Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

Dephasing via stochastic absorption: A case study in Aharonov-Bohm oscillations

The Aharonov-Bohm ring has been the mainstay of mesoscopic physics research since its inception. In this paper we have dwelt on the problem of dephasing of AB oscillations using a phenomenological model based on stochastic absorption. To calculate the conductance in the presence of inelastic scattering we have used the method due to Brouwer and Beenakker. We have shown that conductance is symmetric under flux reversal and visibility of AB oscillations decay to zero as a function of the incoherence parameter thus signalling dephasing in the system. Some comments are made on the relative merits of stochastic absorption with respect to optical potential model, which have been used to mimic dephasing.Comment: 4 pages, 4 figures Minor corrections made and journal reference adde

Impact of co-application of biomethanated spent wash with bio-char on soil micronutrients and crop growth

Biomethanated spentwash (BMS) and biochar are novel soil conditioners considered as value addition to the bi-products from agro-industry. The high nutrient content and organic matter of BMS and high retention of nutrient and organic carbon on biochar has potential of benefits for co-application. We studied the effect of BMS, biochar and their co-application on soybean, which is a common rotation crop in Sugarcane. A field experiment was conducted in randomized block design in vertisols. BMS was produced at Ugar sugar works ltd. and biochar from agriculture waste. Treatments comprised of BMS application@ 60, 66 and 72 m3 ha-1, as sole amendment and in combination with biochar @ 2.5 t ha-1. Post-harvest soil analysis demonstrated a non-significant effect of treatments on soil pH, electrical conductivity and micro-nutrients. However, available Zn, Fe and Mn were numerically increased for all BMS treatments. BMS and biochar or their co-application had no significant effect on germination and plant height of soybean. However the number of soybean pods and grain yield was significantly improved. Grain yield of soybean in BMS 60 m3 ha-1 plus biochar co-applied treatment was significantly higher than all other treatments. Grain yield of BMS 66 m3 ha-1 and other BMS plus BC treatments were at par with each other and significantly higher than sole biochar 2.5 t ha-1, RDF and control

3D evolution of a filament disappearance event observed by STEREO

A filament disappearance event was observed on 22 May 2008 during our recent campaign JOP 178. The filament, situated in the southern hemisphere, showed sinistral chirality consistent with the hemispheric rule. The event was well observed by several observatories in particular by THEMIS. One day before the disappearance, H$\alpha$ observations showed up and down flows in adjacent locations along the filament, which suggest plasma motions along twisted flux rope. THEMIS and GONG observations show shearing photospheric motions leading to magnetic flux canceling around barbs. STEREO A, B spacecraft with separation angle 52.4 degrees, showed quite different views of this untwisting flux rope in He II 304 \AA\ images. Here, we reconstruct the 3D geometry of the filament during its eruption phase using STEREO EUV He II 304 \AA\ images and find that the filament was highly inclined to the solar normal. The He II 304 \AA\ movies show individual threads, which oscillate and rise to an altitude of about 120 Mm with apparent velocities of about 100 km s$^{-1}$, during the rapid evolution phase. Finally, as the flux rope expands into the corona, the filament disappears by becoming optically thin to undetectable levels. No CME was detected by STEREO, only a faint CME was recorded by LASCO at the beginning of the disappearance phase at 02:00 UT, which could be due to partial filament eruption. Further, STEREO Fe XII 195 \AA\ images showed bright loops beneath the filament prior to the disappearance phase, suggesting magnetic reconnection below the flux rope

A Case of Problematic Diffusion

Sex determination techniques have diffused rapidly in India, and are being used to detect female fetuses and subsequently to abort them. This technology has spread rapidly because it imparts knowledge that is of great value within the Indian context, and because it fits in neatly with the modernization dynamic within India, which itself has enmeshed with traditional patriarchal institutions to oppress Indian women. More research needs to be done on ways to stem the adoption of problematic innovations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68396/2/10.1177_107554709401500301.pd

Search for lepton-flavor-violating τ→ℓV0\tau\to\ell V^0 decays at Belle

We have searched for neutrinoless $\tau$ lepton decays into $\ell$ and $V^0$, where $\ell$ stands for an electron or muon, and $V^0$ for a vector meson ($\phi$, $\omega$, $K^{*0}$, $\bar{K}^{*0}$ or $\rho^0$), using 543 fb$^{-1}$ of data collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. No excess of signal events over the expected background has been observed, and we set upper limits on the branching fractions in the range $(5.9-18) \times 10^{-8}$ at the 90% confidence level. These upper limits include the first results for the $\ell \omega$ mode as well as new limits that are significantly more restrictive than our previous results for the $\ell \phi$, $\ell K^{*0}$, $\ell \bar{K}^{*0}$ and $\ell \rho^0$ modes.Comment: 7 pages, 16 figure

Measurement of the ratio B(D0->pi+pi-pi0)/B(D0->K-pi+pi0) and the time-integrated CP asymmetry in D0->pi+pi-pi0

We report a high-statistics measurement of the relative branching fraction B(D0->pi+pi-pi0)/B(D0->K-pi+pi0) using a 532 fb^{-1} data sample collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. The measured value of the relative branching fraction is B(D0->pi+pi-pi0)/B(D0->K-pi+pi0) = (10.12 +/- 0.04(stat) +/- 0.18(syst))x10^{-2} which has an accuracy comparable to the world average. We also present a measurement of the time-integrated CP asymmetry in D0->pi+pi-pi0 decay. The result, A_{CP} = (0.43 +/- 1.30)%, shows no significant CP violation.Comment: 15 pages, 11 figures, submitted to Physics Letters

Search for B -> h(*) nu nubar Decays at Belle

We present a search for the rare decays B -> h(*) nu nubar, where h(*) stands for a light meson. A data sample of 535 million BBbar pairs collected with the Belle detector at the KEKB e+e- collider is used. Signal candidates are required to have an accompanying B meson fully reconstructed in a hadronic mode and signal-side particles consistent with a single h(*) meson. No significant signal is observed and we set upper limits on the branching fractions at 90% confidence level. The limits on B0 -> K*0 nu nubar and B+ -> K+ nu nubar decays are more stringent than the previous constraints, while the first searches for B0 -> K0 nu nubar, pi0 nu nubar, rho0 nu nubar, phi nu nubar and B+ -> K*+ nu nubar, rho+ nu nubar are reported.Comment: 6 pages, 2 figures, submit to PR