Holomorphic Mappings between Domains in C-2

An extension theorem for holomorphic mappings between two domains in C-2 is proved under purely local hypotheses.

Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

The factorization theorem for exclusive processes in perturbative QCD predicts the behavior of the pion electromagnetic form factor F(t) at asymptotic spacelike momenta t(= -Q(2)) < 0. We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from pi pi elastic scattering, and the modulus measured from threshold up to 3 GeV by the BABAR Collaboration. The method leads to almost model-independent upper and lower bounds on the spacelike form factor. Further inclusion of the value of the charge radius and the experimental value at -2.45 GeV2 measured at JLab considerably increases the strength of the bounds in the region Q(2) less than or similar to 10 GeV2, excluding the onset of the asymptotic perturbative QCD regime for Q(2) < 7 GeV2. We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region.

Conversion between electromagnetically induced transparency and absorption in a three-level lambda system

We show that it is possible to change from a subnatural electromagnetically induced transparency (EIT) feature to a subnatural electromagnetically induced absorption (EIA) feature in a (degenerate) three-level. system. The change is effected by turning on a second control beam counter-propagating with respect to the first beam. We observe this change in the D-2 line of Rb in a room temperature vapor cell. The observations are supported by density-matrix analysis of the complete sublevel structure including the effect of Doppler averaging, but can be understood qualitatively as arising due to the formation of N-type systems with the two control beams. Since many of the applications of EIT and EIA rely on the anomalous dispersion near the resonances, this introduces a new ability to control the sign of the dispersion. Copyright (C) EPLA, 2012

Dynamics of end-to-end loop formation: A flexible chain in the presence of hydrodynamic interaction

Based on the Wilemski-Fixman approach G. Wilemski, M. Fixman, J. Chem. Phys. 60 (1974) 866], we show that, for a flexible chain in theta solvent, hydrodynamic interaction treated with a pre-averaging approximation makes ring closing faster if the chain is not very short. We also show that the ring closing time for a long chain with hydrodynamic interaction in theta solvent scales with the chain length (N) as N-1.5, in agreement with the previous renormalization group calculation based prediction by Freidman and O'Shaughnessy B. Friedman, B. O'Shaughnessy, Phys. Rev. A 40 (1989) 5950]. (C) 2012 Elsevier B.V. All rights reserved.

The force distribution function of an oscillator model of polymer stretching at constant velocity

Recent simulations of the stretching of tethered biopolymers at a constant speed v (Ponmurugan and Vemparala, 2011 Phys. Rev. E 84 060101(R)) have suggested that for any time t, the distribution of the fluctuating forces f responsible for chain deformation is governed by a relation of the form P(+ f)/ P(- f) = expgamma f], gamma being a coefficient that is solely a function of v and the temperature T. This result, which is reminiscent of the fluctuation theorems applicable to stochastic trajectories involving thermodynamic variables, is derived in this paper from an analytical calculation based on a generalization of Mazonka and Jarzynski's classic model of dragged particle dynamics Mazonka and Jarzynski, 1999 arXiv:cond-\textbackslashmat/9912121v1]. However, the analytical calculations suggest that the result holds only if t >> 1 and the force fluctuations are driven by white rather than colored noise; they further suggest that the coefficient gamma in the purported theorem varies not as v(0.15)T-(0.7), as indicated by the simulations, but as vT(-1).

On the structure of analytic vectors for the Schrodinger representation

This article deals with the structure of analytic and entire vectors for the Schrodinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and their connection with Hermite expansions we obtain very precise representation theorems for analytic and entire vectors.

The Dπ form factors from analyticity and unitarity

We study the shape parameters of the Dπ scalar and vector form factors using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(α 2 s) terms in perturbative QCD. For the scalar form factor, a low energy theorem and phase information on the unitarity cut are implemented to further constrain the shape parameters. We finally determine points on the real axis and isolate regions in the complex energy plane where zeros of the form factors are excluded.

The Kπ form factors from analyticity and unitarity

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic K l3 decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of Kπ form factors up to an energy t in = 1GeV 2. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.

A unified approach to known and unknown cases of Berge's conjecture

Berge's elegant dipath partition conjecture from 1982 states that in a dipath partition P of the vertex set of a digraph minimizing , there exists a collection Ck of k disjoint independent sets, where each dipath P?P meets exactly min{|P|, k} of the independent sets in C. This conjecture extends Linial's conjecture, the GreeneKleitman Theorem and Dilworth's Theorem for all digraphs. The conjecture is known to be true for acyclic digraphs. For general digraphs, it is known for k=1 by the GallaiMilgram Theorem, for k?? (where ?is the number of vertices in the longest dipath in the graph), by the GallaiRoy Theorem, and when the optimal path partition P contains only dipaths P with |P|?k. Recently, it was proved (Eur J Combin (2007)) for k=2. There was no proof that covers all the known cases of Berge's conjecture. In this article, we give an algorithmic proof of a stronger version of the conjecture for acyclic digraphs, using network flows, which covers all the known cases, except the case k=2, and the new, unknown case, of k=?-1 for all digraphs. So far, there has been no proof that unified all these cases. This proof gives hope for finding a proof for all k.

Energy-dependent orbital modulation of X-rays and constraints on emission of the jet in Cyg X-3

We study the orbital modulation of X-rays from Cyg X-3, using data from Swift, INTEGRAL and RXTE. Using the wealth of data presently available and an improved averaging method, we obtain energy-dependent folded and averaged light curves with unprecedented accuracy. We find that above similar to 5?keV the modulation depth decreases with increasing energy, which is consistent with the modulation being caused by both boundfree absorption and Compton scattering in the stellar wind of the donor, with minima corresponding to the highest optical depth, which occurs around the superior conjunction. We find a decrease of the depth below similar to 3?keV, which appears to be due to re-emission of the absorbed continuum by the wind in soft X-ray lines. Based on the shape of the folded light curves, any X-ray contribution from the jet in Cyg X-3, which emits ?-rays detected at energies >0.1?GeV in the soft spectral states, is found to be minor up to similar to 100?keV. This implies the presence of a rather sharp low-energy break in the jet MeV-range spectrum. We also calculate phase-resolved RXTE X-ray spectra and show that the difference between the spectra corresponding to phases around superior and inferior conjunctions can indeed be accounted for by the combined effect of boundfree absorption in an ionized medium and Compton scattering.

3-MANIFOLD GROUPS, KÄHLER GROUPS AND COMPLEX SURFACES

Let G be a Kahler group admitting a short exact sequence 1 -> N -> G -> Q -> 1 where N is finitely generated. (i) Then Q cannot be non-nilpotent solvable. (ii) Suppose in addition that Q satisfies one of the following: (a) Q admits a discrete faithful non-elementary action on H-n for some n >= 2. (b) Q admits a discrete faithful non-elementary minimal action on a simplicial tree with more than two ends. (c) Q admits a (strong-stable) cut R such that the intersection of all conjugates of R is trivial. Then G is virtually a surface group. It follows that if Q is infinite, not virtually cyclic, and is the fundamental group of some closed 3-manifold, then Q contains as a finite index subgroup either a finite index subgroup of the three-dimensional Heisenberg group or the fundamental group of the Cartesian product of a closed oriented surface of positive genus and the circle. As a corollary, we obtain a new proof of a theorem of Dimca and Suciu in Which 3-manifold groups are Kahler groups? J. Eur. Math. Soc. 11 (2009) 521-528] by taking N to be the trivial group. If instead, G is the fundamental group of a compact complex surface, and N is finitely presented, then we show that Q must contain the fundamental group of a Seifert-fibered 3-manifold as a finite index subgroup, and G contains as a finite index subgroup the fundamental group of an elliptic fibration. We also give an example showing that the relation of quasi-isometry does not preserve Kahler groups. This gives a negative answer to a question of Gromov which asks whether Kahler groups can be characterized by their asymptotic geometry.

A model for growth and engulfment of gas microporosity during aluminum alloy solidification process

A new coupled approach is presented for modeling the hydrogen bubble evolution and engulfment during an aluminum alloy solidification process in a micro-scale domain. An explicit enthalpy scheme is used to model the solidification process which is coupled with a level-set method for tracking the hydrogen bubble evolution. The volume averaging techniques are used to model mass, momentum, energy and species conservation equations in the chosen micro-scale domain. The interaction between the solid, liquid and gas interfaces in the system have been studied. Using an order-of-magnitude study on growth rates of bubble and solid interfaces, a criterion is developed to predict bubble elongation which can occur during the engulfment phase. Using this model, we provide further evidence in support of a conceptual thought experiment reported in literature, with regard to estimation of final pore shape as a function of typical casting cooling rates. The results from the proposed model are qualitatively compared with in situ experimental observations reported in literature. The ability of the model to predict growth and movement of a hydrogen bubble and its subsequent engulfment by a solidifying front has been demonstrated for varying average cooling rates encountered in typical sand, permanent mold, and various casting processes. (C) 2012 Elsevier B.V. All rights reserved.

Heat fluctuations and coherences in a quantum heat engine

Quantum coherence can affect the thermodynamics of small quantum systems. Coherences have been shown to affect the power generated by a quantum heat engine (QHE) which is coupled to two thermal photon reservoirs and to an additional cavity mode. We show that the fluctuations of the heat exchanged between the QHE and the reservoirs strongly depend on quantum coherence, especially when the engine operates as a refrigerator, i.e., heat current flows from the cold bath to the hot bath. Intriguingly, we find that the ratio of positive and negative (with respect to the thermodynamic force) fluctuations in the heat current satisfies a universal coherence-independent fluctuation theorem.

c-theorems in arbitrary dimensions

The dilaton action in 3 + 1 dimensions plays a crucial role in the proof of the a-theorem. This action arises using Wess-Zumino consistency conditions and crucially relies on the existence of the trace anomaly. Since there are no anomalies in odd dimensions, it is interesting to ask how such an action could arise otherwise. Motivated by this we use the AdS/CFT correspondence to examine both even and odd dimensional conformal field theories. We find that in even dimensions, by promoting the cutoff to a field, one can get an action for this field which coincides with the Wess-Zumino action in flat space. In three dimensions, we observe that by finding an exact Hamilton-Jacobi counterterm, one can find a non-polynomial action which is invariant under global Weyl rescalings. We comment on how this finding is tied up with the F-theorem conjectures.

Model independent bounds on the modulus of the pion form factor on the unitarity cut below the omega pi threshold

We calculate upper and lower bounds on the modulus of the pion electromagnetic form factor on the unitarity cut below the omega pi inelastic threshold, using as input the phase in the elastic region known via the Fermi-Watson theorem from the pi pi P-wave phase shift, and a suitably weighted integral of the modulus squared above the inelastic threshold. The normalization at t = 0, the pion charge radius and experimental values at spacelike momenta are used as additional input information. The bounds are model independent, in the sense that they do not rely on specific parametrizations and do not require assumptions on the phase of the form factor above the inelastic threshold. The results provide nontrivial consistency checks on the recent experimental data on the modulus available below the omega pi threshold from e(+)e(-) annihilation and tau-decay experiments. In particular, at low energies the calculated bounds offer a more precise description of the modulus than the experimental data.