Results 11 to 20 of about 22,566 (155)

Smooth Solutions to a Class of Mixed Type Monge-Ampere Equations

, 2012
We prove the existence of C^{\infty} local solutions to a class of mixed type Monge-Ampere equations in the plane. More precisely, the equation changes type to finite order across two smooth curves intersecting transversely at a point.
Han, Qing, Khuri, Marcus
core   +1 more source

Statistical mechanics approach to some problems in conformal geometry

, 2000
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical measure ...
Aubin, Aviles, Beckner, Billingsley, Branson, Branson, Branson, Caglioti, Caglioti, Campbell, Carlen, Chang, Chang, Chang, Chang, Chanillo, Chanillo, Chen, Chen, Cheng, Cheng, Chou, de Finetti, Diaconis, Dynkin, Eyink, Fröhlich, Han, Hewitt, Joyce, Kazdan, Kida, Kiessling, Kiessling, Kiessling, Kiessling, Lin, Liouville, Lundgren, Marchioro, McOwen, Messer, Michael K.-H. Kiessling, Montgomery, Montgomery, Moser, Moser, Ni, O'Neil, Onofri, Onsager, Osserman, Poincaré, Pointin, Ramsey, Saff, Sattinger, Struik, Trudinger   +58 more
core   +2 more sources

Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem

, 2007
We establish an extension of Liouville's classical representation theorem for solutions of the partial differential equation $\Delta u=4 e^{2u}$ and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps with ...
Kraus, Daniela, Roth, Oliver
core   +1 more source

Hard‐Magnetic Soft Millirobots in Underactuated Systems

Advanced Robotics Research, EarlyView.
This review provides a comprehensive overview of hard‐magnetic soft millirobots in underactuated systems. It examines key advances in structural design, physics‐informed modeling, and control strategies, while highlighting the interplay among these domains.
Qiong Wang, Zixuan Zhang, Bingyan Li, Junkai Wang, Hongcheng Gu   +4 more
wiley   +1 more source

Morphing of Geometric Composites via Residual Swelling

, 2015
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade.
Holmes, Douglas P., Nardinocchi, Paola, Pezzulla, Matteo, Shillig, Steven A.   +3 more
core   +1 more source

A State‐Adaptive Koopman Control Framework for Real‐Time Deformable Tool Manipulation in Robotic Environmental Swabbing

Advanced Robotics Research, EarlyView.
This work presents a state‐adaptive Koopman linear quadratic regulator framework for real‐time manipulation of a deformable swab tool in robotic environmental sampling. By combining Koopman linearization, tactile sensing, and centroid‐based force regulation, the system maintains stable contact forces and high coverage across flat and inclined surfaces.
Siavash Mahmoudi, Amirreza Davar, Dongyi Wang   +2 more
wiley   +1 more source

Design and Optimization of Full‐Stokes Hyperspectro‐Polarimetric Encoding Metasurfaces Based on Conditional Multi‐Task Deep Learning

Advanced Science, EarlyView.
A conditional multi‐task deep learning framework is developed for designing and optimizing Full‐Stokes Hyperspectro‐Polarimetric Encoding Metasurfaces (FHPEMs). This framework achieves joint spectro‐polarimetric learning and unified forward–inverse design.
Chenjie Gong, Haodong Shi, Qi Wang, Yingchao Li, Hongyu Sun, Jiayu Wang, Guanlin Li, Jian Zhang, Qiang Fu, Huilin Jiang   +9 more
wiley   +1 more source

What to Make and How to Make It: Combining Machine Learning and Statistical Learning to Design New Materials

Advanced Intelligent Discovery, EarlyView.
Combining machine learning and probabilistic statistical learning is a powerful way to discover and design new materials. A variety of machine learning approaches can be used to identify promising candidates for target applications, and causal inference can help identify potential ways to make them a reality.
Jonathan Y. C. Ting, Amanda S. Barnard
wiley   +1 more source

Deep Learning‐Assisted Design of Mechanical Metamaterials

Advanced Intelligent Discovery, EarlyView.
This review examines the role of data‐driven deep learning methodologies in advancing mechanical metamaterial design, focusing on the specific methodologies, applications, challenges, and outlooks of this field. Mechanical metamaterials (MMs), characterized by their extraordinary mechanical behaviors derived from architected microstructures, have ...
Zisheng Zong, Pu Wen, Zhiping Chai, Dunxuan Wu, Han Ding, Zhigang Wu   +5 more
wiley   +1 more source

Local solvability of degenerate Monge-Ampere equations and applications to geometry

Electronic Journal of Differential Equations, 2007
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally prescribed Gaussian curvature for surfaces in $mathbb{R}^{3}$, and the local
Marcus A. Khuri
doaj