Search Results (130)

Mechanical properties such as viscoelastic, rheological, and textural properties, particularly adhesiveness and cohesiveness, play a significant role in the optimization of handling, processing and drying of dewatered sludge. However, there is no currently standardized methodology for quantifying these properties, leading researchers to adopt various techniques based on economic feasibility, equipment availability, and research objectives. This review systematically compiles and analyzes the most relevant experimental methodologies for evaluating the mechanical properties of dewatered sewage sludge (DSS). This work presents a general overview of the composition and structure of DSS, followed by a comprehensive bibliometric analysis that revealed literature gaps (particularly in adhesiveness evaluation) and identified regulatory frameworks that incremented interest in researching DSS’ properties in the broader push for sustainability. Consequently, a discussion of the experimental set-ups, data treatment and visualization, advantages and disadvantages, and mathematical models with their physical significance is presented for the different techniques identified. The methods analyzed include oscillatory rheology, penetrometry (cylinder and cone), uniaxial compression tests (TPA), shear testing (e.g., Jenike shear test, Atterberg limit test, direct box shear test, triaxial shear test, unconfined shear test, and vane shear test), tomography and slump tests. By comparing these techniques, this study provides insights into the most appropriate approaches for sludge characterization, emphasizing the need for a unified framework to standardize the evaluation of viscoelastic and textural properties in DSS. Full article

This study analyzes the combined effects of non-Newtonian rheology and electrostatics on the transient electroosmotic flow of Maxwell fluids in soft channels. The walls of the rigid channels are hydrophobic, ionically charged, and coated with a polyelectrolyte layer (PEL). This design is intended to regulate both the surface electric potential and the flow velocity. The mathematical model is based on modified Poisson–Boltzmann and momentum equations, which are solved numerically using a one-dimensional (1D) approach. The results indicate that high potentials, exceeding the Debye–Hückel limit, are achieved under conditions of thick polyelectrolyte layers, high surface charge density, and a higher concentration of fixed charges compared to the electrolyte ionic concentration. In this regime, steric effects increase the electric potential; however, this potential increase is limited by the formation of a Donnan potential. The hydrodynamic analysis demonstrates that the velocity magnitude is influenced not only by the wall potential but also by the spatial distribution of free charge density and electroosmotic force, which, in turn, are affected by steric effects. Additionally, changing the polarity and concentration of fixed charge in the PEL produces asymmetric flows, and while hydrodynamic slip enhances velocity, the drag parameter reduces it. Finally, the dimensionless parameters that control the time required to dampen the oscillatory flow induced by viscoelastic effects and reach steady-state are mainly the relaxation time, the drag parameter, the PEL thickness, and the electrokinetic parameter of the PEL, while the surface charge density and the external pressure gradient exert a comparatively minor influence. Full article

Pipes conveying fluids are important fluid–structure interaction systems encountered in aerospace, energy, marine, and industrial applications. Their dynamic behavior is strongly influenced by the interaction between structural motion and internal or external flow, leading to complex phenomena such as divergence, flutter, and flow-induced vibration. This review presents a comprehensive assessment of the dynamics and stability of pipes conveying fluids by integrating classical theories with recent developments in modeling, computation, materials, and control. The review covers mathematical formulations based on Euler–Bernoulli, Rayleigh, Timoshenko, and shell theories, together with analytical and numerical solution methods used for stability and vibration analysis. The effects of geometry, boundary conditions, flow configuration, damping, and material properties on dynamic response and instability thresholds are discussed. Special attention is given to composite, viscoelastic, functionally graded, and smart materials, as well as micro- and nanoscale pipe systems. Recent advances in vibration suppression, reduced-order modeling, machine learning, and physics-informed computational approaches are also reviewed. Finally, the paper identifies current challenges and future research directions, including multiphysics coupling, experimental validation, digital twins, and AI-assisted predictive modeling for fluid-conveying pipe systems. Full article

An artificial neural network (ANN) prediction model based on the Levenberg–Marquardt (LM) algorithm has been developed to predict the nonlinear heat and mass transfer characteristics of Cattaneo–Christov Carreau–Yasuda tri-hybrid nanofluid (CCHMF–THNF) flow over a porous stretching sheet. A mathematical model of the phenomenon was developed based on a number of elements, including the combined effect of magnetohydrodynamic forces, thermal and solutal relaxation and the influence of viscoelastic fluid behavior and is numerically analyzed utilizing MATLAB bvp4c software. A set of standard data was generated as a reference for developing the ANN-LM model with one hidden layer containing 10 neurons and log-sigmoid activation function, to achieve rapid predictions of velocity, temperature and concentration profiles from the identified data set. This study introduces a novel methodology to provide fast prediction capabilities for transport characteristics through integration of the ANN–LM model with the non-linear CCHMF-THNF model, producing computational savings by providing prediction accuracy of transport characteristics with MSE values on the order of $1.0\times {10}^{-10}$ using ANN–LM in place of repeated bvp4c solutions. Furthermore, the predictive capability of the developed ANN–LM framework may be beneficial in the areas of thermal management systems, polymer processing, energy transport applications, and magnetically controlled cooling technologies since they all share a need for fast access to transportation characteristic evaluation data. Full article

This work develops an analytical framework for nonlinear fractional partial differential equations that combine Kirchhoff-type terms, double-phase operators, and $\psi$-Hilfer fractional derivatives. This paper investigates two classes of problems involving variable-exponent growth conditions. The first problem analyzes general nonlinear sources and formulates the solution as a fixed point of a nonlinear operator. Precisely, by proving that the functional energy is coercive, hemicontinuous, and strictly monotone, we establish the existence and the uniqueness of weak solutions via monotone operator theory. The second problem incorporates a convection-type nonlinearity, which breaks variational structure and requires the more robust theory of pseudomonotone operators. Under suitable growth and mixed-order assumptions on the nonlinearity, we prove the existence of at least one weak solution. The main tools are grounded in variable-exponent Lebesgue and Musielak–Orlicz–Sobolev spaces, with compact embeddings, modular estimates, and fractional integral identities playing a key role in the proofs. We note that the results contribute to the mathematical modeling of phenomena involving nonlocal elasticity, viscoelastic materials, phase-transition media, and fractional dynamical systems where the stiffness of the medium depends on the total deformation (Kirchhoff effect) and the energy density alternates between distinct growth regimes (double-phase). The $\psi$-Hilfer derivative enhances the scope by enabling models with tunable memory and hereditary effects. Full article

Dynamic knowledge representation in curved manifolds conventionally relies on integer-order Markovian sequence encoders, intrinsically yielding exponential memory decay. This paradigm fails to model the anomalous diffusion and heavy-tailed historical dependencies inherent in complex evolutionary networks and dense physical environments. This manuscript proposes the Fractional–Temporal Lorentz Graph Convolutional Network (FTL-GCN), formalizing temporal evolution as a continuous fractional geometric flow explicitly defined on the tangent bundle of the Lorentz manifold. Analytical derivations demonstrate that the discrete Grünwald–Letnikov memory kernel establishes a non-exponential, power-law lower bound for historical state retention, preventing topological manifold collapse over extended temporal horizons. Empirical evaluations demonstrate that FTL-GCN achieves competitive forecasting accuracy against the latest 2025–2026 state-of-the-art discrete models within specific temporal windows, while uniquely mitigating predictive degradation by up to 52% in long-horizon dependency stress tests and maintaining sub-millisecond latency for physical control. The architecture is subsequently deployed within an in silico biophysical simulation for autonomous micro–nano robotic navigation in the Tumor Microenvironment (TME). By establishing a physical-mathematical structural analogy—mapping the empirical fractional viscoelasticity of the extracellular matrix to the cognitive network’s fractional derivative order—FTL-GCN sustains continuous-space navigation policies in dense anomalous environments where standard integer-order models experience mechanical slip. Full article

In this research article, we introduce and develop the notion of complex-valued b-suprametric spaces as a natural generalization of existing metric-type structures. Fundamental concepts, including convergence, Cauchy sequences, and completeness, are examined in this new setting. We establish new common fixed point theorems for generalized and cyclic rational contractive mappings. The obtained results extend and unify various known fixed point theorems available in the current literature. To demonstrate the applicability and effectiveness of our theoretical findings, illustrative nontrivial examples are provided. As an application, we investigate the existence and uniqueness of solutions for Caputo fractional differential equations, which naturally arise in systems with hereditary and memory effects, particularly in biomedical modeling of viscoelastic biological tissues such as arteries, cartilage, and brain tissue. This demonstrates both the mathematical strength and the practical relevance of the proposed framework. Full article

Non-dilute emulsions are emulsions where the concentration of the droplets is high enough for the neighbouring droplets to interact with each other hydrodynamically but is still smaller than the packed bed concentration where the droplets are packed and deformed against each other. Thus, they cover a broad range of droplet concentrations. Many emulsions encountered in industrial applications fall under this category. Non-dilute emulsions exhibit rich rheological behaviour, from a simple Newtonian fluid to a highly non-Newtonian fluid, reflecting shear-thinning, shear-thickening, yield stress, viscoelasticity, etc. In this article, the rheology of non-dilute emulsions is reviewed comprehensively. Emulsions of hard-sphere-type droplets and deformable droplets, with and without surfactants, are covered. The mathematical models describing the rheological behaviour of non-dilute emulsions are discussed. The influences of electric charge and interfacial rheology on the rheological behaviour of emulsions are covered in detail. The flocculation of droplets caused by different mechanisms, such as depletion and bridging induced by additives, and their effect on emulsion rheology are investigated thoroughly. Finally, the dynamic rheology of non-dilute emulsions is discussed, covering both pure oil–water interfaces and additive-laden interfaces. The mathematical models describing the dynamic rheological behaviour of non-dilute emulsions are described. Based on the existing theoretical and empirical models, it is possible to a priori predict the rheology of non-dilute emulsions. However, serious gaps in the existing knowledge on non-dilute emulsion rheology remain. This review identifies the gaps in existing knowledge and points out future directions in research related to non-dilute emulsion rheology. Full article

While anisotropic extrudate swell in polymer processing is fundamentally driven by physical viscoelastic recovery, this paper proposes a theoretical framework to explicitly isolate and map the purely geometric and kinematic components of this phenomenon. Serving as a mathematical proof-of-concept, a multi-velocity-centre hypothesis is proposed. By introducing a semi-empirical, lumped material-flow calibration parameter, the macroscopic diameter swell ratio is mathematically extended to the discrete local flow field of a rectangular slit die. To evaluate its validity, the analytical framework is subjected to a numerical test for kinematic consistency utilizing isothermal, inelastic power-law fluid CFD simulations, thereby separating geometric mapping from complex viscoelastic stress relaxation. Results indicate that analytical predictions show good agreement with CFD data (error < 5%) strictly within the core zone of high-aspect-ratio dies. However, due to the infinite-slit assumption, 3D flow kinematics near die edges induce velocity decay, leading to local deviations that require future empirical corrections. Although comprehensive physical extrusion experiments and non-isothermal viscoelastic coupling are required for industrial deployment, this semi-empirical kinematic mapping provides a foundational mathematical basis that could potentially inform future inverse die-profile design and shape distortion compensation. Full article

Self-organizing systems arise in complex biomechanical structures, human locomotion, and neural control hierarchies, yet quantitative methods for describing order formation and loss of stability remain limited. This study develops a mathematical framework for analyzing self-organization using entropy-based measures, indicators of chaotic dynamics, and network-theoretic structure. The approach (the LET framework) combines Lyapunov exponents with entropy families and graph metrics (algebraic connectivity, Load-Path Heterogeneity Index) to: (i) examine transitions between ordered and disordered states, (ii) assess sensitivity to perturbations, and (iii) characterize structural coherence in evolving cervical spine kinematics. Analytical models and computational validations are presented for cervical stability and post-operative Adjacent Segment Disease (ASD) using the Branney–Breen dataset. The findings indicate that entropy and chaos measures identify regime shifts and the emergence of a “stability corridor” more clearly than task-oriented indices, and provide finer resolution of dynamical variability within self-organizing processes. Network metrics complement these results by linking local segmental interactions to global structural fragility transfer. The study shows that entropy, chaos indicators, and network structure together form a consistent basis for describing self-organization in biomechanical systems, enabling quantitative comparison of dynamical regimes and improved interpretation of emergent pathological behavior. The approach utilizes a hybrid kinematic surrogate model to resolve passive and active components, bypassing direct force measurements by employing viscoelastic mechanotransduction principles. Full article

To address the lack of systematic comparison regarding rheological properties and the unclear structure–property relationships among three core fracturing fluid materials including synthetic polymers, vegetable gums, and microbial polysaccharides, this study selected acrylamide-based polymers, hydroxypropyl guar gum and xanthan gum as the representative systems. The steady-state viscosity, rheological curves, thixotropy, viscoelasticity, and temperature-shear resistance of the three samples were systematically characterized at concentrations ranging from 0.1 to 0.7 wt% using an MCR301 rotational rheometer. The outcomes indicate that the structural strength values of all three materials increase with rising concentration, but their rheological behaviors and stability differ significantly due to distinct molecular structures. The acrylamide-based copolymer forms a temporary network via weak hydrogen bonds (amide-carboxyl or amide-amide) and physical entanglements, exhibiting thixotropy and a stress pre-elastic response. The most significant effects occur at 0.7 wt%, with a thixotropic loop area of 2.874 Pa·s⁻¹ and a stress overshoot of 4.97 Pa.; hydroxypropyl guar gum has insufficient thermal stability and poor heat resistance. Its viscosity retention rate is as low as 31%, and it always exhibits a solution-type rheological property of G′ < G″; the xanthan gum exhibits elastic gel properties with tanδ < 1 due to its double-helix molecular structure. It has excellent temperature shear tolerance and the viscosity retention value can reach up to 98.6 mPa·s. Two mathematical models were established and demonstrated strong applicability: a modified Carreau model for flow curve fitting yielded a coefficient of determination (R²) greater than 0.95, enabling accurate description of fluid-type transitions; a four-parameter equation for temperature–shear resistance curves also achieved an R² above 0.95, effectively characterizing viscosity evolution with temperature. Full article

The numerical analysis of dissipative energy in dynamic problems involving impact and contact phenomena relies on the physical principles of classical thermodynamics and on the constitutive equations of the material, supplemented by some additional considerations of potential contact interfaces. From the mathematical perspective, we come to a weak form of partial differential equation(s) of evolution with initial, boundary, and interface conditions, whose numerical analysis is required using the method of discretisation in time and typically the finite element technique. Dissipative energy is an important metric for quantifying the portion of mechanical work that is permanently converted to plastic work and thermal energy, among other applications. Crucially, the localised accumulation of this energy, often expressed as the plastic work density, is the primary physical parameter driving microstructural changes, damage initiation, and crack propagation under intense loading. This paper demonstrates how the dissipative energy resulting from material nonlinearities can be evaluated in dynamic problems involving the impact of one body on another and provides a quantitative comparison of numerically calculated dissipated energy using three types of nonlinear constitutive material models, namely the plastic material model with Rankine–Hill criterion, the Mazars damage model, and the Kelvin–Voigt viscoelastic model. Full article

This Editorial introduces the Symmetry Special Issue “Theory and Applications of Special Functions II” and summarizes the nine contributions collected therein. The papers span the analytic continuation of multivariate hypergeometric functions; stability theory for differential equations via integral transforms; numerical schemes for multi-space fractional partial differential equations based on nonstandard finite differences and orthogonal polynomials; applications of the Lambert W function to viscoelastic creep modeling; algebraic constructions of new Hermite-type polynomial families via the monomiality principle; higher-level generalizations of poly-Cauchy numbers; Bell-polynomial expansions for Laplace transforms of higher-order nested functions; and two complementary studies on the physical implementation and algebraic description of Gaussian quantum states. Beyond the contributions of the Special Issue, we highlight methodological connections—continued fractions and complex analysis, transform techniques, special polynomials, and combinatorial sequences—and emphasize the unifying role of symmetry across mathematical structures and applications. Full article

The present article relates to the description of phenomenological relations of amorphous material behavior within the framework of viscoelasticity and elastic-viscoplasticity theory, as well as to the creation of its digital analog. Ultra-high-molecular-weight polyethylene (UHMWPE) is considered in the study. The model is based on the results of a series of experimental studies. Free compression of cylindrical specimens in a wide range of temperatures [−40; +80] °C and strain rates [0.1; 4] mm/min was performed. Cylindrical specimens were also used to determine the thermal expansion coefficient of the material. Dynamic mechanical analysis (DMA) was performed on rectangular specimens using a three-point bending configuration. Maxwell and Anand models were used to describe the material behavior. In the framework of the study, the temperature dependence of a number of parameters was established. This influenced the mathematical formulation of the Anand model, which was adapted by introducing the temperature dependence of the activation energy, the initial deformation resistance, and the strain rate sensitivity coefficient. Testing of the material models was carried out in the process of analyzing the deformation of a spherical bridge bearing with a multi-cycle periodic load. The load corresponded to the movement of a train on a bridge structure, without taking into account vibrations. It is shown that the viscoelastic model does not describe the behavior of the material accurately enough for a quantitative analysis of the stress–strain state of the structure. It is necessary to move on to more complex models of material behavior to minimize the discrepancy between the digital analog and the real structure; it has been established that taking into account plastic deformation while describing UHMWPE would allow this to be performed. Full article

In this study, a nonlinear mathematical model of a thin string oscillating in an isotropic viscoelastic medium is developed. The model addresses external and internal mechanical energy dissipation in the string using components described by nonlinear exponential functions. The differential state equation of the studied item is based on a modified Hamilton–Ostrogradsky integral variation principle. The principle is modified by expanding the Lagrangian with two additional components: one addressing the external and internal mechanical energy dissipation in a system and the other addressing the energy of external non-potential forces acting on a system. To substantiate the existence and uniqueness of the solution to a mixed initial boundary problem, the general theory of nonlinear differential equations is applied. A long, single power line is used as an example; its elements oscillate between two support points of the wire. The computer simulation results for the nonlinear vibrations of the object are presented and analysed. Full article