Search Results (1,869)

Non-destructive and destructive test methods are applied to wood to characterize this heterogeneous natural material. There have been multiple studies to characterize and investigate the change after the treatment (impregnation, thermal modification, etc.). In terms of thermal modification, there have been few studies on thermo–vacuum treatment, which is performed in a continuous vacuum atmosphere. With this method, the objective was to attempt to reduce the strength decrease after the thermal treatment. The aim of this study was to estimate the flexural properties of thermo–vacuum-treated Scots pine wood with destructive and acoustic-based non-destructive test methods. Wood was treated at 180 °C and 360 mm Hg. Both treated and untreated samples were cut into small specimens to ensure they were free of defects and were tested with acoustic-based non-destructive (longitudinal vibration and stress wave) and static bending test methods. The results show a decrease in equilibrium moisture content, demonstrating the efficiency of the treatment. When the results were compared with destructive test results, higher correlations (R² > 0.858) were found when estimating the modulus of elasticity (MOE) for both the untreated and treated wood, while lower correlations (R² < 0.440) were found for the modulus of rupture (MOR). When an additional equation was developed, stronger correlations (R² > 0.8986) were obtained between the non-destructive and destructive test results. Full article

This paper examines the dynamics of positive solutions to a system of fuzzy difference equations, which provide effective tools for modeling dynamical systems with uncertain or imprecise parameters. The main objective is to establish the existence, uniqueness, and qualitative properties of positive solutions within a fuzzy framework. After recalling some fundamental notions from fuzzy set theory, we analyze the dynamics of the proposed system. The main results prove the existence of a unique positive fuzzy solution under suitable conditions and establish the boundedness, continuity, and convergence of the solutions. In particular, all solutions converge to a unique positive equilibrium point. Numerical experiments for $(l_1,l_2)=(2,3)$ and $(l_1,l_2)=(4,1)$ with uncertainty levels $\gamma =0.2$ and $\gamma =0.8$ illustrate the theoretical results and confirm the convergence toward the unique positive equilibrium. Full article

This article presents the results of a study on an axisymmetric gravity-driven slender free-surface flow down a cone by deriving depth-averaged conservation equations on a cone-adapted coordinate system and obtaining a backwater-type differential equation for steady, axisymmetric films with prescribed apex discharge. Analysis of this equation reveals a location-dependent critical condition separating supercritical and subcritical regimes and shows that a classical constant normal depth does not exist; instead, the flow approaches an equilibrium between gravity and resistance forces as it develops downstream. Asymptotic expansions for the flow and critical depths recover previously established results for the laminar leading-order and first-order corrections under consistent velocity shape coefficients, confirming that capillarity affects only first-order terms. The framework predicts a critical length beyond which the flow must be subcritical, Reynolds number decays inversely with the distance, leading to inevitable relaminarization on sufficiently long cones, and the potential need for hydraulic jumps to compatibilize supercritical and subcritical flow regimes, paralleling open-channel hydraulics on mild slopes. Numerical solutions of the backwater equation agree with existing measurements where the slender-film assumptions hold, providing a practical basis to compute flow depth and regime transitions on conical surfaces. Full article

The Compact Strip Production (CSP) process is the latest version of thin-slab continuous casting, combining both casting and rolling, thus improving the CSP process’s energy efficiency and the strip quality. Modeling the combined phenomena of fluid flow, heat transfer and solidification in CSP casting remains an unresolved multiphysics problem, particularly when boron and other alloying elements enter the system and modify the thermal properties and solidification behavior. In this study, we propose a more integrated approach by executing a computational fluid dynamics (CFD) model at different scales, blending macroscale fluid flow and heat transfer with meso-solidification that is molten in a CSP casting model. For the macroscale model, we solve the Reynolds-Averaged Navier–Stokes (RANS) equations with one of the energy equations, while the mesoscale model uses the solid fraction evolution algorithm to model the multiphase latent heat of solidification and the motion of solid and liquid phases of a non-equilibrium system. Mold heat flux, free surface cooling and secondary spray zones were used to set the boundary conditions. The model simulates temperature distributions at different times, the solid fraction below the liquidus and the trends in shell growth for different process parameters and the time profile of the solidification. The improved prediction capability of the model, demonstrated by the results, opens the opportunity to reduce the process parameters of casting speed and cooling to defect-free results. Comparisons with the most recent studies on continuous casting processes (including CSP and thin slabs) demonstrate alignment with the thermal gradient and solidification behavior characteristics. The thermal gradients and solidification behavior characteristics were obtained. The research yields the basis for developing microstructure and segregation models with boron-alloyed steels. Full article

In this paper, we examine the inherent mathematical and physical inconsistencies of strain-gradient theories. It is shown that strain gradients are not proper measures of deformation, because their corresponding energetically conjugate stresses are non-physical and cannot represent the state of internal stresses in the continuum. Furthermore, the governing equations in these theories do not describe the equilibrium or motion of infinitesimal elements of matter properly. In the first strain-gradient theory (F-SGT), there are nine explicit governing equations of motion for infinitesimal elements of matter at each point: three force equations and six unsubstantiated artificial moment equations that violate Newton’s third law of action and reaction. This shows that F-SGT is not an extension of rigid-body mechanics, which is, therefore, recovered in the absence of deformation. Moreover, F-SGT would require the existence of six additional fictitious symmetries of space-time according to Noether’s theorem, and a complete revision of the well-established concept of static indeterminacy in introductory mechanics. The inconsistencies of F-SGT also manifest themselves in the appearance of strains as boundary conditions. Full article

This research addresses a structural cybernetic anomaly within strategic management precipitated by the integration of artificial intelligence into the organizational core. Traditional paradigms, specifically the resource-based view and the dynamic capabilities framework, operate under closed-system, first-order cybernetic assumptions that fail to capture the dissipative nature of algorithmic agents. By conceptualizing the enterprise as a complex adaptive system operating far from thermodynamic equilibrium, this study introduces the theory of dynamic cognitive advantage. Grounded in second-order cybernetics, the framework posits that competitive differentiation emerges from the historical, recursive, structural coupling of human semantic intent and machine syntactic processing. This research formalizes this co-evolutionary dynamic utilizing coupled non-linear differential equations and time decay integrals. Furthermore, it operationalizes the central mechanism of this capability—the cognitive flywheel—and proposes a fractal governance architecture to mitigate systemic vulnerabilities such as automation bias. To transition these propositions into management science, a proposed mixed-methods empirical research agenda is presented. It outlines a future partial least squares–structural equation modeling (PLS-SEM) approach to test the mediating role of the cognitive flywheel and the moderating effect of fractal governance on organizational resilience. This research provides a mathematically formalized, empirically testable architecture for navigating the artificial intelligence economy. Full article

In this study, we propose a compartmental mathematical model that considers two interacting populations (citrus plants and insect vectors) and investigate the transmission dynamics of Huanglongbing in citrus crops. This disease is caused by the bacterium Candidatus Liberibacter asiaticus and is vectored by the psyllid Diaphorina citri. The disease is modeled under the following three main assumptions: there is vital dynamics with constant recruitment rates of citrus plants, the force of infection in both populations is a spatially dependent function varying with geographic location, and there is a spatial displacement of the vectors. In the main results of the paper, we formulate a coupled ordinary and partial differential equation system with initial and zero flux boundary conditions, establish the existence and uniqueness of solutions to the proposed model by applying semigroup theory, and introduce a numerical approximation of the system. Moreover, we develop a stability and persistence analysis. From the analytical point of view, we calculate the basic reproduction number $R_0$ and prove three facts: the disease-free equilibrium is globally asymptotically stable when $R_0<1$; the disease-free equilibrium is globally asymptotically stable when $R_0>1$; and the hybrid system exhibits uniform persistence of infection when $R_0>1$. In addition, we present some numerical examples. Full article

We investigate a nonlinear convection—diffusion equation involving a non-polynomial square-root flux. By applying a travelling-wave reduction and introducing a structurally motivated square-root transformation, we show that the resulting ordinary differential equation possesses an intrinsic logistic first-order structure. This reduction yields an explicit closed-form monotone travelling-wave solution connecting two equilibrium states and uniquely determines the admissible wave speed $c=2/3$. The solution describes the diffusive smoothing of an initial discontinuity into a propagating transition layer. Direct finite-difference simulations with Riemann-type initial data confirm convergence toward the analytical profile and verify the predicted wave speed. These results demonstrate that convection—diffusion equations with non-algebraic flux functions can admit exact travelling-wave solutions when appropriate structural transformations are identified, providing both theoretical insight and reliable benchmarks for numerical methods. Full article

In this study, density functional theory (DFT) within the generalized gradient approximation (GGA) is employed to investigate the structural, electronic, mechanical, and thermoelectric properties of perovskite hydrides XZrH₃ (X = Mg, Ca, Sr, Ba). Mechanical stability and ductility are evaluated through the Cauchy pressure, Pugh’s ratio, and Poisson’s ratio, all of which point to ductile behavior with a dominant ionic-bonding character. Electronic structure calculations reveal metallic behavior arising from band overlap at the Fermi level. Equilibrium energy–volume data are fitted with the Murnaghan equation of state, and transport coefficients are extracted using the BoltzTraP package as implemented in WIEN2k. The absence of a band gap and the overlap between valence and conduction bands confirm conductor-like behavior. Lattice thermal conductivity for MgZrH₃, CaZrH₃, SrZrH₃, and BaZrH₃ increases monotonically with temperature. Overall, the results identify MgZrH₃ in particular as a promising candidate for thermoelectric devices and solid-state hydrogen storage, thereby supporting progress toward a sustainable hydrogen economy. Full article

This paper investigates the optimal investment and reinsurance problem for insurers in a financial market with contagion risk. The prices of risky assets are assumed to follow a jump–diffusion model, where the jump component is driven by a multidimensional dynamic contagion process with diffusion (DCPD). This process simultaneously captures jumps triggered by endogenous and exogenous excitations, effectively characterizing the dynamic contagion effects arising from the joint influence of multiple factors in financial markets. The insurer aims to maximize a mean-variance (MV) utility function by purchasing per-loss reinsurance and investing the surplus in the contagion financial market. By solving the extended Hamilton–Jacobi–Bellman (HJB) equations, we derive the time-consistent equilibrium investment and reinsurance strategies, as well as explicit expressions for the equilibrium value function. These results are characterized by two nonlocal partial differential equations (PDEs), whose probabilistic solutions are obtained through the Feynman–Kac formula. Finally, numerical experiments illustrate how equilibrium strategies respond to changes in contagion intensity and confirm the effectiveness of the proposed model. Full article

We study a rigidity problem for functions $F:{\mathbb{R}}_{>0}\to {\mathbb{R}}_{\ge 0}$ that penalize deviation of a positive ratio from equilibrium $x=1$. Assuming (i) a d’Alembert-type composition law on ${\mathbb{R}}_{>0}$, and (ii) a single quadratic calibration at the identity (in logarithmic coordinates), we prove that F is uniquely determined. The composition law implies the normalization $F\left(1\right)=0.$ The unique solution is called the canonical reciprocal cost, namely the difference between the arithmetic and geometric means of x and its reciprocal. Our proof uses the logarithmic coordinates $H\left(t\right)=F\left(e^t\right)+1$, where the composition law becomes d’Alembert’s functional equation on $\mathbb{R}$. The calibration provides the minimal regularity needed to invoke the classical classification of continuous solutions and fixes the remaining scaling freedom, selecting the hyperbolic-cosine branch. We also establish the necessity of each assumption: without calibration the composition law admits a continuous one-parameter family; without the composition law the calibration does not determine the global form; and without regularity the composition law admits pathological non-measurable solutions. Finally, we establish a stability estimate for approximate solutions under bounded defect and characterize some properties of the canonical cost. Full article

The objective of this study was to develop a predictive methodology for assessing the leakage phenomenon of gelatin-based soft capsules under various storage conditions. The equilibrium moisture content of the soft capsules was influenced by the temperature and humidity. The leakage phenomenon was attributable to the swelling of gelatin, as revealed by Fourier Transform Infrared spectroscopy (FT-IR) and Scanning Electron Microscopy (SEM) imaging techniques. Additionally, the moisture diffusion mechanism of soft capsule shells was systematically investigated based on the principles of hygroscopic kinetics, enabling quantitative evaluation of their hygroscopic performance under different environmental conditions. Based on macromechanical analysis, the mechanical failure curves of soft capsule shells under different environmental conditions were investigated, enabling successful determination of the shelf life of the soft capsules. Importantly, the Arrhenius equation and the generalized Eyring model were introduced to successfully predict the occurrence of leakage during storage. The developed prediction method performs successful and accurate stability assessment under various conditions, which is crucial for the development of soft capsules. Full article

Theoretical models of polyelectrolyte systems with cross-linked polymer networks are often simplified to linear differential equations by means of the linearized Poisson–Boltzmann approximation, whose validity is traditionally limited to cases where the electrostatic potentials are small. However, the limits of applicability of the linear theory remain debatable in many cases. Moreover, the Poisson–Boltzmann equation is, in principle, not applicable to the description of non-equilibrium systems, particularly those through which an electric current flows. In the present work, a direct comparison is carried out between the exact solution and the approximate solution (i.e., the solution obtained within the framework of the linearization procedure) of the equations describing the contact region between a cross-linked polyelectrolyte network and a low-molecular-mass salt solution. This makes it possible to determine the conditions under which the linear model is applicable, including for the analysis of promising systems in the field of organic electronics. The conclusions obtained in this work are based on basic electrostatics equations and transport equations of low-molecular-mass ions. The proposed approach also makes it possible to obtain a generalized linear differential equation that is not subject to a Boltzmann distribution approximation and is valid for polyelectrolyte systems rather far from thermodynamic equilibrium and even carrying steady electric currents. Full article

We develop a dual-time topological framework for the mathematical description of non-equilibrium systems, aimed at reconciling time-reversible microscopic dynamics with irreversible macroscopic behavior. The formulation introduces two independent but coupled temporal parameters: a reversible time associated with microscopic or generative dynamics, and an irreversible time governing dissipation, entropy production, and macroscopic evolution. Physical states are defined on a dual-time manifold, allowing reversible and irreversible processes to be treated within a unified geometric setting. Temporal evolution is described using independent temporal connections and their associated curvature. We show that nonvanishing temporal curvature induces path dependence in temporal evolution, providing a geometric origin for memory effects, non-Markovian dynamics, and aging phenomena. Temporal asymmetry emerges dynamically through symmetry breaking between the temporal sectors and through projection from the bi-temporal domain onto a single observable time parameter. The relationship between the dual-time formalism and conventional single-time non-equilibrium models is analyzed. Standard evolution equations are recovered in integrable or decoupling limits, demonstrating that the proposed framework constitutes a genuine generalization compatible with established approaches. By encoding irreversibility in the geometry and topology of temporal evolution, this work provides a mathematically consistent geometric framework for analyzing the emergence of the arrow of time in non-equilibrium theoretical physics. Unlike conventional approaches in which irreversibility and memory are encoded phenomenologically at the level of effective equations, the present framework reformulates non-Markovian dynamics and temporal asymmetry in terms of the geometry and topology of coupled temporal evolution. In particular, a representation theorem is established showing that a broad class of convolution-type non-Markovian equations arises as projections of local dual-time dynamics. Full article

Spacecraft pursuit–evasion in contested environments is complicated by strategic incompleteness: the evader can switch maneuvering modes and deploy multi-domain countermeasures that degrade the pursuer’s perception, leading to non-stationary information and distributionally ambiguous interference statistics. A dynamic time-window Nash equilibrium framework is developed for linearized Local Vertical Local Horizontal (LVLH) relative motion under interference-induced uncertainty. Perceptual degradation is modeled via an evidence–theoretic belief representation, and the Jensen–Shannon (JS) divergence is introduced to quantify discrepancies between nominal and interference-corrupted beliefs. The divergence metric drives an adaptive time-window partitioning policy and an uncertainty-aware running cost that balances nominal performance objectives with robustness regularization during high-degradation intervals. In each time window, sufficient conditions are provided for the existence of a local Nash equilibrium, and equilibrium strategies are characterized by the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. A global consistency result is established: assuming state continuity, additive cost decomposition, and dynamic-programming compatibility at window boundaries, concatenating the window-wise equilibria yields a Nash equilibrium over the entire horizon. Unlike conventional receding-horizon differential games with a fixed replanning grid, the proposed policy partitions the horizon online in response to perceptual-degradation events and stitches adjacent windows through a continuation value. This boundary stitching enables the global consistency guarantee under additive costs and state continuity. To hedge against ambiguity in interference intensity, a variational distributionally robust optimization (DRO) problem with moment-constrained ambiguity sets is formulated, and the dual worst-case distribution is derived. The resulting Karush–Kuhn–Tucker (KKT) system is reformulated as a finite-dimensional variational inequality, for which an accelerated Alternating Direction Method of Multipliers (ADMM) operator-splitting solver is proposed for efficient real-time computation. Numerical simulations validate the framework and demonstrate improved robustness and computational scalability under time-varying interference compared with fixed-window baselines. Full article