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Although delta ferrite is a very common phase in most austenitic stainless steels, studies about its formation and evolution during slab processing from industrial heats of tens of tons are scarce. The main objective of this research is to study the evolution of delta ferrite (quantity, chemical composition, morphology, and distribution) along the production route from the cast slab to the coil of an industrial heat of 80 tons of 304 stainless steel. Samples were extracted after the following processing steps: continuous casting, first and second hot-rolling pass, and solution-heat-treating, arriving at the final commercial condition. Sample analyses were carried out with several complementary microstructural characterization techniques: optical microscopy, scanning electron microscopy with energy dispersive spectroscopy (EDS), X-ray diffraction, and magnetic measurements of delta ferrite content (feritscope). Thermocalc® indicates that the present continuous cast slab solidifies according to the FA (ferrite-austenite) mode and the final microstructure should be completely austenitic in equilibrium conditions. Nevertheless, delta ferrite is detected along the processing steps, indicating that the steel is out of phase equilibrium. The ferrite content measured after solidification varies significantly across the as-cast slab thickness. Lower values are detected on the surfaces, followed by a gradual increase when moving into the slab, reaching a peak, and finally decreasing at the slab center. This pattern of delta ferrite content is named "M type" distribution. The average content of delta ferrite decreases after each subsequent processing step, namely the two hot-rolling passes and the solution heat-treating. [ABSTRACT FROM AUTHOR]

We report a characterization of the relative stability and structural behavior of various micellar crystals of an athermal model of AB-diblock copolymers in solution. We adopt a previously developed coarse-graining representation of the chains which maps each copolymer on a soft dumbbell. Thanks to this strong reduction of degrees of freedom, we are able to investigate large aggregated systems and for a specific length ratio of the blocks f = MA/(MA + MB) = 0.6, to locate the order-disorder transition of the system of micelles. Above the transition, mechanical and thermal properties are found to depend on the number of particles per lattice site in the simulation box, and the application of a recent methodology for multiple occupancy crystals [B. M. Mladek et al., Phys. Rev. Lett. 99, 235702 (2007)] is necessary to correctly define the equilibrium state. Within this scheme we have performed free energy calculations at two reduced density ρ/ρ* = 4, 5 and for several cubic structures such as fcc, bcc, and A15. At both densities, the bcc symmetry is found to correspond to the minimum of the unconstrained free energy, that is to the stable symmetry among the few considered, while the A15 structure is almost degenerate, indicating that the present system prefers to crystallize in less packed structures. At ρ/ρ* = 4 close to melting, the Lindemann ratio is fairly high (∼0.29) and the concentration of vacancies is roughly 6%. At ρ/ρ* = 5 the mechanical stability of the stable bcc structure increases and the concentration of vacancies accordingly decreases. The ratio of the corona layer thickness to the core radius is found to be in good agreement with experimental data for poly(styrene-b-isoprene)(22-12) in isoprene selective solvent which is also reported to crystallize in the bcc structure. [ABSTRACT FROM AUTHOR]

A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of ∼60 at 500 K and more at room temperature. We describe the implementation of the methodology in the molecular dynamics package AMBER 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering et al., [J. Am. Chem. Soc. 128, 9080 (2006); J. Am. Chem. Soc.129, 2488 (2007)] confirming the accuracy of the most recent measurement on 2,4,6,7,9-pentamethyl-5-(5,5-2H2)methylene-11,11a-dihydro-12H-naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2-methyl-10-(10,10-2H2)methylenebicyclo[4.4.0]dec-1-ene. [ABSTRACT FROM AUTHOR]

Using first-principles density-functional theory and nonequilibrium Green’s function formalism for quantum transport calculation, we study the electronic and transport properties of C20 fullerene molecule. Our results show that the equilibrium conductance of C20 molecule is near 1G0. It is found that the I-V curve displays a linear region centered about V=0 and nonlinear behavior under higher bias voltages and an obvious negative differential resistance phenomenon in a certain bias voltage range. The mechanism for the negative differential resistance behavior of C20 is suggested. The present findings could be helpful for the application of the C20 molecule in the field of single molecular devices or nanometer electronics. [ABSTRACT FROM AUTHOR]

Using first principles method we report the oxidation of Al doped Au clusters. This work is divided into two parts: (i) the equilibrium structures and stability of Al doped Aun-1 clusters (n=2–7,21) and (ii) the interaction of O2 with stable clusters. The calculations are performed using the plane wave pseudopotential approach under the density functional theory and generalized gradient approximation for the exchange and correlation functional. The optimized geometries of Aun-1Al clusters indicate that the substitution of Au by Al results an early onset of three-dimensional structures from tetramer onwards. This is different from the results of transition metal doped Au clusters, where the planar conformation of Au clusters retains up to heptamer. The stability of Aun-1Al clusters has been analyzed based on the binding energy, second difference in energy, and the energy gaps between the highest occupied molecular orbital and lowest unoccupied molecular orbital energy levels. Based on the energetics, the Au3Al and Au5Al clusters are found to have extraordinary stability. The oxidation mechanism of Al doped Au clusters have been studied by the interaction of O2 with Al, Au, AuAl, Au3Al, and Au20Al clusters. It is found that the oxidation of Aun-1Al clusters undergoes via dissociative mechanism, albeit significant charge transfer from Al to Au. Moreover, the O2 molecule prefers to attach at the Al site rather than at the Au site. [ABSTRACT FROM AUTHOR]

An adaptive minimum action method is proposed for computing the most probable transition paths between stable equilibria in metastable systems that do not necessarily have an underlying energy function, by minimizing the action functional associated with such transition paths. This new algorithm uses the moving mesh strategy to adaptively adjust the grid points over the time interval of transition. Numerical examples are presented to demonstrate the efficiency of the adaptive minimum action method. [ABSTRACT FROM AUTHOR]

The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system’s dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model. [ABSTRACT FROM AUTHOR]

We perform microscopic simulations of a reactive dilute gas and study the propagation of an exothermic chemical wave front in an infinite, one-dimensional medium. The simulation results concerning front propagation speed and concentrations, temperature and stream velocity profiles are compared with the results of the integration of the macroscopic continuity equations in the case of fast reactions. The discrepancies between the two approaches are related to a chemically induced departure from local equilibrium. [ABSTRACT FROM AUTHOR]

To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning’s hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to improvements comparable to or even better than those obtained by increasing the cardinal number in the used basis set by one. However, BSE alone is insufficient to improve agreement with experiment, even after additional consideration of inner-shell correlation and quadruple-excitation effects (mean error and standard deviation with extrapolation are -0.014 and 0.047 pm in comparison with mean error and standard deviation of -0.002 and 0.036 pm without extrapolation). Improvement is obtained only when other contributions of similar magnitude as the BSE contributions (e.g., pentuple-excitation effects and relativistic effects) are also considered. A rather large discrepancy (of the order of a few tenths of a picometer) is observed for the F2 molecule indicating an enhanced basis-set requirement for the various contributions in this case. [ABSTRACT FROM AUTHOR]

A thermostatted dynamical model with five degrees of freedom is used to test the fluctuation relation of Evans and Searles (Ω-FR) and that of Gallavotti and Cohen (Λ-FR). In the absence of an external driving field, the model generates a time-independent ergodic equilibrium state with two conjugate pairs of Lyapunov exponents. Each conjugate pair sums to zero. The fluctuation relations are tested numerically both near and far from equilibrium. As expected from previous work, near equilibrium the Ω-FR is verified by the simulation data while the Λ-FR is not confirmed by the data. Far from equilibrium where a positive exponent in one of these conjugate pairs becomes negative, we test a conjecture regarding the Λ-FR [Bonetto et al., Physica D 105, 226 (1997); Giuliani et al., J. Stat. Phys. 119, 909 (2005)]. It was conjectured that when the number of nontrivial Lyapunov exponents that are positive becomes less than the number of such negative exponents, then the form of the Λ-FR needs to be corrected. We show that there is no evidence for this conjecture in the empirical data. In fact, when the correction factor differs from unity, the corrected form of Λ-FR is less accurate than the uncorrected Λ-FR. Also as the field increases the uncorrected Λ-FR appears to be satisfied with increasing accuracy. The reason for this observation is likely to be that as the field increases, the argument of the Λ-FR more and more accurately approximates the argument of the Ω-FR. Since the Ω-FR works for arbitrary field strengths, the uncorrected Λ-FR appears to become ever more accurate as the field increases. The final piece of evidence against the conjecture is that when the smallest positive exponent changes sign, the conjecture predicts a discontinuous change in the “correction factor” for Λ-FR. We see no evidence for a discontinuity at this field strength. [ABSTRACT FROM AUTHOR]

Recent work has demonstrated the Bennett acceptance ratio method is the best asymptotically unbiased method for determining the equilibrium free energy between two end states given work distributions collected from either equilibrium and nonequilibrium data. However, it is still not clear what the practical advantage of this acceptance ratio method is over other common methods in atomistic simulations. In this study, we first review theoretical estimates of the bias and variance of exponential averaging (EXP), thermodynamic integration (TI), and the Bennett acceptance ratio (BAR). In the process, we present a new simple scheme for computing the variance and bias of many estimators, and demonstrate the connections between BAR and the weighted histogram analysis method. Next, a series of analytically solvable toy problems is examined to shed more light on the relative performance in terms of the bias and efficiency of these three methods. Interestingly, it is impossible to conclusively identify a “best” method for calculating the free energy, as each of the three methods performs more efficiently than the others in at least one situation examined in these toy problems. Finally, sample problems of the insertion/deletion of both a Lennard-Jones particle and a much larger molecule in TIP3P water are examined by these three methods. In all tests of atomistic systems, free energies obtained with BAR have significantly lower bias and smaller variance than when using EXP or TI, especially when the overlap in phase space between end states is small. For example, BAR can extract as much information from multiple fast, far-from-equilibrium simulations as from fewer simulations near equilibrium, which EXP cannot. Although TI and sometimes even EXP can be somewhat more efficient in idealized toy problems, in the realistic atomistic situations tested in this paper, BAR is significantly more efficient than all other methods. [ABSTRACT FROM AUTHOR]

The anomaly of specific heat in systems out of equilibrium, especially the measurement procedure dependence of specific heat, is investigated by means of free energy landscape. Introducing measurement procedure which is based on experimental method, we propose a calculation method of specific heat in systems out of equilibrium and find an abrupt change in specific heat between annealed and quenched states. For longer observation time the change in specific heat occurs at lower temperature and becomes sharper. For slower cooling of a system the transition temperature becomes lower. This cooling rate dependence of the transition temperature is consistent with experiments and thus the abrupt change in specific heat can be regarded as the glass transition which is thermally identified. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the elements Si–Cl. Their performance for atomization energies, equilibrium geometries, harmonic vibrational frequencies, and associated infrared intensities is compared with other commonly used basis sets. Atomization energies can be predicted to within 0.01 kJ/mol per atom of the basis set limit by extrapolation of the pc-2, -3, and -4 results. Equilibrium bond distances and harmonic vibrational frequencies can be calculated to within 10-5 Å and 0.5 cm-1, respectively, of the basis set limit. The pc-n basis sets are shown to give comparable or better accuracy than other alternatives, while containing fewer or equal number of primitive basis functions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Microscale contact between two solid surfaces induced by liquid-bridging force was studied in this article. Attention was placed on configurational stability of the liquid between the two contacting bodies. By examining the solutions for describing the shape of the liquid under equilibrium, it was found that these solutions become physically infeasible as the volume of the liquid vanishes. A linear stability analysis was carried out by perturbing the relevant equilibrium configurations and examining the change of the free energy of the system under consideration. The analysis leads to the conclusion that the equilibrium shape of the liquid, that bridges two solids in contact, may become unstable under certain conditions. As its volume diminishes, the liquid may break into smaller droplets. [ABSTRACT FROM AUTHOR]

Abstract This paper presents conditions for self-equilibrium as well as super-stability of the truncated regular hexahedral and octahedral tensegrity structures. Their symmetry can be described by octahedral group in group representation theory, and furthermore, their force density matrix is analytically rewritten in the symmetry-adapted form. The condition for self-equilibrium, in terms of force densities, is found by satisfying the non-degeneracy condition for a tensegrity structure. The condition for super-stability, also in terms of force densities, is further presented by guaranteeing positive semi-definiteness of the force density matrix. [ABSTRACT FROM AUTHOR]

The relationship between the volume fraction of one phase of an equilibrium two-phase medium and other characteristics of the equilibrium state is studied. [ABSTRACT FROM AUTHOR]

Highlights • Six equilibrium attitude configurations are identified in the rotational model formulated by polyhedral approach. • The necessary conditions of stability of equilibrium attitudes are provided. • The linear solutions of periodic attitudes around stable equilibrium attitudes are explicitly presented. • The periodic attitude solutions and families are determined. Abstract In this work, equilibrium attitude configurations, attitude stability and periodic attitude families are investigated for rigid spacecrafts moving on stationary orbits around asteroid 216 Kleopatra. The polyhedral approach is adopted to formulate the equations of rotational motion. In this dynamical model, six equilibrium attitude configurations with non-zero Euler angles are identified for a spacecraft moving on each stationary orbit. Then the linearized equations of attitude motion at equilibrium attitudes are derived. Based on the linear system, the necessary conditions of stability of equilibrium attitudes are provided, and stability domains on the spacecraft's characteristic plane are obtained. It is found that the stability domains are distributed in the first and third quadrants of the characteristic plane and the stability domain in the third quadrant is separated into two regions by an unstable belt. Subsequently, we present the linear solution around a stable equilibrium attitude point, indicating that there are three types of elemental periodic attitudes. By means of numerical approaches, three fundamental families of periodic solutions are determined in the full attitude model. [ABSTRACT FROM AUTHOR]

Abstract Fluid–structure interaction of an inverted flag, which has a free leading edge and a clamped trailing edge, has drawn attention recently because of its novel properties such as divergence stability, a low stability threshold, and large-amplitude flapping motion. In this study, the stability and flapping behaviors of dual inverted flags with finite height are investigated for a side-by-side arrangement, and their noticeable characteristics are compared to those of dual conventional flags. The critical velocity at which the inverted flags break the equilibrium of a straight configuration reduces monotonically when a gap distance between the two flags becomes smaller and an aspect ratio becomes larger, which is also predicted by our linear stability analysis using simple theoretical models of two-dimensional flags and slender flags. After bifurcation, in addition to the synchronized in-phase and out-of-phase modes commonly observed in dual conventional flags, a novel attached mode appears which is mainly observed for small gap distance and small aspect ratio. In this non-linear mode, the leading edges of the two inverted flags touch each other on a midline, and the deformed inverted flags maintain static equilibrium. In a non-linear flapping regime, a new mechanism of a mode transition from an out-of-phase mode to an in-phase mode is identified, which is allowed by the collision of the two flags flapping with large amplitude. [ABSTRACT FROM AUTHOR]

Aristotle ascribes to Anaximander a conception according to which the Earth remains in its place due to uniformity. Plato shows that this argument's validity is based on both the Earth and the universe being spherical. Anaximander, however, believed the Earth to be flat. Since Aetius ascribes the abovementioned reasoning also to Parmenides, in whose work we find hits to spherical shapes, the argument might be based on Parmenides' thoughts. [ABSTRACT FROM AUTHOR]

A chemical Turing instability resulting in steady spatial patterns is examined here when we superimpose a perturbatively small time periodic modulation on its control parameter. Results for both the modified instability threshold and the corresponding growth of the bifurcating solutions are explicitly obtained. In particular, quasiresonant effects originating significant stabilization or destabilization of the system, depending on the model parameters, are predicted for particular values of the forcing frequency. [ABSTRACT FROM AUTHOR]

This study demonstrates the use of wireline logs for the overpressure- mechanisms analysis in a field in the southwestern Malay basin. The development of overpressure means that the fluid movement in the pores is retarded, both vertically and laterally. In many Tertiary basins, overpressure is mainly generated by compaction disequilibrium caused by a high deposition rate and low permeability in shales. In the Malay basin, temperature and highheat flow also play an important role in generating overpressure at a shallow depth, because the geothermal gradient is very high (40-60°C/km). Pore-pressure profiles and crossplots of sonic velocity/vertical effective stress and of velocity/density are used to derive the overpressure-generating mechanisms. The results obtained from the crossplots of 10 wells reveal that in the study area, overpressure is generated by both primary (compactiondisequilibrium) and secondary (fluid-expansion) mechanisms. The overpressure-magnitude analysis suggests that the overpressure generated by the secondary mechanism is very high compared with the primary mechanism. In all the wells, the Eaton (1972) method with an exponent of 3 gives good prediction when overpressure is the result of the compaction-disequilibrium mechanism, but it underpredicted the high pore pressure where the fluidexpansion mechanism is also present. However, by use of a higher Eaton exponent of 5 for the fluid-expansion mechanism, the overpressures are predicted quite well. The Bowers (1995) method, by use of the unloading parameter (U) of 6, is also used for pressure prediction and it gives a reasonably good prediction in the highoverpressure zone of all the wells. [ABSTRACT FROM AUTHOR]

This paper proposes a novel design of a high order closed-loop Sigma-Delta modulator using a fractional-order disturbance observer, which can reduce the influence of possible dispersions of the sensing element and offset the effect of the external disturbance. The proof mass can maintain near its position of equilibrium by using the proposed fractional-order disturbance observer, which ensures a better control of the proof mass displacement, and the small proof mass displacement can enhance the sensor resolution and the overall system performance. Fractional-order disturbance observer possesses stronger robust stability of interference elimination, because the introduction of fractional calculus makes Q-filter expanding from an integer domain to a real-number domain. Experimental results from the proposed architecture shows an increase of more than 2X improved in signal quantization noise ratio compared to the pure high-order closed-loop Sigma-Delta modulator, and also the proposed Sigma-Delta modulator with a fractional-order disturbance observer improves the performance of disturbance attenuation and system robustness. [ABSTRACT FROM AUTHOR]

We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of such tubes, commonly encountered in applications, is represented by quarter- or semi-circular tubular joints used at pipe’s turning points. The stability theory for pipes with non-straight equilibrium configurations, especially for collapsible tubes, allowing dynamical change of the cross-section, has been elusive as it is difficult to accurately develop the dynamic description via traditional methods. We develop a methodology for studying the three-dimensional dynamics of collapsible tubes based on the geometric variational approach. We show that the linear stability theory based on this approach allows for a complete treatment for arbitrary three-dimensional helical configurations of collapsible tubes by reduction to an equation with constant coefficients. We discuss new results on stability loss of straight tubes caused by the cross-sectional area change. Finally, we develop a numerical algorithm for computation of the linear stability using our theory and present the results of numerical studies for both straight and helical tubes. [ABSTRACT FROM AUTHOR]

The Earth masses reside in a near-hydrostatic equilibrium, while the deviations are, for example, manifested in the geoid, which is nowadays well determined by satellite gravimetry. Recent progress in estimating the density distribution of the Earth allows us to examine individual Earth layers and to directly see how the sum approaches the observed anomalous gravitational field. This study evaluates contributions from the crust and the upper mantle taken from the LITHO1.0 model and quantifies the gravitational spectra of the density structure to the depth of 435 km. This is done without isostatic adjustments to see what can be revealed with models like LITHO1.0 alone. At the resolution of 290 km (spherical harmonic degree 70), the crustal contribution starts to dominate over the upper mantle and at about 150 km (degree 130) the upper mantle contribution is nearly negligible. At the spatial resolution <150km, the spectra behavior is driven by the crust, the mantle lid and the asthenosphere. The LITHO1.0 model was furthermore referenced by adding deeper Earth layers from ak135, and the gravity signal of the merged model was then compared with the observed satellite-only model GOCO05s. The largest differences are found over the tectonothermal cold and old (such as cratonic), and over warm and young areas (such as oceanic ridges). The misfit encountered comes from the mantle lid where a velocity–density relation helped to reduce the RMS error by 40%. Global residuals are also provided in terms of the gravitational gradients as they provide better spatial localization than gravity, and there is strong observational support from ESA’s satellite gradiometry mission GOCE down to the spatial resolution of 80–90 km. [ABSTRACT FROM AUTHOR]

Small time-periodic perturbations of an oscillator whose restoring force has a conservative as well as a dissipative component are studied. The stability of the equilibrium and the bifurcation of an invariant two-dimensional torus from the equilibrium are considered. The focus quantity and the bifurcation equation determining the stability and branching character of the equilibrium are constructed. [ABSTRACT FROM AUTHOR]

This paper describes a fish prey–predator model with a new functional response. The dynamics of the system is discussed mainly from the point of view of permanence and stability. We obtain conditions that affect the persistence of the system. Local asymptotic stability of various equilibrium solutions is explored to understand the dynamics of the model system. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional. We then examine possibilities of the existence of bionomic equilibrium. Lastly, the optimal harvesting policy is obtained by using the Pontryagin’s maximum principle. The objective is to maximize the monetary social benefit as well as conservation of the ecosystem. [ABSTRACT FROM AUTHOR]

We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions. [ABSTRACT FROM AUTHOR]

Experiments depict that the physico-mechanical response of miniature devices is microstructure-dependent. However, the classic continuum theory cannot correctly predict the microstructure-dependency. In this paper, the strain gradient theory is employed to examine the dynamic behavior and instability characteristics of miniature varactor with trapezoidal geometry. The governing equation of the varactor is obtained incorporating the effects of Coulomb force, van der Waals (vdW) attraction, squeeze film damping and structural damping. The influences of microstructure on the dynamic instability of equilibrium points are studied by plotting the phase portrait and bifurcation diagrams. It is found that increase in the microstructure parameter enhances the torsional stability. In the presence of the applied voltage, the phase portrait shows the saddle-node bifurcation while for free-standing varactor a subcritical pitchfork bifurcation is observed. [ABSTRACT FROM AUTHOR]

The dynamical behaviors of a diffusive predator-prey model with Beddington-DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones. [ABSTRACT FROM AUTHOR]

Toppling failure is a common mode of instability in layered and blocky rock slopes where rock blocks rotate about their toes and overturn. One of the most important types of toppling failure is slide-toe-toppling. In this failure, rock blocks at the toe of the slope are overturned by the pressure of sliding mass from the upper part of the slope. In the present study, this type of failure is examined through physical and theoretical modeling. The literature on toppling failures is reviewed briefly first and, then, the mechanism of slide-toe-toppling failure is described. To clarify the mechanism of the failure, a series of physical model tests is conducted under static condition by means of a new tilting table apparatus. Then, a theoretical approach is proposed based on limit equilibrium analysis and some new equations are developed for stability analysis of this type of failure. Finally, the results of physical modeling are compared with outcomes of proposed theoretical approach. This comparison shows a good agreement between the theoretical and experimental results. [ABSTRACT FROM AUTHOR]

Due to the X-point singularity, the safety factor tends to infinity as approaching to the last closed flux surface. The numerical treatments of the near X-point behavior become challenging both for equilibrium and stability. The usual solution is to cut off a small fraction of edge region for system stability evaluation or simply use an up-down symmetric equilibrium without X-point as an approximation. In this work, we assess the sensitivity of this type of equilibrium treatments on the stability calculation. It is found that the system stability can depend strongly on the safety factor value (qa) at the edge after the cutting-off. When the edge safety factor value falls in the vicinity of a rational mode number (referred to as the resonant gap), the system becomes quite unstable due to the excitation of the peeling type modes. Instead, when the edge safety factor is outside the resonant gaps, the system is much more stable and the predominant modes become the usual external kink (or ballooning and infernal) type. It is also found that the resonant gaps become smaller and smaller as qa increases. The ideal magnetohydrodynamic peeling ballooning stability diagram is widely used to explain the experimental observations, and the current results indicate that the conventional peeling ballooning stability diagram based on the simplified equilibrium needs to be reexamined. [ABSTRACT FROM AUTHOR]

We show how to compute the spectral function for a scalar theory in two different scenarios: one which disregards backreaction, i.e. the response of the environment to the external particle, and the other one where backreaction is considered. The calculation was performed using the Kadanoff-Baym equation through the Keldysh formalism. When backreaction is neglected, the spectral function is equal to the equilibrium one, which can be represented as a Breit-Wigner distribution. When backreaction is introduced we observed a damping in the spectral function of the thermal bath. Such behavior modifies the damping rate for particles created within the bath. [ABSTRACT FROM AUTHOR]

The problem of changes in the expressions for effective operators of physical quantities (including an effective Hamiltonian) of a nonrigid molecule upon a change in its equilibrium configurations, in the case in which different possible geometries of such configurations correspond to different point groups, is considered for the example of the nonrigid dimethylacetylene molecule CHCCH in the ground electronic state. [ABSTRACT FROM AUTHOR]

In 2015, there were an estimated 10.4 million new (incident) Tuberculosis cases worldwide, of which 5.9 million (56%) were among men, 3.5 million (34%) among women and 1.0 million (10%) among children. People living with HIV accounted for 1.2 million (11%) of all new TB cases. Six countries accounted for 60% of the new cases: India, Indonesia, China, Nigeria, Pakistan and South Africa [3]. In this study we present a deterministic compartmental mathematical model for the dynamics of tuberculosis and incorporate parameters for slow and fast progression from latently infected tuberculosis to infectious tuberculosis using a modified SIS model to show the effect of HIV/AIDS on the spread of Tuberculosis. The disease free and endemic equilibrium states were established. The disease free equilibrium state was analyzed for stability using a modified version of Bellman and Cooke theorem [1]. [ABSTRACT FROM AUTHOR]

In Nigeria, the National Tuberculosis and Leprosy Control Program concentrates only on Infectious Tuberculosis treatment leaving the Latently infected ones on the waiting list at the mercy of their immune system. In this research we modeled the effect of combining Immunization with Latent Tuberculosis treatment in controlling the spread of Tuberculosis. We established the existence of equilibrium states and analyzed the Disease free equilibrium state for stability using Routh-Hurwitz Theorem. The disease free equilibrium state (i.e., the state of total eradication of Tuberculosis) will be stable if effort is intensified in bringing down both the contraction rate β and the rate of break down to Infectious Tuberculosis T. [ABSTRACT FROM AUTHOR]

Present work is devoted to the investigation of equilibrium composition and thermodynamic characteristics of Ni-0.5C-15Cr-3.2Si-2B alloy in the wide range of temperatures at the common pressure ( P) of 10 Pa. Investigations were carried out using the thermodynamic modeling method. As a software the program complex TERRA was used. The temperature dependences of the integral and partial excess thermodynamic characteristics (enthalpy, entropy and Gibbs energy) and equilibrium composition of alloys were obtained. [ABSTRACT FROM AUTHOR]

The rate-controlled constrained-equilibrium (RCCE) method is a thermodynamics-based dimension reduction method that enables representation of chemistry involvingnschemical species in terms of a smaller number,nr, of constraints, and thus reduces the computational burden imposed by detailed chemical kinetics. The accuracy in the reduced description by RCCE strongly depends on the specification of constraints. In this work, the connection between the RCCE method and the conventional partial equilibrium assumption (PEA) method is revisited. It is shown that with the constraints being specified based on rate-controlling slow reactions, the RCCE method is equivalent to PEA. A criterion based on time scale analysis is then employed for the identification of fast reactions. Then the importance index, which represents the contribution of individual species to the slow dynamics of a reactive system, is proposed for the selection of species constraints in RCCE. This makes the thermodynamics-based constrained equilibrium manifolds (CEMs) a good approximation to the actual kinetics-controlled slow invariant manifolds (SIMs) in reactive systems. The method is demonstrated in the reduced descriptions of perfectly stirred reactors (PSRs) burning stoichiometric methane/air mixtures. Sample reaction states ranging from near-equilibrium conditions to the extinction turning points on theS-curve are examined for the identification of fast reactions and species constraints. Reduced descriptions of transient PSRs by RCCE are subsequently performed with their accuracy assessed against the full descriptions, in which all the chemical species are transported. The study shows that the dynamics predicted by RCCE agrees well with that from the full description and that near-limit reaction states are important for the selection of species constraints in RCCE. [ABSTRACT FROM PUBLISHER]

Engineering students on control courses lack a deep understanding of equilibrium and stability that are crucial concepts in this discipline. Several studies have shown that students find it difficult to understand simple familiar or academic static equilibrium cases as well as dynamic ones from mechanics even if they know the discipline’s criteria and formulae. Our aim is to study the impact of a specific and innovative classroom session, containing well-chosen situations that address students’ misconceptions. We propose an example of Active Learning experiment based both on the Didactical Engineering methodology and the Conceptual Fields Theory that aims at promoting a conceptual change in students. The chosen methodology allows, at the same time, a proper design of the student learning activities, an accurate monitoring of the students’ rational use during the tasks and provides an internal tool for the evaluation of the session’s efficiency. Although the expected starting conceptual change was detected, it would require another activity in order to be reinforced. [ABSTRACT FROM PUBLISHER]

Models used in simulation may give accurate shortterm trajectories but distort long-term (statistical) properties. In this work, we augment a given approximate model with a control law (a 'thermostat') that gently perturbs the dynamical system to target a thermodynamic state consistent with a set of prescribed (possibly evolving) observations. As proof of concept, we provide an example involving a point vortex fluid model on the sphere, for which we show convergence of equilibrium quantities (in the stationary case) and the ability of the thermostat to dynamically track a transient state. [ABSTRACT FROM AUTHOR]

In this paper, for vector equilibrium problems where the ordering relations are defined via improvement sets, linear scalarization characterizations are established, which include the well-known ones for vector optimization problems in the literature as special cases. By applying the obtained results, some continuity (both lower and upper semicontinuities) conclusions of parametric problems with respect to vector equilibria through improvement sets are deduced using scalarization approaches. Several unsolved or interesting problems are also proposed. [ABSTRACT FROM PUBLISHER]

Spacing distance control for an autonomous vehicle-following system is studied in this paper. An improved active disturbance rejection control (ADRC) technique is proposed. The extended state observer (ESO) in traditional ADRC is replaced by a predictive extended state observer (PESO), which is used to estimate virtual disturbance, i.e., the total effect caused by unmodeled dynamics and internal/external disturbances. A confidence function is proposed to describe the reliability of the PESO. A controller based on the PESO is designed to suppress virtual disturbance and maintain system stability around equilibrium. Based on the proposed method, spacing distance control for a vehicle-following system is modeled as a single-input single-output linear time invariant system with disturbance. The stability of the PESO is analyzed with the prescribed H∞ attenuation level. The simulation results also show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The motion of Lagrange's top in the homogeneous gravity field is considered under the assumption that its suspension point accomplishes a specified high-frequency periodic motion with small amplitude (fast vibrations) in the three-dimensional space. The investigation is carried out in the framework of the approximate autonomous system of canonical equations of motion. Stationary rotations of Lagrange's top around its dynamical symmetry axis for a number of particular cases of the suspension point motions are found as positions of equilibriums of the reduced two-degree-of-freedom system. The linear and nonlinear analysis for their stability is carried out. The problems discussed in the report are new and have no analogues in domestic and foreign literature. [ABSTRACT FROM AUTHOR]

The stratified rock of Jurassic strata is widely distributed in Three Gorges Reservoir Region. The limit equilibrium method is generally utilized in the stability analysis of rock slope with single failure plane. However, the stratified rock slope cannot be accurately estimated by this method because of different bedding planes and their variable shear strength parameters. Based on the idealized model of rock slope with bedding planes, a modified limiting equilibrium method is presented to determine the potential sliding surface and the factor of safety for the stratified rock slope. In this method, the S-curve model is established to define the spatial variations of the shear strength parameters c and  φ of bedding plane and the tensile strength of rock mass. This method was applied in the stability evaluation of typical stratified rock slope in Three Gorges Reservoir Region, China. The result shows that the factor of safety of the case study is 0.973, the critical sliding surface for the potential slip surface appears at bedding plane C, and the tension-controlled failure occurs at 10.5 m to the slope face. [ABSTRACT FROM AUTHOR]

The response of spatially extended systems to a force leading their steady state out of equilibrium is strongly affected by the presence of disorder. We focus on the mean velocity induced by a constant force applied on one-dimensional interfaces. In the absence of disorder, the velocity is linear in the force. In the presence of disorder, it is widely admitted, as well as experimentally and numerically verified, that the velocity presents a stretched exponential dependence in the force (the so-called 'creep law'), which is out of reach of linear response, or more generically of direct perturbative expansions at small force. In dimension one, there is no exact analytical derivation of such a law, even from a theoretical physical point of view. We propose an effective model with two degrees of freedom, constructed from the full spatially extended model, that captures many aspects of the creep phenomenology. It provides a justification of the creep law form of the velocity-force characteristics, in a quasistatic approximation. It allows, moreover, to capture the non-trivial effects of short-range correlations in the disorder, which govern the low-temperature asymptotics. It enables us to establish a phase diagram where the creep law manifests itself in the vicinity of the origin in the force-system-size-temperature coordinates. Conjointly, we characterise the crossover between the creep regime and a linear-response regime that arises due to finite system size. [ABSTRACT FROM AUTHOR]

Using several theoretical tools $$\ldots $$ (i) the nucleation theorem, (ii) an equivalent cavity, (iii) the reversible work of adding a cavity to an open hard sphere system, and (iv) the theory of 'stability'... the authors estimated the density at which the hard sphere freezing transition occurs. No direct involvement of the equilibrium solid phase is involved. The reduced density $$\uppi a^3\rho _f/6$$ (where a is the hard sphere diameter and $$\rho _f $$ is the actual density at which freezing occurs) is found to be 0.4937 while the value obtained by computer simulation is 0.494. The agreement is good, but the new method still contains some approximation. However, the approximation is based on the idea that at a density just below $$\rho _f $$ the fluid adopts a distorted structure resembling the solid, but different enough so that long-range order vanishes. Initial loss of stability may not be involved in every fluid-solid transition, but it may be an early step in the hard sphere and related systems. [ABSTRACT FROM AUTHOR]