KAM tori for higher dimensional beam equation with a fixed constant potential

2009 ◽  
Vol 52 (9) ◽  
pp. 2007-2018 ◽  
Author(s):  
XinDong Xu ◽  
JianSheng Geng
Keyword(s):  
Beam Equation ◽  
Kam Tori ◽  
Higher Dimensional ◽  
Constant Potential ◽  
Fixed Constant

KAM Tori for Higher Dimensional Quintic Beam Equation

2018 ◽  
Vol 31 (1) ◽  
pp. 305-319 ◽  
Author(s):  
Chuanfang Ge ◽  
Jiansheng Geng
Keyword(s):  
Beam Equation ◽  
Kam Tori ◽  
Higher Dimensional

scholarly journals SHORTEST PATH QUERIES IN RECTILINEAR WORLDS

1992 ◽  
Vol 02 (03) ◽  
pp. 287-309 ◽  
Author(s):  
MARK DE BERG ◽  
MARC VAN KREVELD ◽  
BENGT J. NILSSON ◽  
MARK OVERMARS
Keyword(s):  
Data Structure ◽  
Shortest Path ◽  
Simple Solution ◽  
Single Shot ◽  
Fixed Target ◽  
Higher Dimensional ◽  
Axis Parallel ◽  
Fixed Constant ◽  
Path Queries

In this paper, a data structure is given for two and higher dimensional shortest path queries. For a set of n axis-parallel rectangles in the plane, or boxes in d-space, and a fixed target, it is possible with this structure to find a shortest rectilinear path avoiding all rectangles or boxes from any point to this target. Alternatively, it is possible to find the length of the path. The metric considered is a generalization of the L1-metric and the link metric, where the length of a path is its L1-length plus some (fixed) constant times the number of turns on the path. The data structure has size O((n log n)d−1), and a query takes O( log d−1 n) time (plus the output size if the path must be reported). As a byproduct, a relatively simple solution to the single shot problem is obtained; the shortest path between two given points can be computed in time O(nd log n) for d≥3, and in time O(n2) in the plane.

KAM tori for higher dimensional beam equations with constant potentials*

Nonlinearity ◽  
2006 ◽  
Vol 19 (10) ◽  
pp. 2405-2423 ◽  
Author(s):  
Jiansheng Geng ◽  
Jiangong You
Keyword(s):  
Kam Tori ◽  
Higher Dimensional ◽  
Beam Equations

Reducible KAM tori for higher dimensional wave equations under nonlocal and forced perturbation

2020 ◽  
Vol 61 (6) ◽  
pp. 062702
Author(s):  
Yin Chen ◽  
Jiansheng Geng ◽  
Shuaishuai Xue
Keyword(s):  
Wave Equations ◽  
Kam Tori ◽  
Higher Dimensional ◽  
Dimensional Wave

Microstructure simulation of early paper forming using immersed boundary methods

TAPPI Journal ◽  
2011 ◽  
Vol 11 (11) ◽  
pp. 23-30 ◽  
Author(s):  
ANDREAS MARK ◽  
ERIK SVENNING ◽  
ROBERT RUNDQVIST ◽  
FREDRIK EDELVIK ◽  
ERIK GLATT ◽  
...  
Keyword(s):  
Early Paper ◽  
Contact Model ◽  
Fiber Suspension ◽  
Beam Equation ◽  
Immersed Boundary ◽  
Paper Machine ◽  
Immersed Boundary Methods ◽  
Element Discretization ◽  
Microstructure Simulation ◽  
Boundary Methods

Paper forming is the first step in the paper machine where a fiber suspension leaves the headbox and flows through a forming fabric. Complex physical phenomena occur as the paper forms, during which fibers, fillers, fines, and chemicals added to the suspension interact. Understanding this process is important for the development of improved paper products because the configuration of the fibers during this step greatly influences the final paper quality. Because the effective paper properties depend on the microstructure of the fiber web, a continuum model is inadequate to explain the process and the properties of each fiber need to be accounted for in simulations. This study describes a new framework for microstructure simulation of early paper forming. The simulation framework includes a Navier-Stokes solver and immersed boundary methods to resolve the flow around the fibers. The fibers were modeled with a finite element discretization of the Euler-Bernoulli beam equation in a co-rotational formulation. The contact model is based on a penalty method and includes friction and elastic and inelastic collisions. We validated the fiber model and the contact model against demanding test cases from the literature, with excellent results. The fluid-structure interaction in the model was examined by simulating an elastic beam oscillating in a cross flow. We also simulated early paper formation to demonstrate the potential of the proposed framework.

Spectroscopy-Based Mapping with Scanning Microwave Impedance Microscopy

2018 ◽  
Author(s):  
Peter De Wolf ◽  
Zhuangqun Huang ◽  
Bede Pittenger
Keyword(s):  
Single Point ◽  
Electrical Characterization ◽  
Principal Component ◽  
High Sensitivity ◽  
Data Cube ◽  
Nanometer Scale ◽  
Learning Approaches ◽  
Data Set ◽  
3D Data ◽  
Higher Dimensional

Abstract Methods are available to measure conductivity, charge, surface potential, carrier density, piezo-electric and other electrical properties with nanometer scale resolution. One of these methods, scanning microwave impedance microscopy (sMIM), has gained interest due to its capability to measure the full impedance (capacitance and resistive part) with high sensitivity and high spatial resolution. This paper introduces a novel data-cube approach that combines sMIM imaging and sMIM point spectroscopy, producing an integrated and complete 3D data set. This approach replaces the subjective approach of guessing locations of interest (for single point spectroscopy) with a big data approach resulting in higher dimensional data that can be sliced along any axis or plane and is conducive to principal component analysis or other machine learning approaches to data reduction. The data-cube approach is also applicable to other AFM-based electrical characterization modes.

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