Scaling Coefficients Research Articles

On a reaction diffusion problem with a moving impulse on boundary

Abstract We study an asymptotic problem of a semilinear partial differential equation (PDE) with Neumann boundary condition, periodic coefficients and highly oscillating drift and nonlinear terms. Our analysis focuses on the double limiting behavior of the PDE-solution perturbed by ε (viscosity parameter) and δ (scaling coefficient) both tending to zero. To do so, we state basic properties of the large deviations principle (LDP) and we express the logarithmic asymptotic of the PDE-solution. Particularly, we provide it for the case when ε converges more quickly than δ.

Reliability and validity of the Chinese version of the COMPI Fertility Problem Stress Scale-Short Form for infertile women.

To translate and culturally adapt the COMPI Fertility Problem Stress Scale-Short form (COMPI-FPSS-SF) and to test its reliability and validity in China. The cross-sectional study adopted Brislin's translation model to translate, synthesize, back-translate, and cross-culturally adapt the COMPI-FPSS-SF for the Chinese setting. A total of 279 infertile women were invited to participate in the study to test the reliability and validity of the scale between March and June 2021. It was verified that the Chinese version of the COMPI-FPSS-SF has three domains with nine items. The Cronbach's α coefficient of the total scale was 0.907, and the coefficient for each dimension ranged from 0.760 to 0.855. The test-retest validity was 0.891. The exploratory factor analysis extracted three common factors with eigenvalues of 4.499, 1.124, and 1.011 and a cumulative variance contribution of 73.706. The validity factor analysis showed good results for the three-factor structure fit. The criterion-related validity with the Fertility Inventory Short-Form Scale was 0.649. The above analysis revealed statistically significant differences (P < 0.001). The Chinese version of the COMPI-FPSS-SF can be used for the assessment of fertility-related stress in infertility patients in China with good reliability and validity.

Development and Validation of Breastfeeding Expectations Scale-A (BES-A): A Questionnaire for Pregnant Women

The aim of this work was to develop a measurement for the expectations of pregnant women about breastfeeding and examine the psychometric properties of the scale. The study was conducted with two separate samples, including women who were ≥28 weeks pregnant. The first sample, comprising 322 women aged 19 to 49 years (M = 28.19; SD = 4.86), was formed to conduct an exploratory factor analysis (EFA). The second sample, which consisted of 274 women aged 18 to 42 years (M = 28.16; SD = 4.85), was formed to conduct a confirmatory factor analysis (CFA). The Prenatal Attachment Inventory and the Depression Anxiety Stress Scale were administered. Data were collected between April and November 2021. In the EFA, two factors were obtained: "1: Enthusiastic Expectations of Breastfeeding" and "2: Fearful/Anxious Expectations of Breastfeeding." In the CFA, path diagrams and goodness-of-fit criteria showed that psychometric properties of 12-item and two-factor structure of the scale were sufficient. The Cronbach’s alpha reliability coefficient of the overall scale and subscales were 0.88, 0.81, and 0.89, respectively. The scale was valid and reliable, and it performed well in measurement of pregnant women’s expectations of breastfeeding about their future breastfeeding experiences.

Association between Depressive Mood, Antidepressant Therapy and Neuropsychological Performances: Results from a Cross-Sectional Study on Elderly Patients.

Currently, the global demographic landscape is undergoing a transformative shift towards an increasingly aging population. This leads to an increase in chronic pathologies, including depression and cognitive impairment. This study aimed to evaluate the association between depressive mood, whether in treatment or not, and cognitive capacities, assessed using the Repeatable Battery for the Assessment of Neuropsychological Status (RBANS). This study included 259 subjects, aged 65 years or older, evaluated at the Geriatric Outpatient Service of the University Hospital of Monserrato, Cagliari, between July 2018 and May 2022, who experienced subjective depressive mood and/or cognitive deficits. Only 25.1% of the sample showed no cognitive impairment on the RBANS. Education was a significant regressor of the RBANS Total Scale scores (p < 0.0001) and was negatively associated with mood deflection (r = -0.15, p = 0.0161). Subjects with depressive mood had more impaired attention and visuospatial/constructional abilities compared to untreated euthymic patients. Post-hoc analysis, conducted with the Conover test, showed that untreated euthymic patients (GDS-15 ≤ 5, group 2) had a higher score on the RBANS total scale than patients with mood deflection (GDS-15 > 5, group 1), and treated euthymic patients (GDS-15 ≤ 5, group 3). Finally, different logistic regression analyses revealed a significant negative coefficient for GDS as a regressor of the RBANS total scale (coefficient: -0.04, p = 0.0089), visuospatial/constructional abilities (coefficient: -0.03, p = 0.0009), language (coefficient: -0.05, p = 0.0140), and attention (coefficient: -0.05, p < 0.0001). Our analysis demonstrated that "naturally" euthymic people show better cognitive performances than people with depressive mood and subjects with acceptable mood due to antidepressants. Furthermore, the gender-based difference observed in the language domain suggests the potential utility of incorporating an alternative category for male patients in the Semantic Fluency test.

Lattice Boltzmann modelling of multicomponent and multiphase flow with high density ratio

Thermodynamic consistency is a key factor in heat and mass transfer simulation. A modified lattice Boltzmann pseudopotential model with the ability to simulate multiphase and multicomponent flow with a large density and viscosity ratio is proposed. Relative to a model using the exact difference method, a better thermodynamic consistency is obtained through introducing an improved external force term, a multi-relaxation-time collision operator, and a scaling coefficient k of the equation of state. The coefficient of scale k = 0.1 is preferred due to its better thermodynamic consistency, lower spurious current and a smaller surface tension. The inter-particle interaction strength has little influence over the thermodynamic consistency due to its limited contributions to the surface tension. With the model, the bubble dissolution under pressure is investigated and Henry’s law is validated.

A degradation feature extraction technique based on static divided symbol sequence entropy

Due to the doping of considerable noise and impact components in vibration signals of quay crane gearboxes, some traditional methods have difficulty uncovering degradation patterns. To accurately extract degradation features from vibration monitoring signals, a degradation feature extraction technique based on static divided symbol sequence entropy is proposed. Based on the basic scale entropy technique, considering the uniformity of the symbolization standard, the technique takes the root mean square of the health condition signal as the basis and incorporates the scale coefficient to establish a uniform basic scale. Simultaneously, the symbol set is expanded to enhance the information content and the ability of the approach to characterize the complexity levels of signals in large-value regions. Therefore, the proposed static divided symbol sequence entropy technique can accurately and flexibly characterize performance degradations. The logistic chaotic sequence and the lifetime signal of hoisting mechanism gearbox are separately used for analysis. It shows that the proposed technique can characterize the complexity of the nonlinear time series and sensitively describe the performance degradation exhibited by hoisting mechanism gearbox. This technique is computationally fast, and it can be implemented as a foundation for developing new methods for evaluating the health conditions of quay crane gearboxes.

The Aesthetic Value of Caravaggio’s Light and Shadow Technique from a Geometric Perspective

Abstract Caravaggio was an influential Italian painter of the 17th century who made important contributions to the development of later European art, both in terms of light and shadow techniques and in terms of ideas. This study first explores the characteristics of Caravaggio’s paintings and briefly explains Caravaggio’s painting style, light and shadow processing techniques, and their significant influence. Secondly, based on the visual perception art understanding method and aesthetic law, the curvelet geometric transformation is utilized to interpret the characteristics of different styles of Caravaggio’s light and shadow techniques in terms of three geometric features: multi-scale amplitude, coefficient distribution curve, and image non-smoothness. Finally, the aesthetic value of Caravaggio’s light and shadow techniques is interpreted from the geometric point of view by using six works from different periods: Caravaggio’s The Doubt of St. Thomas, The Supper at Emmaus, The Basket of Fruits, The Diviner, Narcasus and Judith Cutting down Hierophant as the research materials. The results show that Caravaggio’s light and shadow technique in the early stage of his creative career is characterized by a high low-scale coefficient and a low high-scaled coefficient, which indicates that there are more thick lines and fewer details. The maximum smoothness value of the works is 0.4035 respectively. The light and shadow technique in the later stage of his creative career is characterized by a low scale coefficient and a high scale coefficient, which means that he uses more fine lines to depict the details and less thick lines, reflecting the fact that the light and shadow technique in the later stage of his creative career is characterized by a low scale coefficient and a high high scale coefficient. Caravaggio’s light and shadow technique is characterized by a low scale factor, a high scale factor, and the use of fine lines to depict details and fewer thick lines, reflecting the light and shadow characteristics of Caravaggio’s light and shadow technique, which is depicted by the use of brushes and mineral pigments, and highly demonstrating the aesthetic value of his realist painting.

RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES

Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective gas permeability of the adjacent finger seals annulus considering the gas slip effect and the temperature change is established, and a finite element calculation method of the two-way thermo-mechanical coupling for the finger seal is proposed. The results show that the solid-phase thermal conductance decreases with the increase of the scale coefficient. When the axial pressure difference is greater than 0.4[Formula: see text]MPa, the rotor speed is greater than 11,000[Formula: see text]r/min, the radial displacement excitation is [0.03[Formula: see text]mm, 0.09[Formula: see text]mm], and the temperature is less than 600[Formula: see text]K, the gas-phase thermal conductance between the finger seal and the rotor shows an increasing trend. The gas-phase thermal conductance of the finger seal and the rotor is always the main position under different working conditions. Under different fractal dimensions, the solid-phase thermal conductance gradually occupies the dominant position. Temperature has a certain effect on the effective gas permeability, and fractal dimension, scale coefficient, and axial pressure difference have less effect on the effective gas permeability. At an axial pressure difference of 0.08[Formula: see text]MPa, the numerical calculation results of the two-way thermo-mechanical coupling calculation method for finger seal are closer to the experimental results, with a maximum error rate of 1.96%. The above results further improve the theoretical research system of the heat transfer characteristics of the finger seal.

A validity and reliability of the atraumatic care education model questionnaire based on family-centred care in minimising the stress of hospitalisation in children

Background/Aim: Hospitalisation is a traumatic occurrence in which children must be admitted for acute or chronic diseases. The purpose of this study was to test the validity and reliability of the atraumatic care education model test, instrument based on family-centred care of mother behaviour in minimising children's hospitalisation stress. Methods: Questionnaires were developed based on each parameter of each variable. After the questionnaires were developed, the researcher conducted a pilot study with 50 respondents to assess their validity and reliability. The validity test used the Product Moment test, while the reliability test used Croncbach's Alpha value. Results: All questionnaire statement items on the nurse factor, the mother factor, the service factor, the learning process, the atraumatic care education factor and on mother behaviour variables were declared valid (r count = 0.280-0.854), (r count = 0.292-0.767), (r count = 0.517-0.779), (r count = 0.737-0.918), (r count = 0.303-0.781; r table = 0.275) and (r count = 0.315-0.815; r table = 0.275), respectively. All questionnaires to measure nurse factors, maternal factors, service factors, learning process factors, atraumatic care education, maternal behaviour variables and distress questionnaires were reliable. The internal consistency (alpha coefficient) of the total scale ranged between 0.713-0.925. Conclusion: All questionnaires developed to assess the atraumatic care education model based on family-centred care on mother behaviour in minimising children's hospitalisation stress were valid and reliable and thus have certain application value.

When you avoid your feelings, you may feel even worse: how depersonalization puts you at risk of depression.

The clinical form of depersonalization affects approximately 1%-2% of the adult population. This study aimed to describe the symptoms of depersonalization in a non-clinical sample and to operationalize depersonalization as a regulatory mechanism. This article introduces the Depersonalization Mechanism Scale, 41-item measure developed to assess one's tendency for depersonalization in response to overstimulation. The aim of the study is to explore how depersonalization mechanism is associated with cognitive and behavioral emotion regulation strategies, depression, and anxiety. The study included a sample of 300 Polish adults (149 men) from the general population, ranging in age from 18 to 60. Participants were administered the following questionnaires: Depersonalization Mechanism Scale (DMS), Behavioral Emotion Regulation Questionnaire (BERQ), Cognitive Emotion Regulation Questionnaire (CERQ), Occupational Depression Inventory (ODI), Patient Health Questionnaire (PHQ), and Trait Anxiety Scale (SL-C). An exploratory factor analysis revealed a two-factor structure of Depersonalization Mechanism Scale, with very high reliability coefficients for both subscales and full scale. A regression analysis revealed that depersonalization mechanism is a significant predictor of depressive symptoms. Depersonalization mechanism is strongly correlated with maladaptive regulation strategies such as withdrawal, ignoring, rumination, catastrophizing, self-blame, and blaming others. Weaker but significant connections were identified with certain adaptive strategies: acceptance, positive refocusing, putting into perspective, and seeking social support. Women were more prone to depersonalization than men. Further research on depersonalization in non-clinical samples may improve understanding of this mechanism in the general population. This knowledge, combined with greater education about non-clinical forms of depersonalization, may support preventive programs against depression and professional assistance for people facing acute or chronic stressful life events.

Turkish adaptation of motivation scale for instructional podcast material

The study aims to adapt the Instructional Podcast Material Motivation Scale developed by Asoodar et al. (2014) into Turkish. The study group consists of Cag University Preparatory Year students. The original scale is in English and is a five- point Likert-type tool consisting of a total of 36 items in four dimensions. For the adaptation study, language validity was ensured. The findings obtained from the CFA regarding the construct validity of the scale support the four-factor structure in the original study. As a result of the analysis, the scale consists of 31 items and 4 sub-dimensions. The sub-dimensions of the scale are Attention, Relevance, Confidence, and Satisfaction. Cronbach Alpha internal consistency coefficients for the whole scale (.95) and the sub-dimensions of Attention (.78), Interest (.91), Confidence (.75), and Satisfaction (.93) are high. The results of the analysis show that the scale is valid and reliable in determining students' motivation levels for podcast material.

Cooperative Training Program and Member Satisfaction in Calamba City, Laguna, Philippines

Implementing a training program was a practical relief for the government to eradicate the effect of modern economic scale on marginalized business communities like cooperatives. This study evaluated the effectiveness of the Cooperative Training Program in Calamba City, providing insights into its impact on micro and small cooperative enterprises. It offered detailed feedback on member satisfaction and program outcomes, which can guide necessary improvements to meet participants' needs better. The research utilized a descriptive design and surveyed 14 CLDD employees and 64 Cooperative members operating in Calamba City through a stratified random sampling technique. Specifically, all regular employees of CLDD and Cooperative members from micro-scaled cooperative enterprises who had received the training program were selected as the research sample. Data were collected using Australian Government Standards for a community-based training program called AQTF Survey Form 2007 based on the Quality Indicator Reporting Requirements (2021) and analyzed through statistical treatments, including the simple mean, four-point Likert scale, standard deviation, and Pearson correlation coefficient. The findings show that the CLDD training program was fully implemented, with no notable difference in how CLDD employees and cooperative members rated its execution. Cooperative members expressed high satisfaction with the training, and there was a strong link between how well the program was implemented and their satisfaction levels. In line with these results, the research proposed an enhancement program to improve key areas of the current CLDD training program implementation: training resources, trainer quality, potential and service quality, and product enhancement. The goal is to enhance the overall program and increase satisfaction among cooperative members.

Oral Hygiene Behaviors and Oral Health Literacy Among Informal Thai Workers in Rural Areas

Background: Informal Thai workers experience disparities in accessing health services. Improper oral healthcare behavior is the main cause of oral diseases. Promoting oral health literacy (OHL) is an essential strategy for achieving positive oral health outcomes. This study aimed to investigate OHL, oral hygiene behavior (OHB), and associated factors of OHB among informal Thai workers in a rural context. Methods: A cross-sectional community-based survey was conducted among 274 informal Thai workers aged 20–59 years. The data were collected through face-to-face interviews with questionnaires. Cronbach’s alpha coefficient of the OHL scale was 0.86. Data were analyzed using simple and multiple logistic regression with a 95% confidence interval (CI). Results: The findings revealed that 138 of the participants (50.4%) had proper OHB, and 46.4% had proficiency in overall OHL. Seven factors were significantly associated with OHB, namely, educational attainment, the job sector, the sufficiency of family income, and three OHL dimensions, including understand, appraise, and apply. However, three predictors of proper OHB were those who attained secondary school and higher education (adjusted odds ratio [AOR]: 2.24, 95% CI: 1.31–3.85) and OHL proficiency in the understand and appraise components (AOR: 2.23, 95% CI: 1.25–4.00 and AOR: 1.98, 95% CI: 1.11–3.52, respectively). Conclusion: Therefore, public health dental care units should organize activities to improve workers’ capacity and ability to exhibit OHB. The OHL promotion program should be developed with an emphasis on providing the public with a detailed understanding of oral hygiene. Dental health education is enhanced by inquiring, verifying, and looking at skills to help them gain the skills and confidence to provide consistent oral care.

Interference Response Prediction of Receiver Based on Wavelet Transform and a Temporal Convolution Network

In order to improve the prediction performance of existing methods amidst multi modulation coupling interference in complex electromagnetic environments, this paper introduces a novel approach that integrates wavelet transform with a temporal convolutional network. The model begins with a data preprocessing stage, where wavelet transform decomposes the original signal into various scales. This step generates scale coefficients across different frequency categories, effectively reducing the signal length. To enhance the model’s ability to capture long-term dependencies in time series data, temporal convolutional networks are employed for feature extraction. Moreover, the model’s performance is further refined by incorporating an attention mechanism-driven feature fusion strategy. This strategy methodically combines high and low frequency features along with local and global characteristics. The model’s efficacy is validated using a custom MATLAB dataset, with simulation results confirming a significant improvement in prediction accuracy.

Development of the Pharmacist’s Stress Scale for Home Care (PSS) and evaluation of its reliability and validity

BackgroundAs the needs for home care increase, contact with patients and jobs out of the pharmacy such as the patients’ homes have increased, and there is concern that the situation increases pharmacists’ work-related stress. Stress deteriorates pharmacists’ quality of life (QOL) and affects the quality of services they provide. In this study, we developed a scale for the measurement of stress of pharmacists engaged in home care and evaluated it in pharmacists in 3 prefectures of the Tokai district, Japan.MethodsBased on the stress factors of pharmacists in home care extracted by previous studies, a 59-item questionnaire was developed. The questionnaires were sent to 1785 pharmacies engaged in home care in 3 prefectures of the Tokai district, and anonymous responses were obtained from 399 (valid response rate: 22.4%). The answers to each question were scored using 5-point scale (1: I feel no stress to 5: I always feel strong stress).ResultsAs a result of factor analysis, the Pharmacist’s Stress Scale for Home Care (PSS) was prepared with 51 items, i.e., 14 related to the first factor, “difficulty and feeling of incompetence in patient care”, 9 related to the second factor, “relationship with superiors and work environment”, 13 related to the third factor, “burdens related to work load and work contents”, 10 related to the fourth factor, “communication with patients and families”, and 5 related to the fifth factor, “communication with other professions”. Cronbach’s α coefficients for the entire scale and each factor were ≥ 0.833, and sufficient internal consistency was obtained.ConclusionsThe scale developed in this study is considered to be useful for the measurement of stress of pharmacists derived from interpersonal work and home care services. Leaving the job and burnout are expected to be prevented by perceiving the stress level of the pharmacists by themselves using this scale and coping with stress.

Tensor reduction of loop integrals

The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the number of independent tensor elements that can be constructed using the metric and external momenta. In this article, we present a closed-form solution of this diagonalisation problem in arbitrary tensor integrals. We employ a basis of tensors whose building blocks are the external momentum vectors and a metric tensor transverse to the space of external momenta. The scalar integral coefficients of the basis tensors are obtained by mapping the basis elements to the elements of an orthogonal dual basis. This mapping is succinctly expressed through a formula that resembles the ordering of operators in Wick’s theorem.Finally, we provide examples demonstrating the application of our tensor reduction formula to Feynman diagrams in QCD 2 → 2 scattering processes, specifically up to three loops.

A Study on Tourism Carbon Emission Efficiency in Guangxi Region Through Spatiotemporal Evolution

Currently, there are high emissions and high pollution in the tourism industry around the world, particularly due to carbon emissions from transportation. At the same time, attention is being paid to improving tourism carbon emission efficiency as tourist accommodations and activities consume significant amounts of energy. This article used the slack-based model (SBM) to calculate the tourism carbon emission efficiency in different years and explored its spatiotemporal evolution in the Guangxi region. The factors that affected tourism carbon emission efficiency in Guangxi were selected and examined through Tobit model regression. The results showed that the correlation coefficient of the tourism scale was the largest, reaching 0.6572, making it the variable factor with the greatest impact. The second factor was the tourism industry structure coefficient, which had a correlation coefficient of 0.5688. The impact of tourism industry size and transportation facilities on tourism carbon emission efficiency in Guangxi Province was relatively small, with coefficients of 0.0451 and 0.0357, respectively, i.e., both significance levels were below 0.1, indicating that spatiotemporal evolution can be applied to analyze Guangxi’s tourism carbon emission efficiency.

Ontogenetic and static scaling of antler mass in White-tailed Deer (Odocoileus virginianus)

Abstract Antlers are a costly trait that require skeletal reserves to grow to a large size. Thus, insight into variation in antler size requires understanding the connection between antler and body size, which can be summarized through ontogenetic and static scaling relationships. Both types of scaling relationships are also needed to examine the influence of factors besides body mass on antler growth at different ages and whether the effects of these factors diminish with age. Dietary and maternal effects might decline with age as individuals attempt to mitigate size deficits. We examined the potential effects of diet and maternal attributes of dam (mother) age at birth and litter size on body–antler mass relationships throughout ontogeny and at discrete ages. Data on age, maternal characteristics, body mass, and antler mass were gathered from captive, pen-raised White-tailed Deer (n = 168) that consumed either a low-energy (1.77 kcal/g) or standard-energy diet (2.65 kcal/g) from the time they were weaned until they perished by 5.5 years of age. Both types of scaling relationships were estimated with linear mixed-effects models to account for repeated measurements of males, dams, and sires. Diet affected ontogenetic scaling relationships. Males eating the low-energy diet had faster antler growth when young and lighter in body mass than when they were older and heavier—whereas males fed the standard-energy diet had a similar rate of antler growth across the range of body masses. A Bayesian Information Criterion model selection analysis indicated that diet and litter size (singleton, multiple births), but not dam age at birth influenced static scaling relationships. Static scalar coefficients up to 3.5 years of age were positively allometric (&amp;gt;1.0), but isometric (1.0) in 4.5- and 5.5-year-old males. Furthermore, diet and litter size influenced both intercepts and slopes in only the youngest males (1.5 years) indicating that dietary and maternal effects can diminish with age. Body–antler mass relationships are complex. Young males that are small because of maternal effects, for example, might still be able to mitigate smaller body and antler sizes at older ages.

Scaling of earthquake waiting time distributions in northern Chile

SUMMARY In this study, we examine the scaling of earthquake waiting time distributions in Northern Chile. For this purpose, we analysed 7-yr high spatial resolution and low completeness magnitude IPOC seismic catalogue and 43-yr USGS catalogue. A unified earthquake moment–space–time scaling relation is empirically evaluated by calculating waiting times for different ranges of magnitude and epicentral area linear dimension and estimating the associated scaling coefficients, β analogue to b-value and γ, the correlation fractal dimension. We find a scaling function that can be characterized with three distinct regions, regions whose behaviour depends on whether seismicity is in the coastal area or at intermediate depth. Moreover, high resolution localizations from the IPOC catalogue allows us to further observe differences: the lower plane seismicity of the double seismic zone behaves just like that at intermediate depth, while the crustal upper plate and the upper plane from the double seismic zone seismicity behaves more like interface seismicity. Thus, the earthquake waiting time distribution primarily depends on whether seismicity is located in a crust-on-crust or in a crust–mantle system: having, respectively, high/low correlated behaviour in the short scale region, non-exponential/exponential decay in the transition middle region and, in all cases, long-term clustering with a slower than exponential decay in the long scale.

Modeling the single particle crushing behavior by random discrete element method

Microscopic properties of granular materials typically exhibit significant heterogeneity. Realistic particle crushing simulation in granular materials requires the use of model that incorporate the spatial heterogeneity of its microscopic properties. This study introduces a novel approach, the Random Field Theory-Discrete Element Method (RFT-DEM) model, to simulate the single-particle crushing behavior of granular materials, considering the spatial heterogeneity of microscopic properties within particles. The material heterogeneity was characterized through Random Field Theory, demonstrating reasonable consistency between simulated and experimental results. The size-dependent characteristics of crushing strength and Weibull modulus were confirmed through a series of single-particle crushing simulations, emphasizing the model's capability to capture such features. Systematic analyses explored the impact of coefficient of variation (COV) and scale of fluctuation (SOF) on single-particle crushing behavior. Increasing COV resulted in reduced characteristic crushing strength and Weibull modulus, with larger particles exhibiting greater sensitivity. Furthermore, increasing SOF initially increased these parameters until a threshold SOF value of 0.0005 m, beyond which they stabilized. Reduced COV or increased SOF diminished the size effect in characteristic crushing strength, and once COV exceeded a threshold of 0.03, the size effect became independent of its variations. These findings contribute to a comprehensive understanding of the intricate interplay between microscopic properties and crushing behavior in granular materials.