Articles tagged with Partial Differential Equations
Researchers developed a new framework, 'Mollifier Layers,' to tackle challenging inverse PDEs. This advance could benefit fields such as genetics and weather forecasting by inferring hidden forces that produce observable patterns.
Scientists from Tokyo Metropolitan University have re-engineered the Lattice-Boltzmann Method to store certain data, reducing memory usage and overcoming a key bottleneck. The new algorithm achieves significant accuracy and stability in simulations of fluids and heat.
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 from the University of Utah have developed an 'optical neural engine' that encodes partial differential equations in light and feeds them into a device to accelerate machine learning. The optical approach accelerates the process and requires less energy compared to electronic methods.
The new AI framework, DIMON, solves ubiquitous math problems known as partial differential equations in nearly all scientific and engineering research. It enables faster prediction of solutions for complex engineering designs, such as crash testing, orthopedics research, and bridge stress resistance.
The Polymathic AI team has released two massive datasets for training artificial intelligence models to find and exploit transferable knowledge between seemingly disparate fields. The datasets include data from dozens of sources, covering astrophysics, biology, acoustics, chemistry, fluid dynamics, and more.
The project aims to develop methods that fuse physics and data for decision making in the presence of uncertainty. The research will benefit scientists working in various fields, including numerical analysis, optimization, structural engineering, and bioengineering.
Researchers at Newcastle University developed a novel approach using electromagnetic waves to solve partial differential equations, specifically the Helmholtz wave equation. The innovative structure, known as a metatronic network, effectively behaves like a grid of T-circuits and allows for control over PDE parameters.
A team of researchers at Pusan National University developed a pricing formula for perpetual American strangle options (PASOs) using a stochastic volatility model. The formula is accurate and provides a better understanding of the risks and returns associated with PASOs, especially in low-volatility environments.
A new mathematical proof developed by Dr. Markus Tempelmayr and colleagues provides a method to solve certain classes of stochastic partial differential equations. This approach allows for the solution of complicated equations by combining solutions of simpler ones, offering a flexible tool for researchers.
Dr. Harbir Antil is leading a project to create efficient algorithms for solving optimization problems with partial differential equations (PDEs), which will be applied in various fields such as dynamics and fluid mechanics.
A mathematical breakthrough provides new insights into typhoon dynamics, enabling more accurate predictions and advancements in weather forecasting. The study confirms the stability of specific vortex structures, which can be encountered in real-world fluid flows.
Researchers from University of Cambridge and Cornell University have developed a method to build machine learning models that can understand complex equations using far less training data. This breakthrough enables the construction of more time- and cost-efficient models for physics, engineering, and climate modeling applications.
Researchers investigated space B's behavior, proving no blowing up occurs under certain conditions. This achievement provides mathematical proof for one of the previously expected similarities between A-side and B-side.
Researchers have proved that a long-standing game theory dilemma does not exist in the wall pursuit game, introducing a new method of analysis that proves there is always a deterministic solution. This discovery opens doors to resolving other similar challenges and enables better reasoning about autonomous systems.
Researchers create new 'roadmap' for turbulence by analyzing weak turbulent flow between two independently rotating cylinders. They discover that turbulence follows a predictable pattern of recurrent solutions, which explain the emergence of coherent structures in turbulent flows.
Researchers have found a fundamental connection between two basic integrable hierarchies of solitonic type, KdV and BKP, revealing surprising relationships between these equations. The discovery makes Schur Q-functions a natural basis for expansion of KdV tau-functions.
Researchers at George Washington University have created a nanophotonic analog processor capable of solving partial differential equations. The processor can process arbitrary inputs at the speed of light and is integrated at chip-scale.
A researcher from Ural Federal University developed a new approach to solving optimal control problems for groups of objects. By applying the concept of dynamic stability, he created partial differential equations that predict the behavior of multiple agents in conflict situations.
A mathematician from RUDN University developed a stable difference scheme to solve inverse problems in elliptic-telegraph and differential equations. The scheme was tested both analytically and numerically, demonstrating absolute stability and independence from calculation step size.
Researchers developed mathematical models to study microswimmers in clean and surfactant-covered viscous drops, revealing significant alterations in behavior due to the presence of surfactant. These models may aid in designing artificial microswimmers for targeted drug delivery, micro-surgery, and other applications.
Mahamadi Warma will study optimization problems and nonlocal transmission issues in fractional partial differential equations. Funding started in September 2020 and ended in May 2021.
The four newest 2019 Balzan Prize winners were announced today in Milan for their groundbreaking contributions to film studies, Islamic studies, theory of partial differential equations, and pathophysiology of respiration. The winners will receive a prize of CHF 750,000 each, with half going towards research projects.
Alessio Figalli, a CNRS researcher, has been awarded the 2018 Fields Medal for his groundbreaking contributions to calculus of variations, optimal control, and partial differential equations. His work focuses on optimal transport theory, which has far-reaching implications in fields such as economics, geometry, and probability.
Alessio Figalli, a mathematician at ETH Zurich, has been awarded the Fields Medal for solving the Monge-Ampere equation, a famous partial differential equation with applications in urban planning, imaging, and meteorology. He has also made significant contributions to optimal transport and its connections to probability.
Alessio Figalli, an ERC grantee, wins the 2018 Fields Medal for his work on Partial Differential Equations and Calculus of Variations. His research on optimal transport theory has deep connections with fundamental problems in the field.
Researchers have developed a memory-processing unit using memristors, which can perform numerical calculations in parallel, reducing the need for manual multiplication and summation. This innovation has potential applications in machine learning, artificial intelligence, and simulations for weather forecasting.
Researchers found a single compressed stent produces a denser mesh than two overlapping stents, covering at least half of the aneurysm opening. The technique is more effective for large necked saccular aneurysms.
Andras Vasy's prize-winning paper resolves a 35-year-old conundrum in geometric scattering theory, developing a systematic framework for analyzing certain partial differential equations. The paper has had a major impact and stimulated subsequent research, including Vasy's own work.
Andrew J. Majda has made groundbreaking contributions to partial differential equations, merging asymptotic methods, numerical methods, and rigorous analysis. His work has had a significant impact in science and engineering, particularly in the study of multidimensional shock fronts and their stability.
Researchers translate microscopic concepts to study polar sea ice, capturing dynamic forces with a tractable equation. The new approach opens up climate science to nonequilibrium statistical mechanics methods, solving the long-standing challenge of measuring sea ice volume.
Louis Nirenberg, a NYU mathematician, and John Nash, a Princeton professor, have been awarded the Abel Prize for their work on nonlinear partial differential equations. Their contributions significantly impact geometric analysis, with far-reaching consequences felt more strongly today than ever before.
A new PDE model computes the value of a defined pension plan, including the option for early retirement. The authors provide mathematical analysis and numerical methods to solve the problem, allowing users to identify optimal retirement dates.
Researchers Hu et al. developed a new detonation model named the least-action detonation model (LADM) that takes into account complex movement and transport effects, differing from the classical ZND model. The LADM model predicts detonation product particles to be in a stationary state, which has been observed in experiments.
Mathematicians from the University of Pennsylvania have found solutions to the 140-year-old Boltzmann equation, a 7-dimensional equation that predicts gas molecule behavior. The solution provides new insights into gaseous collisions and confirms the predictions made by James Clerk Maxwell and Ludwig Boltzmann.
Max Gunzburger, a FSU professor, will receive the Reid Prize for his contributions to control of distributed parameter systems and computational mathematics. He will also deliver the Reid Prize Lecture on July 9, showcasing his research interests in various fields including geophysical flows and partial differential equations.
David I. Gottlieb, a Brown University professor and expert in spectral and high-order accurate numerical methods, will be honored as the John von Neumann Lecturer at the SIAM Annual Meeting. He is recognized for his work on partial differential equations and their applications to science and engineering.
Researchers found that smaller spatial resolutions are necessary for accurate modeling of soil water dynamics, especially at large scales. The critical limit for grid resolution can be estimated using soil water retention characteristics, and is typically on the order of decimeters or millimeters.
Drs. Stefano Bianchini and Alberto Bressan's paper on nonlinear hyperbolic systems has solved a 50-year-old problem, proving the existence and uniqueness of solutions as viscosity tends to zero. Their work has far-reaching implications for various physical phenomena, including fluid dynamics and astrophysics.
The article describes mathematical techniques used to assist cranio-maxillofacial surgeons in predicting surgical outcomes. The techniques involve modeling and solving partial differential equations to create a virtual lab for testing operative strategies.
Andrei Okounkov, Terence Tao and Wendelin Werner are honored with the Fields Medal for their work in probability, representation theory and algebraic geometry. Their contributions have brought new insights into problems in physics and mathematics.
Dr. Peter D. Lax received the 2006 Distinguished Service to Applied Mathematics prize for his outstanding leadership and contributions to applied mathematics. He is recognized for his services to the mathematical community, including government service and advisory roles in high-performance computing.
Golse and Saint-Raymond received the prize for their paper connecting weak solutions of the Boltzmann equation to Leray solutions of the incompressible Navier-Stokes equation. Their research focuses on mathematical physics problems, including kinetic equations and fluid dynamics.
Carnegie Mellon University's Irene Fonseca is a renowned mathematician who has made significant contributions to applied and computational mathematics. She has initiated programs to attract young researchers and serves on several major institute boards, inspiring the women's mathematics community.
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.