Critical Number Research Articles

Stability of penetrative convective currents in local thermal non-equilibrium

The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the basic state, with particular regard to the behaviour of stability thresholds with respect to the relevant physical parameters characterizing the problem. The Chebyshev- τ method and the shooting method are employed and accurately implemented to solve the differential eigenvalue problems arising from linear and nonlinear analyses to determine critical Rayleigh numbers. Via numerical simulations, the stabilizing effect of the upper bounding plane temperature, of the Darcy number and of the interaction coefficient for the heat exchange, is demonstrated.

Bounce and contact mode regimes for drop impact on smooth surfaces: The influence of gas kinetics and electrostatics

When liquid drops impact on solid surfaces, an air layer forms in between the drop and the surface, acting as a cushion to mitigate the impact. In this work, we focus on delineating the bounce and contact mode regimes of impacting drops on smooth surfaces, specifically discerning whether drops rebound from the air layer or make contact with the solid surfaces, and pinpointing the precise contact modes between the drop and solid surfaces by resolving the gas film evolution and rupture. Our simulation model incorporates gas kinetics and electrostatics effects, both of which have been validated by experiments documented in the literature or theoretical models regarding thin film instabilities. We undertake a comprehensive review and categorization of the contact modes and elucidate how they change under different conditions of impact velocities, ambient pressures, and electric field intensities. We also provide some perspectives on the regime map for the lubricated surfaces, which contains an unresolved issue that the critical Weber number for bouncing-wetting transition is significantly reduced compared to the solid smooth surfaces like mica. These insights have noteworthy practical implications offering guidance for a wide range of scenarios, from normal-pressure environments to low-pressure conditions at high altitudes, encompassing high electric field conditions such as nanogenerators as well as low electric field conditions resembling glass surfaces with static electricity.

Unifying model for the rheological behavior of hygroresponsive materials.

Hygroresponsive materials exhibit a complex structure-to-property relationship. The interactions of water within these materials under varying hygric and mechanical loads play a crucial role in their macroscopic deformation and final application. While multiple models are available in literature, many lack a comprehensive physical understanding of these phenomena. In this paper, we introduce a stick-slip fiber bundle model that captures the fundamental behaviors of hygroresponsive materials. We incorporate moisture-dependent elements and rules governing the initiation and relaxation of slip strains as well as failure to the statistical approach offered by fiber bundle models. The additional features are based on well-founded interpretations of the structure-to-property relationship in cellulosic materials. Slip strains are triggered by changes in load and moisture, as well as by creep deformations. When subjected to moisture cycles, the model accumulates slip strains, resulting in mechanosorptive behavior. When the load is removed, slip strains are partially relaxed, and subsequent moisture cycles trigger further relaxation, as expected from observations with mechanosorptive material. Importantly, these slip strains are not considered plastic strains; instead, they are unified, nonlinear frozen strains, activated by various stimuli. Failure of fibers is defined by a critical number of slip events allowing for an integrated simulation from intact, via damaged, failed states. We investigate the transition between these regimes upon changes in the hygric and mechanical loading history for relevant parameter ranges. Our enhanced stick-slip fiber bundle model increases the understanding of the intricate behavior of hygroresponsive materials and contributes to a more robust framework for analyzing and interpreting their properties.

Influence of Two-Frequency Rotational Modulation on the Dynamics of the Rayleigh–Bénard Convection in Water-Based Nanoliquids with Either AA7072 or AA7075 Nanoparticles

The effect of time-periodic two-frequency rotation modulation on Rayleigh–Bénard convection in water with either AA7072 or AA7075 nanoparticles is investigated. The single-phase description of the Khanafer–Vafai–Lightstone model is used for modeling the nanoliquids. An asymptotic expansion procedure is adopted in the case of the linear stability to obtain the correction (due to modulation) to the Rayleigh number at marginal stability of unmodulated convection. A nonlinear regime of convection is considered with a nonautonomous generalized Lorenz model as the governing equation. The method of multiscales is then employed to obtain the coupled nonautonomous Ginzburg–Landau equations with cubic nonlinearity from the Lorenz model. These equations are presented in the phase-amplitude form and the amplitude is used to quantify the heat transport. The modulation amplitude is considered to be small (of order less than unity) and moderate frequencies of modulation are considered. We found that there is a threshold frequency beyond which the system behavior reverses. At frequencies below the threshold, the mean Nusselt number increases with an increase in the amplitude of modulation while an opposite influence is seen for values above the threshold. Such a behavior is a consequence of what is analogously seen in the case of the critical Rayleigh number. The influence of two-frequency modulation is more pronounced on the results of the linear and nonlinear regimes compared to that of the single-frequency one. The heat transport is enhanced due to the presence of dilute concentration of suspended nanoparticles (either AA7072 or AA7075 nanoalloys) in water. The influence of nanoparticles is to modify the threshold values generating chaos but it does not qualitatively alter the dynamical behavior of the system. The plots of Lyapunov exponents reveal that there is no possibility of hyper-chaos in the generalized Lorenz model when there is a rotational modulation.

Double Buffers CEM-TD3: More Efficient Evolution and Richer Exploration

CEM-TD3 is a combination scheme using the simple cross-entropy method (CEM) and Twin Delayed Deep Deterministic policy gradient (TD3), and it achieves a satisfactory trade-off between performance and sample efficiency. However, we find that CEM-TD3 cannot fully address the low efficiency of policy search caused by CEM, and the policy gradient learning introduced by TD3 will weaken the diversity of individuals in the population. In this paper, we propose Double Buffers CEM-TD3 (DBCEM-TD3) that optimizes both CEM and TD3. For CEM, DBCEM-TD3 maintains an actor buffer to store the population required for evolution. In each iteration, it only needs to generate a small number of actors to replace the poor actors in the policy buffer to achieve more efficient evolution. The fitness of individuals in the actor buffer decreases exponentially with time, which can avoid premature convergence of the mean actor. For TD3, DBCEM-TD3 maintains a critic buffer with the same number of critics as the number of actors generated in each iteration, and each critic is trained independently by sampling from the shared replay buffer. In each iteration, each newly generated actor uses different critics to guide learning. This ensures more diverse behaviors among the learned actors, enabling richer experiences to be collected during the evaluation phase. We conduct experimental evaluations on five continuous control tasks provided by OpenAI Gym. DBCEM-TD3 outperforms CEM-TD3, TD3, and other classic off-policy reinforcement learning algorithms in terms of performance and sample efficiency.

Explosive epidemic transitions induced by quarantine fatigue

Quarantine measures are one of the first lines of defense against the spread of infectious diseases. However, maintaining these measures over extended periods can be challenging due to a phenomenon known as quarantine fatigue. In this paper, we investigate the impact of quarantine fatigue on the spread of infectious diseases by using an epidemic model on random networks with cliques. In our model, susceptible individuals can be quarantined up to n times, after which they stop complying with quarantine orders due to fatigue. Our results show that quarantine fatigue may induce a regime in which increasing the probability of detecting and isolating infected individuals (along with their close contacts) could subsequently increase the expected number of cases at the end of an outbreak. Moreover, we observe that quarantine fatigue can trigger an abrupt phase transition at the critical reproduction number R0=1. Finally, we explore a scenario where a non-negligible number of individuals are infected at the beginning of an epidemic, and our results show that, depending on the value of n, an abrupt transition between a controlled epidemic and a large epidemic event can occur for R0<1.

Investigation on the intrinsic instabilities of ethyl methyl carbonate flames

The intrinsic instabilities of ethyl methyl carbonate flames are investigated at equivalence ratios (0.6–1.8) and initial pressures (70–160 kPa) by using a 36-liter constant volume combustion chamber. The unstable laminar premixed flame is evaluated by the laminar burning velocity, explosion characteristics, flame cellularity, and flame self-acceleration. The experimental laminar burning velocity is well reproduced by the chemical kinetic mechanism. The extent of cellularization characterized by the crack length and average cell area non-monotonically varies with increasing equivalence ratio but monotonically increases with increasing initial pressure. Meanwhile, the critical flame radius for the onset of cellularity exhibits non-monotonic variation with the equivalence ratio, while it decreases monotonically with increasing initial pressure. The experimental critical Peclet number and critical flame radius are well captured by flame stability theory. The linear correlation between the critical Peclet number and the Markstein number is Pecl = 26.46 Ma + 122.22. In addition, the dependence of the critical Karlovitz number on the Markstein number is predicted as Kacl = 0.0226e-0.0880Ma. The flame self-acceleration increases as the flame instabilities increase. The acceleration exponent and fractal dimension are smaller than 1.5 and 2.33, respectively, which are the suggested values for flame self-turbulization.

Nonlinear ice sheet/liquid interaction in a channel with an obstruction

The interaction between the flow in a channel with an obstruction on the bottom and an elastic sheet representing the ice covering the liquid is considered for the case of steady flow. The mathematical model based on the velocity potential theory and the theory of thin elastic shells fully accounts for the nonlinear boundary conditions at the elastic sheet/liquid interface and on the bottom of the channel. The integral hodograph method is employed to derive the complex velocity potential of the flow, which contains the velocity magnitude at the interface in explicit form. This allows one to formulate the coupled ice/liquid interaction problem and reduce it to a system of nonlinear equations in the unknown magnitude of the velocity at the interface. Case studies are carried out for a semi-circular obstruction on the bottom of the channel. Three flow regimes are studied: a subcritical regime, for which the interface deflection decays upstream and downstream; an ice supercritical and channel subcritical regime, for which two waves of different lengths may exist; and a channel supercritical regime, for which the elastic wave is found to extend downstream to infinity. All these regimes are in full agreement with the dispersion equation. The obtained results demonstrate a strongly nonlinear interaction between the elastic and the gravity wave near the first critical Froude number where their lengths approach each other. The interface shape, the bending moment and the pressure along the interface are presented for wide ranges of the Froude number and the obstruction height.

Instability of Jeffrey Fluid Throughflow in a Porous Layer Induced by Heat Source and Soret Effect

Abstract In this study, we investigated the instability of thermosolutal convection of Jeffrey fluid in a porous layer with internal heating and the Soret effect. The layer is bounded by two fixed permeable parallel plates which are assumed to be isothermal and isosolutal. An existing initial flow in the vertical direction is passing the layer at a constant speed. The flow fields are adequately presented by PDEs and transformed into dimensionless forms. A small perturbation to the basic flow profiles with linear stability analysis results the problem in an eigenvalue problem. The Runge-Kutta method is used to derive the numerical value of the critical thermal Rayleigh number. The convective instability for asymptotic cases for Le = 1 and Pe = 0 are also examined as special cases. The analysis reveals that for a non-positive Soret parameter, the flow is stable for all Lewis numbers and independent of the heat source. But with a positive Soret parameter in the absence of a heat source, the fluid flow is stable for Le = 3 while the influence of a heat source destabilizes the flow for Le &amp;gt; 2. In high and low shear flows with increasing solutal gradient, the solutal Rayleigh number shows a highly destabilizing nature for all Le. Moreover, smaller relaxation and higher retardation time are the most unstable characteristics of the heat source system. In convective longitudinal rolls, the uni-cellular streamline patterns tend to become bi-cellular by the influence of positive Soret parameters and energy sources.

Double-diffusive thermosolutal Hadley–Prats flow: stability analysis

ABSTRACT A mathematical model is formulated to study the onset of double-diffusion fluid flow through an infinite permeable channel with internal heat source and viscous dissipation effects under the influence of convection conditions. Numerically, the dimensionless emerging eigenvalue problem is tackled using the fourth-order Runge–Kutta scheme, specifically applied to longitudinal roll disturbances. Critical values of wave number and vertical thermal Rayleigh number are determined. A higher value of Gebhart number is observed to correlate significantly with the destabilizing phenomena in Hadley–Prats flow. Concentration-based internal heat generation also strongly modifies the critical thermal Rayleigh number. Also, it is found that the horizontal mass flow and viscous dissipation exert a substantial influence on the onset of instability in the flow regime. Linear instability analysis indicates that greater values of Lewis number in the porous medium stabilize the convection process for both values of mass diffusion parameter ( C z ) . Enhancing C z from negative to positive values diminishes the critical thermal Rayleigh ( R z ) value and consequently induces instability in the porous medium. Increased concentration-based internal heat generation generates the destabilization process in the flow region.

Growth and static stability of bubble clouds in yield stress fluids

This study explores the growth and static stability of bubble clouds in yield-stress fluids using an experimental approach. Carbopol gels with varying concentrations and initial gas contents as well as Laponite gels are used as model yield stress fluids in our experiments. A vacuum system is exploited to generate the bubbles and control their growth in the gels. The focus of this study is on determining the maximum gas concentration which could be held trapped in the system and the critical yield number, i.e. the ratio of the yield stress to the buoyancy stress at the onset of motion. Our findings demonstrate the effect of the bubbles proximity as well as the gel structure and rheology on both the maximum gas concentration and critical yield number. Our results confirm that for higher gas fractions, the critical yield number is larger. Also, they show that the size and degree of elongation of the bubbles at the onset of motion are controlled by their proximity as well as the gel rheology. Moreover, our results reveal two different scenarios for the bubble release depending on the uniformity of the structure of the gel. In the case of low concentration Carbopol gels, characterized by uniform structures, quasi mono-dispersed bubble suspensions are formed. At a pretty high gas concentration, this might lead to a bubble cloud burst upon static instability onset. Conversely, in the case of high concentration Carbopol gels or Laponite gels, the polydisperse bubble suspensions emerge and the bubble release occurs gradually rather than suddenly. It can be associated with the heterogeneous structure of these gels stemming from their significant shear history dependence.

Elasto-visco-plastic flows in benchmark geometries: I. 4 to 1 planar contraction

We present predictions for the flow of elastoviscoplastic (EVP) fluids in the 4 to 1 planar contraction geometry. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method with the OpenFOAM software. Both the constitutive model and the solution method require using transient simulations. In this benchmark geometry, whereas viscoelastic fluids may exhibit two vortices, referred to as lip and corner vortices, we find that EVP materials are unyielded in the concave corners. They are also unyielded along the mid-plane of both channels, but not around the contraction area where all stress components are larger. The unyielded areas using this EVP model are qualitatively similar to those using the standard viscoplastic models, when the Bingham or the Weissenberg numbers are lower than critical values, and then, a steady state is reached. When these two dimensionless numbers increase while they remain below the respective critical values, which are interdependent, (a) the unyielded regions expand and shift in the flow direction, and (b) the maximum velocity increases at the entrance of the contraction. Increasing material elasticity collaborates with increasing the yield stress, which expands the unyielded areas, because it deforms the material more prior to yielding compared to stiffer materials. Above the critical Weissenberg number, transient variations appear for longer times in all variables, including the yield surface, instead of a monotonic approach to the steady state. They may lead to oscillations which are damped or of constant amplitude or approach a flow with rather smooth path lines but complex stress field without a plane of symmetry, under creeping conditions. These patterns arise near the entrance of the narrow channel, where the curvature of the path lines is highest and its coupling with the increased elasticity triggers a purely elastic instability. Similarly, a critical value of the yield stress exists above which such phenomena are predicted.

Influence of a magnetic field on double‐diffusive convection in an inclined porous layer

AbstractThe present study investigates the impact of a magnetic field on double‐diffusive convection in an inclined porous layer, employing linear instability theory. The perturbed state is solved using the normal mode technique, and the stability eigenvalue problem is numerically analyzed for longitudinal and traveling rolls using the Runge‐Kutta method coupled with the shooting method. Various dimensionless physical parameters, including solutal and thermal Rayleigh numbers, inclination angle, Hartmann number, and Lewis number, are examined for their influence on system stability. The findings reveal that, for , the Hartmann number, solute Rayleigh number, and inclination angle act as stabilizing factors, with greater stability observed for traveling rolls compared to longitudinal rolls. In the case of , the critical Rayleigh number shows a monotonic relationship with the solute Rayleigh number and inclination angle, while its relationship with the Hartmann number is non‐monotonic for traveling rolls. Moreover, for , the Hartmann number stabilizes the system by raising the onset threshold value, favouring longitudinal modes. The solute Rayleigh number also contributes to system stability. The impact of the inclination angle on system stability is contingent upon its magnitude, with small angles favouring the stability of longitudinal rolls and larger angles leading to an initial transition from traveling to longitudinal rolls, indicating a complex non‐monotonic behavior.

Dynamic deformation and meso-structure of coarse-grained saline soil under cyclic loading with freeze-thaw cycles

The cumulative deformation properties of subgrade soil under cyclic traffic loads are critical for optimizing pavement structure design and ensuring long-term highway structural performance. This study aims to investigate the coupling effect of freeze-thaw cycles and cyclic loads on the cumulative deformation behaviors and meso-structure of coarse-grained saline soil (CGSS) subgrade filling in high-cold areas. Dynamic triaxial tests and computed tomography (CT) scanning were conducted to analyze the CGSS under different working conditions. The research focused on the dynamic deformation development and damage evolution under varying freeze-thaw cycles and load amplitudes. The research results show that the cumulative deformation behavior of CGSS under cyclic loading is relatively sensitive to the freeze-thaw process. The cumulative dynamic strain increases as the freeze-thaw cycles, with a critical freeze-thaw cycle number of five. The stable cumulative dynamic strain curve exhibits clear three-stage characteristics when plotted in semi-log coordination, with critical loading cycles at 20 and 1,000. After 10–100 loading cycles, the cumulative strain curve quickly shows failure. The CGSS’s low density and pore regions greatly increase after a freeze-thaw cycle. The rise in dynamic stress amplitude notably affects the bonding between soil particles and crystalline salts. The coupling effect of the freeze-thaw cycle and dynamic activity exacerbates the deterioration of soil structure, resulting in variations in CT values within the scanning layer in the final state.

Breaking bubbles across multiple time scales in turbulence

The familiar process of bubbles generated via breaking waves in the ocean is foundational to many natural and industrial applications. In this process, large pockets of entrained gas are successively fragmented by the ambient turbulence into smaller and smaller bubbles. The key question is how long it takes for the bubbles to reach terminal sizes for a given system. Despite decades of effort, the reported breakup time from multiple experiments differs significantly. Here, to reconcile those results, rather than focusing on one scale, we measure multiple time scales associated with the process through a unique experiment that resolves bubbles’ local deformation and curvature. The results emphasize that the scale separation among various time scales is controlled by the Weber number, similar to how the Reynolds number determines the scale separation in single-phase turbulence, but shows a distinct transition at a critical Weber number.

Low cycle fatigue of doped tetrahedral amorphous carbon coatings by repetitive micro scratch tests

In contrast to the conventional progressive scratch testing where load is increased up to a critical damage level, the repetitive scratch testing is an assessment of coating behavior under repeatedly applied subcritical load. It often represents a better approximation to actual application conditions of well-designed coating systems where overcritical conditions typically do not occur. In this work, the cyclic micro scratch behavior of differently doped amorphous carbon coatings with similar coating thicknesses were studied using repetitive scratch tests at loads that correspond to 40 %, 60 % and 80 % of the critical loads from progressive scratch testing. Depending on the doping element, the structural and mechanical properties changed, in some cases considerably, which also had a clear effect on the test results. The damage progression was examined using optical microscopy, friction coefficient, and residual depth measurements. The progression of failure phenomena was categorized into different stages. Furthermore, the critical number of cycles for coating failure was recorded at the various load levels. For the identification of the critical cycles, the use of the deviation of the friction coefficient from its mean value has proven to be a valuable parameter. The approach of testing at different load levels allows the creation of low cycle fatigue curves to evaluate the coating behavior. It was found that the hardness and residual stresses of the coatings had different effects on the lifetime of the coatings at the various load levels, i.e. higher hardness and residual compressive stresses were only beneficial for moderate stress levels with low plastic substrate deformation. The results demonstrate that the cyclic scratch test is a powerful tool for comparative damage assessment at different load scenarios.

Manifestation of the hexatic phase in confined two-dimensional systems with circular symmetry

Quasi-two-dimensional systems play an important role in the manufacture of various devices for the needs of nanoelectronics. Obviously, the functional efficiency of such systems depends on their structure, which can change during phase transitions under the influence of external conditions (for example, temperature). Until now, the main attention has been focused on the search for signals of phase transitions in continuous two-dimensional systems. One of the central issues is the analysis of the conditions for the nucleation of the hexatic phase in such systems, which is accompanied by the appearance of defects in the Wigner crystalline phase at a certain temperature. However, both practical and fundamental questions arise about the critical number of electrons at which the symmetry of the crystal lattice in the system under consideration will begin to break and, consequently, the nucleation of defects will start. The dependences of the orientational order parameter and the correlation function, which characterize topological phase transitions, as functions of the number of particles at zero temperature have been studied. The calculation results allows us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, 187, considered as an example.

The effect of macular visual field test density on central structure-function concordance in glaucoma

ABSTRACT Clinical relevance Central visual field (VF) testing often requires focussed high-density test grids. The critical number of test locations for maximising structure-function concordance in the macula is not known. Purpose The aim of this work is to determine the impact of the number of test locations in the central VF on binarized structure-function concordance in glaucoma. Methods Humphrey Field Analyser (HFA) 10–2 test grid and Cirrus optical coherence tomography Ganglion Cell Analysis (GCA) results from one eye of 155 glaucoma patients were extracted. Following anatomical correction for retinal ganglion cell displacement, the pointwise results of the central 36 locations of the 10–2 pattern deviation map and their corresponding locations within the GCA deviation map were recorded. The number of test locations was systematically reduced from 36 (4 locations per step) and added from 1 (1 location per step) and binarized structure-function concordance (p < 0.05 for both) at each step was evaluated. Eleven test point subtraction and addition models were developed. Concordance rates (proportion) were plotted as a function of number of test locations, and were fitted using segmental nonlinear regression to identify the critical point of inflection at which concordance was maximised and discordance minimised. Results Subtractive and additive approaches returned two-way estimates of the critical number, with, on average 8–14 test locations being the range at which structure-function concordance was optimised in the present cohort across all models. A randomised approach to subtracting or adding test locations returned critical numbers that were similar to systematic and empirical models, suggesting that specific test location was not as critical in optimising structure-function concordance compared to the number of test locations. Conclusion There is a potential critical number (8–14) in macular visual field testing where binarized structure-function concordance is optimised, providing a framework for guiding the development of integrated macular test locations in VF testing for glaucoma.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

Revisiting the face stability of rock tunnels in the Hoek–Brown strength criterion with tension cutoff

AbstractIn this work, the three‐dimensional stability of deep tunnel faces is evaluated in rock masses characterized by the generalized Hoek–Brown (H–B) criterion from the perspective of the limit analysis theorem. Considering that underground engineering is gradually developing towards larger burial depths and larger sizes, and the tensile strength of rocks is usually overestimated, the concept of tension cutoff (T‐C) is introduced to substitute the parabolic form of the H–B envelope in the tensile region with a circular arc. The multitangent technique is used to piecewise approximate the H–B envelope, instead of the conventional linear substitution, accounting for the nonlinear dependence of the shear strength on the pressure. Meanwhile, the earthquake loading is considered by the classic pseudostatic method. The tunnel face stability is measured by a stability number, which is calculated based on a newly developed multicone failure mechanism. Parameter studies indicate that the T‐C has almost no impact on the critical support pressure, while has a significant effect on the critical stability number, especially in the presence of earthquakes. Nearly all stress points back‐calculated from the rupture angles fall within the T‐C region, except for the first stress point associated with the first segment. Interestingly, the influence of the geological strength index (GSI) on the face stability is inverse to that of mi due to the brittleness of rocks. Moreover, the critical stability number is not sensitive to mi, but sensitive with the introduction of earthquake loadings.