Monotonic Behavior Research Articles

Monotonicity and the Precision of Program Analysis

It is widely known that the precision of a program analyzer is closely related to intensional program properties, namely, properties concerning how the program is written. This explains, for instance, the interest in code obfuscation techniques, namely, tools explicitly designed to degrade the results of program analysis by operating syntactic program transformations. Less is known about a possible relation between what the program extensionally computes, namely, its input-output relation, and the precision of a program analyzer. In this paper we explore this potential connection in an effort to isolate program fragments that can be precisely analyzed by abstract interpretation, namely, programs for which there exists a complete abstract interpretation. In the field of static inference of numeric invariants, this happens for programs, or parts of programs, that manifest a monotone (either non-decreasing or non-increasing) behavior. We first formalize the notion of program monotonicity with respect to a given input and a set of numerical variables of interest. A sound proof system is then introduced with judgments specifying whether a program is monotone relatively to a set of variables and a set of inputs. The interest in monotonicity is justified because we prove that the family of monotone programs admits a complete abstract interpretation over a specific class of non-trivial numerical abstractions and inputs. This class includes all non-relational abstract domains that refine interval analysis (i.e., at least as precise as the intervals abstraction) and that satisfy a topological convexity hypothesis.

Cyclic mechanical behavior of electro-welded meshes used as structural reinforcement

In this work, the monotonic and cyclic behavior of 6, 7 and 8 mm diameter electro welded meshes manufactured in Colombia and used as reinforcement in construction is studied experimentally. The cyclic mechanical behavior of the material is modeled using the Ramberg-Osgood model, and the model parameters are adjusted based on experimental data and using linear regression. The results show that the material undergoes cyclic softening, and that the Ramberg-Osgood Ramberg -Osgood model accurately predicts the monotonic and cyclic mechanical behavior.

Graph-Represented Distribution Similarity Index for Full-Reference Image Quality Assessment.

In this paper, we propose a graph-represented image distribution similarity (GRIDS) index for full-reference (FR) image quality assessment (IQA), which can measure the perceptual distance between distorted and reference images by assessing the disparities between their distribution patterns under a graph-based representation. First, we transform the input image into a graph-based representation, which is proven to be a versatile and effective choice for capturing visual perception features. This is achieved through the automatic generation of a vision graph from the given image content, leading to holistic perceptual associations for irregular image regions. Second, to reflect the perceived image distribution, we decompose the undirected graph into cliques and then calculate the product of the potential functions for the cliques to obtain the joint probability distribution of the undirected graph. Finally, we compare the distances between the graph feature distributions of the distorted and reference images at different stages; thus, we combine the distortion distribution measurements derived from different graph model depths to determine the perceived quality of the distorted images. The empirical results obtained from an extensive array of experiments underscore the competitive nature of our proposed method, which achieves performance on par with that of the state-of-the-art methods, demonstrating its exceptional predictive accuracy and ability to maintain consistent and monotonic behaviour in image quality prediction tasks. The source code is publicly available at the following website https://github.com/Land5cape/GRIDS.

Monotonic and cyclic behaviour of sand-silt mixtures through the equivalent state parameter

This paper presents the results of a laboratory investigation into the effect of non-plastic fines on the monotonic and cyclic behaviour of sand-silt mixtures. For this purpose, drained and undrained triaxial monotonic and undrained stresscontrolled cyclic triaxial tests were performed on clean sand and its mixtures with non-plastic silt. The Critical State theory known as a characteristic state of soil behaviour and the equivalent state concept were used to the interpretation of the laboratory tests results. By estimating parameter b, which recognizes that different percentages of fines contribute differently to the strength of the sand and consequently the equivalent intergranular void ratio, (eg)eq, a single Critical State Line, CSL, is determined in the (eg)eq-log(p΄) plane, and a single liquefaction resistance curve at the CRR15-(eg)eq, independently of fines content, fc, based on the monotonic and cyclic tests results, respectively. It is shown that parameter b depends on the fines content, fc, and on the loading type of the laboratory test conducted, while (eg)eq proves to be a suitable parameter for the estimation of the monotonic behavior and undrained critical state strength as well as the liquefaction resistance of granular mixtures up to the threshold fines content value, fcth, independently of their fines content. The effectiveness of state parameter, ψ, and equivalent state parameter, (ψg)eq, in the estimation of the undrained critical state strength and liquefaction resistance of sand-silt mixtures is confirmed.

Understanding the glassy dynamics from melting temperatures in binary glass-forming liquids.

It is natural to expect that small particles in binary mixtures move faster than large ones. However, in binary glass-forming liquids with soft-core particle interactions, we observe the counterintuitive dynamic reversal between large and small particles along with the increase of pressure by performing molecular dynamics simulations. The structural relaxation (dynamic heterogeneity) of small particles is faster (weaker) than large ones at low pressures, but becomes slower (stronger) above a crossover pressure. In contrast, this dynamic reversal never happens in glass-forming liquids with hard-core interactions. We find that the difference of the effective melting temperatures felt by large and small particles can be used to understand the dynamic reversal. In binary mixtures, we derive effective melting temperatures of large and small particles simply from the conversion of units and find that particles with a higher effective melting temperature usually undergo a slower and more heterogeneous relaxation. The presence (absence) of the dynamic reversal in soft-core (hard-core) systems is simply due to the non-monotonic (monotonic) behavior of the melting temperature as a function of pressure. Interestingly, by manipulating the relative softness between large and small particles, we obtain a special case of soft-core systems, in which large particles always have higher effective melting temperatures than small ones. As a result, the dynamic reversal is totally eliminated. Our work provides another piece of evidence of the underlying connections between the properties of non-equilibrium glass-formers and equilibrium crystal-formers.

Using X-ray micro CT imaging data to obtain particle morphology and soil fabric parameters

In addition to the well-understood effects of void ratio and effective confining stress on the mechanical behavior of finegrained soils, past experimental research at the University of British Columbia (UBC), Vancouver, Canada, has revealed a considerable effect of particle fabric on the monotonic and cyclic shear behavior of silts. With this background, an experimental research program was undertaken to further investigate the particulate nature and arrangement of silts. The fabric of soils has been traditionally associated with the matrix void ratio, but can be directly associated with fabric parameters like the coordination number. Furthermore, grain morphology has a significant impact on these characteristics. Advancements in acquiring digital images and associated processing have made it possible to obtain individual soil particle parameters such as length, width, breath, thickness, volume, etc., along with information on spatial location and orientation of a given particle - thus providing the data needed to determine contact fabric and morphology of a soil matrix. In order to calculate these parameters and look for any potential correlations, commercially available, precalibrated, standard-size silica having particles within the size range from 40 μm to 60 μm, were imaged and analyzed. This study establishes an approach for extracting void and morphological information from tomographic images using image analysis techniques and algorithms developed in-house. Initial observations related to particle morphology and preliminary fabric scalar parameters are discussed. This work contributes to the accounting for fabric in understanding the macroscopic shear behavior of silts from the Fraser River Delta, British Columbia, Canada.

A proposal for the numerical modelling of monotonic and cyclic behaviour of masonry infilled reinforced concrete frames

A proposal for the numerical modelling of monotonic and cyclic behaviour of masonry infilled reinforced concrete frames

The monotonic behaviour of a low- to medium-density chalk through in-situ and laboratory characterisation

Chalk is a highly variable cemented biomicrite limestone that can show widely different rock strengths and patterns of micro to macro fissuring and jointing, due to variations in depositional environments and local geological histories. This paper describes the characterisation of a very weak to weak, low- to medium-density chalk through in situ profiling and laboratory testing, which provided new insights into the geomaterial’s mechanical behaviour. The chalk de-structures when taken to large strains, leading to remarkably high pore pressures beneath penetrating cones and degraded responses in full-displacement pressuremeter tests. Laboratory tests on carefully formed specimens explored the chalk’s unstable structure and marked time-, rate- and pressure dependency. A clear hierarchy was found between profiles of peak strength with depth from Brazilian tension, drained and undrained triaxial and direct simple shear tests conducted from in-situ stress conditions. Highly instrumented triaxial tests sheared from low confining stresses indicated stiffness anisotropy and showed very brittle failure behaviour from small strains. Progressively more ductile behaviour was seen as confining pressures were raised, with failures being delayed until increasingly large strains and finally stable critical states were attained. The chalk’s mainly sub-vertical jointing and micro-fissuring led to properties depending on specimen scale, with high-quality laboratory stiffness measurements significantly exceeding those obtained from in-situ geophysical testing, which far exceed the operational stiffnesses of the chalk mass. While compressive strength and stiffness appear relatively insensitive to effective stress levels, consolidation to higher pressures closes micro-fissures and reduces anisotropy. The results provided the basis for numerical analysis with advanced constitutive models that inform the interpretation of axial and lateral tests on driven piles and inform the development of new practical design methods.

Performance evaluation of the Generalized Bounding Surface Model in the simulation of Cajicá clay subjected to monotonic loading

Different constitutive models, based on principles of mechanics and experimental evidence, have been developed over several decades to represent and predict the stress-strain behavior of soils subjected to various loading conditions. The Generalized Bounding Surface Model (GBSM) is one of them and is defined as a fully three-dimensional elastoplastic constitutive model for saturated cohesive soils that employ the bounding surface plasticity in conjunction with a nonassociative flow rule and a soil microfabric-inspired rotational hardening rule. The GBSM has been successfully validated on numerous laboratory reconstituted soils, but not on natural or undisturbed soil samples. Hence, in this paper the predictive capabilities of the GBSM are evaluated in the simulation of the monotonic behavior of an undisturbed cohesive soil called “Cajicá clay” from the high plain of Bogotá in Colombia. In the first instance, an isotropic consolidation test and a set of axisymmetric triaxial compression and extension tests are conducted using an automated triaxial equipment, to experimentally describe the response of the undisturbed soil. From experimental data, the parameters associated with the GBSM model are calibrated to finally evaluate its capabilities in the simulation of a cohesive natural soil. A comparison between experimental data and numerical simulations is presented to show both performance and advantages of the GBSM model.

Cyclic and Monotonic Behavior of Non-plastic Silts with the Presence of Initial Static Shear Stress Using Strain Energy Approach: A Case Study for a Tailings Dam

Cyclic and Monotonic Behavior of Non-plastic Silts with the Presence of Initial Static Shear Stress Using Strain Energy Approach: A Case Study for a Tailings Dam

Predicting the monotonic horizontal behavior of tripod bucket foundations in clay

The requirements for the foundation bearing characteristics become higher due to the evolution of offshore wind turbines in the abyssal sea. Tripod bucket foundations have good bearing performance and has gradually become a trend. To investigate the horizontal dynamic behavior of the tripod bucket foundation and the dynamic characteristics relationship between the tripod bucket and the single bucket under horizontal monotonic loadings, the predictive model of the dynamic characteristics of the tripod bucket is established through formula derivation, and extensive numerical analyses were conducted under horizontal monotonic loadings in clay. It was confirmed that the limit bearing moment of the tripod bucket enhances with increment of bucket spacing and length. The ultimate bearing moment has an exponential positive correlation with the ratio of length and diameter (L/D) for the single bucket and a linear positive correlation with the ratio of space and diameter (S/D) for the bucket. Predicting the dynamic characteristics of tripod bucket foundations under horizontal monotonic loadings based on the horizontal bearing capacity coefficient model and the single bucket foundations horizontal dynamic characteristics. Simplified prediction of the tripod bucket foundations' rotation angle and moment has been verified under horizontal monotonic loadings. That can provide a certain design reference of the multi-bucket foundation by studying the relationship between single and jacket foundation.

The effect of particle breakage on the dilatancy and shear behavior of marine calcareous and siliceous deposits

A large part of ocean surface is covered by calcareous deposits. The Low stiffness and weak particles of calcareous soils deposited by marine organisms showed significant particle breakage under applied loads, which resulted in different behavior compared to terrigenous soils. A series of compression drained triaxial tests were carried out to evaluate the monotonic shear behavior of crushable and non-crushable soils. Three different soils, including Firoozkuh siliceous sand (as a non-crushable soil) and Hormuz and Bushehr calcareous sands (as crushable soils) which were different in mineralogy compositions were obtained from northern and southern Iran. The specimens were prepared in different relative densities (i.e., loose, medium and dense conditions) and consolidated under confining pressures ranging from 100 to 600 kPa. The monotonic shear and dilatancy behaviors of the soils have been presented in detail and the effect of particle breakage has been discussed. The results showed that particle breakage has a significant effect on the mobilized friction and dilatancy angles of marine crushable soils. There is a linear relationship between the amount of particle breakage occurring during a triaxial test and breakage angle. In addition, the mineralogical difference influences the breakage properties of calcareous deposits.

Solvent exchange creates transient memory with regulatable lifespan

Generally, a synthetic smart material exhibits a monotonic response behavior. Its material property shifts reversibly between two equilibrium states upon switching a pair of reverse external stimuli. This paper reports that a solvent-swollen elastomeric film turns opaque and then autonomously reverts to transparency through a single trigger of exchanging the swelling solvent with a poorer solvent. We demonstrate this method capable of recording optical information with a regulatable lifespan into the soft material, which is reminiscent of the memory in the brain. The intriguing non-monotonic response behavior is proved to arise from the fast molecular mixing of solvents during solvent exchange, which pushes the system far from its swelling equilibrium. As a result, excess solvent molecules separate into a new phase and are temporally trapped within the gel film, creating an off-equilibrium heterogeneous structure that scatters light. The heterogenous structure later autonomously vanishes, as the excess network elasticity relative to swelling equilibrium drives the excess solvent molecules out of the gel film. By adjusting the solvation ability of the poorer solvent, the lifespan of off-equilibrium structure can be continuously regulated from mere hours to several months.

Quantum enhancement of qutrit dynamics of a three-level giant atom coupling to a one-dimensional waveguide

Dynamics of quantum coherence and non-Markovianity of a three-level giant atom coupling to a one-dimensional waveguide and a classical field are investigated theoretically. The time delay of the photo propagation in the waveguide is taken into account and our aim is to access the collective impact of a waveguide and classical control of the system on the time evolution of coherence and non-Markovianity. For a giant atom, we find that the various values of the accumulated phase and time delay does not make much difference for the coherence evolution but there exists non-Markovian behavior for the vast majority of the chosen parameter values. With regard to the initial relative phase, the quantum coherence takes a monotonic behavior for a small atom but decreases with oscillations for a giant atom with majority values of the initial relative phase. Quantum coherence of a small atom decreases monotonically with regardless of the Rabi frequency and the atom’s detuning to a large extent but a large Rabi frequency or a large atom’s detuning will induce non-Markovian behavior for a giant atom. With a comparative analysis, the coherence evolution is enhanced significantly in that there is non-Markovian behavior for the dynamics of quantum coherence in a much larger range of scaled time for a giant atom than that for a small atom. Our study provide clues to preserve and to enhance quantum coherence in qutrit systems.

Some New Results Involving Past Tsallis Entropy of Order Statistics.

This work focuses on exploring the properties of past Tsallis entropy as it applies to order statistics. The relationship between the past Tsallis entropy of an ordered variable in the context of any continuous probability law and the past Tsallis entropy of the ordered variable resulting from a uniform continuous probability law is worked out. For order statistics, this method offers important insights into the characteristics and behavior of the dynamic Tsallis entropy, which is associated with past events. In addition, we investigate how to find a bound for the new dynamic information measure related to the lifetime unit under various conditions and whether it is monotonic with respect to the time when the device is idle. By exploring these properties and also investigating the monotonic behavior of the new dynamic information measure, we contribute to a broader understanding of order statistics and related entropy quantities.

Predicting monotonic lateral load-displacement behavior of offshore flexible piles in saturated MCC soils: An application of the cavity expansion theory

This paper proposes an application of the cavity expansion theory to predict the load-displacement response of monotonically laterally loaded piles and the effective stress distribution of saturated modified Cam-clay (MCC) soil surrounding the pile. This approach incorporates geometric relationship, equilibrium equation, and boundary conditions to derive governing equations. These equations are subsequently solved to obtain monotonic p-y curves, which encompass the elastic, elastoplastic, and critical processes. To determine the load-displacement behavior and effective stress distribution of the soil, the proposed approach combines the deflection equilibrium differential equation with the finite-difference method. The accuracy and effectiveness of the approach are validated through a comparison with a Finite Element Method (FEM) simulation. Parametric studies are also presented to investigate the effects of overconsolidation ratio, in-situ coefficient, and mean effective stress. The validity and capacity of the proposed model are further demonstrated using model pile tests. The results affirm that this approach can well predict the monotonic load-displacement response of the pile and effectively captures important phenomena observed in pile tests.

Compressive behavior and modeling of concrete wrapped by hybrid low-high elongation capacities FRP

This paper experimentally investigated the monotonic and cyclic compressive behavior of concrete confined with hybrid carbon fiber-reinforced polymer (CFRP) and large rupture strain (LRS) FRP. A total of 34 concrete cylinders wrapped by FRP were prepared and tested under monotonic/cyclic axial compression. The effects of FRP types and thickness on the failure mode, efficiency factor, hybrid effect, stress-strain response, and energy dissipation were carefully investigated. Test results verified that the hybrid confinement mechanism can fully utilize the advantages of both types of FRP and avoid their essential shortcomings. LRS FRP effectively improved the utilization of CFRP and increased the deformation and energy dissipation capacity of concrete. Hybrid inner CFRP and outer LRS FRP serve as a confinement device that can achieve a progressive failure mechanism for concrete. In addition, an analysis-oriented model was developed and constructed to simulate the monotonic stress-strain behavior of hybrid-wrapped concrete. This analysis-oriented model focuses on the lateral stress-strain relationship and the localized CFRP fracture effect. Finally, a cyclic stress-strain model of hybrid-wrapped concrete was developed using the analysis-oriented model as an envelope model. The proposed model can accurately capture monotonic/cyclic stress-strain behaviors.

Monotonic and cyclic behaviour of deficient reinforced concrete slabs retrofitted with externally bonded carbon fibre reinforced polymer

Fibre reinforced polymer (FRP) retrofitting of reinforced concrete (RC) slabs has been widely investigated; however, the flexural behaviour of deficient RC slabs retrofitted with FRP under cyclic loading are limitedly explored. Towards this aim, this study experimentally and theoretically investigated the behaviour of RC slabs retrofitted with carbon fibre reinforced polymer (CFRP) under monotonic/cyclic loadings. Seven full-scale RC slabs, including one control slab and six slabs retrofitted by 1/2 and one CFRP layer, namely retrofitting types I and II, were tested under monotonic and cyclic loadings until failure. The results indicated that FRP retrofitted slabs failed by CFRP debonding while the control slab failed by steel yielding. CFRP retrofitted slabs exhibited tri-linear behaviour. CFRP retrofitting types I and II improved the yield load-carrying capacity by 43.5% and 83.5%, and the maximum load-carrying capacity by 81.9% and 217.4% compared with the capacity of the control slab, respectively. The stiffness of the retrofitted slabs increased significantly, leading to a substantial reduction in the deflection capacity. Although the ductility decreased, the safety factors based on load-carrying capacity of CFRP retrofitted slabs were much higher than the safety factor of the control slab. Cyclic loading caused a marginal strength degradation while it slightly reduced the ultimate deflections. Finally, a model to compute the moment capacity of CFRP retrofitted slabs was proposed, which can be useful for engineers in practice due to its simplicity and reasonable accuracy.

The influence of soil fabric on the monotonic and cyclic shear behaviour of consolidated and compacted specimens

While the fabric of soil can significantly influence its behaviour, the effect of varying fabric parameters on the subgrade shear response is still not well understood. This study creates soil specimens with different fabrics which are then captured through X-ray microscopic-computed tomography scanning and quantified by image processing techniques. A comprehensive laboratory investigation is conducted to understand how the soil fabric affects its monotonic and cyclic shear behaviour. The results indicate that the consolidation method creates a more homogeneous fabric with mainly small-to-medium interconnected pores, whereas the compaction technique creates significantly large and mostly inter-aggregate pores with lower connectivity. In this regard, the consolidated specimens exhibit an elastic-perfectly plastic behaviour, while the compacted specimens show strain-hardening transformation during isotropic monotonic shearing. Under anisotropic conditions, the compacted specimens exhibit a greater strain softening response and excess pore pressure than the consolidated specimens because they have a weaker fabric. Furthermore, the compacted specimens show a smaller threshold strain at a lower critical number of cycles due to the collapse of large pores. These current findings prove the decisive role that soil fabric plays in determining the shear response and failure of subgrade soils.

Transport Properties of Equiatomic CoCrFeNi High-Entropy Alloy with a Single-Phase Face-Centered Cubic Structure

The key thermophysical properties necessary for the successful design and use of CoCrFeNi alloy in thermophysical applications have been measured experimentally, and the results have been compared with literature values and results previously obtained for commercial Ni-Cr alloys and equiatomic CoCrFeNi alloy. In particular, the thermal diffusivity, coefficient of thermal expansion (CTE), and specific heat capacity were measured for the as-cast and homogenized equiatomic CoCrFeNi alloy over a temperature range allowing the thermal conductivity to be calculated up to 1173 K. The thermal conductivity and thermal diffusivity of the equiatomic CoCrFeNi alloy were found to deviate from monotonic behavior in the temperature range from 773 to 1100 K. Such a deviation was previously observed in the behavior of the temperature dependence of CTE and specific heat capacity of the equiatomic CoCrFeNi alloy. The non-linear behavior is primarily the result of order/disorder phenomena for the as-cast and homogenized sample, as well as non-equilibrium solidification under arc melting conditions for the as-cast sample. The measured data of thermophysical properties are provided for thermally differently treated samples, and it is shown that there is a difference in the behavior of the temperature dependences of CTE, thermal diffusivity, and heat capacity.