H, we demonstrate an efficient method for recovering the higher dimensional theories, essentially by decomposition into subgroups. The equations of motion, Bianchi identities, Kaluza-Klein modifications and Chern-Simons terms are easily extracted from the root lattice of the group G. We briefly discuss some aspects of oxidation from the E_{8(8)}/SO(16) coset, and demonstrate that our formalism reproduces the Chern-Simons term of 11-d supergravity, knows about the T-duality of IIA and IIB theory, and easily deals with self-dual tensors, like the 5-tensor of IIB supergravity.Comment: LaTeX, 8 pages, uses IOP style files; Talk given at the RTN workshop ``The quantum structure of spacetime and the geometric nature of fundamental interactions'', Leuven, September 200