Search Results (41)

This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article

In this paper, we propose an approach for constructing quasiparticle-like asymptotic solutions within the weak diffusion approximation for the generalized population Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation, which incorporates nonlocal quadratic competitive losses and a fractal time derivative of non-integer order ($\alpha$, where $0<\alpha \le 1$). This approach is based on the semiclassical approximation and the principles of the Maslov method. The fractal time derivative is introduced in the framework of $F^{\alpha }$ calculus. The Fisher–KPP equation is decomposed into a system of nonlinear equations that describe the dynamics of interacting quasiparticles within classes of trajectory-concentrated functions. A key element in constructing approximate quasiparticle solutions is the interplay between the dynamical system of quasiparticle moments and an auxiliary linear system of equations, which is coupled with the nonlinear system. General constructions are illustrated through examples that examine the effect of the fractal parameter ($\alpha$) on quasiparticle behavior. Full article

This paper delves into a comprehensive analysis of a generalized impulsive discrete reaction–diffusion system under periodic boundary conditions. It investigates the behavior of reactant concentrations through a model governed by partial differential equations (PDEs) incorporating both diffusion mechanisms and nonlinear interactions. By employing finite difference methods for discretization, this study retains the core dynamics of the continuous model, extending into a discrete framework with impulse moments and time delays. This approach facilitates the exploration of finite-time stability (FTS) and dynamic convergence of the error system, offering robust insights into the conditions necessary for achieving equilibrium states. Numerical simulations are presented, focusing on the Lengyel–Epstein (LE) and Degn–Harrison (DH) models, which, respectively, represent the chlorite–iodide–malonic acid (CIMA) reaction and bacterial respiration in Klebsiella. Stability analysis is conducted using Matlab’s LMI toolbox, confirming FTS at equilibrium under specific conditions. The simulations showcase the capacity of the discrete model to emulate continuous dynamics, providing a validated computational approach to studying reaction-diffusion systems in chemical and biological contexts. This research underscores the utility of impulsive discrete reaction-diffusion models for capturing complex diffusion–reaction interactions and advancing applications in reaction kinetics and biological systems. Full article

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of $R^3$ bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail. Full article

The transport–diffusion problem of point-source solutes in water environmental flows is an important issue in environmental fluid mechanics, with significant theoretical and practical implications for sustainable development and the ecological management and environmental protection of water. This study presents a model for instantaneously released multi-point-source solutes, utilizing the separation of variables method and Duhamel’s principle to solve classical mathematical physics equations. The zeroth-order and first-order concentration moment equations, which are crucial for predicting the cross-sectional average concentration of instantaneously released point-source solutes, are systematically addressed. The accuracy of the analytical results is confirmed by comparing them with the relevant literature. Furthermore, a general discussion is provided based on the study’s findings (including an ideal physical model of Couette flow), and an analytical solution (a recursive relationship) for higher-order concentration moments is deduced. Finally, this study quantitatively discusses downstream environmental ecological effects by examining the movement of released point-source solute centroids in the river, illustrating that the time needed for the released point-source solute to have an environmental–ecological impact downstream of the river is dependent on the initial release location. Under the specified engineering parameters, for the release location at the bottom boundary point of the channel (z₀ = 0 m), the midpoint (z₀ = 5 m), and the water-surface point (z₀ = 10 m), the time for additional displacement of released solute centroid to reach the asymptotic value in three cases is 4.0 h, 1.0 h, and 4.5 h; the asymptotic values are approximately −0.087 km, 0.012 km, and 0.055 km, respectively. These results not only correspond with the conclusions of previous research but also provide a more extensive range of numerical results. This study establishes the groundwork for theoretical research on more complex water environmental flow models and provides a theoretical basis for engineering computations aimed at contributing to the environmental management of rivers and lakes. Full article

To protect the environment and preserve natural resources, it is crucial to use recycled aggregate (RA) in construction. The recycled coarse aggregate reinforced concrete columns with the addition of steel fiber evaluated under concentric and eccentric loadings for short and slender columns were examined experimentally and analytically in this research. Twenty-four column specimens were built for this study to examine the impact of steel fiber, recycled aggregate, slenderness, and eccentricity on the behavior of reinforced concrete columns. This research examined the failure mode, maximum load-carrying capacity, strain in the concrete, strain in the reinforcement, and ductility. Based on the results, it can be concluded that employing recycled concrete aggregate is a potential approach to meet design codes. The addition of 1% steel fiber effectively prevents concrete from crushing and spalling. Steel fiber, however, improved the columns’ ductility and strength. The results showed the maximum load-carrying capacity of the specimens and the results of using ACI-318 code equations agreed very well. Furthermore, a model is proposed for columns with both natural and recycled aggregate and which accounts for the eccentricity and slenderness to forecast the load-carrying capacity. The outcomes demonstrated that the design principles were met well. Plots of load–moment interaction diagrams for short and slender columns made with the ACI-318 method are compared to the findings of the experiments. Full article

In reinforced concrete flat slab buildings, the transference of unbalanced moments in the slab–column connections usually results from the asymmetry of spans, vertical loads, and horizontal forces from the wind. The punching strength of the slab–column connections can limit the load-carrying capacity of the structure in these cases, leading to structural collapse. The design code provisions are still based on empirical or semi-empirical equations; as the punching shear failure mechanisms are complex, and the ultimate strength is affected by several parameters. In this context, this paper presents the results of the computational investigation of the mechanical behaviour of flat slabs subjected to balanced and unbalanced moments using numerical Finite Element models. The numerical models were calibrated and accurately reproduced the behaviour and the punching resistance for concentric and eccentric loading. Furthermore, a parametric study was conducted to evaluate the mechanical behaviour of flat slabs under different load eccentricities, confirming that the increase in the unbalanced moment negatively impacts the load-carrying capacity of the slab–column connection. Furthermore, it was observed that all computational results obtained from models with unbalanced bending moments were higher than those estimated by the design codes. Full article

This study introduces a novel particle model for biomass fast pyrolysis, incorporating an anisotropic cylindrical particle to address mass and energy transport coupled with aerosol ejection, which previous models have overlooked. The main contribution lies in developing a model that considers aerosol generation in anisotropic cylindrical particles for the first time, addressing bubbling dynamics and bursting within the liquid phase. The population balance equation describes bubble dynamics and aerosol formation, capturing phenomena like nucleation, growth, coalescence, and bursting. The model employs the method of moments with bubble volume as an internal variable, substantially reducing computational costs by eliminating dependence on this variable. Results highlight the significant impact of anisotropy and particle size on aerosol ejection: smaller, less elongated particles experience faster heating, quicker conversion, and the increased accumulation of the liquid intermediate phase. Specifically, 1 mm diameter particles yield higher concentrations of metaplast and bio-oil aerosols, exceeding 15%, compared to concentrations below 11% for 3 mm particles. This model provides insights into aerosol structure (volume, surface area), aiding in understanding aerosol reactivity at the reactor scale. Full article

The study investigated the effect of the molecular weight of three difunctional poly(propylene glycol) diacrylates on the temperature-dependent ionic conductivity of these monomers and their blends with an eutectic nematic liquid crystal mixture (E7). The results revealed two distinct regions. At low temperatures, ionic conduction can be described by the Vogel–Tamman–Fulcher (VTF) equation, while at high temperatures, the conductivity data follow the prediction of the Arrhenius model. The Arrhenius and VTF parameters and their corresponding activation energies were determined using the least squares method. In addition, a conductivity analysis based on an ionic hopping model is proposed. Estimates of ion concentrations and diffusion constants were calculated. It was found that both the ionic concentration and the diffusion constant decrease with the increase in the molecular weight of the monomers. The static dielectric permittivity decreases in the following order: TPGDA, PPGDA540, and PPGDA900. This can be explained by the higher dipole moment of TPGDA, which is caused by an enhanced volume density of carbonyl groups. Full article

The Winkler foundation modulus is key to evaluating the response of underground structures using the elastic foundation beam model. In this paper, an improved formula of the Winkler foundation modulus for a beam embedded in a full space is proposed to overcome the limitation of inconsistent assumptions in previous studies. To achieve this goal, the bending responses of the beam are obtained using the elastic foundation beam model and three-dimensional elastic continuum model, respectively, wherein a consistent assumption is proposed that tangential interactions at the beam–ground interface are ignored in the two models. In addition, as deformation of the site is an important source of the underground structure response, the beam is applied to standard soil displacement of the free field on the Winkler foundation to improve the accuracy of the Winkler modulus obtained by fitting solutions based on the concentrated force on the beam. The formula for the Winkler foundation is obtained by equating the first zero of the bending moment in the two models. The Winkler foundation modulus is verified by comparing the results with numerical solutions and previous studies. Full article

A system of two equations based on one of the classical electricity laws was used to determine the sizes and temperatures of ohmic areas formed under action of overcritical nanosecond electrical pulses. Calculations were performed at five points for three experimentally obtained voltage–current (V-I) dependences for samples with the same geometry but different critical current density values. The system included two additional conditions to satisfy the known descriptive model of transition from superconducting (SC) to a normal (N) state—S-N switching—and to obtain physically acceptable solutions over the entire current range of V-I dependence. The solution for each point takes the form of a function, since the initial temperature increase of the primary channel across the film is entered as a parameter. Two modes of concentrated energy release in the channel were disclosed. Their random appearance leads to an unexpected degradation of the sample. As such, the obtained results correspond to the situations occurring during the experiments. The validity of applying additional conditions to the system is discussed. In the discussion, it is also explained at which moments the moving S-N border acquires the velocity of the order of ~10⁶ m/s, comparable to the Fermi velocity. Consideration to describe the moving unstable S-N border as being constantly in a state of Richtmyer–Meshkov instability is presented. Full article

An approach to estimate the behavior of stiffened rafts under column loads of a lightweight-reinforced concrete structure resting on expansive soils is presented in this paper. The analysis was conducted using the computer program SLAB97, which estimates the 3D distorted mound shape using the finite difference method by solving the transient suction diffusion equation in 3D and computing the corresponding soil movements. The interaction between the stiffened rafts and the 3D distorted mound shape is then analyzed using the finite element method. The SLAB97 program has been validated by comparing its results with the results of others that were shown to be valid. The goal of the study is to make the expansive soil structure interaction models that the previous researchers proposed more logical. Assuming the worst initial 3D distorted mound shapes of the two cases of edge heave and edge shrinkage, an upper-bound solution is obtained. Using the two scenarios of edge shrinkage and edge heave, the program was utilized in a parametric investigation to examine the impact of various parameters on the behavior of stiffened rafts on expansive soils. These parameters include the stiffening beam depth, the maximum differential movement of the distortion mound shape, and the raft dimensions. The behavior of the stiffened rafts subjected to concentrated column loads is concluded to be similar to that of the stiffened rafts subjected to uniform and perimeter line loads in both cases of distortion modes, with regard to the shape of raft deformation and distribution of the bending moments; however, the values of the design parameters such as maximum deflection, maximum differential deflection, and maximum moments are entirely different in these two situations. Full article

This study discusses the influence of the composition of a ternary gas mixture on the possibility of occurrence of convective instability under isothermal conditions due to the difference in the diffusion abilities of the components. A numerical study was carried out to study the change in “diffusion–concentration gravitational convection” modes in an isothermal three-component gas mixture He + CO₂ − N₂. The mixing process in the system under study was modeled at different initial carbon dioxide contents. To carry out a numerical experiment, a mathematical algorithm based on the D2Q9 model of lattice Boltzmann equations was used for modeling the flow of gases. We show that the model presented in the paper allows one to study the occurrence of convective structures at different heavy component contents (carbon dioxide). It has been established that in the system under study, the instability of the mechanical equilibrium occurs when the content of carbon dioxide in the mixture is more than 0.3 mole fractions. The characteristic times for the onset of convective instability and the subsequent creation of structural formations, the values of which depend on the initial content of carbon dioxide in the mixture, have been determined. Distributions of concentration, pressure and kinetic energy that allow one to specify the types of mixing and explain the occurrence of convection for a situation where, at the initial moment of time, the density of the gas mixture in the upper part of the diffusion channel is less than in the lower one, were obtained. Full article

This study proposes a new numerical method for the free vibration analysis of elastically restrained tapered Rayleigh beams with concentrated mass and axial force. The beam model had elastic support, concentrated mass at both ends, and axial force at the right end. The elastic supports were modeled as translational and rotational springs. The shear force and bending moment were determined under the assumption that the sum of the forces at arbitrary positions and the joint between the beam and elastic supports always becomes zero. Therefore, a frequency determinant is established considering the free-free end condition at both ends, but various boundary conditions were constructed by adjusting the values of the elastic springs in the frequency equation. This assumption simplified the deduction procedure, and the method’s efficiency was demonstrated through various comparisons. In particular, the value of compressive loading at which the first natural frequency vanished was investigated by considering the taper ratio based on the relationship between the elastic support and compressive loading. The analyzed results can be adopted as benchmark solutions for other approaches. The frequency determinant employs the transfer matrix method; however, numerical methods can easily be utilized in other approaches. Full article

Peridynamics is a continuum theory that operates with non-local deformation measures as well as long-range internal force/moment interactions. The resulting equations are of the integral type, in contrast to the classical theory, which deals with differential equations. The aim of this paper is to analyze peridynamic governing equations for elastic beams. To this end, the strain energy density is formulated as a function of the non-local curvature. By applying the Lagrange principle, the peridynamic equations of motion are derived. Examples of non-local boundary conditions, including simple support, clamped edge, roller clamped edge, and free edge, are presented by introducing the interaction domain. Novel closed-form analytical solutions to integral equations are presented for beams with various boundary conditions, including clamped—simply supported, clamped–clamped, simply supported–roller-clamped, and clamped–roller-clamped beams. Furthermore, different types of loadings, including uniformly distributed load, concentrated force, and concentrated moment, are considered. The results are validated by comparing the derived solutions against solutions to the classical Bernoulli–Euler beam theory. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes, which shows the capability of the derived equations of motion and proposed boundary conditions. Full article