Generic Stability Research Articles

A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1s. Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

A measurement-based VSI for voltage dependent loads using angle difference between tangent lines of load and PV curves

In this short communication, a generic measurement-based voltage stability indicator (VSI) is presented with voltage dependent load models incorporated. It uses the angle difference between the tangent lines of the load characteristic curve and the PV curve. Based on the Thevenin equivalent estimated from the measurements, the proposed VSI can be easily applied to both the ZIP and the exponential load models. Time domain simulation results on both load models demonstrate that the proposed VSI accurately indicates voltage instability and outperforms a conventional VSI which is based on a constant power load model.

Spatial decision support for nature-based shoreline stabilization options in subtropical estuarine environments

In response to shoreline erosion and potentially more severe storm damage due to climate change and sea level rise, armouring of shorelines using traditional hard structures is likely to increase. An emerging alternative to seawalls and other hard structures is to create ‘living shorelines’ where natural habitats are incorporated into a resilient shoreline stabilization design. Research has shown that functional, multiuse living shorelines provide options for reducing erosion rates and sustaining shoreline stability while supporting intertidal and nearshore habitat. Drawing upon the scientific literature, shoreline management best practices, and the results from an expert opinion survey, we propose a spatial decision framework for multiclass suitability analysis of generic shoreline stabilization options with a focus on the unique challenges and opportunities of South Florida. The results have been incorporated into a web application that can facilitate decision-making in support of nature-based stabilization infrastructure.

Robust Bifunctional Lanthanide Cluster Based Metal-Organic Frameworks (MOFs) for Tandem Deacetalization-Knoevenagel Reaction.

A series of 12-connected lanthanide cluster based metal-organic frameworks (MOFs) have been constructed by [Ln6(μ3-OH)8(COO-)12] secondary building units (SBUs) and 2-aminobenzenedicarboxylate (BDC-NH2) ligands. These obtained materials exhibit high chemical stability and generic thermal stability, especially in acidic and basic conditions. They also present commendable CO2 adsorption capacity, and Yb-BDC-NH2 was further confirmed by a breakthrough experiment under both dry and wet conditions. Moreover, these materials possess both Lewis acid and Brønsted base sites that can catalyze one-pot tandem deacetalization-Knoevenagel condensation reactions.

Phylogeny, new generic-level classification, and historical biogeography of the Eucera complex (Hymenoptera: Apidae)

The longhorn bee tribe Eucerini (Hymenoptera: Apidae) is a diverse, widely distributed group of solitary bees that includes important pollinators of both wild and agricultural plants. About half of the species in the tribe are currently assigned to the genus Eucera and to a few other related genera. In this large genus complex, comprising ca. 390 species, the boundaries between genera remain ambiguous due to morphological intergradation among taxa. Using ca. 6700 aligned nucleotide sites from six gene fragments, 120 morphological characters, and more than 100 taxa, we present the first comprehensive molecular, morphological, and combined phylogenetic analyses of the ‘Eucera complex’. The revised generic classification that we propose is congruent with our phylogeny and maximizes both generic stability and ease of identification. Under this new classification most generic names are synonymized under an expanded genus Eucera. Thus, Tetralonia, Peponapis, Xenoglossa, Cemolobus, and Syntrichalonia are reduced to subgeneric rank within Eucera, and Synhalonia is retained as a subgenus of Eucera. Xenoglossodes is reestablished as a valid subgenus of Eucera while Tetraloniella is synonymized with Tetralonia and Cubitalia with Eucera. In contrast, we suggest that the venusta-group of species, currently placed in the subgenus Synhalonia, should be recognized as a new genus. Our results demonstrate the need to evaluate convergent loss or gain of important diagnostic traits to minimize the use of potentially homoplasious characters when establishing classifications. Lastly, we show that the Eucera complex originated in the Nearctic region in the late Oligocene, and dispersed twice into the Old World. The first dispersal event likely occurred 24.2–16.6 mya at a base of a clade of summer-active bees restricted to warm region of the Old World, and the second 13.9–12.3 mya at the base of a clade of spring-active bees found in cooler regions of the Holarctic. Our results further highlight the role of Beringia as a climate-regulated corridor for bees.

Impedance-Sum Stability Criterion for Cascaded Power Electronic Systems

: The impedance-ratio criterion has been widely adopted to analyze the stability of cascaded power electronic systems. However, for different cascaded systems, the impedance ratio takes different forms. For cascaded systems with a voltage-controlled source, it is the ratio of the output impedance of the source converter to the input impedance of the load converter. For cascaded systems with a current-controlled source, it is the ratio of the input impedance of the load converter to the output impedance of the source converter. In this paper, a generic stability criterion in terms of the sum of the impedances of individual subsystems is proposed. A cascaded system with individually stable subsystems is stable if and only if the sum of the impedances of the subsystems does not encircle the origin clockwise or equivalently the impedance sum does not have right-half-plan (RHP) zeros. Real-time simulation results are presented to validate this generic stability criterion.

On base sizes for algebraic groups

Let G be a permutation group on a set \Omega . A subset of \Omega  is a base for G if its point-wise stabilizer is trivial; the base size of G is the minimal cardinality of a base. In this paper we initiate the study of bases for algebraic groups defined over an algebraically closed field. In particular, we calculate the base size for all primitive actions of simple algebraic groups, obtaining the precise value in almost all cases. We also introduce and study two new base measures, which arise naturally in this setting. We give an application concerning the essential dimension of simple algebraic groups, and we establish several new results on base sizes for the corresponding finite groups of Lie type. The latter results are an important contribution to the classical study of bases for finite primitive permutation groups. We also indicate some connections with generic stabilizers for representations of simple algebraic groups.

Geometric sigma model of the Universe**Supported by Serbian Ministry of Education, Science and Technological Development (171031)

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity. Although they look like ordinary sigma models, they have the peculiarity that their complete matter content can be gauged away. The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory. The fact that background configuration is specified in advance is another peculiarity of geometric sigma models. In this paper, I construct geometric sigma models based on different background geometries of the Universe. Whatever background geometry is chosen, the dynamics of its small perturbations is shown to have a generic classical stability. This way, any freely chosen background metric is made a stable solution of a simple model. Three particular models of the Universe are considered as examples of how this is done in practice.

Donaldson–Thomas invariants versus intersection cohomology of quiver moduli

Abstract The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure of the stable locus inside the associated coarse moduli space of semistable quiver representations. In fact, we prove an even stronger result relating the Donaldson–Thomas “function” to the intersection complex. The proof of our main result relies on a relative version of the integrality conjecture in Donaldson–Thomas theory. This will be the topic of the second part of the paper, where the relative integrality conjecture will be proven in the motivic context.

Spinors and essential dimension

We prove that spin groups act generically freely on various spinor modules, in the sense of group schemes and in a way that does not depend on the characteristic of the base field. As a consequence, we extend the surprising calculation of the essential dimension of spin groups and half-spin groups in characteristic zero by Brosnan et al. [Essential dimension, spinor groups, and quadratic forms, Ann. of Math. (2) 171 (2010), 533–544], and Chernousov and Merkurjev [Essential dimension of spinor and Clifford groups, Algebra Number Theory 8 (2014), 457–472] to fields of characteristic different from two. We also complete the determination of generic stabilizers in spin and half-spin groups of low rank.

Distance Verification for Classical and Quantum LDPC Codes

The techniques of distance verification known for general linear codes are first applied to the quantum stabilizer codes. Then, these techniques are considered for classical and quantum (stabilizer) low-density-parity-check (LDPC) codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks’ sparsity for both the classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of the quantum stabilizer LDPC codes.

Generic injectivity and stability of inverse problems for connections

ABSTRACTWe consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a compact Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral geometry question of some attenuated geodesic ray transform through a pseudolinearization argument. We show injectivity (up to natural obstructions) and stability estimates for both the linear and nonlinear problems for generic simple metrics and generic connections and Higgs fields, including the real-analytic ones. We consider the problems on simple manifolds to make the exposition of the main ideas clear and concise, many results of this paper still hold under some assumptions weaker than simplicity.

Projectivity and birational geometry of Bridgeland moduli spaces on an Enriques surface

We construct moduli spaces of semistable objects on an Enriques surface for generic Bridgeland stability condition and prove their projectivity. We further generalize classical results about moduli spaces of semistable sheaves on an Enriques surface to their Bridgeland counterparts. Using Bayer and Macr\`{i}'s construction of a natural nef divisor varying with the stability condition, we begin a systematic exploration of the relation between wall-crossing on the Bridgeland stability manifold and the minimal model program for these moduli spaces. We give three applications of our machinery to obtain new information about the classical moduli spaces of Gieseker-stable sheaves: 1) We obtain a region in the ample cone of the moduli space of Gieseker-stable sheaves which works for all unnodal Enriques surfaces. 2) We determine the nef cone of the Hilbert scheme of $n$ points on an unnodal Enriques surface in terms of the classical geometry of its half-pencils and the Cossec-Dolgachev $\phi$-function. 3) We recover some classical results on linear systems on Enriques surfaces and obtain some new ones about $n$-very ample line bundles.

Essential dimension of algebraic groups, including bad characteristic

We give upper bounds on the essential dimension of (quasi-) simple algebraic groups over an algebraically closed field that hold in all characteristics. The results depend on showing that certain representations are generically free. In particular, aside from the cases of spin and half-spin groups, we prove that the essential dimension of a simple algebraic group G of rank at least two is at most dim G - 2(rank G) - 1. It is known that the essential dimension of spin and half-spin groups grows exponentially in the rank. In most cases, our bounds are as good as or better than those known in characteristic zero and the proofs are shorter. We also compute the generic stabilizer of an adjoint group on its Lie algebra.

Robust Stability of Scaled-Four-Channel Teleoperation with Internet Time-Varying Delays.

We describe the application of a generic stability framework for a teleoperation system under time-varying delay conditions, as addressed in a previous work, to a scaled-four-channel (γ-4C) control scheme. Described is how varying delays are dealt with by means of dynamic encapsulation, giving rise to mu-test conditions for robust stability and offering an appealing frequency technique to deal with the stability robustness of the architecture. We discuss ideal transparency problems and we adapt classical solutions so that controllers are proper, without single or double differentiators, and thus avoid the negative effects of noise. The control scheme was fine-tuned and tested for complete stability to zero of the whole state, while seeking a practical solution to the trade-off between stability and transparency in the Internet-based teleoperation. These ideas were tested on an Internet-based application with two Omni devices at remote laboratory locations via simulations and real remote experiments that achieved robust stability, while performing well in terms of position synchronization and force transparency.

Tracking evolution of myoglobin stability in cetaceans using experimentally calibrated computational methods that account for generic protein relaxation

The evolution of cetaceans (whales, dolphins, and porpoises) from land to water is one of the most spectacular events in mammal evolution. It has been suggested that selection for higher myoglobin stability (∆G of folding) allowed whales to conquer the deep-diving niche. The stability of multi-site protein variants, including ancient proteins, is however hard to describe theoretically. From a compilation of experimental ∆∆G vs. ∆G we first find that protein substitutions are subject to large generic protein relaxation effects. Using this discovery, we develop a simple two-parameter model that predicts multi-site ∆∆G as accurately as standard methods do for single-site mutations and reproduces trends in contemporary myoglobin stabilities. We then apply this new method to the study of the evolution of Mb stability in cetaceans: With both methods the main change in stability (about 1kcal/mol) occurred very early, and stability was later relaxed in dolphins and porpoises, but was further increased in the sperm whales. This suggests that single proteins can affect whole organism evolution and indicates a role of Mb stability in the evolution of cetaceans. Transition to the deep-diving niche probably occurred already in the ancestor of contemporary baleen and toothed whales. In summary, we have discovered generic stability relaxation effects in proteins that, when incorporated into a simple model, improves the description of multi-site protein variants.

Kinetic model of metabolic network for xiamenmycin biosynthetic optimisation.

Xiamenmycins, a series of prenylated benzopyran compounds with anti‐fibrotic bioactivities, were isolated from a mangrove‐derived Streptomyces xiamenensis. To fulfil the requirements of pharmaceutical investigations, a high production of xiamenmycin is needed. In this study,, the authors present a kinetic metabolic model to evaluate fluxes in an engineered Streptomyces lividans with xiamenmycin‐oriented genetic modification based on generic enzymatic rate equations and stability constraints. Lyapunov function was used for a viability optimisation. From their kinetic model, the flux distributions for the engineered S. lividans fed on glucose and glycerol as carbon sources were calculated. They found that if the bacterium can utilise glucose simultaneously with glycerol, xiamenmycin production can be enhanced by 40% theoretically, while maintaining the same growth rate. Glycerol may increase the flux for phosphoenolpyruvate synthesis without interfering citric acid cycle. They therefore believe this study demonstrates a possible new direction for bioengineering of S. lividans.

Dimer models and crepant resolutions

We study variations of tautological bundles on moduli spaces of representations of quivers with relations associated with dimer models under a change of stability parameters. We prove that if the tautological bundle induces a derived equivalence for some stability parameter, then the same holds for any generic stability parameter, and any projective crepant resolution can be obtained as the moduli space for some stability parameter. This result is used in [IU] to prove the abelian McKay correspondence without using the result of Bridgeland, King and Reid [BKR01].

Existence and generic stability of cooperative equilibria for multi-leader-multi-follower games

In this paper, we first introduce the notion of cooperative equilibria in multi-leader-multi-follower games, and then establish an existence theorem. Next, we shift out attention to the generic stability of these cooperative equilibria. After studying the class of games satisfying the sufficient conditions of the existence theorem, we identify a dense residual subset of these games whose cooperative equilibria are all essential.

Generic stability of the solution mapping for set-valued optimization problems

In this paper, we consider the generic stability of the weakly efficient solution mapping for set-valued optimization problems. Firstly, we obtain the upper semicontinuity of the weakly efficient solution mapping for set-valued optimization problems. Secondly, we show that, in the sense of Baire category, most set-valued optimization problems are stable. Finally, we give sufficient conditions ensuring the existence of essential. Our results extend and improve the corresponding results of Song et al. (J. Optim. Theory Appl. 156:591-599, 2013).