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In this paper, we propose a parallel shooting algorithm for solving nonlinear model predictive control problems using sequential quadratic programming. This algorithm is built on a two-phase approach where we first test and assess sequential convergence over many initial trajectories in parallel. However, if none converge, the algorithm starts varying the Newton step size in parallel instead. Through this parallel shooting approach, it is expected that the number of iterations to converge to an optimal solution can be decreased. Furthermore, the algorithm can be further expanded and accelerated by implementing it on GPUs. We illustrate the effectiveness of the proposed Parallel Shooting Sequential Quadratic Programming (PS-SQP) method in some benchmark examples for nonlinear model predictive control. The developed PS-SQP parallel solver converges faster on average and especially when significant nonlinear behaviour is excited in the NMPC horizon., Comment: 7 pages, 6 figures, submitted and accepted for the 7th IEEE Conference on Control Technology and Applications (CCTA) 2023

Around fifty years ago, LiTi$_2$O$_4$ was reported to be first spinel oxide to exhibit a superconducting transition with highest T$_c$ $\approx$ 13.7 K. Recently, MgTi$_2$O$_4$ has been found to be the only other spinel oxide to reveal a superconducting transition with a T$_c$ $\approx$ 3 K, however, its superconducting state is realized only in thin film superlattices involving SrTiO$_3$. We find that a V-doped Mg$_{1-x}$Ti$_2$O$_4$ phase, which gets stabilized as a thin surface layer on top of stoichiometric and insulating V-doped MgTi$_2$O$_4$ bulk sample, exhibits high-temperature superconductivity with T$_c$ $\approx$ 16 K. The superconducting transition is also confirmed through a concomitant sharp diamagnetic transition immediately below T$_c$. The spinel phase of the superconducting surface layer is elucidated through grazing-incidence X-ray diffraction and Micro-Raman spectroscopy. A small shift of the sharp superconducting transition temperature ($\sim$ 4 K) with application of a high magnetic field (upto 9 Tesla) suggests a very high critical field for the system, $\sim$ 25 Tesla. Thus, V-doped Mg$_{1-x}$Ti$_2$O$_4$ exhibits the highest T$_c$ among spinel superconductors and also possesses a very high critical field., Comment: 5 pages, 4 figures

We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{\ast}$-algebra. As an application, we prove that any faithful smooth action by a compact quantum group on a compact smooth (not necessarily connected) manifold is injective. A similar result is proved for actions on $C^{\ast}$- algebras obtained by Rieffel-deformation of compact, smooth manifolds., Comment: arXiv admin note: text overlap with arXiv:1507.08407, arXiv:1309.1294

During cell division, sister chromatids are segregated by the mitotic spindle, a bipolar assembly of interdigitating antiparallel polar filaments called microtubules. Establishing a stable overlap region is essential for maintenance of bipolarity, but the underlying mechanisms are poorly understood. Using a particle-based stochastic model, we find that the interplay of motors and passive cross linkers can robustly generate partial overlaps between antiparallel filaments. Our analysis shows that motors reduce the overlap in a length-dependent manner, whereas passive cross linkers increase it independently of the length. In addition to maintaining structural integrity, passive cross linkers can thus also have a dynamic role for size regulation., Comment: 10 pages 4 figures

Motivated by recent experiments on the supersolid behavior of $^4$He, we study the effect of an edge dislocation in promoting superfluidity in a Bose crystal. Using Landau theory, we couple the elastic strain field of the dislocation to the superfluid density, and use a linear analysis to show that superfluidity nucleates on the dislocation before occurring in the bulk of the solid. Moving beyond the linear analysis, we develop a systematic perturbation theory in the weakly nonlinear regime, and use this method to integrate out transverse degrees of freedom and derive a one-dimensional Landau equation for the superfluid order parameter. We then extend our analysis to a network of dislocation lines, and derive an XY model for the dislocation network by integrating over fluctuations in the order parameter. Our results show that the ordering temperature for the network has a sensitive dependence on the dislocation density, consistent with numerous experiments that find a clear connection between the sample quality and the supersolid response., Comment: 10 pages, 6 figures

We investigate bound state solutions of the 2D Schr\"odinger equation with a dipole potential originating from the elastic effects of a single edge dislocation. The knowledge of these states could be useful for understanding a wide variety of physical systems, including superfluid behavior along dislocations in solid $^4$He. We present a review of the results obtained by previous workers together with an improved variational estimate of the ground state energy. We then numerically solve the eigenvalue problem and calculate the energy spectrum. In our dimensionless units, we find a ground state energy of -0.139, which is lower than any previous estimate. We also make successful contact with the behavior of the energy spectrum as derived from semiclassical considerations., Comment: 6 pages, 3 figures, submitted to PRB

We have carried out scanning tunneling microscopy experiments under ultrahigh vacuum condition to study the morphology of ultrathin Ge films eposited on pristine Si(100) and ion-irradiated Si(100) self-affine fractal surfaces. The pristine and the ion-irradiated Si(100) surface have roughness exponents of alpha=0.19+/-0.05 and alpha=0.82+/-0.04 respectively. These measurements were carried out on two halves of the same sample where only one half was ion-irradiated. Following deposition of a thin film of Ge (~6 A) the roughness exponents change to 0.11+/-0.04 and 0.99+/-0.06, respectively. Upon Ge deposition, while the roughness increases by more than an order of magnitude on the pristine surface, a smoothing is observed for the ion-irradiated surface. For the ion-irradiated surface the correlation length xi increases from 32 nm to 137 nm upon Ge deposition. Ge grows on Si surfaces in the Stranski-Krastanov or layer-plus-island mode where islands grow on a wetting layer of about three atomic layers. On the pristine surface the islands are predominantly of square or rectangular shape, while on the ion-irradiated surface the islands are nearly diamond shaped. Changes of adsorption behaviour of deposited atoms depending on the roughness exponent (or the fractal dimension) of the substrate surface are discussed., Comment: 5 pages, 2 figures and 1 table

Accurate knowledge of absorption coefficient of a sample is a prerequisite for measuring the third order optical nonlinearity of materials, which can be a serious limitation for unknown samples. We introduce a method, which measures both the absorption coefficient and the third order optical nonlinearity of materials with high sensitivity in a single experimental arrangement. We use a dual-beam pump-probe experiment and conventional single-beam z-scan under different conditions to achieve this goal. We also demonstrate a counterintuitive coupling of the non-interacting probe-beam with the pump-beam in pump-probe z-scan experiment., Comment: to appear in "Advances in Laser and Optics Research", Nova Science Publishers, 2004

Growth and strain behavior of thin Ag films on Si substrate have been investigated by scanning tunneling microscopy, cross-sectional transmission electron microscopy and high resolution x-ray diffraction studies. Ag islands formed on Si at room temperature growth show strongly preferred heights and flat top. At low coverage, islands containing two atomic layers of Ag are overwhelmingly formed. At higher coverages island height distribution shows strong peaks at relative heights corresponding to an even number of Ag atomic layers. This appears to be a quantum size effect. Hexagonal disc-like islands with flat top are formed upon annealing. The annealed film shows two closely-spaced Ag(111) diffraction peaks - one weak and broad and the other narrow and more intense. The intense peak corresponds to a shorter Ag(111) planar spacing compared to the bulk value. This can be explained in terms of changes in the Ag lattice during the heating-cooling cycle due to thermal expansion coefficient mismatch between Ag and Si., Comment: 9 pages, 11 figures

Topography of silicon surfaces irradiated by a 2 MeV Si$^+$ ion beam at normal incidence and ion fluences in the range $10^{15}-10^{16}$ ions/cm$^{2}$ has been investigated using scanning tunneling microscopy. At length scales below $\sim$~50 nm, surface smoothing is observed; the smoothing is more prominent at smaller length scales. The smoothed surface is self-affine with a scaling exponent $\alpha=0.53\pm0.02$., Comment: 11 pages, 4 figures

Accurate knowledge of absorption coefficient of a sample is a prerequisite for measuring the third order optical nonlinearity of materials, which could become a serious limitation for unknown samples. We introduce a new method, which measures both the absorption coefficient and the third order optical nonlinearity of materials with high sensitivity in a single experimental setup. We use a dual-beam pump-probe experiment under different conditions to achieve this goal. We also demonstrate a counterintuitive coupling of the non-interacting probe-beam with the pump-beam in pump-probe z-scan experiment., Comment: 8 pages, 4 figures, submitted to APL