Transforming frontiers: The next decade of differential equations and control processes

Advances in Differential Equations and Control Processes, Journal Year: 2025, Volume and Issue: 32(1), P. 2589 - 2589

Published: Jan. 22, 2025

Mathematics serves as the fundamental basis for innovation, propelling technological advancement. In forthcoming decade, convergence of differential equations and control processes is poised to redefine frontiers scientific exploration. The integration artificial intelligence machine learning with set inaugurate a new era problem-solving, enabling extraction latent physical insights accelerating solution discovery. Multi-scale modeling, its capacity span disparate domains, has potential resolve long-standing puzzles in fields such fluid mechanics nanoscience. Furthermore, fractal geometry holds promise novel perspectives understanding optimizing complex systems, ranging from urban landscapes turbulent flows. (AI) innovations play pivotal role development next-generation technologies, transform diverse sectors medicine, communication, autonomous systems. This paper explores these developments, highlighting their impacts emphasizing necessity interdisciplinary collaboration leverage full potential.

Language: Английский

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The old Babylonian algorithm: reborn with a bang and its application in non-linear vibration

Frontiers in Applied Mathematics and Statistics, Journal Year: 2025, Volume and Issue: 10

Published: Jan. 15, 2025

The Old Babylonian Algorithm, a remarkable mathematical gem from ancient Mesopotamia (around 1800-1600 BC), has long been subject of fascination for scholars. This algorithm not only represents the advanced intellectual capabilities Babylonians but also holds great relevance in modern times. It is particularly renowned its ingenious method approximating square roots [1].In recent research, an exciting transformation occurred. traditional Algorithm ingeniously modified to solve differential equations, breathing new life into this technique [1]. In paper, we aim reveal how revival led significant role within complex and captivating realm Non-linear Vibration theory, thereby bridging demonstrating timelessness concepts.Nonlinear vibration analysis presents several specific challenges. Strongly nonlinear oscillators, such as one considered study (in form shown equation ( 1)), are characterized by presence higher-order terms. These nonlinearities can lead dynamic behaviors that difficult analyze using methods [3][4][5]. For instance, homotopy perturbation method, while widely used, attempts convert original problem sequence linear subproblems through introduction parameter, yet it may still face difficulties accurately handling highly systems [2][3][4]. variational iteration another commonly employed approach, limitations dealing with intricacies vibrations [5]. He's frequency formulation, originating Chinese algorithm, offers relatively simple effective means treating demonstrated unique value field dynamics straightforward efficient nature [6,7,8]. However, proposed Ref. [1] provides novel perspective potentially more solution strongly oscillator comparison these methods. combines wisdom adaptations better suit context analysis.By exploring application vibration, hope contribute deeper understanding both heritage practical implications contemporary scientific research. research sheds light on historical significance paves way further advancements dynamics.We consider 35 0 u au bu + =(1)This distinguished existence high-order terms, where b constants. initial conditions set )0 uA = ) 00 u= , A amplitude.Traditionally, numerous have adopted address problems.The gained extensive application. endeavors sub-problems introducing parameter -used approach Moreover, formulation [6,7,8], which stems systems. characteristics [9][10][11][12][13].However, apply old suggested [1]:( 2 1 n nn bu uu   -(2)Where  weighting factor. viewpoint contrast methods.To understand derivation let's following step -bystep explanation.Suppose cos t  (3)where frequency. Utilizing obtain )u aA bA At - -(4)By setting 31 = Figure elaborate -depth between approximate exact diverse range values parameters b. vividly showcases performance scope domain. excellent agreement solutions effectively validates effectiveness algorithm. solid evidence theoretically sound practically applicable.( conclusion, emerged promising oscillators. Through combination adaptations, alternative compared techniques.The successful theoretical soundness applicability. solutions, presented study, compelling effectiveness.Looking ahead, findings future studies applications. MEMS (Micro-Electro-Mechanical Systems), could be enhance optimization behavior devices. By modeling analyzing miniature systems, possible improve their performance, reliability, lifespan.Furthermore, exploration algorithm's capabilities. Future investigations focus extending those time -varying or multiple degrees freedom. Additionally, there potential integrating other computational analytical tools, machine learning algorithms identification system optimization.Overall, resurgence promise advancing our ability handle opening up avenues innovation various engineering disciplines.13.

Language: Английский

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A variational principle of an electrohydrodynamic fluid

Modern Physics Letters A, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 24, 2025

Electrohydrodynamic fluids possess extensive applications, spanning from the formation of magnetic fields in planets and stars to oil recovery. In this paper, a variational principle for an electrohydrodynamic fluid is presented, formulated through semi-inverse method. The Ritz method utilized derive approximate solution. Furthermore, potential application optimal control problems constrained by explored.

Language: Английский

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Scrutinizing highly nonlinear oscillators using He’s frequency formula

Sound&Vibration, Journal Year: 2025, Volume and Issue: 59(2), P. 2358 - 2358

Published: March 5, 2025

Highly nonlinear oscillators are examined in their capacity to simulate intricate systems engineering, physics, biology, and finance, as well diverse behavior, rendering them essential the development of resilient technological advancement. Therefore, fundamental purpose current work is analyze He’s frequency formula (HFF) get theoretical explanations many types very oscillators. We investigate, both analytical computational, relationship between elastic forces solution a specific oscillator. This oscillator exhibits significant damping. It assumed that required quantity trigonometric functions matches strong ordinary differential equation (ODE) explains motion. The novel approach definitely takes less processing time complex than traditional perturbation methods were widely used this field. method, which essentially giving linearization ODE, known non-perturbative (NPA). procedure produces new similar linear much harmonic scenario. Readers will benefit from an in-depth account NPA. findings validated by numerical examination using Mathematical Software (MS). (NS) tests yielded fairly findings. well-established principle classical trust on Taylor expansions approximate restoring forces, therefore simplifying situation. When NPA used, vulnerability does not present. Furthermore, enables thorough assessment problems’ stability analysis, was possible prior conventional methodology. Consequently, more appropriate responsibility tool for examining approximations extremely MS.

Language: Английский

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A fast and accurate estimation of amperometric current response in reaction kinetics

Journal of Electroanalytical Chemistry, Journal Year: 2024, Volume and Issue: unknown, P. 118884 - 118884

Published: Dec. 1, 2024

Language: Английский

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Application of MEMS technology in anti-electromagnetic radiation maternity clothes: state of the art and future perspectives

Frontiers in Physics, Journal Year: 2025, Volume and Issue: 12

Published: Jan. 14, 2025

This review provides a comprehensive analysis of the application Micro-Electro-Mechanical Systems (MEMS) technology in anti-electromagnetic radiation maternity wear. The commences with an elaboration electromagnetic shielding principles traditional materials and principle radiation. Subsequently, role MEMS clothing is detailed, including real-time monitoring via sensors, enhancement fabric through electrospinning material deposition, realization intelligent functions such as micro-actuators communication modules. Furthermore, considers optimization performance, taking into account factors shielding, air permeability comfort. article addresses challenges ensuring comfort power supply. concludes by emphasizing potential protecting pregnant women fetuses proposes future research directions, in-depth exploration working principles, technical specifications, performance characteristics key components (sensors micro-actuators), well on combination existing anti-radiation technologies, metal fiber fabrics nanomaterials, has to yield significant synergistic effects. optimization, durability washing stability clothes, essential. Additionally, emerging bubble could lead innovative applications this field.

Language: Английский

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An efficient space–time two-grid difference approach to symmetric regularized long waves: Enhanced efficiency and accuracy

Alexandria Engineering Journal, Journal Year: 2025, Volume and Issue: 121, P. 53 - 65

Published: Feb. 25, 2025

Language: Английский

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Introducing Monotone Enriched Nonexpansive Mappings for Fixed Point Approximation in Ordered CAT(0) Spaces

Computation, Journal Year: 2025, Volume and Issue: 13(4), P. 81 - 81

Published: March 21, 2025

The aim of this paper is twofold: introducing the concept monotone enriched nonexpansive mappings and a faster iterative process. Our examples illustrate novelty our newly introduced concepts. We investigate estimation fixed points for such first time within an ordered CAT(0) space. It done by proving some strong Δ-convergence theorems. Additionally, numerical experiments are included to demonstrate validity theoretical results establish superiority convergence behavior As application, we use concepts find solution integral equation. outcomes study expand upon enhance certain established findings in current body literature.

Language: Английский

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Modified Lagrange Interpolating Polynomial (MLIP) Method: A Straightforward Procedure to Improve Function Approximation

AppliedMath, Journal Year: 2025, Volume and Issue: 5(2), P. 34 - 34

Published: March 27, 2025

This work presents the modified Lagrange interpolating polynomial (MLIP) method, which aims to provide a straightforward procedure for deriving accurate analytical approximations of given function. The method introduces an exponential function with several parameters multiplies one terms polynomial. These will adjust their values ensure that proposed approximation passes through points target function, while also adopting correct its derivative at points, showing versatility. polynomials (LIPs) present problem introducing oscillatory and are, therefore, expected poor We see relevant contributions MLIPs is contain fewer compared those obtained by LIPs when both pass same be represented; consequently, better MLIP are expected. A comparison results from other methods reported in literature highlights method’s potential as useful tool obtaining set points. It this contributes break paradigm effective modification known has lengthy complex.

Language: Английский

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Generating Mandelbrot and Julia sets using PV iterative technique

Chaos Solitons & Fractals, Journal Year: 2025, Volume and Issue: 196, P. 116346 - 116346

Published: April 4, 2025

Language: Английский

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