Construction of stability multipliers for non-linear feedback systems

This paper is concerned with the analysis of the absolute stability of a non-linear autonomous system which consists of a single non-linearity belonging to a particular class, in an otherwise linear feedback loop. It is motivated from the earlier Popovlike frequency-domain criteria using the ' multiplier ' eoncept and involves the construction of ' stability multipliers' with prescribed phase characteristics. A few computer-based methods by which this problem can be solved are indicated and it is shown that this constitutes a stop-by-step procedure for testing the stability properties of a given system.

Zero miss distance guidance using feedforward and periodic control

There have been attempts at obtaining robust guidance laws to ensure zero miss distance (ZMD) for interceptors with parametric uncertainties. All these laws require the plant to be of minimum phase type to enable the overall guidance loop transfer function to satisfy strict positive realness (SPR). The SPR property implies absolute stability of the closed loop system, and has been shown in the literature to lead to ZMD because it avoids saturation of lateral acceleration. In these works higher order interceptors are reduced to lower order equivalent models for which control laws are designed to ensure ZMD. However, it has also been shown that when the original system with right half plane (RHP) zeros is considered, the resulting miss distances, using such strategies, can be quite high. In this paper, an alternative approach using the circle criterion establishes the conditions for absolute stability of the guidance loop and relaxes the conservative nature of some earlier results arising from assumption of in�nite engagement time. Further, a feedforward scheme in conjunction with a lead-lag compensator is used as one control strategy while a generalized sampled hold function is used as a second strategy, to shift the RHP transmission zeros, thereby achieving ZMD. It is observed that merely shifting the RHP zero(s) to the left half plane reduces miss distances signi�cantly even when no additional controllers are used to ensure SPR conditions.

Charge and color breaking constraints in MSSM after the Higgs discovery at LHC

We revisit the constraints on the parameter space of the Minimal Supersymmetric Standard Model (MSSM), from charge and color breaking minima in the light of information on the Higgs from the LHC so far. We study the behavior of the scalar potential keeping two light sfermion fields along with the Higgs in the pMSSM framework and analyze the stability of the vacuum. We find that for lightest stops a parts per thousand(2) 1 TeV and small mu a parts per thousand(2) 500 GeV, the absolute stability of the potential can be attained only for . The bounds become stronger for larger values of the mu parameter. Note that this is approximately the value of Xt which maximizes the Higgs mass. Our bounds on the low scale MSSM parameters are more stringent than those reported earlier in literature. We reanalyze the stau sector as well, keeping both staus. We study the connections between the observed Higgs rates and vacuum (meta)stability. We show how a precision study of the ratio of signal strengths, (mu (gamma gamma) /mu (ZZ) ) can shed further light.

Absolute/Convective Instability Transition in a Backward Facing Step Combustor: Fundamental Mechanism and Influence of Density Gradient

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms-(1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are colocated. Regions in the space of parameters characterizing the base flow velocity profile, i.e., shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on understanding prior experimental studies of combustion instability in backward facing step combustors and hydrodynamic instability in other flows such as heated jets and bluff body stabilized flames is discussed.

ABSOLUTE/CONVECTIVE INSTABILITY TRANSITION IN A BACKWARD FACING STEP COMBUSTOR: FUNDAMENTAL MECHANISM AND INFLUENCE OF DENSITY GRADIENT

Hydrodynamic instabilities of the flow field in lean premixed gas turbine combustors can generate velocity perturbations that wrinkle and distort the flame sheet over length scales that are smaller than the flame length. The resultant heat release oscillations can then potentially result in combustion instability. Thus, it is essential to understand the hydrodynamic instability characteristics of the combustor flow field in order to understand its overall influence on combustion instability characteristics. To this end, this paper elucidates the role of fluctuating vorticity production from a linear hydrodynamic stability analysis as the key mechanism promoting absolute/convective instability transitions in shear layers occurring in the flow behind a backward facing step. These results are obtained within the framework of an inviscid, incompressible, local temporal and spatio-temporal stability analysis. Vorticity fluctuations in this limit result from interaction between two competing mechanisms - (1) production from interaction between velocity perturbations and the base flow vorticity gradient and (2) baroclinic torque in the presence of base flow density gradients. This interaction has a significant effect on hydrodynamic instability characteristics when the base flow density and velocity gradients are co-located. Regions in the space of parameters characterizing the base flow velocity profile, i.e. shear layer thickness and ratio of forward to reverse flow velocity, corresponding to convective and absolute instability are identified. The implications of the present results on prior observations of flow instability in other flows such as heated jets and bluff-body stabilized flames is discussed.

The effect of pH on the unfolding pathway and stability of ribosome-inactivating protein abrin-II

The effect of pH on the unfolding pathway acid the stability of the toxic protein abrin-II have been studied by increasing denaturant concentrations of guanidine hydrochloride and by monitoring the change in 8,1-anilino naphthalene sulfonic acid (ANS) fluorescence upon binding to the hydrophobic sites of the protein. Intrinsic protein fluorescence, far and near UV-circular dichroism (CD) spectroscopy and ANS binding studies reveal that the unfolding of abrin-II occurs through two intermediates at pH 7.2 and one intermediate at pH 4.5. At pH 7.2, the two subunits A and B of abrin-II unfold sequentially. The native protein is more stable at pH 4.5 than at pH 7.2. However, the stability of the abrin-II A-subunit is not affected by a change in pH. These observations may assist in an understanding of the physiologically relevant transmembrane translocation of the toxin.

Thermodynamic characterization of the conformational stability of the homodimeric protein, pea lectin

The conformational stability of the homodimeric pea lectin was determined by both isothermal urea-induced and thermal denaturation in the absence and presence of urea. The denaturation profiles were analyzed to obtain the thermodynamic parameters associated with the unfolding of the protein. The data not only conform to the simple A(2) double left right arrow 2U model of unfolding but also are well described by the linear extrapolation model for the nature of denaturant-protein interactions. In addition, both the conformational stability (Delta G(s)) and the Delta C-p for the protein unfolding is quite high, at about 18.79 kcal/ mol and 5.32 kcal/(mol K), respectively, which may be a reflection of the relatively larger size of the dimeric molecule (M-r 49 000) and, perhaps, a consequent larger buried hydrophobic core in the folded protein. The simple two-state (A(2) double left right arrow 2U) nature of the unfolding process, with the absence of any monomeric intermediate, suggests that the quaternary interactions alone may contribute significantly to the conformational stability of the oligomer-a point that may be general to many oligomeric proteins.

Glass forming ability and stability: Ternary Cu bearing Ti, Zr, Hf alloys

Four Cu bearing alloys of nominal composition Zr25Ti25Cu50, Zr34Ti16Cu50, Zr25Hf25Cu50 and Ti25Hf25Cu50 have been rapidly solidified in order to produce ribbons. All the alloys become amorphous after meltspinning. In the Zr34Ti16Cu50 alloy localized precipitation of cF24 Cu5Zr phase can be observed in the amorphous matrix. The alloys show a tendency of phase separation at the initial stages of crystallization. The difference in crystallization behavior of these alloys with Ni bearing ternary alloys can be explained by atomic size, binary heat of mixing and Mendeleev number. It has been observed that both Laves and Anti-Laves phase forming compositions are suitable for glass formation. The structures of the phases, precipitated during rapid solidification and crystallization can be viewed in terms of Bernal deltahedra and Frank-Kasper polyhedra.

Stability of a Random Diffusion with Linear Drift

We consider a Linear system with Markovian switching which is perturbed by Gaussian type noise, If the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable, We also shaw that under certain conditions the linear system with Markovian switching can be stabilized by such noisy perturbation.

Hingeless-rotor aeromechanical stability in axial and forward flight with wake dynamics

A finite-state wake model is used to investigate aeromechanical stability of hingeless-rotor helicopters in the ground-contact, hover and trimmed-night conditions. The investigation covers three items: (1) the convergence of the damping with increasing number of wake harmonics for the lag regressing, and body pitch and roll modes; (2) a parametric study of the damping over a range of thrust level, advance ratio and number of blades; and (3) correlations, primarily with the damping and frequency measurements of these lag and body modes. The convergence and parametric studies are conducted in the hover and trimmed-flight conditions; they include predictions from the widely used dynamic inflow model. The correlations are conducted in the ground-contact conditions and include predictions from the dynamic inflow and vortex models; recently, this vortex model is proposed for the axial-flight conditions and is used to investigate the coupled free vibrations of rotor flapping and body modes. The convergence and parametric studies show that a finite-state wake model that goes well beyond the dynamic inflow model is required for fairly converged damping, Moreover, the correlations from the finite-state wake, dynamic inflow and vortex models are generally satisfactory.

A new intelligent algorithm for online voltage stability assessment and monitoring

This paper presents a new approach for assessing power system voltage stability based on artificial feed forward neural network (FFNN). The approach uses real and reactive power, as well as voltage vectors for generators and load buses to train the neural net (NN). The input properties of the NN are generated from offline training data with various simulated loading conditions using a conventional voltage stability algorithm based on the L-index. The performance of the trained NN is investigated on two systems under various voltage stability assessment conditions. Main advantage is that the proposed approach is fast, robust, accurate and can be used online for predicting the L-indices of all the power system buses simultaneously. The method can also be effectively used to determining local and global stability margin for further improvement measures.

Stability of Dimeric Interface in Banana Lectin: Insight from Molecular Dynamics Simulations

Banana lectin (Banlec) is a homodimeric non-glycosylated protein. It exhibits the b-prism I structure. High-temperature molecular dynamics simulations have been utilized to monitor and understand early stages of thermally induced unfolding of Banlec. The present study elucidates the behavior of the dimeric protein at four different temperatures and compares the structural and conformational changes to that of the minimized crystal structure. The process of unfolding was monitored by following the radius of gyration, the rms deviation of each residue, change in relative solvent accessibility and the pattern of inter- and intra-subunit interactions. The overall study demonstrates that the Banlec dimer is a highly stable structure, and the stability is mostly contributed by interfacial interactions. It maintains its overall conformation during high-temperature (400–500 K) simulations, with only the unstructured loop regions acquiring greater momentum under such condition. Nevertheless, at still higher temperatures (600 K) the tertiary structure is gradually lost which later extends to loss of secondary structural elements. The pattern of hydrogen bonding within the subunit and at the interface across different stages has been analyzed and has provided rationale for its intrinsic high stability.

Response And Stability Of A Stochastic Beam-Column Using Stochastic Fem

A beam-column resting on continuous Winkler foundation and discrete elastic supports is considered. The beam-column is of variable cross-section and the variation of sectional properties along the axis of the beam-column is deterministic. Young's modulus, mass per unit length and distributed axial loadings of the beam-column have a stochastic distribution. The foundation stiffness coefficient of the Winkler model, the stiffnesses of discrete elastic supports, stiffnesses of end springs and the end thrust, are all considered as random parameters. The material property fluctuations and distributed axial loadings are considered to constitute independent, one-dimension uni-variate homogeneous real stochastic fields in space. The foundation stiffness coefficient, stiffnesses of the discrete elastic supports, stiffnesses of end springs and the end thrust are considered to constitute independent random variables. Static response, free vibration and stability behaviour of the beam-column are studied. Hamilton's principle is used to formulate the problem using stochastic FEM. Sensitivity vectors of the response and stability parameters are evaluated. Using these statistics of free vibration frequencies, mode shapes, buckling parameters, etc., are evaluated. A numerical example is given.

Stability of pargasite during ultrahigh-temperature metamorphism:A consequence of titanium and REE partitioning

Orthopyroxene-clinopyroxene-plagioclase needles and symplectite along the cleavage planes and grain boundaries of fluorine-bearing titanian-ferroan pargasite from the Highland Complex, Sri Lanka, are interpreted as evidence for dehydration melting at ultrahigh-temperature conditions. High Ti (up to 0.4 pfu) and F (XF up to 0.56) content in pargasite extends its stability to higher temperatures, and the composition indicates the dehydration melting reaction may take place at ultrahigh-temperatures (~950 °C) at a pressure around 10 kbar, close to peak metamorphic conditions. The increase of Ti content close to the grain boundaries and cleavage planes in pargasite indicates titanium partitioning from the melt during dehydration melting enhanced the stability of the mineral toward ultrahigh-temperature conditions. The REE content in the pargasite shows a similar behavior to that of titanium. The cores with no breakdown assemblage consist of low and flat REE concentrations with respect to the high and Eu-depleted rim. Clinopyroxene in symplectite and needle-shaped lamellae within the pargasite porphyroblasts have similar REE patterns with slightly low-concentrations relative to that of pargasite. In the breakdown assemblage, LREEs are partitioned mainly into plagioclase while the HREEs are partitioned into orthopyroxene. The REE enrichment in the pargasite rims signals their relative partitioning between pargasite rims and melt. Modeling of the partitioning of Ti and REEs associated with pargasite breakdown demonstrates that its stability is greatly enhanced at UHT conditions. This investigation implies that the stability of hydrous minerals such as amphibole can be extended to UHT conditions, and expands our knowledge of metamorphism in the lower crust.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.