Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper we analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. We first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zero or positive, then the robot equations cannot exhibit chaos. We show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, we analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, we resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and we show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.

Badly approximable numbers and vectors in Cantor-like sets

We show that a large class of Cantor-like sets of R-d, d >= 1, contains uncountably many badly approximable numbers, respectively badly approximable vectors, when d >= 2. An analogous result is also proved for subsets of R-d arising in the study of geodesic flows corresponding to (d+1)-dimensional manifolds of constant negative curvature and finite volume, generalizing the set of badly approximable numbers in R. Furthermore, we describe a condition on sets, which is fulfilled by a large class, ensuring a large intersection with these Cantor-like sets.

Life of flame particles embedded in premixed flames interacting with near isotropic turbulence

Flame particles are surface points that always remain embedded on, by comoving with a given iso-scalar surface within a flame. Tracking flame particles allow us to study the fate of propagating surface locations uniquely identified throughout their evolution with time. In this work, using Direct Numerical Simulations we study the finite lifetime of such flame particles residing on iso-temperature surfaces of statistically planar H-2-air flames interacting with near-isotropic turbulence. We find that individual flame particles as well as their ensemble, experience progressively increasing tangential straining rate (K-t) and increasing negative curvature (kappa) near the end of their lifetime to finally get annihilated. By studying two different turbulent flow conditions, flame particle tracking shows that such tendency of local flame surfaces to be strained and cusped towards pinch-off from the main surface is a rather generic feature, independent of initial conditions, locations and ambient turbulence intensity levels. The evolution of the alignments between the flame surface normals and the principal components of the local straining rates are also tracked. We find that the surface normals initially aligned with the most extensive principal strain rate components, rotate near the end of flame particles' lifetime to enable preferential alignment between the surface tangent and the most extensive principal strain rate component. This could explain the persistently increasing tangential strain rate, sharp negative curvature formation and eventual detachment. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

A flame particle tracking analysis of turbulence-chemistry interaction in hydrogen-air premixed flames

Interactions of turbulence, molecular transport, and energy transport, coupled with chemistry play a crucial role in the evolution of flame surface geometry, propagation, annihilation, and local extinction/re-ignition characteristics of intensely turbulent premixed flames. This study seeks to understand how these interactions affect flame surface annihilation of lean hydrogen-air premixed turbulent flames. Direct numerical simulations (DNSs) are conducted at different parametric conditions with a detailed reaction mechanism and transport properties for hydrogen-air flames. Flame particle tracking (FPT) technique is used to follow specific flame surface segments. An analytical expression for the local displacement flame speed (S-d) of a temperature isosurface is considered, and the contributions of transport, chemistry, and kinematics on the displacement flame speed at different turbulence-flame interaction conditions are identified. In general, the displacement flame speed for the flame particles is found to increase with time for all conditions considered. This is because, eventually all flame surfaces and their resident flame particles approach annihilation by reactant island formation at the end of stretching and folding processes induced by turbulence. Statistics of principal curvature evolving in time, obtained using FPT, suggest that these islands are ellipsoidal on average enclosing fresh reactants. Further examinations show that the increase in S-d is caused by the increased negative curvature of the flame surface and eventual homogenization of temperature gradients as these reactant islands shrink due to flame propagation and turbulent mixing. Finally, the evolution of the normalized, averaged, displacement flame speed vs. stretch Karlovitz number are found to collapse on a narrow band, suggesting that a unified description of flame speed dependence on stretch rate may be possible in the Lagrangian description. (C) 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Cinematographic OH-PLIF measurements of two interacting turbulent premixed flames with and without acoustic forcing

This paper describes an experimental investigation into the interactions that occur between two lean turbulent premixed flames stabilised on conical bluff-bodies when they are moved closer together. Cinematographic OH-PLIF measurements were acquired to investigate adjacent flame front interactions as a function of flame separation distance (S). Flame surface density (FSD) and curvature were determined to characterise the unforced flames. Acoustic forcing was then applied to explore the amplitude dependent thermo-acoustic response. Phase-averaged FSD and global heat release measurements in the form of OH * chemiluminescence were obtained for a range of forcing frequencies (f) and amplitudes (A) as a function of S. As the flames were brought closer together the adjacent annular jets were found to merge into a single jet structure. This caused adjacent flame fronts to merge above the wake region between the two flames at a location determined by the jet efflux (flame angle) and S. This region of flame-flame interaction we refer to as 'interacting region'. In the unforced flames, a trend of increasingly negative curvature for decreasing S produced a small net increase in flame surface area via cusp formation. When subjected to acoustic forcing, S-dependent regimes were found in the global heat release response as a function A. The overall trend showed that the occurrence of jet/flame merging reduces the value of A at which non-linear response occurs. In support of previous findings for flames stabilised along shear layers, the phase-averaged FSD showed that the flame dynamics that drive the thermo-acoustic response result from the roll-up of vortices which generate large-scale vortex-flame interactions. Compared with axisymmetric flames, the occurrence of jet merging alters the vortex-flame interactions resulting in an asymmetric contribution to the heat release between the wall and interacting regions. The majority of the heat release was found to occur in the interacting region through the rapid production and destruction of flame surface area. The occurrence of jet merging and large-scale interactions between adjacent flames result in different physical mechanisms that drive the thermo-acoustic response compared with single axisymmetric flames. © 2011.

PHYTOCHROME KINASE SUBSTRATE1 regulates root phototropism and gravitropism.

Light promotes the expression of PHYTOCHROME KINASE SUBSTRATE1 (PKS1) in the root of Arabidopsis thaliana, but the function of PKS1 in this organ is unknown. Unilateral blue light induced a negative root phototropic response mediated by phototropin 1 in wild-type seedlings. This response was absent in pks1 mutants. In the wild type, unilateral blue light enhanced PKS1 expression in the subapical region of the root several hours before bending was detectable. The negative phototropism and the enhanced PKS1 expression in response to blue light required phytochrome A (phyA). In addition, the pks1 mutation enhanced the root gravitropic response when vertically oriented seedlings were placed horizontally. The negative regulation of gravitropism by PKS1 occurred even in dark-grown seedlings and did not require phyA. Blue light also failed to induce negative phototropism in pks1 under reduced gravitational stimulation, indicating that the effect of pks1 on phototropism is not simply the consequence of the counteracting effect of enhanced gravitropism. We propose a model where the background level of PKS1 reduces gravitropism. After a phyA-dependent increase in its expression, PKS1 positively affects root phototropism and both effects contribute to negative curvature in response to unilateral blue light.

The effects of gramicidin on the structure of phospholipid assemblies /

Gramicidin is an antibiotic peptide that can be incorporated into the monolayers of cell membranes. Dimerization through hydrogen bonding between gramicidin monomers in opposing leaflets of the membrane results in the formation of an iontophoretic channel. Surrounding phospholipids, with various associated mechanical properties, have been shown to influence the gating properties of this channel. Conversely, gramicidin incorporation has been shown to affect the structure of spontaneously formed lipid assemblies. Using small-angle x-ray diffraction and model systems composed of phospholipids and gramicidin, the physical effects incurred by gramicidin incorporation were measured. The reverse hexagonal (H^) phase composed of dioleoylphosphatidylethanolamine (DOPE) monolayers decreased in lattice dimension with increasing incorporation of gramicidin. This indicated that gramicidin was adding negative curvature to the monolayers. In this system, gramicidin was measured to have an apparent intrinsic radius of curvature (Rop*™") of -7. 1 A. The addition of up to 4 mol% gramicidin in mixtures with DOPE did not result in the monolayers becoming stiffer, as indicated by unaltered bending moduli for each composition. Dioleoylphosphatidylcholine (DOPC) alone forms the lamellar (LJ phase when hydrated, but undergoes a transition into the H^ phase when mixed with gramicidin. The lattice repeat dimension decreases systematically with increased gramicidin content. Again, this indicated that gramicidin was adding negative curvature to the monolayers. At 12 mol% gramicidin in mixtures with DOPC, the apparent radius of intrinsic curvature of gramicidin (Rop*"^) was measured to be -7.4 A. This mixture formed monolayers that were very resistant to bending under osmotic pressure, with a measured bending modulus of 1 15 kT. The measurements made in this study demonstrate that peptides are able to modulate the spontaneous curvature and other mechanical properties of phospholipid assemblies.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Aggregation behavior of aqueous dioctadecyldimethylammonium bromide/monoolein mixtures: A multitechnique investigation on the composition and temperature

A recently described non-viral gene delivery system [dioctadecyldimethylammonium bromide (DODAB)/monoolein (MO)] has been studied in detail to improve knowledge on the interactions between lamellar (DODAB) and non-lamellar-forming (MO) lipids, as a means to enhance their final cell transfection efficiency. Indeed, the morphology, fluidity, and size of these cationic surfactant/neutral lipid mixtures play an important role in the ability of these systems to complex nucleic acids. The different techniques used in this work, namely dynamic light scattering (DLS), fluorescence spectroscopy, differential scanning calorimetry (DSC), cryogenic transmission electron microscopy (cryo-TEM), light microscopy (LM), and surface pressure-area isotherms, allowed fully characterization of the phase behavior and aggregate morphology of DODAB/MO mixtures at different molar ratios. Overall, the results indicate that the final morphology of DODAB/MO aggregates depends on the balance between the tendency of DODAB to form zero-curvature bilayer structures and the propensity of MO to form non-bilayer structures with negative curvature. These results also show that in the MO-rich region, an increase in temperature has a similar effect on aggregate morphology as an increase in MO concentration. (C) 2012 Elsevier B.V. All rights reserved.

Casimir energy in a small volume multiply connected static hyperbolic preinflationary universe

A few years ago, Cornish, Spergel and Starkman (CSS) suggested that a multiply connected small universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected fat space-times. Because of the interest in small volume hyperbolic universes (e.g., CSS), we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

Casimir energy density in closed hyperbolic universes

The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper we develop the theory of a similar situation, involving a scalar field in spacetimes with closed spatial sections of negative curvature.

Some integrals occurring in a topology change problem

In a paper presented a few years ago, de Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes. The purpose of this present work is to go a step further in that model, by performing some calculations only estimated there for several compact manifolds of constant negative curvature, such as the Weeks and Thurston spaces and the icosahedral hyperbolic space (Best space). ©2000 The American Physical Society.

Dynamical and statistical properties of a rotating oval billiard

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)