OGY Control of Haken Like Systems on Different Poincare Sections

The Chua system, the Lorenz system, the Chen system and The L\"u system are chaotic systems that their state space equations is very similar to Haken system which is a nonlinear model of a optical slow-fast system. These Haken-Like Sys-tems have very similar properties. All have two slow but unstable eigenvalues and one fastest but stable eigenvalue. This lets that an approximation of slow manifold be equivalent with unstable manifold of the system. In other hand, control of discreet model of the system on a defined manifold (Poincare map) is main essence of some important control methods of chaotic systems for example OGY method. Here, by using different methods of defining slow manifold of the H-L systems the efficiency of the OGY control for stabilizing problem investigated.Comment: 4 page

What do you get for "Sixteen Tons"?

Wages

A theoretical study of microwave beam absorption by a rectenna

The rectenna's microwave power beam absorption limit was theoretically confirmed by two mathematical models descriptive of the microwave absorption process; first one model was based on the current sheet equivalency of a large planar array above a reflector and the second model, which was based on the properties of a waveguide with special imaging characteristics, quantified the electromagnetic modes (field configurations) in the immediate vicinity of a Rectenna element spacing which permit total power beam absorption by preventing unwanted modes from propagating (scattering) were derived using these models. Several factors causing unwanted scattering are discussed

Neutrino Signatures and the Neutrino-Driven Wind in Binary Neutron Star Mergers

We present VULCAN/2D multigroup flux-limited-diffusion radiation-hydrodynamics simulations of binary neutron star mergers, using the Shen equation of state, covering ≳ 100 ms, and starting from azimuthal-averaged two-dimensional slices obtained from three-dimensional smooth-particle-hydrodynamics simulations of Rosswog & Price for 1.4M☉ (baryonic) neutron stars with no initial spins, co-rotating spins, or counter-rotating spins. Snapshots are post-processed at 10 ms intervals with a multiangle neutrino-transport solver. We find polar-enhanced neutrino luminosities, dominated by ¯νe and “νμ” neutrinos at the peak, although νe emission may be stronger at late times. We obtain typical peak neutrino energies for νe, ¯νe, and “νμ” of ∼12, ∼16, and ∼22 MeV, respectively. The supermassive neutron star (SMNS) formed from the merger has a cooling timescale of ≾ 1 s. Charge-current neutrino reactions lead to the formation of a thermally driven bipolar wind with (M·) ∼ 10^−3 M☉ s^−1 and baryon-loading in the polar regions, preventing any production of a γ-ray burst prior to black hole formation. The large budget of rotational free energy suggests that magneto-rotational effects could produce a much-greater polar mass loss. We estimate that ≾ 10^−4 M☉ of material with an electron fraction in the range 0.1–0.2 becomes unbound during this SMNS phase as a result of neutrino heating. We present a new formalism to compute the νi ¯νi annihilation rate based on moments of the neutrino-specific intensity computed with our multiangle solver. Cumulative annihilation rates, which decay as ∼t^−1.8, decrease over our 100 ms window from a few ×1050 to ∼ 1049 erg s−1, equivalent to a few ×10^54 to ∼10^53 e−e+ pairs per second

Auctions as a vehicle to reduce airport delays and achieve value capture

Congestion at airports imposes large costs on airlines and their passengers. A key reason for congestion is that an airline schedules its flights without regard to the costs imposed on other airlines and their passengers. As a result, during some time intervals, airlines schedule more flights to and from an airport than that airport can accommodate and flights are delayed. This paper explores how a specific market-based proposal by the Federal Aviation Administration (FAA), which includes the use of auctions to determine the right to arrive or depart in a specific time interval at airports in the New York City area, might be used as part of a strategy to mitigate delays and congestion. By explaining the underlying economic theory and key arguments with minimal technical jargon, the paper allows those with little formal training in economics to understand the fundamental issues associated with the FAA's controversial proposal. Moreover, the basics of the proposed auction process, known as a combinatorial auction, and value capture are also explained.Airlines ; Airports

New Results for Non-preemptive Speed Scaling

We consider the speed scaling problem introduced in the seminal paper of Yao et al.. In this problem, a number of jobs, each with its own processing volume, release time, and deadline needs to be executed on a speed-scalable processor. The power consumption of this processor is $P(s) = s^\alpha$, where $s$ is the processing speed, and $\alpha > 1$ is a constant. The total energy consumption is power integrated over time, and the goal is to process all jobs while minimizing the energy consumption. The preemptive version of the problem, along with its many variants, has been extensively studied over the years. However, little is known about the non-preemptive version of the problem, except that it is strongly NP-hard and allows a constant factor approximation. Up until now, the (general) complexity of this problem is unknown. In the present paper, we study an important special case of the problem, where the job intervals form a laminar family, and present a quasipolynomial-time approximation scheme for it, thereby showing that (at least) this special case is not APX-hard, unless $NP \subseteq DTIME(2^{poly(\log n)})$. The second contribution of this work is a polynomial-time algorithm for the special case of equal-volume jobs, where previously only a $2^\alpha$ approximation was known. In addition, we show that two other special cases of this problem allow fully polynomial-time approximation schemes (FPTASs)

Nonlinear Dynamics of a Bose-Einstein Condensate in a Magnetic Waveguide

We have studied the internal and external dynamics of a Bose-Einstein condensate in an anharmonic magnetic waveguide. An oscillating condensate experiences a strong coupling between the center of mass motion and the internal collective modes. Due to the anharmonicity of the magnetic potential, not only the center of mass motion shows harmonic frequency generation, but also the internal dynamics exhibit nonlinear frequency mixing. We describe the data with a theoretical model to high accuracy. For strong excitations we test the experimental data for indications of a chaotic behavior.Comment: 4 pages, 4 figure

2δ2\delta-Kicked Quantum Rotors: Localization and `Critical' Statistics

The quantum dynamics of atoms subjected to pairs of closely-spaced $\delta$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances which approximate the `critical statistics' relation $\Sigma_2(L) \simeq \chi L \approx {1/2}(1-\nu) L$, where $\nu \approx 0.75$ is related to the fractal classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent is analyzed.Comment: 4 pages, 3 fig

The Proto-neutron Star Phase of the Collapsar Model and the Route to Long-soft Gamma-ray Bursts and Hypernovae

Recent stellar evolutionary calculations of low-metallicity massive fast-rotating main-sequence stars yield iron cores at collapse endowed with high angular momentum. It is thought that high angular momentum and black hole formation are critical ingredients of the collapsar model of long-soft gamma-ray bursts (GRBs). Here, we present 2D multi-group, flux-limited-diffusion MHD simulations of the collapse, bounce, and immediate post-bounce phases of a 35-Msun collapsar-candidate model of Woosley & Heger. We find that, provided the magneto-rotational instability (MRI) operates in the differentially-rotating surface layers of the millisecond-period neutron star, a magnetically-driven explosion ensues during the proto-neutron star phase, in the form of a baryon-loaded non-relativistic jet, and that a black hole, central to the collapsar model, does not form. Paradoxically, and although much uncertainty surrounds stellar mass loss, angular momentum transport, magnetic fields, and the MRI, current models of chemically homogeneous evolution at low metallicity yield massive stars with iron cores that may have too much angular momentum to avoid a magnetically-driven, hypernova-like, explosion in the immediate post-bounce phase. We surmise that fast rotation in the iron core may inhibit, rather than enable, collapsar formation, which requires a large angular momentum not in the core but above it. Variations in the angular momentum distribution of massive stars at core collapse might explain both the diversity of Type Ic supernovae/hypernovae and their possible association with a GRB. A corollary might be that, rather than the progenitor mass, the angular momentum distribution, through its effect on magnetic field amplification, distinguishes these outcomes.Comment: 5 pages, 1 table, 2 figures, accepted to ApJ