Geometric Stabilization Research Articles

Geometric stabilization of discrete‐time systems via dissipativity approach and output feedback control

AbstractGeometric stabilizability is studied for nonlinear discrete‐time systems (DTS) utilizing linear static output feedback (SOF). Initially, a linear SOF controller is designed such that nonlinear DTS achieve geometric stabilizability. Utilizing the concept of geometric QSR‐dissipativity (GQSR‐D), a condition both sufficient and necessary is proffered to guarantee geometric stabilizability for nonlinear DTS. Subsequently, the necessary conditions of linear matrix inequality (LMI) are delineated to ascertain the stability of a system employing linear SOF. A new sufficient and necessary condition is provided aiming to stabilize the linear time‐invariant (LTI) DTS based on GQSR‐D. Lastly, examples are furnished to elucidate the efficacy of the results, thereby reinforcing their practical applicability.

Geometric prescribed‐time control of quadrotors with adaptive extended state observers

AbstractThis article studies an adaptive extended state observer (AESO) based prescribed‐time geometric attitude stabilization problem of quadrotors with endogenous uncertainties, exogenous disturbances, and actuator saturation, which can be estimated and compensated by AESOs. The employment of the geometric representation method for system attitude can effectively avoid ambiguity or singularity problems that may arise with other representations. The temporal and scale transformations are employed to solve the global boundedness problem on infinite time instead of the prescribed‐time convergence problem on finite time. By integrating the proposed controller with the backstepping technique, the system of quadrotors can be prescribed‐time stable. Further, a prescribed‐time geometric attitude control technique is devised such that the control signal is bounded and the state signals converge to a small domain near the equilibrium point in the prescribed time. The prescribed time is determined by the user and is independent of the initial conditions. The comparative simulations with different initial information are performed to demonstrate the effectiveness of the proposed design technique.

On divergent Richtmyer–Meshkov instability of a light/heavy interface

Abstract

Superatom Paramagnetism in Au102(SR)441-/0/1+/2+ Oxidation States.

Gold nanoclusters show distinctive magnetic properties and electronic structure. Nanoclusters of sufficiently small size restructure geometrically to stabilize electronically (e.g., a Jahn-Teller effect), whereas geometric distortion may not be possible in larger nanoclusters. In this work, the charge-state-dependent magnetism of the Au102(SPh)441-/0/1+/2+ nanocluster is investigated through Evans method NMR measurements. The 2+ charge state is shown as paramagnetic. This suggests that the nanocluster does not distort geometrically to pair electrons. Because the nanocluster lies within the transition range of molecule-like to bulk-like properties, this suggests that the geometric stabilization that becomes important in larger "magic number clusters" may be resistant to electronically driven distortions observed in smaller nanoclusters.

Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. II. Non-axisymmetric systems

A non-perturbative analysis for the study non-axisymmetric (3D) effects on the linear ion-temperature-gradient driven mode is introduced. Perturbations and equilibria are considered to be global on the flux surface, yet radially local. The analysis is valid for systems arbitrarily far from axisymmetry. It is found that finite Larmor radius effects can suppress the global (on the surface) instability, in analogy with the local analysis but shift its poloidal location from the position of the greatest local instability. Fourier spectra of the instability whose width grow for increasingly non-axisymmetric systems are predicted. Results are in qualitative agreement with numerical global (on the surface) gyrokinetic simulations.

A geometric stabilization of planar switched systems

In this paper, we investigate a particular class of switching functions between two linear systems in the plan. The considered functions are defined in terms of geometric constructions. More precisely, we introduce two criteria for proving uniform stability of such functions, both criteria are based on the construction of a Lyapunov function. The first criterion is constructed in terms of an algebraic reformulation of the problem and linear matrix inequalities. The second one is purely geometric. Finally, we illustrate these methods with a numerical example.

Motivic random variables and representation stability II: Hypersurface sections

We prove geometric and cohomological stabilization results for the universal smooth degree d hypersurface section of a fixed smooth projective variety as d goes to infinity. We show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed Grothendieck ring of varieties, and deduce from this the stabilization of the Hodge Euler characteristic of natural families of local systems constructed from the vanishing cohomology. We prove explicit formulas for the stable values using a probabilistic interpretation, along with the natural analogs in point counting over finite fields. We explain how these results provide new geometric examples of a weak version of representation stability for symmetric, symplectic, and orthogonal groups. This interpretation of representation stability was studied in the prequel [20] for configuration spaces.

Hydrogen bonded complexes of oxazole family: electronic structure, stability, and reactivity aspects

In the present study, five-membered heterocyclic ring systems containing oxygen with one, two, three, and four nitrogen atoms in the ring along with their isomeric forms and their corresponding 1:1 water complexes have been fully optimized at the ab initio molecular orbital theory and Density Functional Theory (DFT) using aug-cc-pVDZ basis set. The optimized geometric parameters and stabilization energies of the complexes are reported. The study suggests that nitrogen of heterocyclic ring is a stronger hydrogen bond acceptor in comparison to oxygen and ability of nitrogen to act as hydrogen bond acceptor increases in the order oxazole (OZ) > oxadiazole (ODZ) > oxatriazole (OTZ) > oxatetrazole (OTTZ). The results are corroborated by Natural Bond Orbital (NBO) analysis, Quantum Theory of Atoms in Molecules (QTAIM), Symmetry Adapted Perturbation Theory (SAPT), and Molecular Electrostatic Potential (MEP) studies. The blue- and red-shifts in the hydrogen bond donors X-H (X = O, C) stretching frequencies have also been analyzed. Hydrogen bond ability has also been governed in the presence of reactivity descriptors including chemical potential (μ), global hardness (η), and electrophilicity index (ω).

Toxicodynamics of Organophosphates with Human Acetylcholinesterase Interaction at Novel Site Trp-86 for Antidote Action

Molecular Docking, site directed mutagenesis and molecular dynamic (MD) simulation approaches were used to explore mode of binding and inhibition for human acetylcholinesterase (hAChE) and organophosphates (OPs). More than 200 OPs molecules were investigated using Glide docking module of Schrodinger suite as co-crystal structure between two are not available in protein data bank. In initial screening Trp86 was found to be involved in maximum π-cation interaction on anionic subsite of hAChE other than Ser203 (catalytic site). With extra precision glide docking phoxim ethyl phosphonate (PEP) tops among 200 OPs based on glide docking score while interacted with Trp86, Gly121 and Ser203 whereas MMGBSA score shows less binding affinity than heptenophos and dichlorovos. Trp86 preferred π interaction with ring bearing OPs and hydrophobic interactions with smaller OPs without ring bearing structures. Site directed mutagenesis at Trp86 (Trp86 to Ala86) shown the deterioration of the binding site in terms of size reduction, loss of electrostatic and geometric stabilization in binding cavity and significant reduction in binding of OPs in preferred orientation. Dock score of both wild and mutated hAChE shows a perfect qualitative agreement (R 2 =64.1%) towards the study. Molecular dynamic simulation (GROMACS 4.5.5) of hAChE-PEP complex for 4×10 4 pico-second with SPC16 water system at 310K temperature explained the evident role of Trp86 in stabilizing the ligand at P-site of the enzyme. Asp74 and Tyr 124 were noticed in conveying H-bonds. Trp86 have shown consistent and stable distance between residues and ligand. Asp74 and Tyr124 appeared as important residues which contributed H bonds and Ser203 was expected to be closer for interaction to happen as it disappeared during simulation. Study suggests role of Trp86 on binding site is equally important to take consideration. As residue Trp86 plays significant role, it can be taken into consideration for the studies on development of more efficient antidotes to overcome the case of human poisoning.

Geometric stabilization of bearing races by centerless rolling

The geometric stabilization of bearing races by centerless rolling is studied experimentally, for the outer races of ball bearings.

Gyrokinetic study of turbulence suppression in a JET-ILW power scan

For exploring tokamak operation regimes that deliver both high β and good energy confinement, power scans at JET with ITER-like wall have been performed. Relatively weak degradation of the confinement time coincides with increased core temperature of the ions at high power. The changes in core turbulence characteristics during a power scan with an optimized (broad) q profile are analyzed by means of nonlinear gyrokinetic simulations. The increase in β is crucial for stabilizing ion temperature gradient driven turbulence, accompanied by increased ion to electron temperature ratio, the presence of a dynamic fast ion species, as well as the geometric stabilization by increased thermal and suprathermal pressure. A sensitivity study with respect to the q profile reveals that electromagnetic effects are more pronounced at larger values of q. Further, it is confirmed that turbulence suppression due to rotation becomes less effective in such strongly electromagnetic systems. Electrostatic simplified models may thus perform well in present-day devices, in which high β is often correlated with high rotation, but provide poor extrapolation towards low rotation devices. Implications for ITER and reactor plasmas are discussed.

Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems

The effects of a non-axisymmetric (3D) equilibrium magnetic field on the linear ion-temperature-gradient (ITG) driven mode are investigated. We consider the strongly driven, toroidal branch of the instability in a global (on the magnetic surface) setting. Previous studies have focused on particular features of non-axisymmetric systems, such as strong local shear or magnetic ripple, that introduce inhomogeneity in the coordinate along the magnetic field. In contrast, here we include non-axisymmetry explicitly via the dependence of the magnetic drift on the field line label α, i.e., across the magnetic field, but within the magnetic flux surface. We consider the limit where this variation occurs on a scale much larger than that of the ITG mode, and also the case where these scales are similar. Close to axisymmetry, we find that an averaging effect of the magnetic drift on the flux surface causes global (on the surface) stabilization, as compared to the most unstable local mode. In the absence of scale separation, we find destabilization is also possible, but only if a particular resonance occurs between the magnetic drift and the mode, and finite Larmor radius effects are neglected. We discuss the relative importance of surface global effects and known radially global effects.

Smooth Image Sequences for Data‐driven Morphing

AbstractSmoothness is a quality that feels aesthetic and pleasing to the human eye. We present an algorithm for finding “as‐smooth‐as‐possible” sequences in image collections. In contrast to previous work, our method does not assume that the images show a common 3D scene, but instead may depict different object instances with varying deformations, and significant variation in lighting, texture, and color appearance. Our algorithm does not rely on a notion of camera pose, view direction, or 3D representation of an underlying scene, but instead directly optimizes the smoothness of the apparent motion of local point matches among the collection images. We increase the smoothness of our sequences by performing a global similarity transform alignment, as well as localized geometric wobble reduction and appearance stabilization. Our technique gives rise to a new kind of image morphing algorithm, in which the in‐between motion is derived in a data‐driven manner from a smooth sequence of real images without any user intervention. This new type of morph can go far beyond the ability of traditional techniques. We also demonstrate that our smooth sequences allow exploring large image collections in a stable manner.

Polar metals by geometric design.

Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals--it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedral--the structural signatures of perovskites--owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.

Geometric Controllability and Stabilization of Spherical Robot Dynamics

Geometric control of a spherical robot rolling on a horizontal plane with three independent inertia disc actuators is considered in this note. The dynamic model of the spherical robot in the geometric framework is used to establish the strong accessibility and small-time local controllability properties. Smooth stabilizability to an equilibrium fails for the nonholonomic spherical robot. A novel contribution of this note is a smooth, asymptotically stabilizing geometric control law for position and reduced attitude, which corresponds to an equilibrium submanifold of dimension one. From Brockett's condition, this is the best possible dimension of a smoothly stabilized equilibrium submanifold. We also present a novel smooth global tracking controller for tracking position trajectories.

Accurate Bond Energies of Biodiesel Methyl Esters from Multireference Averaged Coupled-Pair Functional Calculations

Accurate bond dissociation energies (BDEs) are important for characterizing combustion chemistry, particularly the initial stages of pyrolysis. Here we contribute to evaluating the thermochemistry of biodiesel methyl ester molecules using ab initio BDEs derived from a multireference averaged coupled-pair functional (MRACPF2)-based scheme. Having previously validated this approach for hydrocarbons and a variety of oxygenates, herein we provide further validation for bonds within carboxylic acids and methyl esters, finding our scheme predicts BDEs within chemical accuracy (i.e., within 1 kcal/mol) for these molecules. Insights into BDE trends with ester size are then analyzed for methyl formate through methyl crotonate. We find that the carbonyl group in the ester moiety has only a local effect on BDEs. C═C double bonds in ester alkyl chains are found to increase the strengths of bonds adjacent to the double bond. An important exception are bonds beta to C═C or C═O bonds, which produce allylic-like radicals upon dissociation. The observed trends arise from different degrees of geometric relaxation and resonance stabilization in the radicals produced. We also compute BDEs in various small alkanes and alkenes as models for the long hydrocarbon chain of actual biodiesel methyl esters. We again show that allylic bonds in the alkenes are much weaker than those in the small methyl esters, indicating that hydrogen abstractions are more likely at the allylic site and even more likely at bis-allylic sites of alkyl chains due to more electrons involved in π-resonance in the latter. Lastly, we use the BDEs in small surrogates to estimate heretofore unknown BDEs in large methyl esters of biodiesel fuels.

Target-directed catalytic metallodrugs

Most drugs function by binding reversibly to specific biological targets, and therapeutic effects generally require saturation of these targets. One means of decreasing required drug concentrations is incorporation of reactive metal centers that elicit irreversible modification of targets. A common approach has been the design of artificial proteases/nucleases containing metal centers capable of hydrolyzing targeted proteins or nucleic acids. However, these hydrolytic catalysts typically provide relatively low rate constants for target inactivation. Recently, various catalysts were synthesized that use oxidative mechanisms to selectively cleave/inactivate therapeutic targets, including HIV RRE RNA or angiotensin converting enzyme (ACE). These oxidative mechanisms, which typically involve reactive oxygen species (ROS), provide access to comparatively high rate constants for target inactivation. Target-binding affinity, co-reactant selectivity, reduction potential, coordination unsaturation, ROS products (metal-associated vs metal-dissociated; hydroxyl vs superoxide), and multiple-turnover redox chemistry were studied for each catalyst, and these parameters were related to the efficiency, selectivity, and mechanism(s) of inactivation/cleavage of the corresponding target for each catalyst. Important factors for future oxidative catalyst development are 1) positioning of catalyst reduction potential and redox reactivity to match the physiological environment of use, 2) maintenance of catalyst stability by use of chelates with either high denticity or other means of stabilization, such as the square planar geometric stabilization of Ni- and Cu-ATCUN complexes, 3) optimal rate of inactivation of targets relative to the rate of generation of diffusible ROS, 4) targeting and linker domains that afford better control of catalyst orientation, and 5) general bio-availability and drug delivery requirements.

What is the best density functional to describe water clusters: evaluation of widely used density functionals with various basis sets for (H2O) n (n = 1–10)

The geometric structures, stabilization energies, dipole moments, and vibrational frequencies of the neutral water clusters (H2O)n, with n = 1–10, were investigated using density functional theory along with a variety of exchange-correlation functionals (LDA with SVWN5 parameterization, GGA with BLYP, PW91, PBE, B3LYP, X3LYP, PBE0, PBE1W, M05-2X, M06-2X and M06-L parameterizations) as well as high-level ab initio MP2 and CCSD(T) methods. Using the MP2 and CCSD(T) results as benchmarks, the effects of exchange-correlation functionals and basis sets were carefully examined. Each functional has its advantage in certain aspects; for example, M05-2X and X3LYP yield better geometries, and the capability of these two functionals to distinguish the relative energies between isomers are more similar to MP2. The size of the split-valence basis set (6-31G or larger), diffuse functions on the oxygen atom, and d(p) polarization on the oxygen (hydrogen) atom are crucial for an accurate description of intermolecular interaction in water clusters. The 6-31+G(2d,p) basis set is thus recommended as a compromise between computational efficiency and accuracy for structural description. We further demonstrated that the numerical basis set, TNP, performs satisfactorily in describing structural parameters of water clusters.

Natural bond orbital (NBO) analysis of the angular group induced bond alternation (AGIBA) substituent effect

AbstractThe geometries, natural charges, and resonance structures of 11 monosubstituted benzene derivatives were analyzed at the B3LYP/6‐311++G(d,p) and HF/6‐311++G(d, p) levels of theory. The following angular substituents were chosen: OCH3, CH2CH3, OH, SH, NHCH3, NHNH2, NO, CHCH2, NCH2, NNH, and CHO. The analysis of resonance structures was performed by using two different methodologies: harmonic oscillator stabilization energies (HOSE) and natural resonance theory (NRT). Also, the natural bond orbital (NBO) donor–acceptor stabilization energies for different resonance structures were calculated. We found that for all the substituents, the purely geometric resonance stabilization parameter (HOSE) is linearly correlated with quantum chemically derived resonance structure weight (NRT) of a given structure. Also, the calculations provide qualitative support for the earlier assumption of a through space angular group induced bond alternation (AGIBA) effect. Copyright © 2010 John Wiley & Sons, Ltd.

484 離散ハミルトン系に基づくホロノミック力学系の定式化と幾何学的拘束安定化

This paper develops discrete holonomic Hamiltonian systems that is based on the discretization by the Backward Differentiation Formula and with geometric constraint stabilization, which enables one to effectively stabilize constraint violations that appear in numerical simulations of holonomic mechanical systems. We illustrate the validity of the proposed discrete holonomic Hamiltonian systems by an illustrative example of linkage mechanisms in comparison with conventional constraint stabilization methods such as the GGL method and the Baumgarte method.