A fractional map with hidden attractors: chaos and control

The European Physical Journal Special Topics - This paper studies the dynamics of a new fractional-order map with no fixed points. Through phase plots, bifurcation diagrams, largest Lyapunov...     

What if supersymmetry breaking unifies beyond the GUT scale?

We study models in which soft supersymmetry-breaking parameters of the MSSM become universal at some unification scale, M _in, above the GUT scale, M _GUT. We assume that the scalar masses and gaugino masses have common values, m ₀ and m _1/2 respectively, at M _in. We use the renormalisation-group equations of the minimal supersymmetric SU(5) GUT to evaluate their evolutions down to M _GUT, studying their dependences on the unknown parameters of the SU(5) superpotential. After displaying some generic examples of the evolutions of the soft supersymmetry-breaking parameters, we discuss the effects on physical sparticle masses in some specific examples. We note, for example, that near-degeneracy between the lightest neutralino and the lighter stau is progressively disfavoured as M _in increases. This has the consequence, as we show in (m _1/2,m ₀) planes for several different values of tan?β, that the stau-coannihilation region shrinks as M _in increases, and we delineate the regions of the (M _in,tan?β) plane where it is absent altogether. Moreover, as M _in increases, the focus-point region recedes to larger values of m ₀ for any fixed tan?β and m _1/2. We conclude that the regions of the (m _1/2,m ₀) plane that are commonly favoured in phenomenological analyses tend to disappear at large M _in.     

Controlling the optical bistability beyond the multi-photon resonance condition in a three-level closed-loop atomic system

We investigate the optical bistability behavior of a three-level closed-loop atomic system beyond the multi-photon resonance condition. Using the Floquet decomposition, we solve the time-dependent equations of motion, beyond the multi-photon resonance condition. By identifying the different scattering processes contributing to the medium response, it is shown that in general the optical bistability behavior of the system is not phase-dependent. The phase dependence is due to the scattering of the driving and coupling fields into the probe field at a frequency, which, in general, differs from the probe field frequency.     

Analysis of 2-D motion tracking in ultrasound with dual transducers

We study displacement and strain measurement error of dual transducers (two linear arrays, aligned orthogonally and coplanar). Displacements along the beam of each transducer are used to obtain measurements in two-dimensions. Simulations (5 MHz) and experiments (10 MHz) are compared to measurements with a single linear array, with and without angular compounding. Translation simulations demonstrate factors of 1.07 larger and 8.0 smaller biases in the axial and lateral directions respectively, for dual transducers compared to angular compounding. As the angle between dual transducers decreases from 90° to 40°, for 1% compression simulations, the lateral RMS error ranges from 2.1 to 3.9 μm compared to 9 μm with angular compounding. Simulation of dual transducer misalignment of 1 mm and 2° result in errors of less than 9 μm. Experiments demonstrate factors of 3.0 and 5.2 lower biases for dual transducers in the axial and lateral directions respectively compared to angular compounding.     

Convoy movement problem: a civilian perspective

We study the convoy movement problem in peacetime from a civilian perspective by seeking to minimize civilian traffic disruptions. We develop an exact hybrid algorithm that combines the k-shortest path algorithm along with finding a minimum weighted k-clique in a k-partite graph. Through this coupling scheme, we are able to exactly solve large instances of the convoy movement problem without relaxing many of its complicating constraints. An experimental study is performed based on pseudo-transportation networks to illustrate the computational viability of the method as well as policy implications.     

Electrocatalytic Reduction of Peroxy Disulfate on the Palladized Aluminum Electrode Modified by Prussian Blue: Application to the Analysis of Decolorizing Powders

The mechanism of catalytic reduction of peroxydisulfate on the palladized aluminum electrode modified by Prussian blue (PB/Pd‐Al) was studied. The charge transfer‐rate limiting step as well as overall reduction reaction of S₂O₈^2? is found to be a one‐electron and two‐electron abstraction respectively. The modified electrode is exploited for the hydrodynamic amperometry of peroxydisulfate. It is found that the calibration graph is linear in the S₂O₈^2?concentration range 5×10^?6–1.5×10^?3 mol L^?1. The detection limit of the method was 2.4×10^?6 mol L^?1 S₂O₈². The method was successfully used for the determination of S₂O₈^2? in decolorizing powders     

The best L 1-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes

For classes of periodic functions defined by constraints imposed on the L ₁-norm of the result of action of differential operators with constant coefficients and real spectrum on these functions, we determine the exact values of the best L ₁-approximations by generalized splines from the classes considered. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1443–1451, November, 1998.