Non-classical Model Research Articles

Selected Reinsurance Models

In this paper, we investigate non-classical reinsurance models. Two kinds of such models are presented. One is based on dependent binomial distributions and the second on fuzzy numbers. First, we study dependent random variables representing claims using copulas. We investigate the number of claims the reinsurer covers and the total value of covered claims. We present the influence of the degree of dependence and different copulas on the number and the value of the claims covered by the reinsurer. Second, we analyze the case in which the main parameter of the model, the probability that the reinsurer covers the claim, is uncertain. We treat such a parameter as a fuzzy number in this case and combine randomness and fuzziness. We also study the case when the parameter of a copula which describes the degree of dependence is uncertain.

In situ atomic observations of aggregation growth and evolution of penta-twinned gold nanocrystals

The twin boundaries and inherent lattice strain of five-fold twin (5-FT) structures offer a promising and innovative approach to tune nanocrystal configurations and properties, enriching nanomaterial performance. However, a comprehensive understanding of the nonclassical growth models governing 5-FT nanocrystals remains elusive, largely due to the constraints of their small thermodynamically stable size and complex twin configurations. Here, we conducted in situ investigations to elucidate the atomic-scale mechanisms driving size-dependent and twin configuration-related aggregation phenomena between 5-FT and other nanoparticles at the atomic scale. Our results reveal that surface diffusion significantly shapes the morphology of aggregated nanoparticles, promoting the symmetrical formation of 5-FT, especially in smaller nanoparticles. Moreover, the inherent structural characteristics of 5-FT mitigate the dominance of surface diffusion in its morphological evolution, retarding the aggregation evolution process and fostering intricate twin structures. These findings contribute to advancing our capacity to manipulate the configuration of twinned particles, enabling more predictable synthesis of functional nanomaterials for advanced engineering applications.

Contour Detection Algorithm for α Phase Structure of TB6 Titanium Alloy fused with Multi-Scale Fretting Features

Aiming at the problems of inaccuracy in detecting the α phase contour of TB6 titanium alloy. By combining computer vision technology with human vision mechanisms, the spatial characteristics of the α phase can be simulated to obtain the contour accurately. Therefore, an algorithm for α phase contour detection of TB6 titanium alloy fused with multi-scale fretting features is proposed. Firstly, through the response of the classical receptive field model based on fretting and the suppression of new non-classical receptive field model based on fretting, the information maps of the α phase contour of the TB6 titanium alloy at different scales are obtained; then the information map of the smallest scale contour is used as a benchmark, the neighborhood is constructed to judge the deviation of other scale contour information, and the corresponding weight value is calculated; finally, Gaussian function is used to weight and fuse the deviation information, and the contour detection result of TB6 titanium alloy α phase is obtained. In the Visual Studio 2013 environment, 484 metallographic images with different temperatures, strain rates, and magnifications were tested. The results show that the performance evaluation F value of the proposed algorithm is 0.915, which can effectively improve the accuracy of α phase contour detection of TB6 titanium alloy.

Proceedings 14th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024)

Proceedings 14th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024)

Proceedings 14th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024)

Proceedings 14th International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024)

On determining residual stresses in a viscoelastic coating of arbitrary thickness formed during multilayer application on the inner surface of the straight pipe wall

Abstract The technological problem of forming a coating of arbitrary thickness on the inner surface of the wall of a straight pipe due to the multilayer application of a material having the property of viscoelasticity is considered. It is assumed that during the forming process, the coating experiences the action of inertia forces due to the relatively intense rotation of the coated wall. To determine the residual stresses in the resulting coating, a non-classical model of deformable solid mechanics, based on the concepts of growing continuum is used. With the help of the developed model, boundary value problems are formulated, the solutions of which make it possible to construct the desired residual stress distributions for arbitrary programs for changing the parameters of the implemented technological process.

A General Nucleation Model for Semiconductor Nanocrystals.

We introduce a nonclassical model for nanocrystal nucleation in solution which centers on the dynamic interplay of chemical bond breakage and formation coupled with the desolvation of precursor molecules, which we term the molecular chemistry (MC) model. Departing from classical theory, our model employs the bond count as the key variable rather than particle size, thereby redefining the role of supersaturation and its role in determining the so-called critical nucleus size. We apply the model to CdSe nanocrystal formation in nonpolar solvents and showcase its efficacy in predicting solvent dynamics, precursor characteristics, crystal phase, stoichiometry, "magic number" behavior, and transition states. While the coupled-cluster method is used to determine the bond energy, we show that it is possible to derive reaction pathways by reducing the calculations to algebraic approximations for the nucleation energy. This singular set of bond energy parameters allows nanocrystal nucleation and growth to be conceptualized as a straightforward chemical reaction.

Discrete-continuum-discrete approach for the modeling of the dynamic behavior of 2D lattice systems

This work presents a new methodology to model elastic lattice systems through a two-step approach that permits to reliably capture its dynamic behavior with a lower computational cost than modeling the lattice explicitly. The first step consists of a non-standard continualization accounting for scale effects. Several methods are explored to derive new continuum models, whose dispersive and vibrational behaviors are compared to that of the lattice, considered as a reference. Non-classical models with micro-inertia reveal high accuracy, not presenting physical inconsistencies. The second step follows a FEM spatial discretization of the developed continua, accounting for micro inertia terms in the mass matrix. Finally, the FEM formulation allows the use of element sizes larger (up to four times) than the physical length scale of the lattice system, thus significantly reducing the computational cost while maintaining accuracy and enabling a versatile application to materials, geometries and boundary conditions. The methodology is tested here for a 2D system with displacements in the plane, but can be extended to other lattice typologies as well.

Nonlocal strain gradient-based dynamic stability of functionally graded piezoelectric nanoshells considering thermo-electro-mechanical coupling effects

In this paper, a nonclassical shell model is utilized to investigate the dynamic stability of functionally graded piezoelectric (FGP) nanoshells considering the thermo-electro-mechanical coupling effects. Also, the FGP nanoshells on elastic foundations are subjected to periodic axial loading. The theoretical formulations are derived by implementing the first-order shear deformation (FSD) shell theory into the nonlocal strain gradient theory (NSGT). Hamilton’s principle is utilized to obtain the equations of motion and related boundary conditions of the present nanoshell model. Moreover, the Mathieu-Hill equations determining the instability regions are presented and analyzed based on Bolotin’s method. Results demonstrate that the external electric voltage, the elastic foundations, the temperature rise, the static load factor, the power-law index and the small-scale parameters have significant influences on the dynamic stability responses of FGP nanoshells.

Application of Modified Couple-Stress Theory to Nonlinear Vibration Analysis of Nanobeam with Different Boundary Conditions

PurposeIn the present study, the nonlinear vibration analysis of a nanoscale beam with different boundary conditions named as simply supported, clamped-clamped, clamped-simple and clamped-free are investigated numerically.MethodsNanoscale beam is considered as Euler-Bernoulli beam model having size-dependent. This non-classical nanobeam model has a size dependent incorporated with the material length scale parameter. The equation of motion of the system and the related boundary conditions are derived using the modified couple stress theory and employing Hamilton’s principle. Multiple scale method is used to obtain the approximate analytical solution.ResultNumerical results by considering the effect of the ratio of beam height to the internal material length scale parameter, h/l and with and without the Poisson effect, υ are graphically presented and tabulated.ConclusionWe remark that small size effect and poisson effect have a considerable effect on the linear fundamental frequency and the vibration amplitude. In order to show the accuracy of the results obtained, comparison study is also performed with existing studies in the literature.

Formula omitted] and its interpretations

In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for = and ∈. Although, these variations coincide with the standard interpretation in Boolean-valued constructions, nonetheless they extend the scope of validity of ZF to new algebra-valued models. This paper presents, for the first time, non-trivial paraconsistent models of full ZF. Moreover, due to the validity of Leibniz's law in these structures, we will show how to construct proper models of set theory by quotienting these algebra-valued models with respect to equality, modulo the filter of the designated truth-values.

A new model for spatial rods incorporating surface energy effects

A new non-classical model for spatial rods incorporating surface energy effects is developed using a surface elasticity theory. A variational formulation based on the principle of minimum total potential energy is employed, which leads to the simultaneous determination of the equilibrium equations and complete boundary conditions. The newly developed spatial rod model contains three surface elasticity constants to account for surface energy effects. The new model recovers the classical elasticity-based Kirchhoff rod model as a special case when the surface energy effects are not considered. To illustrate the new spatial rod model, two sample problems are analytically solved by directly applying the general formulas derived. The first one is the buckling of an elastic rod of circular cross-section with fixed-pinned supports, and the other is the equilibrium analysis of a helical rod deformed from a straight rod. An analytical formula is derived for the critical buckling load required to perturb the axially compressed straight rod, and two closed-form expressions are obtained for the force and couple needed in deforming the helical rod. These formulas reduce to those based on classical elasticity when the surface energy effects are suppressed. For the buckling problem, it is found that the critical buckling load predicted by the current new model is always higher than that given by the classical elasticity-based model, and the difference between the two sets of predicted values is significantly large when the radius of the rod is sufficiently small but diminishes as the rod radius increases. For the helical rod problem, the numerical results reveal that the force and couple predicted by the current model are, respectively, significantly larger and smaller than those predicted by the classical model when the rod radius is very small, but the difference is diminishing with the increase of the rod radius.

Nonlinear modeling of nanoscale interaction forces between atomic force microscope and carbon nanotubes

This paper introduces a non-linear non-classical model of nanoscale interaction forces between atomic force microscope and carbon nanotubes in a manipulation process. To accurately model the 3D manipulation process, Prandtl-Tomlinson friction model and the Hertz, JKR, and Lundberg contact mechanics theories were employed, taking into account the CNT geometry and manipulation conditions. The applied forces exerted by both the substrate and the probe on the CNT were extracted. The dynamic characteristics of the nanorods and nanotubes were investigated by employing the non-linear modified couple stress Timoshenko beam. Additionally, the cantilever was modeled using the Mindlin plate theory. The findings showed a good agreement between the experimental data of multi-walled carbon nanotube with a diameter of 100 nm, and the theoretical simulations. In addition to critical force and time, CNT bending results were presented using various Timoshenko theories. In order to validate the results of the maximum bending, the outcomes derived from the computational modeling of a polystyrene nanorod using the Euler-Bernoulli and Timoshenko theories were juxtaposed with the existing classical bending outcomes. Finally, the effects of the size parameter were investigated in non-classical polystyrene models. The findings indicated that considering the size effects is important; For instance, the variance between classical and non-classical models can exceed 57% for l/D = 0.5.

ДЕЯКІ КРАЙОВІ ЗАДАЧІ ДРОБОВО-ДИФЕРЕНЦІЙНОЇ ФІЛЬТРАЦІЙНОЇ ДИНАМІКИ ЩОДО БІПАРАБОЛІЧНОЇ МАТЕМАТИЧНОЇ МОДЕЛІ

Closed-form solutions are obtained to some one-dimensional boundary-value problems for modeling anomalous filtration dynamics in a layered geoporous medium, posed within the framework of the fractional-differential generalization of the biparabolic evolutionary partial differential equation of the fourth order. In particular, the formulation and solution of the direct and inverse model boundary-value problems of geofiltration dynamics based on the mathematical model with conjugation conditions are presented, and the conditions of the existence of regular solutions to these problems are defined. Keywords: mathematical modeling, fractional-differential dynamics of geofiltration processes, nonclassical models, biparabolic evolutionary equation, the fractional-differential analog of the biparabolic evolutionary equation, nonstationary boundary-value problems on a finite interval, direct and inverse problems, conjugation conditions, closed-form solutions.

ДЕЯКІ КРАЙОВІ ЗАДАЧІ, ВІДПОВІДНІ МОДЕЛІ ДРОБОВО-ДИФЕРЕНЦІЙНОЇ ФІЛЬТРАЦІЙНОЇ ДИНАМІКИ В ТРІЩИНУВАТО-ПОРИСТОМУ СЕРЕДОВИЩІ ЗА УМОВ ЧАСОВОЇ НЕЛОКАЛЬНОСТІ

Closed-form solutions of some boundary-value problems of fractional-differential geofiltration dynamics in a fractured-porous medium are obtained for a model with weakly permeable porous blocks. In particular, the direct and inverse boundary-value problems of filtration for the finite thickness layer are solved, the conditions for the existence of their regular solutions are given, and the solution of the problem of filtration dynamics with nonlocal boundary conditions is found. For a particular case of the filtration model, the problem of modeling the anomalous dynamics of filtration pressure fields on a star-shaped graph is considered. Keywords: mathematical modeling, fractional-differential dynamics of filtration processes, fractured-porous medium, non-classical models, boundary-value problems, inverse problems, problems with non-local conditions, closed-form solutions.

Approximation Solution of Mixed Boundary-Contact Problems and their Applications

In this article non-classical diffusion models of theory coupled-elasticity of static systems for isotropic inhomogeneous elastic materials with thermal and diffusion variables has been investigated. Approximate solutions for boundary-contact problems for theory coupled-elasticity in Cauchy hypothesis conditions has been constructed. The tools applied in this development are based on the boundary integral methods and Greens functions applications.

WHEN THE HEAVEN OBSCURE (VENTURING INTO THE ONTOLOGY OF «RUSSKIY MIR»)

In the endeavor to expound upon the phenomenon of the "russkiy mir", an immediate recognition emerges that the "reality" of this phenomenon can be situated across diverse strata (or within disparate domains) and within the expanse of multifarious exchanges. The attendant representations, delineations, and analyses may be conducted within varying disciplinary frameworks and discourses, encompassing realms as diverse as psychology, psychiatry – both individual and societal, history in its global and regional dimensions, as well as in the quotidian sphere spanning different epochs and methodological paradigms. Cultural studies, social theory, theories of civilizations and ideologies, economics, political economy, and metaeconomics, political and geopolitical studies, natural sciences, humanities, and posthumanism all find their place in classical, non-classical, and post-contemporary models. However, this "reality" is not merely descriptive and analyzable; it also manifests itself, capable of being staged across a spectrum of genres – from quasi-religious ecstasy to the proclamation of the "supreme value," from inebriated effusion to propagandistic performance... Today there are voices that our modernity identifies itself with the end of philosophy. That the current way of existence of philosophy itself is its rejection and deviation from its vocation, purpose, work and destiny. Herein unfolds a nuanced economy: the "Russian world" can be construed as a symbol of philosophy's proclaimed incapacity or, alternatively, as a peculiar manifestation of philosophy's terminus, an alternative nomenclature for this cessation, a self-negation intrinsic to philosophy's existence. It seems as though the "russkiy mir" is expressly fashioned to attest to, and perhaps more provocatively, effectuate the denouement of philosophy. Furthermore, discerning whether there exists an effect/symptom proves challenging. It appears that in the co-definition of the "Russian world" and philosophy's renunciation of philosophizing – an ontological condition of philosophy's current presence – a kind of "aprioristic perfect" transpires. Simultaneously, the presence of the "russkiy mir" in the global milieu unveils a nuanced ambivalence toward philosophy. Alongside the factual legitimation of philosophy's incapacity, this presence poses a challenge to philosophical ruminations. It goads philosophizing, insists upon it, and necessitates an interrogation of its presence: "how is this possible, how did this become possible?" Ergo, the inquiry into the "russkiy mir" is inherently a philosophical one, and we shall endeavor to elucidate as much. However, within this context, an essential question emerges: "What is, what does it signify, and what presupposes the 'philosophical question'?" This inquiry forms the crux of this article. In this regard, the theme of "culture" enters the discourse, specifically within the modality of "Russian culture." Simultaneously, the question of culture in its entirety becomes pertinent. Examining the theme of the "russkiy mir" as a philosophical query prompts questions regarding "Russian culture" and, ultimately, culture at large.

The explicit power series solution formation and computationof Lie point infinitesimals generators: Lie symmetry approach

This work scrutinizes the well-known nonlinear non-classical Sobolev-type wave model which addresses the fluid flow via fractured rock, thermodynamics and many other fields of modern sciences. The nonlinear non-classical Sobolev-type wave model provides a more comprehensive and accurate description of wave phenomena in a wide range of fields. By incorporating both nonlinearity and the complexities of dispersive waves, these models enhance our understanding of natural phenomena and enable more precise predictions and applications in various scientific and engineering disciplines. Therefore, this study is investigating it. Prior to this study, no previous research has performed Lie symmetry analysis and achieved invariant solutions of this kind. The symmetry generators are taking into account the Lie invariance criteria. The suggested approach produces the three dimensional Lie algebra, where translation symmetries in space and time are associated with mass conservation and conservation of energy, respectively and the other symmetries are scaling or dilation. The nonlinear non-classical Sobolev-type wave partial differential equation is transformed into a system of highly nonlinear ordinary differential equations by employing appropriate similarity transformations through using Lie group methodology. The power series technique is used to generate exact wave solutions because the inverse scattering transform cannot solve the Cauchy problem for this equation. The graphical behaviour of certain solutions is demonstrated in 3-D and 2-D for particular quantities of the physical factors in the investigated equation.

Synergetic effect of microfluidic flow and ultrasonication on chains pre-ordering in conjugated polymer solution

Multi-physical fields solution processing strategy provides a universal and facile way to prepare various conjugated polymer (CP) films and high-performance devices, whereas the hierarchical structures evolution and crystallization of the polymer chains are elusive particularly under the far-from-equilibrium state in solution. In this work, we employed a combined microfluidic flow and ultrasonication strategy (FU) for CP solution processing and found a pronounced synergetic effect of these fields in promoting the pre-ordering of chains in solution. This conformation order and anisotropy of the solution were revealed by using UV–Vis absorption, polarized optical microscopy (POM) and cryogenic transmission electron microscopy (Cryo-TEM) characterizations. A non-classical nucleation model for the conjugated polymer crystallization in the procedure of non-equilibrium solution processing was confirmed. The roles of microfluidic flow and ultrasonication on the chain aggregation and crystallization were addressed with the aim of a multi-physical simulation based on pressure acoustics streaming, fluid heat transfer and thermoviscous boundary layer impedance. Compared to pristine solutions, the FU strategy showed improved solution anisotropy and crystallization kinetics, substantially giving rise to a larger crystallinity in films and much increased mobilities for the organic field-effect transistor (OFET) devices by more than an order of magnitude. With an appropriate balance between the solvation and interchain interactions, the FU processing strategy is universal for regulation of chains conformation and aggregation in conjugated polymer solution.

Variance reduction function for a potential inclined slip line in a spatially variable soil

Variance reduction function for a spatially variable soil property is an important factor that affects the spatial average-based characteristic value, which in turn influences the design of a geotechnical structure in the context of Eurocode 7. This study derives the theoretical and approximate variance reduction functions (VRFs) for a potential inclined slip line in a spatially variable soil. Only stationary random fields are studied but more general spatial variability characteristics including smoothness and hole effect are considered. First, the closed-form one-dimensional (1D) VRFs are investigated, including the VRFs for classical one-parameter autocorrelation models, the non-classical two-parameter Whittle-Matérn (WM) model, and the most general three-parameter cosine Whittle-Matérn (CosWM) model proposed to date. It is found that closed-form solutions are not available or not practical to compute in general and the simple approximate VRF (equal to scale of fluctuation/averaging length) is not adequate for the non-classical autocorrelation models (WM and CosWM). Two approximate VRFs are developed in this study for the 1D WM and 1D CosWM models. For a spatial average over an inclined line, this paper derives the theoretical scales of fluctuation (SOFs) and VRFs for five commonly used 2D autocorrelation models. The theoretical solutions show that the equivalent SOFs proposed in the literature are only applicable under special conditions which are clarified in this paper. More general approximations for the VRF over an inclined line are proposed. The range of applicability for each approximation is stated. The proposed approximate VRFs are shown to be reasonably accurate when they are applied to the spatial average-based characteristic value and for the design of a vertical pile and an inclined soil nail.