Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

A continuous and long-term in-situ stress measuring method based on fiber optic. Part I: Theory of inverse differential strain analysis

A method for in-situ stress measurement via fiber optics was proposed. The method utilizes the relationship between rock mass elastic parameters and in-situ stress. The approach offers the advantage of long-term stress measurements with high spatial resolution and frequency, significantly enhancing the ability to measure in-situ stress. The sensing casing, spirally wrapped with fiber optic, is cemented into the formation to establish a formation sensing nerve. Injecting fluid into the casing generates strain disturbance, establishing the relationship between rock mass properties and treatment pressure.Moreover, an optimization algorithm is established to invert the elastic parameters of formation via fiber optic strains. In the first part of this paper series, we established the theoretical basis for the inverse differential strain analysis method for in-situ stress measurement, which was subsequently verified using an analytical model. This paper is the fundamental basis for the inverse differential strain analysis method.

Effects of Intermittent Hypoxia Exposure on Symptoms of Chronic Fatigue Syndrome in Repeated Restraint Stress and Forced Swimming Induced-Mouse Model

Background: Chronic fatigue syndrome (CFS) shows as its main symptoms debilitating fatigue that is not relieved by physiological rest, depression, inflammation, learning disability and memory impairment. But, intermittent hypoxia, consisting of alternating exposure to hypoxia and normoxia, plays a very important role in improving CFS. However, the essential components for improving learning and memory in CFS patients as well as their mechanism are largely unknown. Objectives: This study aims to analyze the effects of 12% and 15% hypoxia on the expression of alpha tumor necrosis factor (TNF-α) and nuclear factor kappa B (NF-κB) in CFS induced-mouse model for clarifying the effects on the learning and memory function. Methods: A total of 48 type IC mice were used. The CFS mouse model was established using restrained stress and repeated forced swimming. Treatment of CFS was done by exposing CFS mice to intermittent hypoxia at 12% and 15%. The effects of intermittent hypoxia on learning and memory as well as its mechanism of action on inflammation were tested respectively with the Morris test, the SDS page, the immunohistochemistry technique and the Nissl staining. Results: We found that 12% and 15% intermittent hypoxia exposure improved learning capacity and memory of CFS induced-mice. SDS page showed that CFS caused higher TNF-α expression. By exposing CFS mice to 12% and 15% intermittent hypoxia, TNF-α expression decreased significantly, with a much better effect at 15%. Both TNF-α and NF-κB increased in CFS state and decreased after treatment with intermittent hypoxia. Conclusion: Intermittent hypoxia improves learning capacity and memory. It acted by decreasing NF-κB come to down-regulating TNF-α and ameliorates learning capacity and memory impairment in CFS mice.

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design.The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads.The topology optimization formula is combined with the ordered solid isotropic material with penalization(ordered-SIMP)multi-material interpolation model.The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function.Furthermore,the sequential optimization and reliability assessment(SORA)is applied to transform the original uncertainty optimization problem into an equivalent deterministic topology optimization(DTO)problem.Stochastic response surface and sparse grid technique are combined with SORA to get accurate information on the most probable failure point(MPP).In each cycle,the equivalent topology optimization formula is updated according to the MPP information obtained in the previous cycle.The adjoint variable method is used for deriving the sensitivity of the stress constraint and the moving asymptote method(MMA)is used to update design variables.Finally,the validity and feasibility of the method are verified by the numerical example of L-shape beam design,T-shape structure design,steering knuckle,and 3D T-shaped beam.

Advances in the Research Application of Ultrasound Non-Invasive Stress-Strain Loop Technology in Cardiovascular Diseases

The ultrasound pressure-strain loop (PSL) technique is a non-invasive method of examining myocardial work, which takes into account the effect of cardiac afterload on deformation and combines the overall longitudinal strain force of the left ventricle with the changes in the left ventricular pressure, allowing earlier detection of possible subclinical cardiac damage in patients, and a more accurate and non-invasive assessment of the patient’s myocardial work performance. In this article, we will discuss the progress of PSL applications in cardiovascular diseases.

Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering,the total vertical stress in the soil layer is not constant due to stress diffusion,and varies with time and depth.Therefore,the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional(2D)plane strain consolidation properties of unsaturated soils when the stress varies with time and depth.A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion.Then,the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump’s method.The reliability of the obtained solutions is proved by the degeneration.Finally,the 2D plots of excess pore pressures and the curves of settlement varying with time,considering different physical parameters of unsaturated soil stratum and depth-dependent stress,are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depthdependent stress.

A novel binary effective medium model to describe the prepeak stressstrain relationship of combined bodies of rock-like material and rock

Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering,such as tunnels and mines.The existing theoretical models describing the stress-strain relationship of a combined body lack a binary feature.Based on effective medium theory,this paper presents the governing equation of the“elastic modulus”for combined and single bodies under triaxial compressive tests.A binary effective medium model is then established.Based on the compressive experiment of concretegranite combined bodies,the feasibility of determining the stress threshold based on crack axial strain is discussed,and the model is verified.The model is further extended to coal-rock combined bodies of more diverse types,and the variation laws of the compressive mechanical parameters are then discussed.The results show that the fitting accuracy of the model with the experimental curves of the concretegranite combined bodies and various types of coal-rock combined bodies are over 95%.The crack axial strain method can replace the crack volumetric strain method,which clarifies the physical meanings of the model parameters.The variation laws of matrix parameters and crack parameters are discussed in depth and are expected to be more widely used in geotechnical engineering.

Effects of intermediate stress on deep rock strainbursts under true triaxial stresses

The effect of intermediate stress(in situ tunnel axial)on a strainburst is studied with a threedimensional(3D)bonded block distinct element method(DEM).A series of simulations of strainbursts under true triaxial in situ stress conditions(i.e.high tangential stress,moderate intermediate stress and low radial stress)of near-boundary rock masses are performed.Compared with the experimental results,the DEM model is able to capture the stress-strain response,failure pattern and energy balance of strainbursts.The fracturing processes of strainbursts are also numerically reproduced.Numerical results show that,as the intermediate stress increases:(1)The peak strain of strainbursts increases,the yield stress increases,the rock strength increases linearly,and the ratio of yield stress to rock strength decreases,indicating that the precursory information on strainbursts is enhanced;(2)Tensile and shear cracks increase significantly,and slabbing and bending of rock plates are more pronounced;and(3)The stored elastic strain energy and dissipated energy increase linearly,whereas the kinetic energy of the ejected rock fragments increases approximately exponentially,implying an increase in strainburst intensity.By comparing the experimental and numerical results,the effect of intermediate stress on the rock strength of strainbursts is discussed in order to address three key issues.Then,the Mogi criterion is applied to construct new strength criteria for strainbursts by converting the one-face free true triaxial stress state of a strainburst to its equivalent true triaxial stress state.In summary,the effect of intermediate stress on strainbursts is a double-edged sword that can enhance the rock strength and the precursory information of a strainburst,but also increase its intensity.

Formulation and procedure for in situ stress back-analysis from borehole strain changes measured during nearby underground excavation

Estimation of in situ stresses based on back-analysis of measured stress changes and displacements has become an alternative to the direct stress measurement methods.In order to help users conduct own measurement and analysis,this paper presents in detail a field stress back-analysis approach directly from borehole strain changes measured during nearby underground excavation.Essential formulations in major steps and the procedure for the entire analysis process are provided to allow users to follow.The instrument for borehole strain change measurement can be the CSIR or CSIRO stress cells and other borehole strain cells that can measure strains on borehole walls.Strain changes corresponding to the stress changes at a borehole location are calculated in borehole environment.The stress changes due to nearby excavation can be calculated by an analytical model for a single circular opening and simulated by a numerical model for non-circular and multiple openings.These models are based on isotropic,homogeneous and linear elastic assumptions.The analysis of borehole strain changes is accomplished by multiple linear regression based on error minimization and an integrated process provides the best-fit solution directly to the in situ stresses.A statistical technique is adopted for screening outliers in the measurement data,checking measurement compatibility and evaluating the reliability of analysis results.An application example is included to demonstrate the practical application and the analysis procedure.

Grain Yield,Biomass Accumulation,and Leaf Photosynthetic Characteristics of Rice under Combined Salinity-Drought Stress

Simultaneous stresses of salinity and drought often coincide during rice-growing seasons in saline lands,primarily due to insufficient water resources and inadequate irrigation facilities.Consequently,combined salinity-drought stress poses a major threat to rice production.In this study,two salinity levels(NS,non-salinity;HS,high salinity)along with three drought treatments(CC,control condition;DJ,drought stress imposed at jointing;DH,drought stress imposed at heading)were performed to investigate their combined influences on leaf photosynthetic characteristics,biomass accumulation,and rice yield formation.Salinity,drought,and their combination led to a shortened growth period from heading to maturity,resulting in a reduced overall growth duration.Grain yield was reduced under both salinity and drought stress,with a more substantial reduction under the combined salinity-drought stress.The combined stress imposed at heading caused greater yield losses in rice compared with the stress imposed at jointing.Additionally,the combined salinity-drought stress induced greater decreases in shoot biomass accumulation from heading to maturity,as well as in shoot biomass and nonstructural carbohydrate(NSC)content in the stem at heading and maturity.However,it increased the harvest index and NSC remobilization reserve.Salinity and drought reduced the leaf area index and SPAD value of flag leaves and weakened the leaf photosynthetic characteristics as indicated by lower photosynthetic rates,transpiration rates,and stomatal conductance.These reductions were more pronounced under the combined stress.Salinity,drought,and especially their combination,decreased the activities of ascorbate peroxidase,catalase,and superoxide dismutase,while increasing the contents of malondialdehyde,hydrogen peroxide,and superoxide radical.Our results indicated a more significant yield loss in rice when subjected to combined salinity-drought stress.The individual and combined stresses of salinity and drought diminished antioxidant enzyme activities,inhibited leaf photosynthetic functions,accelerated leaf senescence,and subsequently lowered assimilate accumulation and grain yield.

Ferroptosis and endoplasmic reticulum stress in ischemic stroke

Ferroptosis is a form of non-apoptotic programmed cell death,and its mechanisms mainly involve the accumulation of lipid peroxides,imbalance in the amino acid antioxidant system,and disordered iron metabolism.The primary organelle responsible for coordinating external challenges and internal cell demands is the endoplasmic reticulum,and the progression of inflammatory diseases can trigger endoplasmic reticulum stress.Evidence has suggested that ferroptosis may share pathways or interact with endoplasmic reticulum stress in many diseases and plays a role in cell survival.Ferroptosis and endoplasmic reticulum stress may occur after ischemic stroke.However,there are few reports on the interactions of ferroptosis and endoplasmic reticulum stress with ischemic stroke.This review summarized the recent research on the relationships between ferroptosis and endoplasmic reticulum stress and ischemic stroke,aiming to provide a reference for developing treatments for ischemic stroke.

Piezo1 channel exaggerates ferroptosis of nucleus pulposus cells by mediating mechanical stress-induced iron influx

To date,several molecules have been found to facilitate iron influx,while the types of iron influx channels remain to be elucidated.Here,Piezo1 channel was identified as a key iron transporter in response to mechanical stress.Piezo1-mediated iron overload disturbed iron metabolism and exaggerated ferroptosis in nucleus pulposus cells(NPCs).Importantly,Piezo1-induced iron influx was independent of the transferrin receptor(TFRC),a well-recognized iron gatekeeper.Furthermore,pharmacological inactivation of Piezo1 profoundly reduced iron accumulation,alleviated mitochondrial ROS,and suppressed ferroptotic alterations in stimulation of mechanical stress.Moreover,conditional knockout of Piezo1(Col2a1-CreERT Piezo1^(flox/flox))attenuated the mechanical injury-induced intervertebral disc degeneration(IVDD).Notably,the protective effect of Piezo1 deficiency in IVDD was dampened in Piezo1/Gpx4 conditional double knockout(cDKO)mice(Col2a1-CreERT Piezo1^(flox/flox)/Gpx4^(flox/flox)).These findings suggest that Piezo1 is a potential determinant of iron influx,indicating that the Piezo1-iron-ferroptosis axis might shed light on the treatment of mechanical stress-induced diseases.

Impact of effective stress on permeability for carbonate fractured-vuggy rocks

To gain insight into the flow mechanisms and stress sensitivity for fractured-vuggy reservoirs,several core models with different structural characteristics were designed and fabricated to investigate the impact of effective stress on permeability for carbonate fractured-vuggy rocks(CFVR).It shows that the permeability performance curves under different pore and confining pressures(i.e.altered stress conditions)for the fractured core models and the vuggy core models have similar change patterns.The ranges of permeability variation are significantly wider at high pore pressures,indicating that permeability reduction is the most significant during the early stage of development for fractured-vuggy reservoirs.Since each obtained effective stress coefficient for permeability(ESCP)varies with the changes in confining pressure and pore pressure,the effective stresses for permeability of four representative CFVR show obvious nonlinear characteristics,and the variation ranges of ESCP are all between 0 and 1.Meanwhile,a comprehensive ESCP mathematical model considering triple media,including matrix pores,fractures,and dissolved vugs,was proposed.It is proved theoretically that the ESCP of CFVR generally varies between 0 and 1.Additionally,the regression results showed that the power model ranked highest among the four empirical models mainly applied in stress sensitivity characterization,followed by the logarithmic model,exponential model,and binomial model.The concept of“permeability decline rate”was introduced to better evaluate the stress sensitivity performance for CFVR,in which the one-fracture rock is the strongest,followed by the fracture-vug rock and two-horizontalfracture rock;the through-hole rock is the weakest.In general,this study provides a theoretical basis to guide the design of development and adjustment programs for carbonate fractured-vuggy reservoirs.

Overexpression of the transcription factor MdWRKY115 improves drought and osmotic stress tolerance by directly binding to the MdRD22 promoter in apple

Abiotic stress reduces plant yield and quality.WRKY transcription factors play key roles in abiotic stress responses in plants,but the molecular mechanisms by which WRKY transcription factors mediate responses to drought and osmotic stresses in apple(Malus×domestica Borkh.)remain unclear.Here,we functionally characterized the apple GroupⅢWRKY gene MdWRKY115.qRT-PCR analysis showed that MdWRKY115 expression was up-regulated by drought and osmotic stresses.GUS activity analysis revealed that the promoter activity of MdWRKY115 was enhanced under osmotic stress.Subcellular localization and transactivation assays indicated that MdWRKY115 was localized to the nucleus and had a transcriptional activity domain at the N-terminal region.Transgenic analysis revealed that the overexpression of MdWRKY115 in Arabidopsis plants and in apple callus markedly enhanced their tolerance to drought and osmotic stresses.DNA affinity purification sequencing showed that MdWRKY115 binds to the promoter of the stress-related gene MdRD22.This binding was further verified by an electrophoretic mobility shift assay.Collectively,these findings suggest that MdWRKY115 is an important regulator of osmotic and drought stress tolerance in apple.

Brain region-specific roles of brain-derived neurotrophic factor in social stress-induced depressive-like behavior

Brain-derived neurotrophic factor is a key factor in stress adaptation and avoidance of a social stress behavioral response.Recent studies have shown that brain-derived neurotrophic factor expression in stressed mice is brain region–specific,particularly involving the corticolimbic system,including the ventral tegmental area,nucleus accumbens,prefrontal cortex,amygdala,and hippocampus.Determining how brain-derived neurotrophic factor participates in stress processing in different brain regions will deepen our understanding of social stress psychopathology.In this review,we discuss the expression and regulation of brain-derived neurotrophic factor in stress-sensitive brain regions closely related to the pathophysiology of depression.We focused on associated molecular pathways and neural circuits,with special attention to the brain-derived neurotrophic factor–tropomyosin receptor kinase B signaling pathway and the ventral tegmental area–nucleus accumbens dopamine circuit.We determined that stress-induced alterations in brain-derived neurotrophic factor levels are likely related to the nature,severity,and duration of stress,especially in the above-mentioned brain regions of the corticolimbic system.Therefore,BDNF might be a biological indicator regulating stress-related processes in various brain regions.

Present-day Upper-crustal Strain Rate Field in Southeastern Tibet and its Geodynamic Implications:Constraints from GPS Measurements with ABIC Method

The Earth’s surface kinematics and deformation are fundamental to understanding crustal evolution.An effective research approach is to estimate regional motion field and deformation fields based on modern geodetic networks.If the discrete observed velocity field is obtained,the velocity related fields,such as dilatation rate and maximum shear strain rate,can be estimated by applying varied mathematical approaches.This study applied Akaike's Bayesian Information Criterion(ABIC)method to calculate strain rate fields constrained by GPS observations in the southeast Tibetan Plateau.Comparison with results derived from other three methods revealed that our ABIC-derived strain rate fields were more precise.The maximum shear strain rate highlighted the Xianshuihe–Xiaojiang fault system as the main boundary for the outward migration of material in southeastern Tibet,indicating rotation of eastern Tibet material around the eastern Himalaya rather than whole extrusion along a fixed channel.Additionally,distinct dilatation rate patterns in the northeast and southwest regions of the fault system were observed.The northeast region,represented by the Longmenshan area,exhibited negative dilatational anomalies;while the southwest region,represented by the Jinsha River area north of 29°N,displayed positive dilatational anomalies.This indicates compression in the former and extension in the latter.Combined with deep geophysical observations,we believe that the upper and lower crusts of the Jinsha River area north of 29°N are in an entire expanding state,probably caused by the escape-drag effect of material.The presence of a large,low-viscosity region south of 29°N may not enable the entire escape of the crust,but instead result in a differential escape of the lower crust faster than the upper crust.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method(DEM)modelling.The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions.A side wall node loading method is used to exert bi-directional shear of various angles.The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials.However,the relationship between bidirectional shear and mechanical responses relies on loading conditions,i.e.constant vertical stress or constant volume conditions.The stress states induced by static shear consolidation are affected by loading angles,which are enlarged by subsequent shear,consistent with the relationship between bidirectional shear and principal stresses.It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials.The presence of bi-directional principal stress rotation(PSR)is demonstrated,which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction.Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts,but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts.It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions.Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined,providing further insights into understanding granular behaviour under bi-directional shear.

Adverse effects of early-life stress:focus on the rodent neuroendocrine system

Early-life stress is associated with a high prevalence of mental illnesses such as post-traumatic stress disorders,attention-deficit/hyperactivity disorder,schizophrenia,and anxiety or depressive behavior,which constitute major public health problems.In the early stages of brain development after birth,events such as synaptogenesis,neuron maturation,and glial differentiation occur in a highly orchestrated manner,and external stress can cause adverse long-term effects throughout life.Our body utilizes multifaceted mechanisms,including neuroendocrine and neurotransmitter signaling pathways,to appropriately process external stress.Newborn individuals first exposed to early-life stress deploy neurogenesis as a stress-defense mechanism;however,in adulthood,early-life stress induces apoptosis of mature neurons,activation of immune responses,and reduction of neurotrophic factors,leading to anxiety,depression,and cognitive and memory dysfunction.This process involves the hypothalamus-pituitary-adrenal axis and neurotransmitters secreted by the central nervous system,including norepinephrine,dopamine,and serotonin.The rodent early-life stress model is generally used to experimentally assess the effects of stress during neurodevelopment.This paper reviews the use of the early-life stress model and stress response mechanisms of the body and discusses the experimental results regarding how early-life stress mediates stress-related pathways at a high vulnerability of psychiatric disorder in adulthood.

A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Pyridinic-N doping carbon layers coupled with tensile strain of FeNi alloy for activating water and urea oxidation

Exploitation of oxygen evolution reaction(OER)and urea oxidation reaction(UOR)catalysts with high activity and stability at large current density is a major challenge for energy-saving H_(2) production in water electrolysis.Herein,we use the pyridinic-N doping carbon layers coupled with tensile strain of FeNi alloy activated by NiFe_(2)O_(4)(FeNi/NiFe_(2)O_(4)@NC)for efficiently increasing the performance of water and urea oxidation.Due to the tensile strain effect on FeNi/NiFe_(2)O_(4)@NC,it provides a favorable modulation on the electronic properties of the active center,thus enabling amazing OER(η_(100)=196 mV)and UOR(E_(10)=1.32 V)intrinsic activity.Besides,the carbon-coated layers can be used as armor to prevent FeNi alloy from being corroded by the electrolyte for enhancing the OER/UOR stability at large current density,showing high industrial practicability.This work thus provides a simple way to prepare high-efficiency catalyst for activating water and urea oxidation.