Concept
Cartesian coordinate system
Related publications (96)
Wandering principal optical axes in van der Waals triclinic materials
Nature is abundant in material platforms with anisotropic permittivities arising from symmetry reduction that feature a variety of extraordinary optical effects. Principal optical axes are essential characteristics for these effects that define light-matte ...
Nature Portfolio2024The first Grushin eigenvalue on cartesian product domains
Joachim Stubbe, Luigi Provenzano, Paolo Luzzini
In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...
WALTER DE GRUYTER GMBH2023Learning Linearized Degradation of Health Indicators using Deep Koopman Operator Approach
With the current trend of increasing complexity of industrial systems, the construction and monitoring of health indicators becomes even more challenging. Given that health indicators are commonly employed to predict the end of life, a crucial criterion fo ...
Research Publishing2023A geometric optimal control approach for imitation and generalization of manipulation skills
Sylvain Calinon, Amirreza Razmjoo Fard, Jie Zhao
Daily manipulation tasks are characterized by regular features associated with the task structure, which can be described by multiple geometric primitives related to actions and object shapes. Only using Cartesian coordinate systems cannot fully represent ...
ELSEVIER2023Modelisation of fiber reinforced DEAs
The aim of this "Face Reconstruction" project is to enable people with paralysis in one half of their face to recover facial expressions. To do this, we’ll replace the paralyzed muscle with an DEA which we’ll connect to the nerve on the other side of the f ...
2023High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics
This paper develops high-order accurate entropy stable (ES) adaptive moving mesh finite difference schemes for the two- and three-dimensional special relativistic hydrodynamic (RHD) and magnetohydrodynamic (RMHD) equations, which is the high-order accurate ...
ACADEMIC PRESS INC ELSEVIER SCIENCE2022Local invertibility and sensitivity of atomic structure-feature mappings
Michele Ceriotti, Sergey Pozdnyakov
Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...
2021Demonstrator Surface For Machine Learning Algorithm
In the field of haptic feedback, LAI is working on a way of localizing impact vibrations through machine learning algorithms. In this semester project, the goal is to extend a one-dimensional system into a two-dimensional system with a demonstrator surface ...
2021Physics-Inspired Structural Representations for Molecules and Materials
Michele Ceriotti, Félix Benedito Clément Musil, Andrea Grisafi
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atom ...
AMER CHEMICAL SOC2021Charge-based modeling of ultra narrow junctionless cylindrical nanowire FETs
This brief proposes an analytical approach to model the DC electrical behavior of extremely narrow cylindrical junctionless nanowire field-effect transistors (JL-NW-FETs). The model includes explicit expressions, taking into account the first-order perturb ...
PERGAMON-ELSEVIER SCIENCE LTD2021