Noise-amplitude dependence of the invariant density for noisy, fully chaotic one-dimensional maps

We present some analytic, non-perturbative results for the invariant density rho(x) for noisy one-dimensional maps at fully developed chaos. Under periodic boundary conditions, the Fourier expansion method is used to show precisely how noise makes rho(x) absolutely continuous and smoothens it out. Simple solvable models are used to illustrate the explicit dependence of rho(x) on the amplitude eta of the noise distribution, all the way from the case of zero noise (eta > 0) to the completely noise-dominated limit (eta=1).Comment: 15 pages, 5 Postscript figures (To appear in Phys. Rev. E

A Value-Based Approach for Sustainable Supplier-Customer Relationships: The Case of the Indian Steel Industry

The steel industry, which has endured years of mediocre performance due to a supply glut and consequent depressed world prices, has seen considerable resurgence during the last several months. The ever-widening demand-supply gap, and greatly increased input costs have resulted in prices firming up. The sharp increase in steel prices without any let-up is an issue that steel customers have found difficult to grapple with. Many customers believe that the steel industry is behaving opportunistically. The paper attempts to understand the dynamics of the Indian steel industry. Although the steel industry caters to both consumer (B2C) and business (B2B) markets, the focus of the paper is on the business markets, which accounts for 80% of the market. After presenting a picture of who the suppliers and customers of the steel industry are, the paper presents the various forces at play in the industry, a conceptual model to understand supplier-customer relationships in the industry, and traces the sources of animosity and hostility between the supplier and the customer firms. Forging meaningful value-based long-term relationships between supplier and customer firms as a way forward is explored. The paper presents possible remedies to the malady of distrust between customer and supplier firms. Collaborative working between competing suppliers and active pan-industry collaborative forums to bring better cooperation and trust between customer and supplier firms are essential first steps to bring normalcy back into the industry’s functioning.

Ladder operators for isospectral oscillators

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.Comment: 13 page

Cosmic acceleration in a model of scalar-tensor gravitation

In this paper we consider a model of scalar-tensor theory of gravitation in which the scalar field, $\phi$ determines the gravitational coupling G and has a Lagrangian of the form, $\mathcal{L}_{\phi} =-V(\phi)\sqrt{1 - \partial_{\mu}\phi\partial^{\mu}\phi}$. We study the cosmological consequence of this theory in the matter dominated era and show that this leads to a transition from an initial decelerated expansion to an accelerated expansion phase at the present epoch. Using observational constraints, we see that the effective equation of state today for the scalar field turns out to be $p_{\phi}=w_{\phi}{\rho}_{\phi}$, with $w_{\phi}=-0.88$ and that the transition to an accelerated phase happened at a redshift of about 0.3.Comment: 12 pages, 2 figures, matches published versio

Quantum revivals, geometric phases and circle map recurrences

Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct revival times can occur, with specified weights. A link is thus established between quantum revivals and recurrences in a coarse-grained discrete-time dynamical system.Comment: 9 page

Superfluid-Insulator transition of ultracold atoms in an optical lattice in the presence of a synthetic magnetic field

We study the Mott insulator-superfluid transition of ultracold bosonic atoms in a two-dimensional square optical lattice in the presence of a synthetic magnetic field with p/q (p and q being co-prime integers) flux quanta passing through each lattice plaquette. We show that on approach to the transition from the Mott side, the momentum distribution of the bosons exhibits q precursor peaks within the first magnetic Brillouin zone. We also provide an effective theory for the transition and show that it involves q interacting boson fields. We construct, from a mean-field analysis of this effective theory, the superfluid ground states near the transition and compute, for q=2,3, both the gapped and the gapless collective modes of these states. We suggest experiments to test our theory.Comment: 4 pages, 4 figs; v

Scalar Field Dark Energy Perturbations and their Scale Dependence

We estimate the amplitude of perturbation in dark energy at different length scales for a quintessence model with an exponential potential. It is shown that on length scales much smaller than hubble radius, perturbation in dark energy is negligible in comparison to that in in dark matter. However, on scales comparable to the hubble radius ($\lambda_{p}>1000\mathrm{Mpc}$) the perturbation in dark energy in general cannot be neglected. As compared to the $\Lambda$CDM model, large scale matter power spectrum is suppressed in a generic quintessence dark energy model. We show that on scales $\lambda_{p} < 1000\mathrm{Mpc}$, this suppression is primarily due to different background evolution compared to $\Lambda$CDM model. However, on much larger scales perturbation in dark energy can effect matter power spectrum significantly. Hence this analysis can act as a discriminator between $\Lambda$CDM model and other generic dark energy models with $w_{de} \neq -1$.Comment: 12 pages, 13 figures, added new section, accepted for publication in Phys. Rev.

Validation of Floating Node Method Using Three-Point Bend Doubler Under Quasi-Static Loading

The NASA Advanced Composite Project (ACP), an industry/government/university partnership, has embarked upon the task of developing technology that can aid in reducing the time line for structural certification of aircraft composite parts using a combination of technologies, one of which is high fidelity damage progression computational methods. Phase II of this project included a task for validating an approach based on the Floating Node Method combined with Directional Cohesive Elements (FNM-DCZE). This paper discusses predicted damage onset and growth in a three-point bend doubler specimen compared to experimental results. Sensitivity of the simulations to mesh refinement as well as key material properties and thermal effects are studied and reported. Overall, qualitative results suggest the main aspects of the damage progression have been captured, with the simulated damage morphology and sequence of events resembling closely what was observed experimentally. Quantitatively, the first load-peak is predicted. However, the re-loading observed in the experiments, after the first load peak, is not captured numerically, suggesting further investigation may be worth pursuing