Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.     

The role of dust particles with large gyroradii in the `2/3'fall-down process

The authors consider the Alfven-Arrhenius fall-down process and propose a mechanism whereby the Rosseland electric field (the field needed to maintain quasineutrality) may be responsible for the capture and confinement of large-gyroradius dust particles within a plasma shell stratified along the direction of the magnetic-field lines. For these particles, the effect of the magnetic force is rather weak, and they move with a constant z component of the angular momentum in a one-dimensional equivalent potential (gravitational plus centrifugal). This has a maximum at the equator and a minimum at the `2/3' points, i.e. the points where the field-aligned components of the gravitational and centrifugal forces balance. It is shown that under suitable initial conditions these are points of maximum dust density and minimum plasma density. The plasma-planetisemal transition is therefore expected to take place at the `2/3' points in accordance with the Alfven-Arrhenius mechanism. It is also shown that the fraction of infalling dust particles that can accrete onto the equatorial plane by the Alfven-Arrhenius and Rosseland mechanisms is rather small (~(L/ R_e)≪1), L being the thickness of the plasma shell, and R_e, a characteristic length scale of the field line     

Toughening of Poly(ethylene terephtalate) (PET) Bottle Wastes by Modified Styrene-Butadiene Rubber (SBR) Elastomer

Summary: Modified SBR was blended with dried PET bottle wastes in an internal mixer. During the process mechanical and morphological properties were studied. When PET bottle wastes were blended with unmodified SBR, the final blend had a rough morphology and low impact strength. In contrary, blending of PET with modified SBR lead to smooth and fine morphology. Utilizing grafted SBR in PET blends creates an enormous difference in particle size and morphology, which is a result of powerful interactions and effective chemical bonding between the components of the blend. The final product had high impact strength in comparison with PET and unmodified SBR blend. These results are mainly related to formation in situ of PET/SBR graft copolymer in interface, which is produced by chemical reaction among active maleic anhydride groups and active PET groups.     

Parameter dependence of vortex interactions on a two-dimensional plunging plate

The structure and dynamics of the flow field created by a plunging flat-plate airfoil are investigated at a chord Reynolds number of 10,000 while varying plunge amplitude and Strouhal number. Digital particle image velocimetry measurements are used to characterize the shedding patterns and the interactions between the leading- and trailing-edge vortex structures (LEV and TEV), resulting in the development of a wake classification system based on the nature and timing of interactions between the leading- and trailing-edge vortices. The streamwise advancement of the LEV during a plunge cycle and its resulting interaction with the TEV is primarily dependent on reduced frequency; however, for Strouhal numbers above approximately 0.4, significant changes are observed in the formation of vortices shed from the leading and trailing edges, as well as the circulation of the leading-edge vortex. The functional form of the relationship between leading-edge vortex circulation and Strouhal number suggests that the Strouhal number dependence is more specifically a manifestation of the effective angle of attack. Comparison with low-Reynolds-number studies of plunging airfoil aerodynamics reveals a high degree of consistency and suggests applicability of the classification system beyond the range examined in the present work.     

Approximating Probability Distributions Using Small Sample Spaces

We formulate the notion of a "good approximation" to a probability distribution over a finite abelian group ?. The quality of the approximating distribution is characterized by a parameter ɛ which is a bound on the difference between corresponding Fourier coefficients of the two distributions. It is also required that the sample space of the approximating distribution be of size polynomial in and 1/ɛ. Such approximations are useful in reducing or eliminating the use of randomness in certain randomized algorithms. We demonstrate the existence of such good approximations to arbitrary distributions. In the case of n random variables distributed uniformly and independently over the range , we provide an efficient construction of a good approximation. The approximation constructed has the property that any linear combination of the random variables (modulo d) has essentially the same behavior under the approximating distribution as it does under the uniform distribution over . Our analysis is based on Weil's character sum estimates. We apply this result to the construction of a non-binary linear code where the alphabet symbols appear almost uniformly in each non-zero code-word. Received: September 22, 1990/Revised: First revision November 11, 1990; last revision November 10, 1997     

Fourier synthesis of 1.8-THz optical-pulse trains by phase locking of three independent semiconductor lasers

Fourier synthesis of ultrafast optical-pulse trains was demonstrated based on optical phase locking of three independent continuous-wave semiconductor lasers. Pulse repetition frequencies as high as 1.81 THz were limited by the gain bandwidth of an erbium-doped fiber amplifier. The waveforms of the pulse trains were maintained over a long period by use of an auxiliary optical phase-locked loop. The repetition frequency could be tuned continuously over a range of 100 MHz.     

Enhanced efficiency and pulse-adjacency effects in high-repetition-rate laser machining

. We observed enhanced efficiency in the machining of copper using a high-repetition-rate (10 kHz) Q-switched Nd:YLF laser. A significant increase of machining efficiency (material removed per unit time) was observed when the speed of lateral translation of the thin copper sheet across the beam focus was decreased. We attribute this increased efficiency to effects caused by pulse adjacency (i.e. partial overlapping) of several pulses at a given point on the target surface. Several mechanisms which might be responsible for the effect are discussed. Similar results were observed in experiments on laser trepanning. The observed increases in ablation rates might lead to improvements in some industrial processes, e.g. laser drilling, cutting and marking. PACS 42.62.Cf; 79.20.Ds     

Measurement of the chromatic dispersion of an optical fiber by use of a Sagnac interferometer employing asymmetric modulation

We describe a novel method, based on asymmetric modulation in a Sagnac interferometer, that measures the chromatic dispersion of single-mode fibers. The interferometer incorporates a phase modulator and a test fiber, so the dispersion can be determined from the interference fringe seen when a sweep rf signal is applied to the modulator. This technique provides picosecond temporal resolution without the need for any fast diagnostic equipment and is capable of accurately measuring the average dispersion of fibers several kilometers long.     

Paths to stability for college admissions with budget constraints

We study two-sided matching problem considered in Abizada (Theor Econ 11(2), 735–756, 2016), where one side (colleges) can make monetary transfers (offer stipends) to the other (students) subject to budget constraints. Colleges have strict preferences over sets of students and value money only to the extent that it allows them to enroll better or additional students. A student can attend at most one college and receive a stipend from it. Each student has preferences over college-stipend bundles. Although in the presence of budget constraints, the conditions that are essential for most of the results on stability in the literature fail, Abizada (Theor Econ 11(2), 735–756, 2016) shows that for this model a pairwise stable allocation always exists. In this paper, we show that starting from an arbitrary allocation, there is a sequence of allocations, each allocation being obtained from the previous one by “satisfying” a blocking pair, such that the final allocation is pairwise stable.     

Synthesis of Novel Tritopic Hydrazone Ligands: Spectroscopy,Biological Activity,DFT, and Molecular Docking Studies

Polytopic organic ligands with hydrazone moiety are at the forefront of new drug research among many others due to their unique and versatile functionality and ease of strategic ligand design. Quantum chemical calculations of these polyfunctional ligands can be carried out in silico to determine the thermodynamic parameters. In this study two new tritopic dihydrazide ligands, N’2, N’6-bis[(1E)-1-(thiophen-2-yl) ethylidene] pyridine-2,6-dicarbohydrazide (L1) and N’2, N’6-bis[(1E)-1-(1H-pyrrol-2-yl) ethylidene] pyridine-2,6-dicarbohydrazide (L2) were successfully prepared by the condensation reaction of pyridine-2,6-dicarboxylic hydrazide with 2-acetylthiophene and 2-acetylpyrrole. The FT-IR, ¹H, and ¹³C NMR, as well as mass spectra of both L1 and L2, were recorded and analyzed. Quantum chemical calculations were performed at the DFT/B3LYP/cc-pvdz/6-311G+(d,p) level of theory to study the molecular geometry, vibrational frequencies, and thermodynamic properties including changes of ∆H, ∆S, and ∆G for both the ligands. The optimized vibrational frequency and (¹H and ¹³C) NMR obtained by B3LYP/cc-pvdz/6-311G+(d,p) showed good agreement with experimental FT-IR and NMR data. Frontier molecular orbital (FMO) calculations were also conducted to find the HOMO, LUMO, and HOMO–LUMO gaps of the two synthesized compounds. To investigate the biological activities of the ligands, L1 and L2 were tested using in vitro bioassays against some Gram-negative and Gram-positive bacteria and fungus strains. In addition, molecular docking was used to study the molecular behavior of L1 and L2 against tyrosinase from Bacillus megaterium. The outcomes revealed that both L1 and L2 can suppress microbial growth of bacteria and fungi with variable potency. The antibacterial activity results demonstrated the compound L2 to be potentially effective against Bacillus megaterium with inhibition zones of 12 mm while the molecular docking study showed the binding energies for L1 and L2 to be −7.7 and −8.8 kcal mol⁻¹, respectively, with tyrosinase from Bacillus megaterium.