Articles tagged with Nonlinear Equations
Comprehensive exploration of living organisms, biological systems, and life processes across all scales from molecules to ecosystems. Encompasses cutting-edge research in biology, genetics, molecular biology, ecology, biochemistry, microbiology, botany, zoology, evolutionary biology, genomics, and biotechnology. Investigates cellular mechanisms, organism development, genetic inheritance, biodiversity conservation, metabolic processes, protein synthesis, DNA sequencing, CRISPR gene editing, stem cell research, and the fundamental principles governing all forms of life on Earth.
Comprehensive medical research, clinical studies, and healthcare sciences focused on disease prevention, diagnosis, and treatment. Encompasses clinical medicine, public health, pharmacology, epidemiology, medical specialties, disease mechanisms, therapeutic interventions, healthcare innovation, precision medicine, telemedicine, medical devices, drug development, clinical trials, patient care, mental health, nutrition science, health policy, and the application of medical science to improve human health, wellbeing, and quality of life across diverse populations.
Comprehensive investigation of human society, behavior, relationships, and social structures through systematic research and analysis. Encompasses psychology, sociology, anthropology, economics, political science, linguistics, education, demography, communications, and social research methodologies. Examines human cognition, social interactions, cultural phenomena, economic systems, political institutions, language and communication, educational processes, population dynamics, and the complex social, cultural, economic, and political forces shaping human societies, communities, and civilizations throughout history and across the contemporary world.
Fundamental study of the non-living natural world, matter, energy, and physical phenomena governing the universe. Encompasses physics, chemistry, earth sciences, atmospheric sciences, oceanography, materials science, and the investigation of physical laws, chemical reactions, geological processes, climate systems, and planetary dynamics. Explores everything from subatomic particles and quantum mechanics to planetary systems and cosmic phenomena, including energy transformations, molecular interactions, elemental properties, weather patterns, tectonic activity, and the fundamental forces and principles underlying the physical nature of reality.
Practical application of scientific knowledge and engineering principles to solve real-world problems and develop innovative technologies. Encompasses all engineering disciplines, technology development, computer science, artificial intelligence, environmental sciences, agriculture, materials applications, energy systems, and industrial innovation. Bridges theoretical research with tangible solutions for infrastructure, manufacturing, computing, communications, transportation, construction, sustainable development, and emerging technologies that advance human capabilities, improve quality of life, and address societal challenges through scientific innovation and technological progress.
Study of the practice, culture, infrastructure, and social dimensions of science itself. Addresses how science is conducted, organized, communicated, and integrated into society. Encompasses research funding mechanisms, scientific publishing systems, peer review processes, academic ethics, science policy, research institutions, scientific collaboration networks, science education, career development, research programs, scientific methods, science communication, and the sociology of scientific discovery. Examines the human, institutional, and cultural aspects of scientific enterprise, knowledge production, and the translation of research into societal benefit.
Comprehensive study of the universe beyond Earth, encompassing celestial objects, cosmic phenomena, and space exploration. Includes astronomy, astrophysics, planetary science, cosmology, space physics, astrobiology, and space technology. Investigates stars, galaxies, planets, moons, asteroids, comets, black holes, nebulae, exoplanets, dark matter, dark energy, cosmic microwave background, stellar evolution, planetary formation, space weather, solar system dynamics, the search for extraterrestrial life, and humanity's efforts to explore, understand, and unlock the mysteries of the cosmos through observation, theory, and space missions.
Comprehensive examination of tools, techniques, methodologies, and approaches used across scientific disciplines to conduct research, collect data, and analyze results. Encompasses experimental procedures, analytical methods, measurement techniques, instrumentation, imaging technologies, spectroscopic methods, laboratory protocols, observational studies, statistical analysis, computational methods, data visualization, quality control, and methodological innovations. Addresses the practical techniques and theoretical frameworks enabling scientists to investigate phenomena, test hypotheses, gather evidence, ensure reproducibility, and generate reliable knowledge through systematic, rigorous investigation across all areas of scientific inquiry.
Study of abstract structures, patterns, quantities, relationships, and logical reasoning through pure and applied mathematical disciplines. Encompasses algebra, calculus, geometry, topology, number theory, analysis, discrete mathematics, mathematical logic, set theory, probability, statistics, and computational mathematics. Investigates mathematical structures, theorems, proofs, algorithms, functions, equations, and the rigorous logical frameworks underlying quantitative reasoning. Provides the foundational language and tools for all scientific fields, enabling precise description of natural phenomena, modeling of complex systems, and the development of technologies across physics, engineering, computer science, economics, and all quantitative sciences.
Researchers from OIST and universities provided a new proof for the BBL inequality using heat and diffusion equations, taking an unconventional approach. The study offers fresh insights on the concept, which has vast applications across many fields, including computer science, medical imaging, and resource distribution.
Physicists Björn Birnir and Luiza Angheluta develop a new mathematical model to characterize Lagrangian turbulence, which captures its complex phenomena. The study reveals the presence of a Lagrangian scaling regime and connects three scaling regimes as the turbulent flow evolves.
Researchers developed a new equation to predict seismic wave propagation in magma containing crystals and bubbles, revealing how crystal content influences wave velocity and waveform properties. The analysis also showed that bubble content affects attenuation effects, with discernible differences emerging between models.
A team of researchers from Osaka University has demonstrated that human tissue can be used to solve complex equations and process information, outperforming traditional computing methods. This breakthrough uses the concept of reservoir computing, where data is input into a complex 'reservoir' that encodes rich patterns.
Dr. Wencai Liu, an associate professor at Texas A&M University, has been selected for the 2024 IUPAP Early Career Scientist Prize in Mathematical Physics. His research focuses on linear and nonlinear Schrodinger equations, contributing to our understanding of quantum mechanics and its applications.
Researchers create an analog system that can learn complex tasks like XOR relationships and nonlinear regression, using local learning rules without centralized processor. The system is fast, low-power, and scalable, offering a unique opportunity for studying emergent learning.
Researchers optimized triticale germination conditions using nonlinear programming to maximize fat content, a crucial parameter in animal feed production. The study identified optimal temperature and moisture levels, resulting in a fat content of 2.83%, improving the nutritional value of triticale grain.
A team of researchers from Korea investigated the dynamics of the p-Laplacian AC equation, finding that solutions maintain three criteria: phase separation, boundedness, and energy decay properties. They also identified an advantage of p-AC equation over classical Laplacian in adjusting interface sharpness.
A team of RUDN University physicists discovered solutions to semi-classical models describing particle-like waves and calculated the ratio between gravitational interaction and charge interactions. The results suggest that gravity may play a significant role in the formation of elementary particles, particularly at the Planck scale.
Professor Dietmar Gallistl from Friedrich Schiller University Jena aims to develop new algorithms and discretization techniques for fully nonlinear equations, with potential applications in financial mathematics and geometry. The project will focus on minimizing computational effort while achieving accurate approximations.
The proposed SA-RBF-TSE algorithm corrects TDOA measurements using a Self-Adaptive RBF neural network and improves position estimation. It adapts the number of RBF nodes and center vector based on error distribution, resulting in high accuracy and reliability compared to other algorithms.
Mathematicians Gino Biondini and Dionyssios Mantzavinos develop a new mathematical model describing wave patterns with small irregularities. Their research shows that many disturbances evolve into single-class wave forms, answering a question scientists have been trying to answer for 50 years.
Researchers have made significant progress in identifying growing localised patterns as early indicators of freak waves. By resolving the nonlinear Schrödinger equation, they can extract pertinent information from localised disturbances' characteristics, shedding light on complex dynamics.
The mathematician's work has led to a better understanding of how fiber optics can be made more stable and robust. His research involves marrying mathematics and physics to study the behavior of solitary waves in various structures, including optical waveguide arrays and granular crystals.
A renowned NJIT mathematician has been awarded the prestigious Steele Prize for his groundbreaking work on the Korteweg-de-Vries equation, a problem that had stumped mathematicians for decades. The award is a testament to Miura's innovative approach and contributions to the field of mathematics.