Rheology of Suspensions Thickened by Cellulose Nanocrystals.

The steady rheological behavior of suspensions of solid particles thickened by cellulose nanocrystals is investigated. Two different types and sizes of particles are used in the preparation of suspensions, namely, TG hollow spheres of 69 µm in Sauter mean diameter and solospheres S-32 of 14 µm in Sauter mean diameter. The nanocrystal concentration varies from 0 to 3.5 wt% and the particle concentration varies from 0 to 57.2 vol%. The influence of salt (NaCl) concentration and pH on the rheology of suspensions is also investigated. The suspensions generally exhibit shear-thinning behavior. The degree of shear-thinning is stronger in suspensions of smaller size particles. The experimental viscosity data are adequately described by a power-law model. The variations in power-law parameters (consistency index and flow behavior index) under different conditions are determined and discussed in detail.

Revealing endogenous conditions for Peto's paradox via an ordinary differential equation model.

Cancer, a disease intimately linked to cellular mutations, is commonly believed to exhibit a positive association with the cell count and lifespan of a species. Despite this assumption, the observed uniformity in cancer rates across species, referred to as the Peto's paradox, presents a conundrum. Recognizing that tumour progression is not solely dependent on cancer cells but involves intricate interactions among various cell types, this study employed a Lotka-Volterra (LV) ordinary differential equation model to analyze the evolution of cancerous cells and the cancer incidence in an immune environment. As a result, this study uncovered the sufficient conditions underlying the absence of correlation in Peto's paradox and provide insights into the reasons for the equitable distribution of cancer incidence across diverse species by applying nondimensionalization and drawing an analogy between the characteristic time interval for the variation of cell populations in the ODE model and that of cell cycles of a species.

Comparison of four rheological models for estimating viscosity and rheological parameters of microwave treated Basil seed gum.

Dispersion of Basil seed gum has high viscosity and exhibits shear-thinning behavior. This study aimed to analyze the influence of microwave treatment (MT) at various time intervals (0, 1, 2, and 3 min) on the viscosity and rheological behavior of Basil seed gum dispersion (0.5%, w/v). The finding of this study revealed that the apparent viscosity of Basil seed gum dispersion (non-treated dispersion) reduced from 0.330 Pa.s to 0.068 Pa.s as the shear rate (SR) increased from 12.2 s-1 to 171.2 s-1. Additionally, the apparent viscosity of the Basil seed gum dispersion reduced from 0.173 Pa.s to 0.100 Pa.s as the MT time increased from 0 to 3 min (SR = 61 s-1). The rheological properties of gum dispersion were successfully modeled using Power law (PL), Bingham, Herschel-Bulkley (HB), and Casson models, and the PL model was the best one for describing the behavior of Basil seed gum dispersion. The PL model showed an excellent performance with the maximum r-value (mean r-value = 0.942) and the minimum sum of squared error (SSE) values (mean SSE value = 5.265) and root mean square error (RMSE) values (mean RMSE value = 0.624) for all gum dispersion. MT had a considerable effect on the changes in the consistency coefficient (k-value) and flow behavior index (n-value) of Basil seed gum dispersion (p < 0.05). The k-value of Basil seed gum dispersion decreased significantly from 3.149 Pa.sn to 1.153 Pa.sn (p < 0.05) with increasing MT time from 0 to 3 min. The n-value of Basil seed gum dispersion increased significantly from 0.25 to 0.42 (p < 0.05) as the MT time increased. The Bingham plastic viscosity of Basil seed gum dispersion increased significantly from 0.029 Pa.s to 0.039 Pa.s (p < 0.05) while the duration of MT increased. The Casson yield stress of Basil seed gum dispersion notably reduced from 5.010 Pa to 2.165 Pa (p < 0.05) with increasing MT time from 0 to 3 min.

Scaling relationships between the total number of leaves and the total leaf area per culm of two dwarf bamboo species.

Total leaf area per plant is an important measure of the photosynthetic capacity of an individual plant that together with plant density drives the canopy leaf area index, that is, the total leaf area per unit ground area. Because the total number of leaves per plant (or per shoot) varies among conspecifics and among mixed species communities, this variation can affect the total leaf area per plant and per canopy but has been little studied. Previous studies have shown a strong linear relationship between the total leaf area per plant (or per shoot) (A T) and the total number of leaves per plant (or per shoot) (N T) on a log-log scale for several growth forms. However, little is known whether such a scaling relationship also holds true for bamboos, which are a group of Poaceae plants with great ecological and economic importance in tropical, subtropical, and warm temperate regions. To test whether the scaling relationship holds true in bamboos, two dwarf bamboo species (Shibataea chinensis Nakai and Sasaella kongosanensis 'Aureostriatus') with a limited but large number of leaves per culm were examined. For the two species, the leaves from 480 and 500 culms, respectively, were sampled and A T was calculated by summing the areas of individual leaves per culm. Linear regression and correlation analyses reconfirmed that there was a significant log-log linear relationship between A T and N T for each species. For S. chinensis, the exponent of the A T versus N T scaling relationship was greater than unity, whereas that of S. kongosanensis 'Aureostriatus' was smaller than unity. The coefficient of variation in individual leaf area increased with increasing N T for each species. The data reconfirm that there is a strong positive power-law relationship between A T and N T for each of the two species, which may reflect adaptations of plants in response to intra- and inter-specific competition for light.

A network model of social contacts with small-world and scale-free features, tunable connectivity, and geographic restrictions.

Small-world networks and scale-free networks are well-known theoretical models within the realm of complex graphs. These models exhibit "low" average shortest-path length; however, key distinctions are observed in their degree distributions and average clustering coefficients: in small-world networks, the degree distribution is bell-shaped and the clustering is "high"; in scale-free networks, the degree distribution follows a power law and the clustering is "low". Here, a model for generating scale-free graphs with "high" clustering is numerically explored, since these features are concurrently identified in networks representing social interactions. In this model, the values of average degree and exponent of the power-law degree distribution are both adjustable, and spatial limitations in the creation of links are taken into account. Several topological metrics are calculated and compared for computer-generated graphs. Unexpectedly, the numerical experiments show that, by varying the model parameters, a transition from a power-law to a bell-shaped degree distribution can occur. Also, in these graphs, the degree distribution is most accurately characterized by a pure power-law for values of the exponent typically found in real-world networks.

Statistical Parameters Extracted from Radar Sea Clutter Simulated under Different Operational Conditions.

A complete framework of predicting the attributes of sea clutter under different operational conditions, specified by wind speed, wind direction, grazing angle, and polarization, is proposed for the first time. This framework is composed of empirical spectra to characterize sea-surface profiles under different wind speeds, the Monte Carlo method to generate realizations of sea-surface profiles, the physical-optics method to compute the normalized radar cross-sections (NRCSs) from individual sea-surface realizations, and regression of NRCS data (sea clutter) with an empirical probability density function (PDF) characterized by a few statistical parameters. JONSWAP and Hwang ocean-wave spectra are adopted to generate realizations of sea-surface profiles at low and high wind speeds, respectively. The probability density functions of NRCSs are regressed with K and Weibull distributions, each characterized by two parameters. The probability density functions in the outlier regions of weak and strong signals are regressed with a power-law distribution, each characterized by an index. The statistical parameters and power-law indices of the K and Weibull distributions are derived for the first time under different operational conditions. The study reveals succinct information of sea clutter that can be used to improve the radar performance in a wide variety of complicated ocean environments. The proposed framework can be used as a reference or guidelines for designing future measurement tasks to enhance the existing empirical models on ocean-wave spectra, normalized radar cross-sections, and so on.

A unified framework for perceived magnitude and discriminability of sensory stimuli.

The perception of sensory attributes is often quantified through measurements of sensitivity (the ability to detect small stimulus changes), as well as through direct judgments of appearance or intensity. Despite their ubiquity, the relationship between these two measurements remains controversial and unresolved. Here, we propose a framework in which they arise from different aspects of a common representation. Specifically, we assume that judgments of stimulus intensity (e.g., as measured through rating scales) reflect the mean value of an internal representation, and sensitivity reflects a combination of mean value and noise properties, as quantified by the statistical measure of Fisher information. Unique identification of these internal representation properties can be achieved by combining measurements of sensitivity and judgments of intensity. As a central example, we show that Weber's law of perceptual sensitivity can coexist with Stevens' power-law scaling of intensity ratings (for all exponents), when the noise amplitude increases in proportion to the representational mean. We then extend this result beyond the Weber's law range by incorporating a more general and physiology-inspired form of noise and show that the combination of noise properties and sensitivity measurements accurately predicts intensity ratings across a variety of sensory modalities and attributes. Our framework unifies two primary perceptual measurements-thresholds for sensitivity and rating scales for intensity-and provides a neural interpretation for the underlying representation.

A mathematical fractal-fractional model to control tuberculosis prevalence with sensitivity, stability, and simulation under feasible circumstances.

BACKGROUND: Tuberculosis, a global health concern, was anticipated to grow to 10.6 million new cases by 2021, with an increase in multidrug-resistant tuberculosis. Despite 1.6 million deaths in 2021, present treatments save millions of lives, and tuberculosis may overtake COVID-19 as the greatest cause of mortality. This study provides a six-compartmental deterministic model that employs a fractal-fractional operator with a power law kernel to investigate the impact of vaccination on tuberculosis dynamics in a population. METHODS: Some important characteristics, such as vaccination and infection rate, are considered. We first show that the suggested model has positive bounded solutions and a positive invariant area. We evaluate the equation for the most important threshold parameter, the basic reproduction number, and investigate the model's equilibria. We perform sensitivity analysis to determine the elements that influence tuberculosis dynamics. Fixed-point concepts show the presence and uniqueness of a solution to the suggested model. We use the two-step Newton polynomial technique to investigate the effect of the fractional operator on the generalized form of the power law kernel. RESULTS: The stability analysis of the fractal-fractional model has been confirmed for both Ulam-Hyers and generalized Ulam-Hyers types. Numerical simulations show the effects of different fractional order values on tuberculosis infection dynamics in society. According to numerical simulations, limiting contact with infected patients and enhancing vaccine efficacy can help reduce the tuberculosis burden. The fractal-fractional operator produces better results than the ordinary integer order in the sense of memory effect at diffract fractal and fractional order values. CONCLUSION: According to our findings, fractional modeling offers important insights into the dynamic behavior of tuberculosis disease, facilitating a more thorough comprehension of their epidemiology and possible means of control.

Power law of path multiplicity in complex networks.

Complex networks describe a wide range of systems in nature and society. As a fundamental concept of graph theory, the path connecting nodes and edges plays a vital role in network science. Rather than focusing on the path length or path centrality, here we draw attention to the path multiplicity related to decision-making efficiency, which is defined as the number of shortest paths between node pairs and thus characterizes the routing choice diversity. Notably, through extensive empirical investigations from this new perspective, we surprisingly observe a "hesitant-world" feature along with the "small-world" feature and find a universal power-law of the path multiplicity, meaning that a small number of node pairs possess high path multiplicity. We demonstrate that the power-law of path multiplicity is much stronger than the power-law of node degree, which is known as the scale-free property. Then, we show that these phenomena cannot be captured by existing classical network models. Furthermore, we explore the relationship between the path multiplicity and existing typical network metrics, such as average shortest path length, clustering coefficient, assortativity coefficient, and node centralities. We demonstrate that the path multiplicity is a distinctive network metric. These results expand our knowledge of network structure and provide a novel viewpoint for network design and optimization with significant potential applications in biological, social, and man-made networks.

Anomalous diffusion of synaptic vesicles and its influences on spontaneous and evoked neurotransmission.

Neurons in the central nervous system communicate with each other by activating billions of tiny synaptic boutons distributed along their fine axons. These presynaptic varicosities are very crowded environments, comprising hundreds of synaptic vesicles. Only a fraction of these vesicles can be recruited in a single release episode, either spontaneous or evoked by action potentials. Since the seminal work by Fatt and Katz, spontaneous release has been modelled as a memoryless process. Nevertheless, at central synapses, experimental evidence indicates more complex features, including non-exponential distributions of release intervals and power-law behaviour in their rate. To describe these features, we developed a probabilistic model of spontaneous release based on Brownian motion of synaptic vesicles in the presynaptic environment. To account for different diffusion regimes, we based our simulations on fractional Brownian motion. We show that this model can predict both deviation from the Poisson hypothesis and power-law features in experimental quantal release series, thus suggesting that the vesicular motion by diffusion could per se explain the emergence of these properties. We demonstrate the efficacy of our modelling approach using electrophysiological recordings at single synaptic boutons and ultrastructural data. When this approach was used to simulate evoked responses, we found that the replenishment of the readily releasable pool driven by Brownian motion of vesicles can reproduce the characteristic binomial release distributions seen experimentally. We believe that our modelling approach supports the idea that vesicle diffusion and readily releasable pool dynamics are crucial factors for the physiological functioning of neuronal communication. KEY POINTS: We developed a new probabilistic model of spontaneous and evoked vesicle fusion based on simple biophysical assumptions, including the motion of vesicles before they dock to the release site. We provide closed-form equations for the interval distribution of spontaneous releases in the special case of Brownian diffusion of vesicles, showing that a power-law heavy tail is generated. Fractional Brownian motion (fBm) was exploited to simulate anomalous vesicle diffusion, including directed and non-directed motion, by varying the Hurst exponent. We show that our model predicts non-linear features observed in experimental spontaneous quantal release series as well as ultrastructural data of synaptic vesicles spatial distribution. Evoked exocytosis based on a diffusion-replenished readily releasable pool might explain the emergence of power-law behaviour in neuronal activity.

Type of probability distribution reflects how close mixing dynamics in river chemistry are to thermodynamic equilibrium.

The distribution of geochemical species are typically either (log)normally distributed or follow power laws. Here we link these types of distributions to the dynamics of the system that generates these distributions, showing that power laws can emerge in dissipative systems far from equilibrium while (log)normal distributions are found for species for which the concentrations are close to equilibrium. We use observations of the chemical composition of river water from the sampling space in central Italy as well as discharge data to test this interpretation. We estimate the dissipation rate that results when groundwater drains into the river and the dissolved chemical species mix with the river water. We show that calcium (Ca2+) and bicarbonate (HCO3-) concentrations are close to saturation along most of the downstream length of the Arno river, with decreasing dissipation rates and a lognormal distribution, while sodium (Na+) and chloride (Cl-) concentrations increase substantially downstream, show increased dissipation rates, and are power-law distributed. This supports our hypothesis that power law distributions appear to be indicative of dissipative systems far from thermodynamic equilibrium, while (log)normal distributions indicate weakly dissipative systems close to equilibrium. What this implies is that probability distributions are likely to be indicative of the thermodynamics of the system and the magnitude of disequilibrium constrains the range over which power-law scaling may be observed. This should help us to better identify the generalities and mechanisms that result in these common types of distributions and to better classify variability in systems according to how dissipative these are.

Assessing internal displacement patterns in Ukraine during the beginning of the Russian invasion in 2022.

Given the worldwide increase of forcibly displaced populations, particularly internally displaced persons (IDPs), it's crucial to have an up-to-date and precise tracking framework for population movements. Here, we study how the spatial and temporal pattern of a large-scale internal population movement can be monitored using human mobility datasets by exploring the case of IDPs in Ukraine at the beginning of the Russian invasion of 2022. Specifically, this study examines the sizes and travel distances of internal displacements based on GPS human mobility data, using the combinations of mobility pattern estimation methods such as truncated power law fitting and visualizing the results for humanitarian operations. Our analysis reveals that, although the city of Kyiv started to lose its population around 5 weeks before the invasion, a significant drop happened in the second week of the invasion (4.3 times larger than the size of the population lost in 5 weeks before the invasion), and the population coming to the city increased again from the third week of the invasion, indicating that displaced people started to back to their homes. Meanwhile, adjacent southern areas of Kyiv and the areas close to the western borders experienced many migrants from the first week of the invasion and from the second to third weeks of the invasion, respectively. In addition, people from relatively higher-wealth areas tended to relocate their home locations far away from their original locations compared to those from other areas. For example, 19 % of people who originally lived in higher wealth areas in the North region, including the city of Kyiv, moved their home location more than 500 km, while only 9 % of those who originally lived in lower wealth areas in the North region moved their home location more than 500 km..

The influence of solvent refractive index on the photoluminescence decay of thick-shell gradient-alloyed colloidal quantum dots investigated in a wide range of delay times.

Colloidal semiconductor quantum dots have many potential optical applications, including quantum dot light-emitting diodes, single-photon sources, or biological luminescent markers. The optical properties of colloidal quantum dots can be affected by their dielectric environment. This study investigated the photoluminescence (PL) decay of thick-shell gradient-alloyed colloidal semiconductor quantum dots as a function of solvent refractive index. These measurements were conducted in a wide range of delay times to account for both the initial spontaneous decay of excitons and the delayed emission of excitons that has the form of a power law. It is shown that whereas the initial spontaneous PL decay is very sensitive to the refractive index of the solvent, the power-law delayed emission of excitons is not. Our results seem to exclude the possibility of carrier self-trapping in the considered solvents and suggest the existence of trap states inside the quantum dots. Finally, our data show that the average exciton lifetime significantly decreases as a function of the solvent refractive index. The change in exciton lifetime is qualitatively modeled and discussed.

Size Distributions of Microplastics in the St Louis Estuary and Western Lake Superior.

Identifying the sources and fate of microplastics in natural systems has garnered a great deal of attention because of their implications for ecosystem health. This work characterizes the size fraction, morphology, color, and polymer composition of microplastics in western Lake Superior and its adjacent harbor sampled in August and September 2021. The results reveal that the overall microplastic counts are similar, with the harbor stations ranging from 0.62 to 3.32 microplastics per liter and the lake stations ranged from 0.83 to 1.4 microplastics per liter. However, meaningful differences between the sample locations can be seen in the size fraction trends and polymer composition. Namely, the harbor samples had relatively larger amounts of the largest size fraction and more diversity of polymer types, which can be attributed to the urbanized activity and shorter water residence time. Power law size distribution modeling reveals deviations that help in the understanding of potential sources and removal mechanisms, although it significantly underpredicts microplastic counts for smaller-sized particles (5-45 µm), as determined by comparison with concurrently collected microplastic samples enumerated by Nile Red staining and flow cytometry.

Relativistic Roots of κ-Entropy.

The axiomatic structure of the κ-statistcal theory is proven. In addition to the first three standard Khinchin-Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom and the scaling axiom. It is shown that both the κ-entropy and its special limiting case, the classical Boltzmann-Gibbs-Shannon entropy, follow unambiguously from the above new set of five axioms. It has been emphasized that the statistical theory that can be built from κ-entropy has a validity that goes beyond physics and can be used to treat physical, natural, or artificial complex systems. The physical origin of the self-duality and scaling axioms has been investigated and traced back to the first principles of relativistic physics, i.e., the Galileo relativity principle and the Einstein principle of the constancy of the speed of light. It has been shown that the κ-formalism, which emerges from the κ-entropy, can treat both simple (few-body) and complex (statistical) systems in a unified way. Relativistic statistical mechanics based on κ-entropy is shown that preserves the main features of classical statistical mechanics (kinetic theory, molecular chaos hypothesis, maximum entropy principle, thermodynamic stability, H-theorem, and Lesche stability). The answers that the κ-statistical theory gives to the more-than-a-century-old open problems of relativistic physics, such as how thermodynamic quantities like temperature and entropy vary with the speed of the reference frame, have been emphasized.

Diffusion in Porous Rock Is Anomalous.

Molecular diffusion of chemical species in subsurface environments─rock formations, soil sediments, marine, river, and lake sediments─plays a critical role in a variety of dynamic processes, many of which affect water chemistry. We investigate and demonstrate the occurrence of anomalous (non-Fickian) diffusion behavior, distinct from classically assumed Fickian diffusion. We measured molecular diffusion through a series of five chalk and dolomite rock samples over a period of about two months. We demonstrate that in all cases, diffusion behavior is significantly different than Fickian. We then analyze the results using a continuous time random walk framework that can describe anomalous diffusion in heterogeneous porous materials such as rock. This methodology shows extreme long-time tailing of tracer advance as compared to conventional Fickian diffusion processes. The finding that distinct anomalous diffusion occurs ubiquitously implies that diffusion-driven processes in subsurface zones should be analyzed using tools that account for non-Fickian diffusion.

Anisotropic power-law viscoelasticity of living cells is dominated by cytoskeletal network structure.

During physiological and pathological processes, cells experience significant morphological alterations with the re-arrangement of cytoskeletal filaments, resulting in anisotropic viscoelasticity. Here, a structure-based cell model is proposed to study the anisotropic viscoelastic mechanical behaviors of living cells. We investigate how cell shape affects its creep responses in longitudinal and perpendicular directions. It is shown that cells exhibit power-law rheological behavior in both longitudinal and perpendicular directions under step stress, with a more solid-like behavior along the longitudinal direction. We reveal that the cell volume and cytoskeletal filament orientation, which have been neglected in most existing models, play a critical role in regulating cellular anisotropic viscoelasticity. The stiffness of the cell in both directions increases linearly with increasing its aspect ratio, due to the decrease of cell volume. Moreover, the increase in the cell's aspect ratio produces the aggregation of cytoskeletal filaments along the longitudinal direction, resulting in higher stiffness in this direction. It is also shown that the increase in cell's aspect ratio corresponds to a process of cellular ordering, which can be quantitatively characterized by the orientational entropy of cytoskeletal filaments. In addition, we present a simple yet robust method to establish the relationship between cell's aspect ratio and cell volume, thus providing a theoretical framework to capture the anisotropic viscoelastic behavior of cells. This study suggests that the structure-based cell models may be further developed to investigate cellular rheological responses to external mechanical stimuli and may be extended to the tissue scale. STATEMENT OF SIGNIFICANCE: The viscoelastic behaviors of cells hold significant importance in comprehending the roles of mechanical forces in embryo development, invasion, and metastasis of cancer cells. Here, a structure-based cell model is proposed to study the anisotropic viscoelastic mechanical behaviors of living cells. Our study highlights the crucial role of previously neglected factors, such as cell volume and cytoskeletal filament orientation, in regulating cellular anisotropic viscoelasticity. We further propose an orientational entropy of cytoskeletal filaments to quantitatively characterize the ordering process of cells with increasing aspect ratios. Moreover, we derived the analytical interrelationships between cell aspect ratio, cell stiffness, cell volume, and cytoskeletal fiber orientation. This study provides a theoretical framework to describe the anisotropic viscoelastic mechanical behavior of cells.

A generic approach to infer community-level fitness of microbial genes.

The gene content in a metagenomic pool defines the function potential of a microbial community. Natural selection, operating on the level of genomes or genes, shapes the evolution of community functions by enriching some genes while depriving the others. Despite the importance of microbiomes in the environment and health, a general metric to evaluate the community-wide fitness of microbial genes remains lacking. In this work, we adapt the classic neutral model of species and use it to predict how the abundances of different genes will be shaped by selection, regardless of at which level the selection acts. We establish a simple metric that quantitatively infers the average survival capability of each gene in a microbiome. We then experimentally validate the predictions using synthetic communities of barcoded Escherichia coli strains undergoing neutral assembly and competition. We further show that this approach can be applied to publicly available metagenomic datasets to gain insights into the environment-function interplay of natural microbiomes.

Nanoscopic Interfacial Hydrogel Viscoelasticity Revealed from Comparison of Macroscopic and Microscopic Rheology.

Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for an interfacial shell around tracers with viscoelastic properties that deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable to the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is applicable to different kinds of viscoelastic fluids and particles.

Multigrid simulations of non-Newtonian fluid flow and heat transfer in a ventilated square cavity with mixed convection and baffles.

The impact of baffles on a convective heat transfer of a non-Newtonian fluid is experimentally studied within a square cavity. The non-Newtonian fluid is pumped into the cavity through the inlet and subsequently departs from the cavity via the outlet. Given the inherent non-linearity of the model, a numerical technique has been selected as the method for obtaining the outcomes. Primarily, the governing equations within the two-dimensional domain have been discretized using the finite element method. For approximating velocity and pressure, we have employed the reliable P 2 - P 1 finite element pair, while for temperature, we have opted for the quadratic basis. To enhance convergence speed and accuracy, we employ the powerful multigrid approach. This study investigates how key parameters like Richardson number (Ri), Reynolds number (Re), and baffle gap b g influence heat transfer within a cavity comprising a non-Newtonian fluid. The baffle gap ( b g ) has been systematically altered within the range of 0.2-0.6, and for this research, three distinct power law indices have been selected namely: 0.5, 1.0, and 1.5. The primary outcomes of the investigation are illustrated through velocity profiles, streamlines, and isotherm visualizations. Furthermore, the study includes the computation of the Nu avg (average Nusselt number) across a range of parameter values. As the Richardson number (Ri) increases, Nu avg also rises, indicating that an increase in Ri results in augmented average heat transfer. Making the space between the baffles wider makes heat flow more intense. This, in turn, heats up more fluid within the cavity.