Instability Line Research Articles

Comparison of two fine sands under torsional loading

In this paper the behaviour of two “standard research sands”, widely used for experimental purposes, is compared in a torsional hollow cylinder apparatus under monotonic and cyclic loading conditions. Both sands are fine and uniform with D50= 0.22 and 0.29 mm, respectively. However, their response to undrained monotonic loading at similar void ratios is dramatically different, with the finer sand showing strength reduction after peak and the coarser sand showing continuous increase in strength with torsional shear. The difference in response is mainly attributed to grain angularity and to a lesser degree to their grading. The results of drained torsional hollow cylinder tests show initial contraction followed by dilation. The stress ratio at phase transformation is uniquely defined by both drained and undrained tests for each sand. Cyclic loading instability is manifested by a sudden increase in shear strain and excess pore-water pressure leading to initial liquefaction. The instability initiates across the instability line for the sand showing strength reduction and across the phase transformation line for the sand showing continuous increase in strength with shearing. Both lines are defined under monotonic loading conditions. The liquefaction, stiffness, and damping characteristics of the sands are given in this paper.

Replica-symmetry breaking: discrete and continuous schemes in the Sherrington–Kirkpatrick model

We study hierarchies of replica-symmetry-breaking solutions of the Sherrington–Kirkpatrick model. Stationarity equations for order parameters of solutions with an arbitrary number of hierarchies are set and the limit to infinite number of hierarchical levels is discussed. In particular, we demonstrate how the continuous replica-symmetry breaking scheme of Parisi emerges and how the limit to infinite-many hierarchies leads to equations for the order-parameter function of the continuous solution. The general analysis is accompanied by an explicit asymptotic solution near the de Almeida–Thouless instability line in the nonzero magnetic field.

Undrained behaviour of Changi sand in triaxial and plane-strain compression

The results of an experimental study of the undrained behaviour of Changi sand under axisymmetric and plane-strain conditions are presented. K0 consolidated undrained plane-strain tests and K0 or isotropically consolidated triaxial tests on very loose and medium dense specimens were conducted. The undrained behaviour of sand at very loose and medium dense states under plane-strain conditions was characterised and compared with that under axisymmetric conditions. It was observed that the undrained behaviour of very loose and medium dense sand under plane strain is similar to that under axisymmetric conditions. However, because of the formation of shear bands in plane-strain tests, the post-peak behaviour of medium dense sand in plane strain is different from that in triaxial tests. It was also established that an instability line for plane-strain conditions can be defined in a way similar to that for axisymmetric conditions. Using the state parameter, a unified relationship between the normalised slope of instability line and the state parameters can be established for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can be used for plane-strain conditions.

Time-Dependent Behaviour and Static Liquefaction Phenomenon of Sand

Recent laboratory and field experiments have confirmed that sand does indeed exhibit time-dependent behaviour. Based on these findings, it was considered necessary to revisit some of the published experimental results on the static liquefaction phenomenon of loose anisotropic Hostun RF sand. Time-dependency might have had a significant influence on the observed undrained response of anisotropic consolidated sand specimens. Specific triaxial tests have been performed and a qualitative analysis is presented in this paper. It is shown that, despite the differences on the anisotropic consolidation path employed, different specimens show qualitatively identical undrained responses if creep periods are performed at identical test stages or if the anisotropic consolidation takes place very slowly. With time, the undrained stiffness and strength are considerably improved and this may explain why the static liquefaction phenomenon is not as common in practice as could be predicted based on an instability line concept. Whereas the original instability line concept was developed independently of time-dependency, in field situations, the liquefaction resistance of the sand can increase with time.

Behavior of Ising Spin Glasses in a Magnetic Field

We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.

Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered, respectively, at +H0 and -H0, presenting the same width sigma . It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely, the single Gaussian distribution (sigma>>H0) and the bimodal one (sigma=0) . The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of sigma , with the possibility of two tricritical points along the same critical frontier. To our knowledge, it is the first time that such a behavior is verified for a spin-glass model in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters H0 and sigma , for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature.

Monotonic and cyclic behaviour of sand under torsional loading

Comprehensive tests were performed to obtain the stress–strain and stiffness characteristics of a fine uniform sand in a hollow cylinder apparatus under monotonic and cyclic torsional loading. Unstable response with a sudden reduction in shear strength after peak was observed under undrained monotonic loading. After a quasi-steady state the specimens showed a phase transformation and a tendency to dilation. Drained torsional hollow cylinder tests showed an equivalent characteristic state marking the transition between contractant and dilatant behaviour and the same line at phase transformation as their undrained counterparts. The instability line, defined under monotonic loading, appears to form a boundary to the behaviour of sand under cyclic loading. Unstable behaviour is introduced when the effective stress path followed by the specimen during cyclic loading reaches the instability line at a shear strain of approximately 0·5%. The first loading cycle is at variance with the following cycles in terms of the stress–dilatancy relationship in drained or the excess pore water pressure generation in undrained torsional hollow cylinder tests. The liquefaction, stiffness and damping characteristics of the sand have been defined.

Instability Conditions of Loose Sand in Plane Strain

When a loose sand specimen is loaded under an undrained condition, it may become unstable. The instability conditions may be specified by an instability line determined using undrained tests. However, the instability behavior of sand has seldom been studied under plane-strain conditions. Experimental data obtained under both triaxial and plane-strain conditions are presented in this paper to define the instability conditions of loose sand under plane-strain conditions. Using the state parameter, a unified relationship can be established between the normalized slope of instability line and the state parameters for both axisymmetric and plane-strain conditions. Using this relationship, the instability conditions established under axisymmetric conditions can also be used for plane-strain conditions.

Static liquefaction of sand in plane strain

Experimental results on the static liquefaction behaviour of sand under plane-strain conditions are presented in this paper. Undrained tests on very loose sand under both plane-strain and axisymmetric conditions were conducted and the results compared. The test data show that the undrained behaviour of sand under plane strain is similar to that under axisymmetric conditions. However, the critical-state line (CSL) on both the q–p′ and the e–p′ planes determined under plane-strain conditions is different from that under axisymmetric conditions. The slope of the CSL is different as a result of the influence of the intermediate principal stress. The state parameter (ψ), which is measured with reference to the CSL in the e – log p′ plane, is also different: the ψ value for plane strain is about 0.05 less than that for axisymmetric conditions for the sand tested. The instability behaviour of very loose sand under undrained plane-strain conditions is also studied. Based on the testing data, a unique relationship between the stress ratio of the instability line and ψ is established to enable the triaxial results to be used for plane-strain conditions.Key words: failure, sands, laboratory tests, liquefaction, shear strength.

Phase diagram of Script N = 4 super-Yang-Mills theory withR-symmetry chemical potentials

The phase diagram of large Nc, weakly-coupled N=4 supersymmetric Yang-Mills theory on a three-sphere with non-zero chemical potentials is examined. In the zero coupling limit, a transition line in the mu-T plane is found, separating a "confined" phase in which the Polyakov loop has vanishing expectation value from a "deconfined" phase in which this order parameter is non-zero. For non-zero but weak coupling, perturbative methods may be used to construct a dimensionally reduced effective theory valid for sufficiently high temperature. If the maximal chemical potential exceeds a critical value, then the free energy becomes unbounded below and no genuine equilibrium state exists. However, the deconfined plasma phase remains metastable, with a lifetime which grows exponentially with Nc (not Nc^2). This metastable phase persists with increasing chemical potential until a phase boundary, analogous to a spinodal decomposition line, is reached. Beyond this point, no long-lived locally stable quasi-equilibrium state exists. The resulting picture for the phase diagram of the weakly coupled theory is compared with results believed to hold in the strongly coupled limit of the theory, based on the AdS/CFT correspondence and the study of charged black hole thermodynamics. The confinement/deconfinement phase transition at weak coupling is in qualitative agreement with the Hawking-Page phase transition in the gravity dual of the strongly coupled theory. The black hole thermodynamic instability line may be the counterpart of the spinodal decomposition phase boundary found at weak coupling, but no black hole tunneling instability, analogous to the instability of the weakly coupled plasma phase is currently known.

Instability of sand–silt mixtures

The instability of the sand–silt mixtures with different amount of fines contents were studied in this paper. It showed that the slope of the instability lines increases with the increasing relative densities, and it approaches the slope of the failure line (steady state line) at a high relative density. The relationship between the peak stress ratio and the intergranular void ratio can be described by a common curve for all the mixtures with fines contents less than the transitional fines content. There may also exist a unique curve for the relationship between the peak stress ratio and interfine void ratio for the mixtures with fines contents higher than the transitional fines content. If the yield strength ratio is used instead of the peak stress ratio, the relationships can be characterized in the same way.

Computer simulation for the precipitation process of Ni75Al7.5V17.5 alloy

Abstract The precipitation mechanism of Ni75Al7.5V17.5 alloy above the L12 instability line, between the L12 and D022 instability lines and below the D022 instability line are studied using microscopic phase-field kinetic equation. This paper is aimed at investigating the effect of temperature on precipitation mechanism and morphological evolution of the alloy. Our simulations demonstrate that the precipitation is a mixed mechanism of non-classical nucleation growth and spinodal decomposition above the L12 instability line. It needs certain thermal fluctuations for nucleation and the number of ϑ phases is small at this temperature. The precipitation mechanism of γ' phase is congruent ordering followed by spinodal decomposition, and ϑ phase is a mixed mechanism of non-classical nucleation growth and spinodal decomposition between the L12 and D022 instability lines. The mechanism below the D022 instability line is similar to that between the L12 and D022 instability lines. With the decrease of the temperature, ordering and phase separation becomes fast, the dimension of γ' phase becomes small, the shape transforms from equiaxed to block, the dimension of ϑ phase becomes large and the shape transforms from strip to circle.

Instability and Static Liquefaction on Proportional Strain Paths for Sand at Low Stresses

The behavior of Hostun RF sand on proportional strain paths at low confining pressures (20 to 100 kPa) is considered in this paper. In such paths, a constant dilation rate is imposed during shear. The usual features of pore pressure increase (contracting material) or decrease (dilating material) are here observed depending upon whether the imposed dilation rate is respectively greater or smaller than the “natural” dilation rate at failure (as measured in a drained test). Particular attention is given to the static liquefaction phenomenon, which is seen to occur for loose as well as dense sand provided the imposed dilation rate is large enough to lead to a continuous pore pressure increase during shear. Instability tests performed at low confining pressures on proportional strain paths show that the instability line is strain path dependent. It does not coincide with the peak deviator stress line in proportional strain paths tests, in general, but does coincide with the line d2W=0 (nil second increment of total work).

Analysis of instability line width and white wall created by the photolithography process

In the photolithography processing of semiconductor, line width is smaller and smaller. Therefore, the requirements of process window are stricter than before. In the small line width, the formation of serious white wall will affect line width and cause rejects in following process. The study conducted research on the control of best focus in which particularly explored the relationship between exposure dose and line width and the phenomenon of white wall generated by focus. The research obtained related coefficients of exposure dose-line width and exposure dose-white wall by coating photo resist of different components with the same thickness on the surface of fused silica wafer. The results of research found that exposure dose might not only change line width but also had important effects on white wall. Among others, the most important factor for exposure dose is the component of sensitivity of photo resist.

Nonergodicity for a van der Waals Glass Model

We examine the question of how glassiness can remain finite in the van der Waals model of structural glass in situations where the Ginzburg criterion near the spinodal line of fluid instability against crystallization is satisfied. For d < 4, d being the dimensionality of space, finite glassiness demands certain conditions for the long-range interaction potential. For 4 < d < 6, no such condition is required, whereas for d > 6, the Ginzburg criterion becomes irrelevant. We comment on the relationship between dynamic and static calculations of the nonergodicity parameter.

Dynamics and criteria for bubble instabilities in a single layer film blowing extrusion

AbstractIn this paper, the performance of a new in‐line scanning camera system for the study of various bubble instabilities in film blowing extrusion is critically evaluated. Three commercial film‐grade polyethylenes, LmPE, LLDPE and LDPE, were used to generate the bubble instabilities. Reliable and objective criteria for differentiating various bubble instabilities such as draw resonance, helicoidal instability, and frost line height instability are proposed by using the new device. Detailed dynamics of each bubble instability was carefully investigated as a function of time in a broad range of the take‐up ratio (TUR), blow‐up ratio (BUR) and frost line height (FLH). In addition, effects of melt temperature and mass flow rates on dynamics of the bubble instabilities are discussed. It was found that the new system could capture the main characteristics of all bubble instabilities quantitatively. It was also found that magnitude and periodicity of radius variation during draw resonance of LmPE decreased as TUR increased at constant FLH and BUR. This implies that the origin of draw resonance in film blowing seems to be different from that observed in fiber spinning. In the case of helicoidal instability, eccentricity, which defines the deviation of the bubble center from the die center, decreased as TUR increased. However, the bubble could not be stabilized as expected. A graphical quantification approach to determine the stable zone in the bubble stability map is also discussed.

Order Stability in Supply Chains: Coordination Risk and the Role of Coordination Stock

The bullwhip effect describes the tendency for the variance of orders in supply chains to increase as one moves upstream from consumer demand. Previous research attributes this phenomenon to both operational and behavioral causes. Operational causes are features of the institutional setting that lead rational agents to amplify changes in demand, while behavioral causes arise from suboptimal decisionmaking. This paper examines causes of the bullwhip through experiments with a serial supply chain, using the Beer Distribution Game. Unlike prior studies, we control all four commonly cited operational causes of the bullwhip, including uncertainty about customer demand. We eliminate demand uncertainty completely by making customer demand constant and known to all participants. Despite these controls, order amplification, instability, and supply line underweighting remain pervasive. We propose a new behavioral cause of the bullwhip, coordination risk, that arises when players place excessive orders to address the perceived risk that others will not behave optimally. We test two strategies to mitigate coordination risk: (1) holding additional on-hand inventory, and (2) creating common knowledge by informing participants of the optimal policy. Both strategies reduce, but not eliminate, the bullwhip effect. Holding excess inventory reduces order amplification by providing a buffer against the endogenous risk of coordination failure. Such coordination stock differs from traditional safety stock, which buffers against exogenous demand uncertainty. Surprisingly, neither strategy reduces supply-line underweighting. We conclude that the bullwhip can be mitigated but its behavioral causes appear robust.

Reply to the discussion by A. Eliadorani and Y.P. Vaid on "Effect of undrained creep on instability behaviour of loose sand"

The discussers stated that the definition used in the note is “misleading.” According to the Oxford Advanced Learner’s Dictionary, the word “misleading” means “giving the wrong idea or impression and make them believe something that is not true.” The definition of instability is clearly defined and used consistently in the note. Therefore, we fail to see in which way it is “misleading.” If the discussers’ disagreement is on the term “undrained creep” or whether the instability should be called creep induced instability, we have explained in the note that the same term has been used and similar behaviour has been studied by Arulanandan et al. (1971) and Sheahan (1995) before for other types of soil. The discussers also stated “drained perturbation will not cause instability” and “there is only one instability line.” This may not be generally true, as it has been observed by a number of researchers (Eckersley 1990; Sasitharan et al. 1993; Chu et al. 2000, 2003b) that instability can occur under drained conditions and the instability line is not unique, but affected by many factors (Imam et al. 2002; Yang 2002). Creep is one of the factors and is studied in this note. The influence of void ratio on the instability line is also illustrated in Fig. 3 of the discussed note.

Unstable behaviour of sand and its implication for slope instability

Results of some constant shear-drained (CSD) tests conducted on both loose and dense sand are presented. Using the critical state line and a modified state parameter, a new framework for analysing the instability of granular soil slopes is proposed. The test data were examined and interpreted using the new framework. Instability lines for sand with different void ratios were established within this framework. The conditions for the occurrence of instability in both contractive and dilative granular soil slopes under various shear stress levels were examined using the proposed framework.Key words: deformation, laboratory tests, liquefaction, sands, shear strength, slope stability.

Charge instabilities in strongly correlated bilayer systems

We investigate the charge-instabilities of the Hubbard-Holstein model with two coupled layers. In this system the scattering processes naturally separate into contributions which are either symmetric or antisymmetric combinations with respect to exchange of the layers. It turns out that the short-range strong correlations suppress finite wave-vector nesting instabilities for both symmetries but favor the occurrence of phase separation in the symmetric channel. Inclusion of a sizeable long-range Coulomb (LRC) interaction frustrates the q=0 instabilities and supports the formation of incommensurate charge-density waves (CDW). Upon reducing doping from half-filling and for small electron-phonon coupling g the CDW instability first occurs in the antisymmetric channel but both instability lines merge with increasing g. While LRC forces always suppress the phase separation instability in the symmetric channel, the CDW period in the antisymmetric sector tends to infinity ( $q_c\to 0$ ) for sufficiently small Coulomb interaction. This feature allows for the possibility of singular scattering over the whole Fermi surface. We discuss possible implications of our results for the bilayer high-T c cuprates.