Key Equations Research Articles

OXFORD-UMAT: An efficient and versatile crystal plasticity framework

The crystal plasticity-based finite element method is widely used, as it allows complex microstructures to be simulated and allows direct comparison with experiments. This paper presents the OXFORD-UMAT for Abaqus®, a novel crystal plasticity code that is publicly available online for researchers interested in using crystal plasticity. The model is able to simulate a wide range of materials and incorporates two different solvers based on the solution of slip increments and Cauchy stress with variants of state update procedures including explicit, semi-implicit, and fully-implicit for computational efficiency that can be set by the user based on the application. Constitutive laws are available for a range of materials with single or multiple phases for slip, creep, strain hardening, and back stress. The model includes geometrically necessary dislocations that can be computed using finite element interpolation functions by four alternative methods, including the total form with and without a correction for the dislocation flux, a widely used rate form, and a slip-gradient formulation. In addition, the initial strengthening and subsequent softening seen in irradiated materials can also be simulated with the model. The analysis is available in 2D (plane stress and plane strain) and 3D, including linear and quadratic elements. Here we include full derivations of the key equations used in the code and then demonstrate the capability of the code by modeling single-crystal and large-scale polycrystal cases. Comparison of OXFORD-UMAT with other available crystal plasticity codes for Abaqus® reveals the efficiency of the proposed approach, with the backup solver offering greater versatility for handling convergence issues commonly found in practical applications.

Entropy generation in radiative motion of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms and activation energy

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1<α<4.0, 0.1<M<1.2, 0.1<Nr<2.2, 0.1<Le<2.2, 0.1<Nb<0.4, 0.1<Nt<1.0, 2.0<⁡Pr⁡<5.0, and 0.1<Lb<2.0, as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.

Comment on “Cellular aggregation dictates universal spreading behaviour of a whole-blood drop on a paper strip”

Laha et al. studied the diffusive behavior of a whole-blood drop on filter paper using the generalized capillary bundle model. However, some model parameters should be further refined to accurately reflect the physics involved in this diffusion process. Moreover, citations are missing for some key equations. Addressing these aspects will improve the model applicability to this application and benefit readers in accessing more accurate and detailed information.

Efficient Study on Westervelt-Type Equations to Design Metamaterials via Symmetry Analysis

Metamaterials have emerged as a focal point in contemporary science and technology due to their ability to drive significant innovations. These engineered materials are specifically designed to couple the phenomena of different physical natures, thereby influencing processes through mechanical or thermal effects. While much of the recent research has concentrated on frequency conversion into electromagnetic waves, the field of acoustic frequency conversion still faces considerable technical challenges. To overcome these hurdles, researchers are developing metamaterials with customized acoustic properties. A key equation for modeling nonlinear acoustic wave phenomena is the dissipative Westervelt equation. This study investigates analytical solutions using ansatz-based methods combined with Lie symmetries. The approach presented here provides a versatile framework that is applicable to a wide range of fields in metamaterial design.

Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE

Hybrid energy supply systems are widely utilized in modern manufacturing processes, where accurately predicting energy consumption is essential not only for managing productivity but also for driving sustainable development. Effective energy management is a cornerstone of sustainable manufacturing, reducing waste and enhancing efficiency. However, conventional studies often focus solely on predicting single types of energy consumption and overlook the integration of physical laws and information, which are essential for a comprehensive understanding of energy dynamics. In this context, this paper introduces a multi-task physics-informed multi-gate mixture-of-experts (pi-MMoE) model that not only considers multiple forms of energy consumption but also incorporates physical principles through the integration of physical information and multi-task modeling. Specifically, a detailed analysis of manufacturing processes and energy patterns is first conducted to study various energy types and extract relevant physical laws. Next, using industry insights and thermodynamic principles, key equations for energy balance and conversion are derived to create a physics-based loss function for model training. Finally, the pi-MMoE model framework is constructed, featuring multi-expert networks and gating mechanisms to balance cross-task knowledge sharing and expert learning. In a case study of a textile factory, the pi-MMoE model reduced electricity and steam prediction errors by 14.28% and 27.27%, respectively, outperforming traditional deep learning methods. This demonstrates that the model can improve prediction performance, providing a novel approach to intelligent energy management and promoting sustainable development in manufacturing.

Potential Power Output from Vehicle Suspension Energy Harvesting Given Bumpy and Random-Surfaced Roads

The energy efficiency of vehicles is a crucial challenge relating to sustainable energy preservation and regeneration methods. Regenerative breaking has proven feasible, and there is interest in whether harvesting energy from a vehicle’s suspension is similarly feasible. We here provide methods for estimating the amount of power that can be regenerated from the suspension for given vehicle and road parameters. We show that a reasonable road model is a generalised Gaussian process known as AR(1). Using this model, we can derive the key equation used in the ISO 8608 standard for measuring road roughness, such that the AR(1) parameters can be related to the measured road roughness data. We find that the road roughness coefficient of ISO 8608 and the diffusion coefficient of the AR(1) road are equal up to a factor. We provide an analytical expression for the maximum amount of power that can be generated for given road and car parameters, derived via Fourier analysis. We further model harvesting from large bumps using Simulink. These results help to estimate the potential power output given the measured road data.

Isometries to Analyze the Stability of Norm-Based Functional Equations in p-Uniformly Convex Spaces

Over the past two decades, significant advancements have been made in understanding the stability according to Hyers–Ulam involving different functional equations (FEs). This study investigates the generalized stability of norm-based (norm-additive) FEs within the framework of arbitrary (noncommutative) groups and p-uniformly convex spaces. Specifically, we analyze two key functional equations, ∥η(gh)∥=∥η(g)+η(h)∥ and ∥η(gh−1)∥=∥η(g)−η(h)∥foreveryg,h∈G, where (G,·) denotes an arbitrary group and B is considered to be a p-uniformly convex space. The surjectivity of the function η:G→B is a critical assumption in our analysis. Drawing upon the foundational works of L. Cheng and M. Sarfraz, this paper applies the large perturbation method tailored for p-uniformly convex spaces, where p≥1. This study extends previous research by offering a deeper exploration of the conditions under which these functional equations demonstrate Hyers–Ulam stability. In this study, the additive functional equation demonstrates a fundamental form of symmetry, where the order of operands does not affect the results. This symmetry under permutation of arguments is crucial for the analysis of stability. In the context of norm-additive FEs, this stability criterion investigates how small changes in the inputs of a functional equation affect the outputs, especially when the function is expected to follow an additive form.

Traffic Traps: An Investigation into Road Congestion Management

Abstract: Urban traffic congestion presents a significant global challenge, necessitating effective traffic management for seamless transportation system operations. This study emphasizes the implementation of an Intelligent Traffic Management System (ITMS) capable of real-time monitoring and control. Focusing on Mattoor Junction in Ernakulam, Kerala, this research applies distinct algorithms in Python and MATLAB, introducing three key equations: Average Traffic Flow (ATF), Traffic Variability Index (TVI), and Time-of-Day Congestion Index (CI). The methodology involves a detailed survey of the route, traffic volume counts, spot speed studies, and roadside interviews to gather data. The ATF, TVI, and CI equations are used to analyze traffic patterns, variability, and congestion levels. The findings reveal significant congestion on critical routes intersecting at Mattoor Junction, particularly during peak hours. To address this, the study proposes the implementation of an automated traffic signal system, optimizing signal timings. This intervention aims to enhance traffic flow and reduce congestion. The research underscores the potential of ITMS for real-time traffic management, offering a data-driven approach to urban traffic challenges. The integration of theoretical models with empirical data provides a comprehensive framework for future ITMS strategies, contributing to more efficient and adaptive urban traffic management

The Scale-Invariant Vacuum Paradigm: Main Results and Current Progress Review (Part II)

This is a summary of the main results within the Scale-Invariant Vacuum (SIV) paradigm based on Weyl integrable geometry. We also review the mathematical framework and utilize alternative derivations of the key equations based on the reparametrization invariance as well. The main results discussed are related to the early universe; that is, applications to inflation, Big Bang Nucleosynthesis, and the growth of the density fluctuations within the SIV. Some of the key SIV results for the early universe are a natural exit from inflation within the SIV in a later time texit with value related to the parameters of the inflationary potential along with the possibility for the density fluctuations to grow sufficiently fast within the SIV without the need for dark matter to seed the growth of structure in the universe. In the late-time universe, the applications of the SIV paradigm are related to scale-invariant dynamics of galaxies, MOND, dark matter, and dwarf spheroidals, where one can find MOND to be a peculiar case of the SIV theory. Finally, within the recent time epoch, we highlight that some of the change in the length-of-the-day (LOD), about 0.92 cm/yr, can be accounted for by SIV effects in the Earth–Moon system.

New simultaneous Diophantine attacks on generalized RSA key equations

RSA stands as a widely adopted method within asymmetric cryptography, commonly applied for digital signature validation and message encryption. The security of RSA relies on the challenge of integer factorization, a problem considered either computationally infeasible or highly intricate, especially when dealing with sufficiently large security parameters. Effective exploits of the integer factorization problem in RSA can allow an adversary to assume the identity of the key holder and decrypt such confidential messages. The keys employed in secure hardware are particularly significant due to the typically greater value of the information they safeguard, such as in the context of securing payment transactions. In general, RSA faces various attacks exploiting weaknesses in its key equations. This paper introduces a new vulnerability that enables the concurrent factorization of multiple RSA moduli. By working with pairs (Ni,ei) and a fixed value y satisfying the Diophantine equation eixi2−y2ϕ(Ni)=zi, we successfully factorized these moduli simultaneously using the lattice basis reduction technique. Notably, our research expands the scope of RSA decryption exponents considered as insecure.

The Lipid–Heart Hypothesis and the Keys Equation Defined the Dietary Guidelines but Ignored the Impact of Trans-Fat and High Linoleic Acid Consumption

In response to a perceived epidemic of coronary heart disease, Ancel Keys introduced the lipid–heart hypothesis in 1953 which asserted that high intakes of total fat, saturated fat, and cholesterol lead to atherosclerosis and that consuming less fat and cholesterol, and replacing saturated fat with polyunsaturated fat, would reduce serum cholesterol and consequently the risk of heart disease. Keys proposed an equation that would predict the concentration of serum cholesterol (ΔChol.) from the consumption of saturated fat (ΔS), polyunsaturated fat (ΔP), and cholesterol (ΔZ): ΔChol. = 1.2(2ΔS − ΔP) + 1.5ΔZ. However, the Keys equation conflated natural saturated fat and industrial trans-fat into a single parameter and considered only linoleic acid as the polyunsaturated fat. This ignored the widespread consumption of trans-fat and its effects on serum cholesterol and promoted an imbalance of omega-6 to omega-3 fatty acids in the diet. Numerous observational, epidemiological, interventional, and autopsy studies have failed to validate the Keys equation and the lipid–heart hypothesis. Nevertheless, these have been the cornerstone of national and international dietary guidelines which have focused disproportionately on heart disease and much less so on cancer and metabolic disorders, which have steadily increased since the adoption of this hypothesis.

On the adaptation of the Lagrange formalism to continuous time stochastic optimal control: A Lagrange-Chow redux

We show how the classical Lagrangian approach to solving constrained optimization problems from standard calculus can be extended to solve continuous time stochastic optimal control problems. Connections to mainstream approaches such as the Hamilton-Jacobi-Bellman equation and the stochastic maximum principle are drawn. Our approach is linked to the stochastic maximum principle, but more direct and tied to the classical Lagrangian principle, avoiding the use of backward stochastic differential equations in its formulation. Using infinite dimensional functional analysis, we formalize and extend the approach first outlined in Chow (1992) within a rigorous mathematical setting using infinite dimensional functional analysis. We provide examples that demonstrate the usefulness and effectiveness of our approach in practice. Further, we demonstrate the potential for numerical applications facilitating some of our key equations in combination with Monte Carlo backward simulation and linear regression, therefore illustrating a completely different and new avenue for the numerical application of Chow's methods.

An enhanced hybrid model for batch sugar crystallization based on the pattern recognition for overall heat transfer coefficient using a machine learning approach

AbstractA hybrid model is developed and evaluated to simulate the heat and mass transfer in the crystallization unit of a sugar factory. While the mass transfer is modeled by using the kinetic growth rate model, the heat transfer is simulated by applying the energy balance to the model. Here, the overall convection heat transfer coefficient of the crystallizer's heat exchanger is considered as a temperature‐dependent function. As this makes the governing equations more realistic, it can help to increase the model accuracy. Additionally, a thorough examination of key practical equations and principles governing the sugar crystallization process is presented. A regression learner method is applied to extract the pattern of the overall heat transfer coefficient. According to our results, the regression learning model successfully predicts the heat transfer coefficient with an average 7% deviation from experimental results. For the hybrid model, an average deviation of about 10% is observed. The crystallizer's behavior is somehow linear, indicating a constant growth rate of sugar crystals. Furthermore, the heat transfer in the crystallizer is improved by increasing the working temperatures.Practical applicationsThe method and obtained results of this work could be used in the following practical purposes: to find the optimum working temperatures of crystallizers used in sugar industry and to predict total working time of batch crystallizers versus working parameters.

ILOSCAR: interactive Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir model v1.0

Computationally inexpensive carbon cycle models serve as critical and efficient tools for illuminating the complex dynamics of the carbon cycle and its interplay with the climate system, offering insights into how our planet has responded to climate perturbations throughout its history. During geologic hyperthermal events, carbon cycle models are employed to trace the trajectory of carbon emissions and establish a connection between the emission trajectory and changes in the Earth's surface environment. To date, the prevalent method to estimate the carbon emission rate relies on coupling the carbon cycle modeling and proxy reconstructions. Most previous studies employ a forward methodology, i.e., they force the model with an array of predefined carbon injection scenarios and select the one that produces the best fit to one or more specific proxy-derived records (e.g., atmospheric pCO2, sea surface pH, and calcite compensation depth) as the optimal solution. However, this forward method has two potential disadvantages. First, it can be computationally expensive, particularly when tens of thousands of scenarios need to be conducted to find the best solution. Second, it might not yield the best injection trajectory if none of the predefined carbon emission curves represents the realistic emission curve. Hence, an inverse model that can reconstruct the carbon emission trajectory directly from the record/records is urgently needed. In this study, building upon the Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir (LOSCAR) Model (Zeebe, 2012), we develop an interactive carbon cycle model (named iLOSCAR) using the open-source Python language and include two options, a forward model and an inverse model. The forward model replicates the original LOSCAR model, while the inverse model calculates the emission trajectory constrained by the proxy records in a single run. Both models are accessible via a web-based interface, which allows users to interactively tune model parameters and conduct experiments. In this paper, we present the details of iLOSCAR, including model structure and derivation of key equations. We then validate iLOSCAR's performance through an identical twin test and model intercomparison. We also apply it to a climatic perturbation event to diagnose features of the emission pattern that were overlooked in previous studies. Finally, we discuss the possible directions for model's future development.

Diamonds in the Current: Navigating Challenges for the Integration of Diamond in Power Electronics

Power electronics, a pivotal field orchestrating electrical energy flow in the modern world, deals with efficient conversion, control, and management of electrical power across diverse applications. While its scope encompasses circuits for energy conversion, its challenges include transporting electrical energy over extended distances. Focusing on electrical‐to‐electrical conversions, the goal is minimal loss for delivering maximum power. The article explores the intricacies of power electronics, presenting key equations, and concepts. The current global power electronics market witnesses growth, driven by demand for energy‐efficient technologies, renewables integration, and the rise of electric vehicles. Future trends indicate continued growth, driven by renewable energy systems, and electric vehicles. Wide bandgap semiconductors, play a crucial role, with ultra‐wide bandgap semiconductors like diamond emerging as potential disruptors. A comparative analysis of semiconductor properties reveals diamond's unique attributes. Despite its challenges, diamond shows promise for power electronic applications, with ongoing research on components like Schottky diodes. Thermal considerations, substrate limitations, and dislocation challenges are discussed, emphasizing the need for advancements to harness the full potential of diamond in power electronics. Finally, some inputs about the importance of overcoming these challenges for the successful integration of diamond in power electronic systems are given.

Method SPH for numerical solution of filtering problems: including capillary forces in fluid flow simulation

This paper explores the theory of filtration within porous media, focusing on multicomponent mixtures’ dynamics and their numerical modeling. Key equations governing filtration, including Darcy’s law and mass conservation, are introduced. The concept of smoothed particle hydrodynamics (SPH) is presented as a powerful numerical technique for approximating these equations. SPH’s integral interpolation approach accommodates complex fluid-solid interactions and is applied to one-dimensional and two-dimensional test cases. Results demonstrate SPH’s effectiveness in capturing intricate dynamics and aligning with traditional methodologies. This study contributes to understanding fluid dynamics in porous media and underscores SPH’s potential for accurate simulations in diverse applications, from hydrocarbon reservoirs to environmental systems. The first section in your paper.

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays.

This study aims to demonstrate the benefits of augmenting commercially available, real-time, in vitro glycolysis assays with phenomenological rate equation-based kinetic models, describing the contributions of the underpinning metabolic pathways. To this end, a commercially available glycolysis assay, sensitive to changes in extracellular acidification (extracellular pH), was used to derive the glycolysis pathway kinetics. The pathway was numerically modelled using a series of ordinary differential rate equations, to simulate the obtained experimental results. The sensitivity of the model to the key equation parameters was also explored. The cellular glycolysis pathway kinetics were determined for three different cell-lines, under nonmodulated and modulated conditions. Over the timescale studied, the assay demonstrated a two-phase metabolic response, representing the differential kinetics of glycolysis pathway rate as a function of time, and this behaviour was faithfully reproduced by the model simulations. The model enabled quantitative comparison of the pathway kinetics of three cell lines, and also the modulating effect of two known drugs. Moreover, the modelling tool allows the subtle differences between different cell lines to be better elucidated and also allows augmentation of the assay sensitivity. A simplistic numerical model can faithfully reproduce the differential pathway kinetics for three different cell lines, with and without pathway-modulating drugs, and furthermore provides insights into the cellular metabolism by elucidating the underlying mechanisms leading to the pathway end-product. This study demonstrates that augmenting a relatively simple, real-time, in vitro assay with a model of the underpinning metabolic pathway provides considerable insights into the observed differences in cellular systems.

Information Fusion for the Training of Public Administrators: Design of a Composite Indicator through the Integration of AHP and TOPSIS Methods

The article addresses the importance of capacity development among public administrators to ensure the efficient functioning of the state and the provision of quality services to the citizenry. This entails acquiring legal knowledge, ethical principles, and technical skills in areas such as strategic planning, financial management, and policy evaluation. In addressing the evaluation of public administrators' training programs, the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods are employed. The methodology delineates the fundamental concepts and key equations to understand the application of these methods in evaluating public administrators' training programs. The findings underscore the significance of specific competencies in public administrators' training. These competencies, combined with comprehensive training encompassing cognitive, attitudinal, and instrumental dimensions, can equip professionals to confront current governmental challenges effectively. The article emphasizes the relevance of capacity development among public administrators and introduces methods such as AHP and TOPSIS to assess and enhance training programs in this field, aiming to bolster the state's capacity to respond efficiently to societal needs.

Time Conservation Principle versus Energy Physics

This article explores the conservation principles that may apply to time, contrasting them with the well-established conservation of energy. Publications of peer reviewed papers enabled the author to derive time to be a tensor, algebraic than merely arithmetic scalar. Here, these are brought out in a dramatic manner to highlight gradation of high rank tensors, which decompose to multiple vectors. This study reexamines time originally as potentially the most conserved attribute in physics, considering the quantum nature of well-known established by thermodynamic fundamentalistic energy conservation. Literature surveys quoting time conservation versus energy physics studies, especially quantum gravity, Page–Wootters formalism, and related areas with concept of time as emergent and travel phenomena associated to time as a wavefunction tensor have been highlighted. Mathematical theory derivations showing conservation of time principle with tensor analysis giving key equations and establishing time invariance with point in space via differential testing in relation to domains of reality of time tensor, = constant proves that conservation of time applies like the general principle of energy quantum conservation well within given conditions. Quantified clocks applying time conservation principle analyze strong gravity versus weak gravity environments like microblackholes and the zero-point fields, showing how branes may produce curled up dimensions, like Kaluza-Klein 5D curled up dimensions. Verifications with experimental methods, especially testing time conservation potentially would uncover new fundamental principles of physics - time conservation principle after establishment will propel to revolutionize our understanding of the universe and drive innovation in both theoretical and applied physics, specifically quantum technologies and astrophysical endeavors, especially measurement techniques with LHC, for example have been considered to launch research efforts of the future.

Concurrent factorization of RSA moduli via weak key equations

<p>The Rivest-Shamir-Adleman (RSA) algorithm is a widely utilized technique in asymmetric cryptography, primarily for verifying digital signatures and encrypting messages. Its security relies on the integer factorization problem's difficulty, which is computationally infeasible with large security parameters. However, this study revealed scenarios where an attacker can concurrently factorize multiple RSA moduli $ N_i = p_i q_i $ under specific conditions. The attack is feasible when the attacker possesses a set of RSA key pairs with certain flaws, allowing each $ N_i $ to be factored in polynomial time. We identified vulnerabilities in RSA keys that satisfy particular equations by applying Diophantine approximation and Coppersmith's lattice-based technique. For instance, the study demonstrates that if RSA public exponents $ e_i $ and moduli $ N_i $ adhere to $ e_i r - (N_i - p_i - q_i + u_i) s_i = t_i $, where $ r, s_i, u_i $, and $ t_i $ are small integers, then all $ N_i $ can be factorized simultaneously. Additionally, another vulnerability arises when RSA parameters satisfy $ e_i r_i - s(N_i - p_i - q_i + u_i) = t_i $, enabling concurrent factorization with small integers $ s, r_i, u_i $, and $ t_i $. This research expands the understanding of RSA security by identifying specific conditions under which RSA public-key pairs can be compromised. These findings are relevant to the broader field of cryptography and the ongoing efforts to secure communication systems against sophisticated adversaries.</p>