Effective Q Criterion for Disk Stability in an External Potential

The standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to the unperturbed rotational field and significantly increases its stability. We obtain the values for the effective Q parameter for the Milky Way and for a low surface brightness galaxy, UGC 7321. We find that in each case the stellar disk by itself is barely stable and it is the dark matter halo that stabilizes the disk against local, axisymmetric gravitational instabilities. Thus, the dark matter halo is necessary to ensure local disk stability. This result has been largely missed so far because in practice the Q parameter for a galactic disk is obtained using the observed rotational field that already includes the effect of the halo

Residue specific contributions to stability and activity inferred from saturation mutagenesis and deep sequencing

Multiple methods currently exist for rapid construction and screening of single-site saturation mutagenesis (SSM) libraries in which every codon or nucleotide in a DNA fragment is individually randomized. Nucleotide sequences of each library member before and after screening or selection can be obtained through deep sequencing. The relative enrichment of each mutant at each position provides information on its contribution to protein activity or ligand-binding under the conditions of the screen. Such saturation scans have been applied to diverse proteins to delineate hot-spot residues, stability determinants, and for comprehensive fitness estimates. The data have been used to design proteins with enhanced stability, activity and altered specificity relative to wild-type, to test computational predictions of binding affinity, and for protein model discrimination. Future improvements in deep sequencing read lengths and accuracy should allow comprehensive studies of epistatic effects, of combinational variation at multiple sites, and identification of spatially proximate residues.

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example. (C) 2014 Elsevier Ltd. All rights reserved.

Solving Axisymmetric Stability Problems by Using Upper Bound Finite Elements, Limit Analysis, and Linear Optimization

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

EFFECTIVE Q CRITERION FOR DISK STABILITY IN AN EXTERNAL POTENTIAL

standard Q criterion (with Q > 1) describes the stability against local, axisymmetric perturbations in a disk supported by rotation and random motion. Most astrophysical disks, however, are under the influence of an external gravitational potential, which can significantly affect their stability. A typical example is a galactic disk embedded in a dark matter halo. Here, we do a linear perturbation analysis for a disk in an external potential and obtain a generalized dispersion relation and the effective stability criterion. An external potential, such as that due to the dark matter halo concentric with the disk, contributes to the unperturbed rotational field and significantly increases its stability. We obtain the values for the effective Q parameter for the Milky Way and for a low surface brightness galaxy, UGC 7321. We find that in each case the stellar disk by itself is barely stable and it is the dark matter halo that stabilizes the disk against local, axisymmetric gravitational instabilities. Thus, the dark matter halo is necessary to ensure local disk stability. This result has been largely missed so far because in practice the Q parameter for a galactic disk is obtained using the observed rotational field that already includes the effect of the halo.

Stability of a circular tunnel in presence of pseudostatic seismic body forces

The stability of a long circular tunnel in a cohesive frictional soil medium has been determined in the presence of horizontal pseudo-static seismic body forces. The tunnel is supported by means of lining and anchorage system which is assumed to exert uniform internal compressive normal pressure on its periphery. The upper bound finite element limit analysis has been performed to compute the magnitude of the internal compressive pressure required to support the tunnel. The results have been presented in terms of normalized compressive normal stress, defined in terms of sigma(i)/c; where sigma(i) is the magnitude of the compressive normal pressure on the periphery of the tunnel and c refers to soil cohesion. The variation of sigma(i)/c with horizontal earthquake acceleration coefficient (alpha(h)) has been established for different combinations of H/D, gamma D/c and phi where (i) H and D refers to tunnel cover and diameter, respectively, and (ii) gamma and phi correspond to unit weight and internal friction angle of soil mass, respectively. Nodal velocity patterns have also been plotted for assessing the zones of significant plastic deformation. The analysis clearly reveals that an increase in the magnitude of the earthquake acceleration leads to a significant increment in the magnitude of internal compressive pressure. (C) 2014 Elsevier Ltd. All rights reserved.

Stability of Unsupported Vertical Circular Excavations

A methodology has been presented for determining the stability of unsupported vertical cylindrical excavations by using an axisymmetric upper bound limit analysis approach in conjunction with finite elements and linear optimization. For the purpose of excavation design, stability numbers (S-n) have been generated for both (1) cohesive-frictional soils and (2) pure cohesive soils, with an additional provision accounting for linearly increasing cohesion with increasing depth by means of a nondimensional factor m. The variation of S-n with H/b has been established for different values of m and phi, where H and b refer to the height and radius of the cylindrical excavation. A number of useful observations have been gathered about the variation of the stability number and nodal velocity patterns as H/b, phi, and m change. The results of the analysis compare quite well with the different solutions reported in the literature. (C) 2014 American Society of Civil Engineers.

Crack stability in edge-notched clamped beam specimens: modeling and experiments

Stability of a fracture toughness testing geometry is important to determine the crack trajectory and R-curve behavior of the specimen. Few configurations provide for inherent geometric stability, especially when the specimen being tested is brittle. We propose a new geometrical construction called the single edge notched clamped bend specimen (SENCB), a modified form of three point bending, yielding stable cracking under load control. It is shown to be particularly suitable for small-scale structures which cannot be made free-standing, (e.g., thin films, coatings). The SENCB is elastically clamped at the two ends to its parent material. A notch is inserted at the bottom center and loaded in bending, to fracture. Numerical simulations are carried out through extended finite element method to derive the geometrical factor f(a/W) and for different beam dimensions. Experimental corroborations of the FEM results are carried out on both micro-scale and macro-scale brittle specimens. A plot of vs a/W, is shown to rise initially and fall off, beyond a critical a/W ratio. The difference between conventional SENB and SENCB is highlighted in terms of and FEM simulated stress contours across the beam cross-section. The `s of bulk NiAl and Si determined experimentally are shown to match closely with literature values. Crack stability and R-curve effect is demonstrated in a PtNiAl bond coat sample and compared with predicted crack trajectories from the simulations. The stability of SENCB is shown for a critical range of a/W ratios, proving that it can be used to get controlled crack growth even in brittle samples under load control.

Coordination of Reactive Power in Grid-Connected Wind Farms for Voltage Stability Enhancement

This paper studies the feasibility of utilizing the reactive power of grid-connected variable-speed wind generators to enhance the steady-state voltage stability margin of the system. Allowing wind generators to work at maximum reactive power limit may cause the system to operate near the steady-state stability limit, which is undesirable. This necessitates proper coordination of reactive power output of wind generators with other reactive power controllers in the grid. This paper presents a trust region framework for coordinating reactive output of wind generators-with other reactive sources for voltage stability enhancement. Case studies on 418-bus equivalent system of Indian southern grid indicates the effectiveness of proposed methodology in enhancing the steady-state voltage stability margin.

Temperature-dependent stability of stacking faults in Al, Cu and Ni: first-principles analysis

We present comparative analysis of microscopic mechanisms relevant to plastic deformation of the face-centered cubic (FCC) metals Al, Cu, and Ni, through determination of the temperature-dependent free energies of intrinsic and unstable stacking faults along 1 (1) over bar 0] and 1 (2) over bar 1] on the (1 1 1) plane using first-principles density-functional-theory-based calculations. We show that vibrational contribution results in significant decrease in the free energy of barriers and intrinsic stacking faults (ISFs) of Al, Cu, and Ni with temperature, confirming an important role of thermal fluctuations in the stability of stacking faults (SFs) and deformation at elevated temperatures. In contrast to Al and Ni, the vibrational spectrum of the unstable stacking fault (USF1 (2) over bar 1]) in Cu reveals structural instabilities, indicating that the energy barrier (gamma(usf)) along the (1 1 1)1 (2) over bar 1] slip system in Cu, determined by typical first-principles calculations, is an overestimate, and its commonly used interpretation as the energy release rate needed for dislocation nucleation, as proposed by Rice (1992 J. Mech. Phys. Solids 40 239), should be taken with caution.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

Small-Signal Stability Analysis of an Open-loop Induction Motor Drive Including the Effect of Inverter Dead-Time

This paper demonstrates light-load instability in open-loop induction motor drives on account of inverter dead-time. The dynamic equations of an inverter fed induction motor, incorporating the effect of dead-time, are considered. A procedure to derive the small-signal model of the motor, including the effect of inverter dead-time, is presented. Further, stability analysis is carried out on a 100-kW, 415V, 3-phase induction motor considering no-load. For voltage to frequency (i.e. V/f) ratios between 0.5 and 1 pu, the analysis brings out regions of instability on the V-f plane, in the frequency range between 5Hz and 20Hz. Simulation and experimental results show sub-harmonic oscillations in the motor current in this region, confirming instability as predicted by the analysis.

Structure, stability and elasticity of DNA nanotubes

DNA nanotubes are tubular structures composed of DNA crossover molecules. We present a bottom up approach for the construction and characterization of these structures. Various possible topologies of nanotubes are constructed such as 6-helix, 8-helix and tri-tubes with different sequences and lengths. We have used fully atomistic molecular dynamics simulations to study the structure, stability and elasticity of these structures. Several nanosecond long MD simulations give the microscopic details about DNA nanotubes. Based on the structural analysis of simulation data, we show that 6-helix nanotubes are stable and maintain their tubular structure; while 8-helix nanotubes are flattened to stabilize themselves. We also comment on the sequence dependence and the effect of overhangs. These structures are approximately four times more rigid having a stretch modulus of similar to 4000 pN compared to the stretch modulus of 1000 pN of a DNA double helix molecule of the same length and sequence. The stretch moduli of these nanotubes are also three times larger than those of PX/JX crossover DNA molecules which have stretch moduli in the range of 1500-2000 pN. The calculated persistence length is in the range of a few microns which is close to the reported experimental results on certain classes of DNA nanotubes.

First-Principles Study on Structural Stability of Belite

A first-principles study was carried out to investigate the stability of the crystal structure of beta-form belite (beta-C2S) substituted by Sr atoms as trace impurities for Ca atoms in CaOx polyhedra. The effect of the connection types of CaOx polyhedral, in the form of common-edge bond and common-face bond, upon the crystal stability is described. The Ca-Ca interatomic distance closely relates to the hydraulic activity of beta-C2S. The beta-C2S substituted by an Sr atom for Ca(1) atoms having seven Ca-O bonds is energetically more stable than that substituted by an Sr atom for Ca(2) atoms having eight Ca-O bonds. The Sr-doped beta-C2S having a common face bond with SrOx polyhedra is energetically more favorable and results in structural stability compared with that having a common edge bond with SrOx polyhedra.

Electrospun SnSb Crystalline Nanoparticles inside Porous Carbon Fibers as a High Stability and Rate Capability Anode for Rechargeable Batteries

In an electrochemical alloying reaction, the electroactive particles become mechanically unstable owing to large volume changes occurring as a result of high amounts of lithium intake. This is detrimental for long-term battery performance. Herein, a novel synthesis approach to minimize such mechanical instabilities in tin particles is presented. An optimal one-dimensional assembly of crystalline single-phase tin-antimony (SnSb) alloy nanoparticles inside porous carbon fibers (abbreviated SnSb-C) is synthesized for the first time by using the electrospinning technique (employing non-oxide precursors) in combination with a sintering protocol. The ability of antimony to alloy independently with lithium is beneficial as it buffers the unfavorable volume changes occurring during successive alloying/dealloying cycles in Sn. The SnSb-C assembly provides nontortuous (tortuosity coefficient, =1) fast conducting pathways for both electrons and ions. The presence of carbon in SnSb-C completely nullifies the conventional requirement of other carbon forms during cell electrode assembly. The SnSb-C exhibited remarkably high electrochemical lithium stability and high specific capacities over a wide range of currents (0.2-5Ag(-1)). In addition to lithium-ion batteries, it is envisaged that SnSb-C also has potential as a noncarbonaceous anode for other battery chemistries, such as sodium-ion batteries.