Phase-dependent interference fringes in the wavelength scaling of harmonic efficiency

We describe phase-dependent wavelength scaling of high-order harmonic generation efficiency driven by ultra-short laser fields in the mid-infrared. We employ both numerical solution of the time-dependent Schr\"{o}dinger equation and the Strong Field Approximation to analyze the fine-scale oscillations in the harmonic yield in the context of channel-closing effects. We show, by varying the carrier-envelope phase, that the amplitude of these oscillations depend strongly on the number of returning electron trajectories. Furthermore, the peak positions of the oscillations vary significantly as a function of the carrier-envelope phase. Owing to its practical applications, we also study the wavelength dependence of harmonic yield in the "single-cycle" limit, and observe a smooth variation in the wavelength scaling originating from the vanishing fine-scale oscillations.Comment: 5 pages, 4 figure

Dielectronic Recombination of Fe XV forming Fe XIV: Laboratory Measurements and Theoretical Calculations

We have measured resonance strengths and energies for dielectronic recombination (DR) of Mg-like Fe XV forming Al-like Fe XIV via N=3 -> N' = 3 core excitations in the electron-ion collision energy range 0-45 eV. All measurements were carried out using the heavy-ion Test Storage Ring at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. We have also carried out new multiconfiguration Breit-Pauli (MCBP) calculations using the AUTOSTRUCTURE code. For electron-ion collision energies < 25 eV we find poor agreement between our experimental and theoretical resonance energies and strengths. From 25 to 42 eV we find good agreement between the two for resonance energies. But in this energy range the theoretical resonance strengths are ~ 31% larger than the experimental results. This is larger than our estimated total experimental uncertainty in this energy range of +/- 26% (at a 90% confidence level). Above 42 eV the difference in the shape between the calculated and measured 3s3p(^1P_1)nl DR series limit we attribute partly to the nl dependence of the detection probabilities of high Rydberg states in the experiment. We have used our measurements, supplemented by our AUTOSTRUCTURE calculations, to produce a Maxwellian-averaged 3 -> 3 DR rate coefficient for Fe XV forming Fe XIV. The resulting rate coefficient is estimated to be accurate to better than +/- 29% (at a 90% confidence level) for k_BT_e > 1 eV. At temperatures of k_BT_e ~ 2.5-15 eV, where Fe XV is predicted to form in photoionized plasmas, significant discrepancies are found between our experimentally-derived rate coefficient and previously published theoretical results. Our new MCBP plasma rate coefficient is 19-28% smaller than our experimental results over this temperature range

Correlation effects and orbital magnetism of Co clusters

Recent experiments on isolated Co clusters have shown huge orbital magnetic moments in comparison with their bulk and surface counterparts. These clusters hence provide the unique possibility to study the evolution of the orbital magnetic moment with respect to the cluster size and how competing interactions contribute to the quenching of orbital magnetism. We investigate here different theoretical methods to calculate the spin and orbital moments of Co clusters, and assess the performances of the methods in comparison with experiments. It is shown that density functional theory in conventional local density or generalized gradient approximations, or even with a hybrid functional, severely underestimates the orbital moment. As natural extensions/corrections we considered the orbital polarization correction, the LDA+U approximation as well as the LDA+DMFT method. Our theory shows that of the considered methods, only the LDA+DMFT method provides orbital moments in agreement with experiment, thus emphasizing the importance of dynamic correlations effects for determining fundamental magnetic properties of magnets in the nano-size regime

The effect of solvent and pressure on polycaprolactone solutions for particle and fibre formation

Polycaprolactone (PCL) is a widely used material in many applications to tackle health problems worldwide. Formed micro- or nanosized PCL particles and fibres benefit from a higher surface area to volume ratio and are valuable in those applications, thus there is always a push to achieve smaller diameters. Electrohydrodynamic (EHD) technologies have been at the forefront in the production of polymeric biomaterials, and pressurised gyration (PG) has also enhanced possibilities by its ability to spin comparable fibres at rapid speeds. In this work, PCL microparticles and fibres were separately produced by changing key operating parameters of EHD and PG systems and PCL solution properties. Initially, PCL microparticles were formed by electrospraying with different binary solvent systems, followed by pressurised gyration fibre production with various singular solvents and a pre-optimised binary solvent system. As anticipated, the use of binary systems altered particle morphologies and diameters, while increased pressure and the use of different solvents greatly affected the characteristics of resulting fibres. The morphology of PCL was found to be highly dependent on the solvents and operating parameters of the technology used

Fixed point results for generalized cyclic contraction mappings in partial metric spaces

Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. P˘acurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic φ-contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak φ- contraction mappings and studied well-posedness problem for such mappings. On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.S. Romaguera acknowledges the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Abbas, M.; Nazir, T.; Romaguera Bonilla, S. (2012). Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 106(2):287-297. https://doi.org/10.1007/s13398-011-0051-5S2872971062Abdeljawad T., Karapinar E., Tas K.: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24(11), 1894–1899 (2011). doi: 10.1016/j.aml.2011.5.014Altun, I., Erduran A.: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. article ID 508730 (2011). doi: 10.1155/2011/508730Altun I., Sadarangani K.: Corrigendum to “Generalized contractions on partial metric spaces” [Topology Appl. 157 (2010), 2778–2785]. Topol. Appl. 158, 1738–1740 (2011)Altun I., Simsek H.: Some fixed point theorems on dualistic partial metric spaces. J. Adv. Math. Stud. 1, 1–8 (2008)Altun I., Sola F., Simsek H.: Generalized contractions on partial metric spaces. Topol. Appl. 157, 2778–2785 (2010)Aydi, H.: Some fixed point results in ordered partial metric spaces. arxiv:1103.3680v1 [math.GN](2011)Boyd D.W., Wong J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)Bukatin M., Kopperman R., Matthews S., Pajoohesh H.: Partial metric spaces. Am. Math. Monthly 116, 708–718 (2009)Bukatin M.A., Shorina S.Yu. et al.: Partial metrics and co-continuous valuations. In: Nivat, M. (eds) Foundations of software science and computation structure Lecture notes in computer science vol 1378., pp. 125–139. Springer, Berlin (1998)Derafshpour M., Rezapour S., Shahzad N.: On the existence of best proximity points of cyclic contractions. Adv. Dyn. Syst. Appl. 6, 33–40 (2011)Heckmann R.: Approximation of metric spaces by partial metric spaces. Appl. Cat. Struct. 7, 71–83 (1999)Karapinar E.: Fixed point theory for cyclic weak $${\phi}$$ -contraction. App. Math. Lett. 24, 822–825 (2011)Karapinar, E.: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011,4 (2011). doi: 10.1186/1687-1812-2011-4Karapinar E.: Weak $${\varphi}$$ -contraction on partial metric spaces and existence of fixed points in partially ordered sets. Math. Aeterna. 1(4), 237–244 (2011)Karapinar E., Erhan I.M.: Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett. 24, 1894–1899 (2011)Karpagam S., Agrawal S.: Best proximity point theorems for cyclic orbital Meir–Keeler contraction maps. Nonlinear Anal. 74, 1040–1046 (2011)Kirk W.A., Srinavasan P.S., Veeramani P.: Fixed points for mapping satisfying cylical contractive conditions. 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(2010, article ID 493298, 6 pages).Romaguera, S.: Fixed point theorems for generalized contractions on partial metric spaces. Topol. Appl. (2011). doi: 10.1016/j.topol.2011.08.026Romaguera S., Valero O.: A quantitative computational model for complete partial metric spaces via formal balls. Math. Struct. Comput. Sci. 19, 541–563 (2009)Rus, I.A.: Cyclic representations and fixed points. Annals of the Tiberiu Popoviciu Seminar of Functional equations. Approx. Convexity 3, 171–178 (2005), ISSN 1584-4536Schellekens M.P.: The correspondence between partial metrics and semivaluations. Theoret. Comput. Sci. 315, 135–149 (2004)Valero O.: On Banach fixed point theorems for partial metric spaces. Appl. Gen. Top. 6, 229–240 (2005)Waszkiewicz P.: Quantitative continuous domains. Appl. Cat. Struct. 11, 41–67 (2003

Kinetic Release Studies of Antibiotic Patches for Local Transdermal Delivery.

This study investigates the usage of electrohydrodynamic (EHD)-3D printing for the fabrication of bacterial cellulose (BC)/polycaprolactone (PCL) patches loaded with different antibiotics (amoxicillin (AMX), ampicillin (AMP), and kanamycin (KAN)) for transdermal delivery. The composite patches demonstrated facilitated drug loading and encapsulation efficiency of drugs along with extended drug release profiles. Release curves were also subjected to model fitting, and it was found that drug release was optimally adapted to the Higuchi square root model for each drug. They performed a time-dependent and diffusion-controlled release from the patches and followed Fick's diffusion law by the Korsmeyer-Peppas energy law equation. Moreover, produced patches demonstrated excellent antimicrobial activity against Gram-positive (Staphylococcus aureus) and Gram-negative (Escherichia coli) strains, so they could be helpful in the treatment of chronic infectious lesions during wound closures. As different tests have confirmed, various types of antibiotics could be loaded and successfully released regardless of their types from produced BC/PCL patches. This study could breathe life into the production of antibiotic patches for local transdermal applications in wound dressing studies and improve the quality of life of patients

Boosting expensive synchronizing heuristics

For automata, synchronization, the problem of bringing an automaton to a particular state regardless of its initial state, is important. It has several applications in practice and is related to a fifty-year-old conjecture on the length of the shortest synchronizing word. Although using shorter words increases the effectiveness in practice, finding a shortest one (which is not necessarily unique) is NP-hard. For this reason, there exist various heuristics in the literature. However, high-quality heuristics such as SynchroP producing relatively shorter sequences are very expensive and can take hours when the automaton has tens of thousands of states. The SynchroP heuristic has been frequently used as a benchmark to evaluate the performance of the new heuristics. In this work, we first improve the runtime of SynchroP and its variants by using algorithmic techniques. We then focus on adapting SynchroP for many-core architectures, and overall, we obtain more than 1000× speedup on GPUs compared to naive sequential implementation that has been frequently used as a benchmark to evaluate new heuristics in the literature. We also propose two SynchroP variants and evaluate their performance

Load displacement relationship for a rigid circular foundation anchored by Mindlin solutions

AbstractIn the present paper, Mindlin’s solutions are used (Mindlin, 1936)  [1] to estimate the load–displacement relationship for a circular foundation for ground anchors. Constant, linearly and parabolically varied anchor loads are applied to the foundation. The closed form analytical solutions derived by Selvadurai are used in the analysis. Effects of the length of the anchor region, its depth of location and the distribution of load within the anchor region are investigated in this article. The analytical solutions are also compared with finite element analysis and the results are given