Curve Evolution Research Articles

Emulsions stability in weightlessness: Droplets size, droplets coalescence and phases spatial distribution

This work presents experiments for the stability study of oil-in-water emulsions at varying gravity conditions. A key factor influencing emulsions stability is droplet size which can be assessed by several techniques employing different physical principles. Experiments are performed during the 79th Parabolic Flight Campaign of European Space Agency (October 2022). A pulsatile miniature emulsification device is used to produce emulsions in ∼0 g conditions while using varying experimental parameters (oil volumetric fraction, surfactant concentration, pulsation frequency, number of strokes). The device resembles the Soft Matter Dynamics facility onboard the International Space Station whereas the examined parameters are also alike to Soft Matter Dynamics experiment. Optical measurements are employed to determine the droplet size distribution as well as, to observe coalescence events in the aqueous phase. Electrical measurements with a non-intrusive, on-line, impedance spectroscopy technique are carried out to track the evolution of oil volumetric fraction at the central region of the emulsification cell. As expected, in the absence of gravity, the buoyancy related phenomena are eliminated and, thus, phase gravitational separation between the two phases (creamy and aqueous) does not take place. Yet, the residual motion at the end of emulsification affects (a) the spatial homogeneity (distribution) of the two phases in the cell and (b) the capacity for coalescence of colliding droplets. In the absence of gravity, these two emulsion parameters are controlled solely by hydrodynamics and interfacial phenomena whereas on earth they are masked by buoyant phenomena. It is found that the oil fraction evolution curves resulting from electrical measurements are compatible with a bidisperse oil droplet size distribution. The characteristic sizes of the two droplet modes are estimated using theoretical arguments. Both the electrically volume-based determined droplet sizes and the number-based ones from high resolution image analysis are discussed in detail.

Digital Medical Images Segmentation by Active Contour Model based on the Signed Pressure Force Function

The signed pressure force (SPF) function has recently become a popular function for guiding the curve evolution of the active contour model (ACM) for image segmentation. The aim is to extract the boundaries of digital medical images for shape and image analysis. The recent SPF-based ACM demonstrates effectiveness in image segmentation. However, it may fail if the targeted object is close to a neighbouring object. Additionally, the presence of intensity inhomogeneity and noise in medical images degrades segmentation accuracy and local target areas. Thus, we proposed a new SPF-based ACM, namely the Selective Segmentation with Signed Pressure Force 1 (SSPF1) model, by incorporating the ideas of the SPF function and the distance fitting term based on geometrical constraints. Then, the new SSPF1 model was extended by incorporating an image enhancement technique to develop our second new model, termed the Selective Segmentation with Signed Pressure Force 2 (SSPF2). Numerical results indicated that the SSPF2 model was more recommended than SSPF1 as the SSPF2 model was approximately 4.7% more accurate, as indicated by the Jaccard value and was about 112 times faster in segmenting noisy images compared to the existing selective segmentation model.

Survival Probability of Tourist Accommodation Establishments in Romania in Relation to the Action of Some Relevant Factors

The units with tourist functions in Romania have a variable duration of activity resulting from the actions of different factors, but which can be analysed mathematically through survival analysis models. The number of establishments offering accommodation for tourism purposes in Romania exceeds 22,000, and the data indicated by the Ministry of Economy, Entrepreneurship and Tourism on the companies that manage them are the inputs of the study. These allowed for the creation of a statistical database showing the total operating time from establishment to the present or to the cessation of activity. Grouping was carried out according to the type of establishment, the location of the companies in rural or urban areas, their belonging to a geographical region of Romania and classification according to the comfort category. The drawing up of evolution curves describing the probability of survival of the establishments, distinctly for the groups mentioned, and the statistical analysis to establish the significance of the differences between the groups provide information that allows for determining and understanding how certain factors influence the chances of survival of the tourist establishment. The type of accommodation unit, the region of development in which the unit is located and the category of comfort are the factors that have a statistically significant influence on the probability of survival of these units. The location of tourism units in rural or urban areas is not a relevant factor. Knowledge of the actions of these factors allows for optimising the measures taken at the start of an activity in the tourism industry. These can result in improving the survivability of tourism. Sustainable tourism involves developing and supporting different forms of tourism by implementing activity management at both the accommodation unit level and at the locality, regional or whole tourist area level. The survival and continuity of the tourism business on the market and, at the same time, respect for the natural, social and economic integrity of the environment can ensure the rational exploitation of natural and cultural resources for future generations.

Destructuration of Canola Protein Gels during In Situ Gastrointestinal Digestion Studied by X-ray Scattering.

We are studying the destructuration of canola protein gels, as a solid food model, during in situ gastrointestinal digestion using synchrotron small-angle X-ray scattering (SAXS). Digestion of two gels, prepared by heating pH 8 and pH 11 solutions, was carried out by diffusion of enzymatic juices into the gel from the top of the capillary and monitored for several tens of hours. Very similar time evolutions of SAXS curves occur at different positions of the gel in the capillary, with a delay determined by the distance from the surface initially in contact with the digestive juice. The main phenomena observed are (i) at the scale of the protein conformation (1-5 nm). The scattering curve is a power law, the exponent of which measures the compactness (related to the degree of unfolding). It can be plotted as a function of the characteristic size of proteins/and interprotein distances and as a function of the scattering intensity. Such diagrams clearly show successive digestion processes. For the pH 11 gel, in which proteins are initially hardly unfolded, the digestive processes are unfolding (1st step), recompaction-aggregation phenomena (2nd step) due to gastrointestinal pH conditions and enzymatic cleavage, further unfolding-disaggregation (3rd step), and final protein cleavage (4th step) down to small peptides. For the pH 8 gel, proteins are initially unfolded, and only the last three steps are observed, showing the influence of easier access for the enzymes. (ii) At the scale of large aggregates (10-50 nm), we observe for both gels a decrease in the size and/or number of these aggregates during digestion and alteration of their interfaces. (iii) At the scale of the secondary protein structure, wide-angle X-ray scattering is very useful for detecting the degradation of the secondary protein structure at different steps of digestion.

Multi-angle property analysis and stress–strain curve prediction of cementitious sand gravel based on triaxial test

In order to further promote the application of cementitious sand gravel (CSG), the mechanical properties and variation rules of CSG material under triaxial test were studied. Considering the influence of fly ash content, water-binder ratio, sand rate and lateral confining pressure, 81 cylinder specimens were designed and made for conventional triaxial test, and the influence laws of stress–strain curve, failure pattern, elastic modulus, energy dissipation and damage evolution of specimens were analyzed. The results showed that the peak of stress–strain curve increased with the increase of confining pressure, and the peak stress, peak strain and energy dissipation all increased significantly, but the damage variable D decreased with the increase of confining pressure. Under triaxial compression, the specimen was basically sheared failure from the bonding surface, and the aggregate generally did not break. Sand rate had a significant effect on the peak stress of CSG, and decreased with the increase of sand rate. Under the conditions of the same cement content, fly ash content and confining pressure, the optimal water-binder ratio 1.2 existed when the sand rate was 0.2 and 0.3. After analyzing and processing the stress–strain curve of triaxial test, a Cuckoo Search-eXtreme Gradient Boosting (CS-XGBoost) curve prediction model was established, and the model was evaluated by evaluation indexes R2, RMSE and MAE. The average R2 of the XGBoost model based on initial parameters under 18 different output features was 0.8573, and the average R2 of the CS-XGBoost model was 0.9516, an increase of 10.10%. Moreover, the prediction curve was highly consistent with the test curve, indicating that the CS algorithm had significant advantages. The CS-XGBoost model could accurately predict the triaxial stress–strain curve of CSG.

Presence of compensatory curve predicts postoperative curve progression in congenital scoliosis after thoracolumbar hemivertebra resection and short fusion.

To investigate the impact of preoperative compensatory curve on the postoperative curve progression in congenital scoliosis (CS) patients following thoracolumbar hemivertebra (HV) resection and short fusion. This study retrospectively reviewed a consecutive cohort of patients with CS who underwent thoracolumbar HV resection and short fusion with a minimum of 2 years follow-up. According to the preoperative curve pattern, patients were divided into compensatory curve group non-compensatory curve group. Based on the postoperative coronal curve evolution, patients were further divided into the progressed group (Group P, with curve decompensation ≥ 20°) and the non-progressed group (Group NP, characterized by well-compensated curves). A total of 127 patients were included in this study, with 31 patients in the compensatory curve group and 96 patients in the non-compensatory curve group. The incidence of postoperative coronal curve progression was significantly higher in the compensatory curve group than that in non-compensatory curve group (35.5% vs. 13.5%, p = 0.007). In the compensatory curve group, patients who experienced postoperative curve progression showed fewer fusion segments (p = 0.001), greater preoperative UIV translation (p = 0.006), greater preoperative LIV tilt (p = 0.017), and larger postoperative UIV tilt (p < 0.001) compared with patients in group NP. Multiple logistic regression demonstrated that the shorter fusion segments and greater postoperative UIV tilt were two independent risk factors for postoperative curve progression. The presence of the compensatory curve was associated with a higher incidence of postoperative curve progression in patients with CS who underwent thoracolumbar HV resection and short fusion. Shorter fusion segments and greater postoperative UIV tilt were found to be the risk factors for postoperative curve progression.

Spin reorientation in premartensite and austenite Ni–Mn–Ga

The premartensite state of Ni–Mn–Ga magnetic shape memory alloy, sometimes called the martensite precursor state, was studied by careful and detailed measurement of the evolution of magnetization curves of magnetically closed samples to evidence local symmetry breaking. During the heating cycle after the martensite transformation, the magnetization loop slowly transforms from a typical sigmoidal shape, corresponding to the magnetization along the easy axis, to a constricted loop indicative of magnetization along a harder magnetic axis. These changes are explained by a switching of the macroscopic magnetic easy axis from [100] to [110]. Above the premartensite transformation temperature, the magnetic easy axis slowly changes back to [100]. After cooling the sample, starting at the Curie temperature, the process reverses.

Existence and convergence of the length-preserving elastic flow of clamped curves

We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document}-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.

In-situ X-ray micro-CT quantitative analysis and modelling the damage evolution in granite rock

Micro-cracking of rock is important mechanism in underground engineering and subsurface energy extraction. Understanding and modeling microcrack evolution and coalescence, and the eventual macroscopic fracture propagation is still a challenge. A micro-mechanically motivated fracture model is developed based on observation and quantitative analysis of in-situ X-CT uniaxial compression test on brittle intact rock with the resolution of 11.98 μm. We performed uniaxial compression test on a micro-granite and acquired real-time X-CT images of crack development under different loadings to investigate cracking pattern, evolution of the crack network and geometric characteristics of the cracks. The experimental results show that the nucleation of isolated microcracks is the main damage pattern before failure. The evolution of damage is subtle under moderate loading but grows stably in density until the unstable coalescence of microcracks, followed by macro-scale failure. Moreover, the damage process is initially dominated by the development of inclined cracks; when failure is approached, the development of relatively more parallel cracks gradually become predominant, indicating the damage transition nature from shear mechanism to tensile mechanism. Based on the X-CT analysis, an improved physics-informed micro-mechanical sliding model is proposed. Compared with previous sliding models, the crack-crack interaction is improved so that this model can well characterize the abrupt failure process. The total surface area of cracks is used to quantify the damage evolution and a relative calibration method is presented. The simulation results show the stress–strain curve and damage evolution are consistent with the experimental results.

Galaxies with grains: unraveling dust evolution and extinction curves with hydrodynamical simulations

Dust in galaxies is an important tracer of galaxy properties and their evolution over time. The physical origin of the grain size distribution, the dust chemical composition, and, hence, the associated ultraviolet-to-optical extinctions in diverse galaxies remains elusive. To address this issue, we introduce a model for dust evolution in the RAMSES code for simulations of galaxies with a resolved multiphase interstellar medium. Dust is modelled as a fluid transported with the gas component, and is decomposed into two sizes, 5 nm and 0.1 μm, and two chemical compositions for carbonaceous and silicate grains. This dust model includes the growth of dust by accretion of elements from the gas phase and by the release of dust in stellar ejecta, the destruction by thermal sputtering, supernovae, and astration, and the exchange of dust mass between the two main populations of grain sizes by coagulation and shattering. Using a suite of isolated disc simulations with different masses and metallicities, the simulations can explore the role of these processes in shaping the key properties of dust in galaxies. The simulated Milky Way analogue reproduces the dust-to-metal mass ratio, depletion factors, size distribution and extinction curves of the Milky Way. Galaxies with lower metallicities reproduce the observed decrease in the dust-to-metal mass ratio with metallicity at around a few 0.1 Z⊙. This break in the dust-to-metal ratio corresponds to a galactic gas metallicity threshold that marks the transition from an ejecta-dominated to an accretion-dominated grain growth, and that is different for silicate and carbonaceous grains, with ≃0.1 Z⊙ and ≃0.5 Z⊙ respectively. This leads to more Magellanic Cloud-like extinction curves, i.e. with steeper slopes in the ultraviolet and a weaker bump feature at 2175 Å, in galaxies with lower masses and lower metallicities. Steeper slopes in these galaxies are caused by the combination of the higher efficiency of gas accretion by silicate relative to carbonaceous grains and by the low rates of coagulation that preserves the amount of small silicate grains. Weak bumps are due to the overall inefficient accretion growth of carbonaceous dust at low metallicity, whose growth is mostly supported by the release of large grains in SN ejecta. We also show that the formation of CO molecules is a key component to limit the ability of carbonaceous dust to grow, in particular in low-metallicity gas-rich galaxies.

Epidemic spreading on spatial higher-order network

Higher-order interactions exist widely in mobile populations and are extremely important in spreading epidemics, such as influenza. However, research on high-order interaction modeling of mobile crowds and the propagation dynamics above is still insufficient. Therefore, this study attempts to model and simulate higher-order interactions among mobile populations and explore their impact on epidemic transmission. This study simulated the spread of the epidemic in a spatial high-order network based on agent-based model modeling. It explored its propagation dynamics and the impact of spatial characteristics on it. Meanwhile, we construct state-specific rate equations based on the uniform mixing assumption for further analysis. We found that hysteresis loops are an inherent feature of high-order networks in this space under specific scenarios. The evolution curve roughly presents three different states with the initial value change, showing different levels of the endemic balance of low, medium, and high, respectively. Similarly, network snapshots and parameter diagrams also indicate these three types of equilibrium states. Populations in space naturally form components of different sizes and isolations, and higher initial seeds generate higher-order interactions in this spatial network, leading to higher infection densities. This phenomenon emphasizes the impact of high-order interactions and high-order infection rates in propagation. In addition, crowd density and movement speed act as protective and inhibitory factors for epidemic transmission, respectively, and depending on the degree of movement weaken or enhance the effect of hysteresis loops.

Alternative View of Inextensible Flows of Curves and Ruled Surfaces via Alternative Frame

In this paper, we present the evolutions of ruled surfaces generated by the principal normal, the principal normal’s derivative, and the Darboux vector fields along a space curve that are the elements of an alternative frame. The comprehension of an object’s rotational behavior is crucial knowledge relevant to various realms, and this can be accomplished by analyzing the Darboux vector along the path of a point on the object as it moves through space. In that regard, examining the evolutions of the ruled surfaces based on the changes in their directrices, including the Darboux vector in the alternative frame along a space curve, is significant. As the first step of this study, we express the evolution of the alternative frame elements of a space curve. Subsequently, the conditions for the ruled surfaces generated by them to be minimal, developable, and inextensible are investigated. These findings can allow some physical phenomena to be well understood through surface evolutions satisfying these conditions. In the final step, we provide graphical representations of some examples of inextensible ruled surfaces and curve evolutions.

Study on compaction characteristics and mechanical model of dry crushing filling material under lateral confinement condition

The compaction characteristics and bearing capacity of dry filling materials in goaf have a significant influence on stope control and surface stability. Through acoustic emission monitoring and mechanical model analysis, a series of confined compression tests were conducted on crushed waste with varying particle sizes and Talbot coefficients. The deformation, fragmentation, and acoustic emission characteristics under corresponding working conditions were determined. The results indicate that the stress–strain curves of crushed stone with different particle sizes and Talbot coefficients exhibit similar nonlinear behavior during confined compression. However, the strain response varies with changing stress levels. By analyzing the slope change rate of the stress–strain curve, the lateral uniaxial compression process of waste rock can be divided into three deformation stages: rapid compression, stable crushing, and slow compaction. The compressive deformation characteristics of gravel differ based on particle size and Talbot coefficient. Specimens with a higher Talbot coefficient demonstrate stronger compressive resistance and weaker deformation resistance during initial compaction loading. Notably, the internal pressure structure strength is influenced by factors such as maximum particle size D, grading coefficient n, and particle size distribution continuity, rather than solely by the proportion of large particles. The evolution of acoustic emission signals and energy-time curve during waste rock confined axial compression synchronizes with the compaction process. Overall, compaction plays a critical role in maintaining the stability of goaf in dry crushed waste filling.

Data-driven mathematical modeling of sleep consolidation in early childhood

Across early childhood development, sleep behavior transitions from a biphasic pattern (a daytime nap and nighttime sleep) to a monophasic pattern (only nighttime sleep). The transition to consolidated nighttime sleep, which occurs in most children between 2- and 5-years-old, is a major developmental milestone and reflects interactions between the developing homeostatic sleep drive and circadian system. Using a physiologically-based mathematical model of the sleep-wake regulatory network constrained by observational and experimental data from preschool-aged participants, we analyze how developmentally-mediated changes in the homeostatic sleep drive may contribute to the transition from napping to non-napping sleep patterns. We establish baseline behavior by identifying parameter sets that model typical 2-year-old napping behavior and 5-year-old non-napping behavior. Then we vary six model parameters associated with the dynamics of and sensitivity to the homeostatic sleep drive between the 2-year-old and 5-year-old parameter values to induce the transition from biphasic to monophasic sleep. We analyze the individual contributions of these parameters to sleep patterning by independently varying their age-dependent developmental trajectories. Parameters vary according to distinct evolution curves and produce bifurcation sequences representing various ages of transition onset, transition durations, and transitional sleep patterns. Finally, we consider the ability of napping and non-napping light schedules to reinforce napping or promote a transition to consolidated sleep, respectively. These modeling results provide insight into the role of the homeostatic sleep drive in promoting interindividual variability in developmentally-mediated transitions in sleep behavior and lay foundations for the identification of light- or behavior-based interventions that promote healthy sleep consolidation in early childhood.

Essential Load-Bearing Characteristics of Steel–Concrete Composite Floor System in Fire Revealed by Structural Stressing State Theory

This study reveals the essential load-bearing characteristics of the steel–concrete composite floor system under fire conditions applying the structural stressing state theory. Firstly, the strain data in the entire process of the fire test are modeled as state variables which can present the slab’s stressing state evolution characteristics. Then, the state variables are used to build the stressing state mode and the parameter characterizing the mode. Further, the Mann–Kendall criterion is adopted to detect the leap points in the evolution curves of the characteristic parameters during the entire fire exposure process. Also, the evolution curves of the stressing state modes are investigated to verify the leap profiles around the leap/characteristic points. Finally, the detected leap points are defined as the failure starting points and elastoplastic branching points, which is unseen in past research focusing on the failure endpoint defined at the ultimate load-bearing state of the composite floor system. The failure starting point and the elastoplastic branching point are the embodiment of natural law from quantitative change to quality change in a system rather than an empirical and statistical judgment. Hence, both characteristic points avoidably exist in the strain data of the composite floor system undergoing the fire process, which can be revealed through the proper modeling methods and update the existing theories and methods on structural analysis and design in fire.

A second-order in time, BGN-based parametric finite element method for geometric flows of curves

Over the last two decades, the field of geometric curve evolutions has attracted significant attention from scientific computing. One of the most popular numerical methods for solving geometric flows is the so-called BGN scheme, which was proposed by Barrett et al. (2007) [8], due to its favorable properties (e.g., its computational efficiency and the good mesh property). However, the BGN scheme is limited to first-order accuracy in time, and how to develop a higher-order numerical scheme is challenging. In this paper, we propose a fully discrete, temporal second-order parametric finite element method, which integrates with two different mesh regularization techniques, for solving geometric flows of curves. The scheme is constructed based on the BGN formulation and a semi-implicit Crank-Nicolson leap-frog time stepping discretization as well as a linear finite element approximation in space. More importantly, we point out that the shape metrics, such as manifold distance and Hausdorff distance, instead of function norms, should be employed to measure numerical errors. Extensive numerical experiments demonstrate that the proposed BGN-based scheme is second-order accurate in time in terms of shape metrics. Moreover, by employing the classical BGN scheme as mesh regularization techniques, our proposed second-order schemes exhibit good properties with respect to the mesh distribution. In addition, an unconditional interlaced energy stability property is obtained for one of the mesh regularization techniques.

Separation and conversion of CO2 reduction products into high-concentration formic acid using bipolar membrane electrodialysis

Electrochemical CO2 reduction to value-added chemicals such as formate represents a crucial pathway in advancing carbon-neutral fuel production. However, the separation of formate from KHCO3 electrolyte solutions and its conversion to formic acid remain cost intensive steps in this process. This study demonstrated the use of bipolar membrane electrodialysis (BMED) to efficiently convert and concentrate formic acid directly from a cathodic solution for CO2 electroreduction. The migration of formate ions during BMED was optimized under different cell configurations and current densities. Mathematical modelling was developed to predict the concentration evolution curves of formic acid production. The results showed that formic acid diffusion through an anion-exchange membrane was more pronounced than that a bipolar membrane; the former diffusion was a key factor that limited the formic acid concentration and reduced the current efficiency. A formic acid concentration of 3.49 mol/L was obtained at an optimum current density of 40 mA/cm2 and a salt-to-acid compartment volume ratio of 25:1. Thus, BMED has emerged as a viable and effective technique for isolating high-purity formic acid from a cathodic solution for CO2 electroreduction.

Effects of multiple relaxation times in the annular flow of pulsatile electro-osmotic flow of a complex biological fluid: blood with low and high cholesterol

This study investigates the electro-osmotic flow of a biological fluid (blood with varying cholesterol levels) in annular flow to simulate a first approximation to arterial occlusion. The fluid´s rheology is characterized by a multi-modal convected Maxwell model equation. The charge density follows the Boltzmann distribution, governing the electrical field. Mathematically, this scenario can be modeled by the Poisson–Boltzmann partial differential equation. Assuming a small zeta potential (less than 25 mV) using the Debye–Huckel approximation and considering a pulsatile electrical field, analytical solutions are derived using the Fourier transform formalism. These solutions, expressed in terms of the modified Bessel function, provide transfer functions for axial velocity and volumetric flow as functions of material parameters represented by characteristic dimensionless numbers. This study further analyzes thermal, electric, inertial, viscoelastic, and various interactions within the plasma, hematocrit, hematocrit–cholesterol, and cholesterol–cholesterol as well as weight concentration through numerical simulations. Finally, the flow and rheology predictions are validated using experimental data on human blood with varying cholesterol levels. The obtained transfer functions reveal that the electric–thermal–viscoelastic effects and the multiple geometric relationships contribute to the dynamic response of the interactions between the input electrical field and output volumetric flow and shear stress functions, leading to and evolution of resonance curves. It is noteworthy that electro-osmotic flow in blood with pathologies associated with low and high cholesterol has been scarcely reported in the literature on rheology. Thus, this work represents a significant contribution to the field.

A frost heave pressure model for fractured rocks subjected to repeated freeze-thaw deterioration

Rock engineering in the Tibetan Plateau is usually suffered severe freeze-thaw (F-T) deterioration, triggering numerous geotechnical engineering disasters. As the essential triggering factor of F-T damage, the frost heave pressure (FHP) in rocks should be quantitatively described and predicted. In this study, a novel theoretical model is established and validated to estimate the critical entire evolution process of FHP in fractured rocks subjected to repeated F-T deterioration, in which the influence of fracture geometric configuration, rock mechanical properties and F-T conditions are comprehensively considered. Besides, given the obvious five-stage manner of FHP evolution, the combination effect of different dominant mechanisms in different stages is theoretically addressed. During freezing, after a silence stage induced by temperature above freezing point of water, volumetric expansion and frost-heave cracking separately controls the generation and reduction stages of FHP, and the solutions are obtained based on elastic mechanics and Griffith energy balance theory, respectively. During thawing, ice segregation dominates the second-arising stage of FHP that is quantitatively described via segregation potential and water migration velocity, and then the FHP enters the dissipation stage owing to complete melting of fracture ice. In addition, a decay coefficient is introduced to estimate the influence of F-T cycle number on FHP, and a piecewise FHP model is finally constructed for fractured rocks subjected to repeated F-T deterioration. To validate our new model, a total of 12 F-T cycle tests with real-time FHP monitoring are conducted on granite and sandstone specimens considering three typical influencing factors, i.e., fracture width, rock types and freezing temperatures. A rational consistency is identified between the theoretical and testing results in terms of the FHP evolution curves and the peak FHPs in rock fracture, demonstrating the generalizability and robustness of our proposed model.

The Evolution of Curve Patterns in Adolescent Idiopathic Scoliosis during Chêneau Brace Treatment.

This retrospective study analyzed bracing outcomes in AIS patients, focusing on curve pattern changes and brace efficacy. To analyze the effectiveness of the Chêneau brace across different curve patterns and to evaluate the tendencies in curve evolution during treatment. Adolescent idiopathic scoliosis (AIS) presents diverse curve patterns, each responding differently to bracing. Understanding these variations is crucial for optimizing treatment strategies. The study included 177 AIS patients treated with Chêneau orthoses, categorized based on curve patterns as per the main curve and modified Lenke (mLenke) classifications. We compared patients according to curve patterns and assessed changes in curve magnitude and pattern before and after treatment. Over an average follow-up of 28.1±10.7 months, the primary curve magnitude decreased from 28.8±6.6° to 25.9±10.5°. Significant reductions were observed in mLenke V and VI patients (P<0.05). Patients with main lumbar curves showed better initial in-brace correction and curve control compared with those with main thoracic curves (P<0.05). In single-curve patterns, binary logistic regression indicated that mLenke V patients demonstrated higher rates of curve control compared with mLenke I patients (P<0.05). No significant differences were found in double-curve patterns between mLenke III and VI (P>0.05). At the final follow-up, thoracolumbar/lumbar curves improved significantly in mLenke III and VI patients (P<0.05), while thoracic curves did not (P>0.05). Furthermore, at the last follow-up, the proportions of mLenke I, II, and IV increased, while mLenke III, V, and VI decreased. Bracing outcomes were more favorable in patients with main lumbar curves than those with main thoracic curves. However, no significant differences were found in patients with double-curve patterns. Thoracic curves exhibited a higher progression risk compared with thoracolumbar/lumbar curves within the same curve pattern. During bracing, a tendency for primary curves to shift proximally was noted.