CLEMENT ATACHEGBE Onate, I. B. Okon, E. S. Eyube
et al.
The computation of partition function (Z) is the bedrock of the study of statistical mechanics as it plays a significant role in the thermodynamic properties (TP) where microscopic properties are connected to macroscopic properties. Several studies have reported TP via the Z using one of the classical limit approach or Poisson summation formula. No study however justifies the agreement or discrepancy between the methods. This study therefore, investigates the two methods for theoretical determination of the vibrational partition function by considering the energy levels of Tietz molecular potential. The first approach employs Poisson summation method with a defined energy levels of the Tietz molecular potential while the second approach adopts the utilization of the classical limit approach with the same energy levels of the Tietz molecular potential. By comparing the results of the two approaches, our result reveals discrepancy between the analytic equations for Z. However, the numerical results obtained for the thermal properties of NaBr and CuCl molecules showed a perfect agreement between the two approaches and the experimental data with the results from classical limit approach closer to the experimental data. This study therefore, provides guidelines for choosing the appropriate approach based on the characteristics of the system under study for theoretical research.
Amirabas Bakhtiari, Benedikt Schumm, Martin Schönfelder
et al.
In this study, we introduce a method, applied for the first time to manipulate human cells, by leveraging the controlled activation and deactivation of microbubble streaming – previously used for rigid polymer particles. This innovative technique enables automatic detection and non-destructive sorting of target cells within a microchannel, directing them into a collection chamber for further analysis or removal. A major focus was the quantification of shear stress distribution induced by the microbubble streaming, which confirmed the method’s biocompatibility. Even with prolonged exposure, no damage to live cells was observed, reinforcing the safety and viability of using microstreaming. These findings demonstrate the potential of microbubble streaming as a powerful tool for lab-on-a-chip systems and biomedical diagnostics.
In this study, we introduced a non-polynomial spline technique to address singularly perturbed differential difference equations involving both delay and advanced parameters. This method exhibits a linear rate of convergence, and we have thoroughly analyzed its convergence properties. To demonstrate the effectiveness of this approach, we provided two numerical examples. We presented the maximum absolute errors in tabular form and displayed the pointwise absolute errors using graphical representations. Additionally, we included tables showing the numerically obtained rate of convergence.
The quadratic B-spline method is a widely recognized numerical technique for solving systems of Volterra integro-differential equations that involve both classical and fractional derivatives (SVIDE’s-CF). This study presents an improved application of the quadratic B-spline approach to achieve highly accurate and computationally efficient solutions. In the method developed in this paper, control points are treated as unknown variables within the framework of the approximate solution. The fractional derivative is considered in the Caputo sense. First, we divide the domain into subintervals, then construct quadratic B-spline basis functions over each subinterval. The approximate solution is presented as a quadratic combination of these B-spline functions over each subinterval, where the control points act as variables. To simplify the system of (VIDE’s-CF) into a solvable set of algebraic equations, the collocation method is applied by discretizing the equations at chosen points within each subinterval. The Jacobian matrix method is employed to perform computations efficiently. In addition, a careful, step-by-step algorithm for employing the proposed method is presented to simplify its use, we implemented the method in a Python program and optimized it for efficiency. Experimental example demonstrates effectiveness and accuracy of the proposed technique and its comparison with present techniques in terms of accuracy and computational efficiency.
In the article the problem of synthesizing uniformly distributed optimal control for nonlinear optimization of oscillatory processes described by integro-differential partial differential equations with the Volterra integral operator was explored. The study was conducted according to the Bellman-Egorov scheme and an algorithm for constructing a uniformly distributed optimal control in the form of a functional from the state of the controlled process was developed. Sufficient conditions for the solvability of the synthesis problem in nonlinear optimization were established.
The present paper establishes a formula of Reidemeister torsion for Schottky representations. The theoretical results are applied to 3-manifolds with boundary consisting orientable surfaces with genus at least 2.
In a rectangular domain, we consider a boundary value problem periodic in one variable for a system of partial differential equations of hyperbolic type. Introducing a new unknown function, this problem is reduced to an equivalent boundary value problem for an ordinary differential equation with an integral condition. Based on the parametrization method, new approaches to finding an approximate solution to an equivalent problem are proposed and its convergence is proved. This made it possible to establish conditions for the existence of a unique solution of a semiperiodic boundary value problem for a system of second-order hyperbolic equations.
A boundary value problem in a rectangular domain for a system of partial differential equations with the Dzhrbashyan–Nersesyan fractional differentiation operators with constant coefficients is studied in the case when the matrix coefficients of the system have complex eigenvalues. Existence and uniqueness theorems for the solution to the boundary value problem under study are proved. The solution is constructed explicitly in terms of the Wright function of the matrix argument.
The article proposes an approximate method based on the "vanishing viscosity"method, which ensures the smoothness of the solution without taking into account the capillary pressure. We will consider the vanishing viscosity solution to the Riemann problem and to the boundary Riemann problem. It is not a weak solution, unless the system is conservative. One can prove that it is a viscosity solution actually meaning the extension of the semigroup of the vanishing viscosity solution to piecewise constant initial and boundary data. It is known that without taking into account the capillary pressure, the Buckley-Leverett model is the main one. Typically, from a computational point of view, approximate models are required for time slicing when creating computational algorithms. Analysis of the flow of a mixture of two immiscible liquids, the viscosity of which depends on pressure, leads to a further extension of the classical Buckley- Leverett model. Some two-phase flow models based on the expansion of Darcy’s law include the effect of capillary pressure. This is motivated by the fact that some fluids, e.g., crude oil, have a pressure-dependent viscosity and are noticeably sensitive to pressure fluctuations. Results confirm the insignificant influence of cross-coupling terms compared to the classical Darcy approach.
This paper investigates the question of the existence of solutions to the semiperiodic Dirichlet problem for a class of singular differential equations of hyperbolic type. The problem of smoothness of solutions is also considered, i.e., maximum regularity of solutions. Such a problem will be interesting when the coefficients are strongly growing functions at infinity. For the first time, a weighted coercive estimate was obtained for solutions to a differential equation of hyperbolic type with strongly growing coefficients.
In this paper, the model-theoretical properties of the algebra of central types of mutually model-consistent fragments are considered. Also, the connections between the center and the Jonsson theory in the permissible signature enrichment are shown, and within the framework of such enrichment, instead of some complete theory under consideration, we can obtain some complete 1-type, and we will call this type the central type, while the theories under consideration will be hereditary. Our work is divided into 3 sections: 1) the outer and inner worlds of the existentially closed model of the Jonsson theory (and the feature between these worlds is considered for two existentially closed models of this theory); 2) the λ- omparison of two existentially closed models (the Schroeder-Bernstein problem is adapted to the study of Jonsson theories in the form of a JSB-problem); 3) an algebra of central types (we carry over the results of Section 2 for the algebra (Fr(C), ×), where C is the semantic model of the theory T). Also in this article, the following new concepts have been introduced: the outer and inner worlds of one existentially closed model of the same theory (as well as the world of this model), a totally model-consistent Jonsson theory. The main result of our work shows that the properties of the algebra of Jonsson theories for the product of theories are used
as an application to the central types of fixed enrichment. And it is easy to see from the definitions of the product of theories and hybrids that these concepts coincide if the product of two Jonsson theories gives a Jonsson theory.
This article is devoted to an experimental study of the effect of rounding off corner points of two-link strain trajectories on complex loading processes during elastoplastic deformation of materials. Replacing corner points in their vicinity with local sections of circles allows a nonanalytic trajectory to be replaced with a smooth trajectory. Experimental studies were performed on thin-walled tubular specimens of the low-carbon steel St3 on an SN-EVM automated testing system. The loading programs for tubular specimens were set in the Ilyushin's deviatoric strain space. The rounding of the corner point of a two-link strain trajectory with an angle of 90° between the branches by arcs of circles with curvatures of 200, 400, as well as the rounding of the corner point of a two-link strain trajectory with an angle of 135° between the branches by arcs with curvatures of 400, 800 are considered. The experimental data characterizing the vector and scalar properties of the material are presented. The experimental data show that the effect of complex loading on the relationship between stresses and strains in a curved section is not immediately apparent. In the curved section, the magnitude of the stress vector modulus first increases, and then decreases with the formation of stress dives. The minimum point of the stress dive is located on the next straight branch of the strain trajectory. In the curvilinear section, the angle of delay increases, and in the next straight branch it decreases, and with the increase of the strain it tends to be zero. The rate of decrease of the angle of delay depends little on the differences in the geometry of the previous history of strain trajectory. In the second straight branch, the experimental results for a smooth and original two-link strain trajectories become little distinguishable from each other. Thus, replacing the original non-analytical strain trajectory to a smooth trajectory affects the complexity of the process of deformation and loading of the materials only in the vicinity of the corner point. This circumstance can be taken into account when numerically modeling the processes of elastoplastic deformation of materials and integrating the defining relations, replacing nonanalytic trajectories with smooth ones. This can be taken into account in the numerical calculation of elastic-plastic deformation and integration of constitutive relations, replacing non-analytical strain trajectories by smooth ones.
The article concerns the description the new concept as core of Jonsson theories, also their combinations, which admit a core model in the class of existentially closed models of this theory. Along with core the property of an existentially algebraically prime theory is considered as an additional property to core Jonsson theory. This article also discusses some combinations of Johnson’s theories, where the authors tried to transfer some results from [1] to Johnson’s theories that satisfy the definition of core or EAP, or their combinations. From the definition of the core and the existentially algebraic primeness of Johnson theory, it can be noted that the core model from [1] in the framework of the study of any Johnson theory will be a unique and rigidly embedded model of the theory were considered. And thus, such a solution to the problem with respect to core models is considered for the first time.
Work fatigue is an important problem that needs to be resolved because can cause work accidents and can have an impact on workers' health. Based on the result of interviews in early 2020, there was one worker who was unconscious due to work fatigue where a similar case had never happened before in the last 5 years. Workers complain of feeling dizzy, tired all over, fever, frequent drowsiness, trembling, feeling heavy in the head, and feeling thirsty while working. The purpose of this study was to identify the factors associated with work fatigue at PT. Indonesia Power Unit Pembangkitan dan Jasa Pembangkitan (UPJP) Priok. This research was a quantitative-analytic study with a cross-sectional design. The population of this research was 81 workers consisting of 11 workers in the main workshop and 70 workers in the mechanical part. The sample of this research was 40 workers in the main workshop and mechanics section which were obtained by a purposive sampling technique. The results show that 57,5% of workers have experienced a high category of work fatigue. Statistical analysis shows that nutritional status (p-value=0,034) and sleep quality (p-value=0,028) were related to work fatigue, while the length of work (p-value=0,299), workload (p-value=0,100) and age (p-value=1,000) were not related to work fatigue. Therefore, workers were suggested to consume foods with high carbohydrate content, adequate-protein, calorie intake, and vitamins, as well as regulating duration and hours of sleep following the Ministry of Health's standards, namely 7-8 hours per day for adults (ages 18-40 year).
The two- and three-body contacts are central to a set of univeral relations between microscopic few-body physics within an ultracold Bose gas and its thermodynamical properties. They may also be defined in trapped few-particle systems, which is the subject of this work. In this work, we focus on the unitary three-body problem in a trap, where interactions are as strong as allowed by quantum mechanics. We derive analytic results for the two- and three-body contacts in this regime and compare them with existing limiting expressions and previous numerical studies.
Nuclear and particle physics. Atomic energy. Radioactivity
In the present study, an identification problem with the Neumann boundary condition for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the identification problem are established. Furthermore, a first order of accuracy difference scheme for the numerical solution of the identification problems for hyperbolic equations with the Neumann boundary condition is presented. Stability estimates for the solution of the difference scheme are established. This difference scheme is tested on an example and some numerical results are presented.
Abstract Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field ϕ (0) as a smeared operator in the CFT. A series of 1/N corrections must be added to ϕ (0) to represent an interacting bulk field ϕ. These corrections have been determined in the literature from several points of view. Here we develop a new perspective. We show that correlation functions involving ϕ (0) suffer from ambiguities due to analytic continuation. As a result ϕ (0) fails to be a well-defined linear operator in the CFT. This means bulk reconstruction can be understood as a procedure for building up well-defined operators in the CFT which thereby singles out the interacting field ϕ. We further propose that the difficulty with defining ϕ (0) as a linear operator can be re-interpreted as a breakdown of associativity. Presumably ϕ (0) can only be corrected to become an associative operator in perturbation theory. This suggests that quantum mechanics in the bulk is only valid in perturbation theory around a semiclassical bulk geometry.
Nuclear and particle physics. Atomic energy. Radioactivity