Analytical Mechanics Research Articles

Single-cell RNA-seq data augmentation using generative Fourier transformer

Single-cell RNA sequencing (scRNA-seq) provides a powerful tool for dissecting cellular complexity and heterogeneity. However, its full potential to achieve statistically reliable conclusions is often constrained by the limited number of cells profiled, particularly in studies of rare diseases, specialized tissues, and uncommon cell types. Deep learning-based generative models (GMs) designed to address data scarcity often face similar limitations due to their reliance on pre-training or fine-tuning, inadvertently perpetuating a cycle of data inadequacy. To overcome this obstacle, we introduce scGFT (single-cell Generative Fourier Transformer), a train-free, cell-centric GM adept at synthesizing single cells that exhibit natural gene expression profiles present within authentic datasets. Using both simulated and experimental data, we demonstrate the mathematical rigor of scGFT and validate its ability to synthesize cells that preserve the intrinsic characteristics delineated in scRNA-seq data. Moreover, comparisons of scGFT with leading neural network-based GMs highlight its superior performance, driven by its analytical mechanism. By streamlining single-cell data augmentation, scGFT offers a scalable solution to mitigate data scarcity in cell-targeted research.

Advances in Theoretical and Applied Mechanics: Selected Contributions from THE 14th NATIONAL CONGRESS ON THEORETICAL AND APPLIED MECHANICS

Advances in Theoretical and Applied Mechanics: Selected Contributions from THE 14th NATIONAL CONGRESS ON THEORETICAL AND APPLIED MECHANICS

Navigating the Cosmos: The Evolution and Impact of Newtonian Mechanics

Mechanics is one of the most fundamental subfields of physics. Founded primarily by Isaac Newton, mechanics has strong relations with astronomy, one of the oldest sciences. It has astronomical origins and exhibits significant applications in astronomical problems. A historical perspective is necessary to grasp the big picture of physics, so this paper traces back to the very beginning of classical mechanics to discover its development through the literature review method. Starting from Keplers planetary motion laws and Newtons theories, then moving to two-body and three-body problems, this essay demonstrates the delicacy of classical mechanics and how it effectively solves different issues. Also, after centuries of development, the implications of Newtonian mechanics have been greatly expanded upon, serving as the foundation for numerous subsequent theories. In the end, this essay provides an outlook for other theories that either derive from or relate to Newtonian mechanics, like chaos theory and analytical mechanics. The paper finds that Newtonian mechanics is essential because it not only provided solutions to many of the modern astronomical difficulties but also encouraged the emergence of other important ideas

Research on the biomechanics and animation assistance of backbasket throwing embroidery ball technique

Objective: This study aims to use biomechanical analysis of sports to create animations and innovate projection methods to improve the competitive level of ethnic sports such as throwing embroidered balls in baskets. Method: Utilizing methods such as analytical mechanics, animation production, and mathematical statistics, the results of training competitions were statistically analyzed to select scientific techniques for throwing embroidered balls into baskets. The prototypes and trajectories of these techniques were then animated to create visual projection technology for training guidance. Innovative projection technology was developed to improve athletic performance. Result: The competitive level of basket throwing embroidered ball is lagging behind, there is a lack of research on projection techniques, and the competition rules are not perfect. Excellent players mainly use short flat (α ≤ 30°) projection method, with a projection speed between 17.32 m/s and 18.97 m/s. The arc top of the projection trajectory is between 4.75 m and 5.5 m from the ground, and the landing point is within the receiving area, forming an effective receiving area. The receiver can easily judge the reception within the effective area, making it easy to achieve good results. Conclusion: The combination of biomechanics and animation production technology can effectively assist in improving the projection technology of basket throwing embroidered balls. Using short flat projection method to control the projection cycle can effectively improve performance, improve and unify the use of balls in competitions, and apply drone aerial photography technology to assist referees in making decisions, thereby improving the competitive level and standardization of embroidered ball throwing.

The concepts of irreversibility and reversibility in research on anthropogenic environmental changes.

The concept of "irreversibility" and its counterpart "reversibility" have become prominent in environmental and ecological research on human-induced changes, thresholds, climate tipping points, ecosystem degradation, and losses in the cryosphere and biosphere. Through a systematic literature review, we show that in these research fields, these notions are not only descriptive terms, but can have different semantic functions and normative aspects. The results suggest that, in the context of environmental and ecological research the concepts of irreversibility and reversibility have taken on additional usages in comparison to their contexts in theoretical thermodynamics and mechanics. Irreversible as a classification of anthropogenic environmental change can be used categorically, in the sense of a finite end, or relatively, i.e. on time or spatial scales of interest. Surprisingly, most of the analyzed scientific articles that use the terminology of (ir)reversibility substantively do not provide an explicit conceptualization or definition (74.7%). The research on potential (ir)reversibility of environmental change may affect the social and political willingness to bear the costs of interventions to mitigate or prevent undesirable environmental change. In particular, classifying a change as reversible or irreversible and determining the timescale(s) and spatial scale(s) involved has implications for policy and ecosystem management decisions, as suggested by its use in several high-level scientific and policy reports on ecosystem and climate change. Therefore, it is important to explicitly present a clear definition of irreversibility or reversibility for the readers from other fields, even if it could be the case that within a specific community an implicit definition was considered to be sufficient. We propose further recommendations for inter- and transdisciplinary reflection and conceptual use in the context of environmental, ecological, and sustainability research.

Exploring Applications of Lagrange’s Equations in Technology: A Systematic Literature Review

Lagrange's equation is a formula in analytical mechanics used to solve problems with physical system dynamics. It allows mathematical modeling to simplify complex mechanical problems by changing the coordinate system, thus providing a deeper understanding of motion. In this research, a literature study was conducted using the Systemic Literature Review (SLR) method from 30 data sources, 24 of which were indexed by Scopus. A total of 11 articles have been reviewed with a focus on the application of Lagrange's equation in various technologies. The review results show that Lagrange multipliers provide a powerful tool for optimizing energy flow within complex smart grids. The benefits extend beyond smart grids. Lagrange's equations are a powerful mathematical tool applicable to various engineering challenges that involve finding optimal solutions under constraints.

On How to Determine Surface Roughness Power Spectra

Analytical contact mechanics theories depend on surface roughness through the surface roughness power spectrum. In the present study, we evaluated the usability of various experimental methods for studying surface roughness. Our findings indicated that height data obtained from optical methods often lack accuracy and should not be utilized for calculating surface roughness power spectra. Conversely, engineering stylus instruments and atomic force microscopy (AFM) typically yield reliable results that are consistent across the overlapping roughness length scale region. For surfaces with isotropic roughness, the two-dimensional (2D) power spectrum can be derived from the one-dimensional (1D) power spectrum using several approaches, which we explored in this paper.Graphical

Theoretical Aspects of Soil Layer Turnover Within the Boundaries of Its Own Furrow

The paper highlights that soil layer turnover remains the most widely used method of primary tillage. Among the existing techniques, smooth plowing without producing back ridges or furrows, which is achieved using reversible plows, best meets the high standards of modern agricultural practices. (Research purpose) The study aims to substantiate the kinematics of soil layer turnover within the boundaries of its own furrow without lateral displacement. (Materials and methods) In analyzing the kinematics, the soil layer is assumed to behave as a cohesive elastic substance undergoing deformation during turnover within its own furrow, without disintegration. This assumption is quite reasonable, as it is well-established that a sodded and moist layer can be extracted as a continuous, intact strip that retains its geometric dimensions when turned 180°. The trajectory of the layer is derived using classical methods of theoretical mechanics. (Results and discussions) The equations governing the motion of the soil layer points during turnover within its own furrow are analyzed. During this process, all points in the cross-section of the layer undergo spatial displacement. Changes in displacement, velocity, and acceleration of the i-th point of the hypothetical layer exhibit smooth dependencies described by trigonometric functions. However, at a rotation angle of ωt = π/2, an abrupt change occurs in the trajectories of displacement, velocity and acceleration graphs, indicating sharply variable loads acting on the soil layer at this point. The abrupt change is attributed to a shift in the support rib which serves as the axis for the rotation of the soil layer's crosssection. The center of gravity of the cross-section moves with variable velocity and acceleration, which indicates the presence of inertial forces. Overcoming these forces requires a certain amount of energy. (Conclusions) The energy required largely depends on the geometric parameters of the layer a, b and its rotation modes (ω). When the layer cross-section rotates by an angle When the layer cross-section rotates by an angle ωt = π/2 – γ, the vertical acceleration of the central point (О) reaches its maximum value. Under certain conditions, the soil layer may detach from the furrow bottom in this position. The kinematics analysis of a soil layer turnover within the boundaries of its own furrow reveals new phenomena occurring during its motion to identifies the patterns of influence that the soil layer's geometric parameters exert on its dynamic characteristics.

The Calcium Hydroxide Controversy: Does Calcium Hydroxide Weaken Teeth?

Calcium hydroxide apexification has been used in the treatment of immature teeth with pulp necrosis and apical periodontitis for more than 50 years. However, the guidelines of the European Academy of Paediatric Dentistry (EAPD) and the American Association of Endodontists (AAE) 'Clinical recommendations for a regenerative procedure' recommend against calcium hydroxide apexification. The American Association of Endodontists "Clinical considerations for a regenerative procedure" do not list calcium hydroxide apexification as a treatment option for immature teeth with pulp necrosis. This review analyses the strength of the science that led to calcium hydroxide no longer being recommended by the EAPD and AAE regenerative guidelines. Many differences in the studies and failure to include adequate controls have resulted in inconsistent outcomes between studies. Furthermore, prior invitro studies have assessed narrow mechanical properties of teeth without a theoretical fracture mechanics model. Cvek's concerns regarding the thinness of the dentinal walls remain as a primary risk for tooth fracture with Class 3 root development fractured with an incidence of 77% compared to a fracture incidence of just 2% for mature teeth. This review develops a simple fracture mechanics approach to the phenomenon of transverse root fracture that provides a theoretical framework to why fragile roots are more likely to fracture when compared to mature teeth. Furthermore, the effect of the varying size access cavities has not been previously considered. Systematic reviews and clinical studies do attest to the success of all approaches for the treatment of immature teeth with pulp necrosis. Calcium hydroxide apexification is one of the recommended treatments in the International Association of Dental Traumatology guidelines. However, mineral trioxide aggregate (MTA) and hydraulic calcium silicate cements (HCSC's) may provide better outcomes and have the convenience for the patient of a shorter treatment time. Regenerative endodontic treatment (RET) is recommended when the tooth roots are very immature with Cvek Class 1-3 root development. However, the treatment of immature teeth with pulp necrosis remains a clinical challenge as does the risk of tooth fracture.

Grounding Analytical Mechanics in Statics: A Didactic Emphasis on the Principle of Virtual Work

Abstract Many textbooks on analytical mechanics introduce the Lagrangian formalism with D'Alembert's or Hamilton's principle. However, the validity of D'Alembert's principle is rooted in an ancient law of statics, the Principle of Virtual Work (PVW), which is rarely discussed in these texts, potentially causing difficulties. Likewise, the well-known tendency of nature to optimize physical phenomena is a straightforward consequence of the PVW, from which Hamilton's principle can also be derived. While Lagrange felt it necessary to dedicate half of his classical book to justify the validity of the PVW, today it is often regarded as a trivial intermediate step when establishing D'Alembert's principle. In this paper, following the path set by Lagrange—though in modern notation—the didactic potential of working with the PVW as an initial step before studying dynamics at the undergraduate level is explored. Beyond elucidating its conceptual richness and historical significance, several practical applications of the PVW are provided, aiming for a deeper understanding of the foundations of dynamics.

Prediction of the Temperature Field Development in Large Heat Storage Tanks for Integration in Network Simulation

Integrating an increasing amount of renewable energy into district heating systems requires thermal energy storages. For the planning and operation of the whole system valid and powerful storage models are essential for implementation in e. g. thermo-hydraulic network simulations and operational optimisation tools. The modelling of large tank thermal energy storages (TTES) up to 60,000 m³ can be insufficient by using a simple energy balance model as it does not provide information about the temperature profile. The detailed model called FreeTTES is capable of predicting the temperature distribution inside a large atmospheric TTES. This model simplifies fluid dynamic processes by assuming horizontal homogeneity and analyses them only in vertical direction. The analytical fluid mechanics approach is combined with numerical, measurement data-based approaches. The validation of the model is performed using DTS (distributed temperature sensing) data

Selected papers from 68th Congress of Indian Society of Theoretical and Applied Mechanics (ISTAM 2023) for the special issue on Innovation in Thermal Systems and Modelling (ITSM 2023)

Selected papers from 68th Congress of Indian Society of Theoretical and Applied Mechanics (ISTAM 2023) for the special issue on Innovation in Thermal Systems and Modelling (ITSM 2023)

Geoeconomic modelling: southwestern trend of vegetable growing in Russia

Relevance. Modern globalization, internationalization, regional competitive differentiation actualize geoeconomic modeling methods for geopolitical planning, management and control. The novelty of the proposed solutions is the proposed concept, based on the translation of the ideas of theoretical mechanics into economics.Methodology. Considering the annual values of statistical indicators of territorial concentrates as a system of geographically distributed objects (subjects of the Russian Federation), it is possible to determine the geographic barycenter. Knowing the values of the geocoordinates of the barycenter, it is possible to determine the tendencies and trend of the barycenter movement as an indicator of the dynamics of the system under consideration through the analysis of the dynamics of these coordinates. Based on Russtat data on the annual gross harvest of agricultural crops (vegetables), population by constituent entities of the Russian Federation for the period 1991-2021, data on the coordinates of the administrative centers of the constituent entities of the Russian Federation, the values of the geographic coordinates of the barycenter of vegetable growing in Russia were calculated.Results. For 2021, the geographic coordinates of the barycenter of vegetable growing in Russia are 50.30° N and 49.49° E with an average regional value with an average regional annual vegetable har-vest of 1722.52 million centners/year and fluctuations in the coordinates of the barycenter in the zone of 3-4 geographic degrees or three hundred territorial kilometers with a pronounced south-west trend Analysis of the dynamics of the barycenter for the period 1991-2021. will allow to reveal a slight shift of the vegetable growing barycenter to the south by 3.5 degrees with an increase in the average regional vegetable harvest by 124.11 million centners per year for each degree (or the all-Russian by more than 9,500 million centners per year for each degree to the south), a slight shift of the vegetable growing barycenter to the west by 4.5 degrees with an increase in the average regional vegetable har-vest by 86.5 million centners per year per degree (or the All-Russian by more than 6,660 million cent-ners per year for each degree to the west). For the period 1991-2021, two opposite trends in the devel-opment of vegetable growing are distinguished. In the period from 1991 to 2000, the movement of the coordinate of the vegetable growing barycenter went in the direction of the northeast of Russia, in the period 2000 to 2021 -- on the contrary, to the southwest.The conclusion is made about the existence of a relationship between the development of vegetable growing and the geopolitics of Russia in the period under review. The obtained method and results can be used in strategic state management of agricultural production in Russia.

Steel Catenary Riser Fatigue Assessment: Fracture Mechanics Approach Versus S-N Curve Method.

In this paper, the fatigue resistance of a full-scale Steel Catenary Riser (SCR) girth weld is investigated using the Strength-Number of cycles (S-N) curve method based on weld formation quality and fracture mechanics approaches. The test results, presented in the form of S-N curves, are superior to the design curve E in BS 7608. Compared with the S-N curve determined by a resonant bending rig, the analytical fracture mechanics, i.e., engineering critical assessment (ECA) based on BS 7910, can provide a rational estimation of full-scale girth welds. For the numerical methods, the short crack growth phase is crucial to improving the accuracy and reliability of the assessment. For the girth weld with a concave root, the geometries of the weld cap are the predominant factors for fatigue life. Although the crack initiation site is always located at the outer surface regardless of the flushed or welded caps, the weld grinding treatment is still effective in promoting fatigue life.

An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems

Motivated by the convenience, in some biomechanical problems, of interpreting the mass balance law of a growing medium as a nonholonomic constraint on the time rate of a structural descriptor known as growth tensor, we employ some results of analytical mechanics to show that such constraint can be studied variationally. Our purpose is to move a step forward in the formulation of a field theory of the mechanics of volumetric growth by defining a Lagrangian function that incorporates the nonholonomic constraint of the mass balance. The knowledge of such Lagrangian function permits, on the one hand, to deduce the dynamic equations of a growing medium as the result of a variational procedure known as Hamilton–Suslov Principle (clearly, up to non-potential generalized forces that are accounted for by extending this procedure), and, on the other hand, to study the symmetries and conservation laws that pertain to a given growth problem. While this second issue is not investigated in this work, we focus on the first one, and we show that the Euler–Lagrange equations of the considered growing medium, which describe both its motion and the evolution of the growth tensor, can be obtained by reformulating a variational method developed by other authors. We discuss the main features of this method in the context of growth mechanics, and we show how our procedure is able to improve them.

Methodology for calculating the support reactions of a statically indeterminate tractor drive axle final drive shaft

BACKGROUND: Currently, in the design of vehicle drive axles, bevel final drives are used, forming both statically determinate structures and statically indeterminate ones. In the first case, the bearings on which the bevel final drive shafts rest form two races of rolling elements, in the second case - three or more. Despite the prevalence of bevel final drive designs that form statically indeterminate structures, in the process of teaching the design and calculation of machine elements, statically determinate structures are considered. The relevance of the work lies in the formalization of the analytical calculation of the reactions of the supports of the bevel final drive, forming a statically indeterminate system, with the derivation of formulas for determining the reactions in the extra support. AIMS: The article aim is the formalization the methodology for calculating the support reactions of the drive axle bevel final drive, forming a statically indeterminate system, for calculating bearings. METHODS: The article uses mathematical dependencies of Analytical Mechanics to calculate reactions in the main supports, a corollary of Castigliano theorem and the Force method to calculate reactions in extra supports. "Mathcad" was used for mathematical calculations. RESULTS: A formalized method for the analytical calculation of support reactions in statically indeterminate systems has been developed and presented, using Castigliano theorem to solve static indetermination. The methodology application for calculating the support reactions of the statically indeterminate the Kirovets K-7 series tractors drive axle bevel final drive is considered. CONCLUSIONS: The dependencies obtained during the calculations make it possible to calculate the bevel final drive support reactions, the design of which forms a statically indeterminate system. The bevel final drive mathematical model obtained during the calculations can be used as a basis for developing software that automates this calculation.

Grundlagen einer 'integralen' Grammatik

Within the framework of an integral grammar, syntax, morphology and lexicology represent three types of consideration of the same reality, which is the linguistic construction of meaning. The distinction between these three linguistic disciplines may be useful in some cases, but in other cases it may hinder the explanation of linguistic phenomena. Integral linguistics is capable of unifying the disciplines - integrating them. It can, however, use modular methods where appropriate. It could therefore be seen as a kind of construction grammar with the option of modularising its descriptions and explanations. This is not to say that this approach advocates methodical indifference; on the contrary, it presupposes a particularly rigorous deduction of its concepts and descriptive methods. The foundations for such a grammar have already been laid in Saussure's Cours de linguistique générale, which – with striking foresight – anticipates the ideas of nowadays' construction grammars and provides them with a hitherto unprecedented theoretical foundation. This is the starting point for the present article, which places Saussure's reflections within the framework of a theory of language centred on the speech event. It defines the functional levels of the sentence on the ground of the dimensions of utterance meaning, deduces the notions of syntactic function and syntactic constituency from the synthetic and analytical mechanisms of the syntagmatic dimension of language, and those of form and category from the abstraction principles of the paradigmatic dimension of language. Finally, it will be shown how the basic ideas of constructional grammars, in particular that of the syntax lexicon continuum, can be convincingly and exhaustively explained by the universal principles of grammar postulated by Saussure: the syntagmatic and paradigmatic structuration of language.

Development of a Lagrange Mechanics E-Module Based on a Flipbook Pendulum Spring System

This research is a type of Research and Development (R D) research that uses the 4D development model, namely Define, Design, Develop, Disseminate. This research produces a Lagrange Mechanics E-Module based on a flipbook pendulum spring system. The aim of this research is to produce a Lagrange Mechanics E-Module that is suitable for use as a learning medium for Analytical Mechanics. The data collection instrument used in this research is a questionnaire as a validation assessment for material experts and students, data analysis uses percentages with predetermined categories. The research sample was 14 Physics Education students. The validation results by material experts were 73% in the feasible category. The student response results were 85% in the very appropriate category. From these results, the Lagrange Mechanics E-Module is suitable for use with revisions as an alternative source of learning.

Mechanism of microwave-assisted coal desulfurization with urea peroxide

To effectively remove organic sulfur from coal for higher resource efficiency, an innovative microwave-assisted urea peroxide for desulfurization system was designed. The experimental group with different microwave frequencies and the conventional pyrolysis control group were set up to prove the desulfurization effect of microwave in coordination with urea peroxide. The experimental results showed that under 1000 W microwave irradiation and the promotion of urea peroxide, the desulfurization efficiency can reach 67.29 %, with an increase of 38.32 % while the conventional pyrolysis is only 28.97 %. According to the Fourier transform infrared (FTIR) analysis, the effectiveness of microwave coordination with urea peroxide for desulfurization is explained from macroscopic point of view. Benzylidene thiol, dibenzyl sulfide, and dibenzyl disulfide were selected as model compounds for the quantum chemical calculation. The simulation results demonstrated that the changes in the pathway energy barriers for desulfurization align with the experimental material transformations, confirming the accuracy of the simulation. The sulfur-containing bonds of mercaptans will be destroyed to form hydrogen sulfide, and the undestroyed bonds will remain in the organic matter. After being oxidized, the sulfur-containing bond will break to form a water-soluble sulfonic acid free radical. The unoxidized sulfur bonds of thioethers will be destroyed to generate unstable phenyl free radicals and free sulfur radicals. To achieve stability, phenyl free radicals can pair to form diphenylethane or combine with other radicals (such as •H). In contrast, sulfur free radicals can only react with hydrogen radicals to form hydrogen sulfide. However, the limited availability of hydrogen radicals in the system restricts the desulfurization efficiency. After oxidation by urea peroxide, the thioethers will form sulfones. The sulfur-containing bonds will be fractured and directly generate phenyl and sulfur dioxide, which reduces the dependence on hydrogen free radicals. The three-dimensional desulfurization path of microwave collaboration with urea peroxide experiment was simulated and converted to the analytical bond breaking and formation mechanism. This study proved that microwave synergizes with urea peroxide can intensify the desulfurization process. It provides a high-efficiency method for the clean and green utilization of coal, which is conducive to supporting environmentally sustainable development.

Mechanical Foundations of the Generalized Second Law and the Irreversibility Principle

We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to establish the generalized second law (GSL) that is applicable to a system of any size, including a single particle system as our example establishes, and that supercedes the celebrated second law (SL) of increase of entropy of an isolated system. It is merely a consequence of the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics and the first law. We justify an irreversibility priciple that covers all processes, spontaneous or not, and having both positive and negative nonequilibrium temperatures temperatures T defined by (dQ/dS)E. Our novel approach to establish GSL/SL is the inverse of the one used in classical thermodynamics and clarifies the concept of spontaneous processes so that dS≥0 for T>0 and dS<0 for T<0. Nonspontaneous processes such as creation of internal constraints are not covered by GSL/SL. Our demonstration establishes that Mec-EQ-P controls spontaneous processes, and that temperature (positive and negative) must be considered an integral part of dissipation.