A Novel Method to Reduce the Fluctuation of Mesh Stiffness by High-order Phasing Gear Sets: Theoretical Analysis and Experiment

2022 ◽  
pp. 116752
Author(s):  
Xiangqian Chen ◽  
Jing Wei ◽  
Jiaxiong Zhang ◽  
Chunpeng Zhang ◽  
Chang-lu Wang ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
High Order ◽  
Mesh Stiffness ◽  
Novel Method

scholarly journals Phyllotaxis instability – exploring the depths of first available space

2011 ◽  
Vol 80 (4) ◽  
pp. 279-284 ◽  
Author(s):  
Marcin Szpak ◽  
Beata Zagórska-Marek
Keyword(s):  
Theoretical Analysis ◽  
Computer Simulations ◽  
Dominant Role ◽  
High Order ◽  
The Other ◽  
Phyllotactic Pattern ◽  
Low Order

The theoretical analysis of the consequences of the phyllotactic pattern being propagated according to the first available space rule has revealed that all monojugate patterns, with the exception of the main Fibonacci pattern, should become developmentally unstable in their low expressions. This fact explains why the main Fibonacci pattern plays the dominant role among other patterns of spiral phyllotaxis. The probability that the pattern becomes unstable varies for different patterns, which likely makes them more or less frequent, and thus easier or more difficult to encounter in nature. The unstable pattern inevitably transforms into another, as the computer simulations show. Theoretically predicted instability of low order phyllotaxis may be treated as one of the causes of natural ontogenetic transitions, occurring in plants. This, however, still does not explain why in nature some patterns with high order of phyllotaxis also change, quite readily one into the other, in shoot apical meristem’s ontogeny.

A Novel Method of Diameter Measurement by Laser Scanning Based on Flat-Crystal

2011 ◽  
Vol 467-469 ◽  
pp. 1604-1609 ◽  
Author(s):  
Yi Wang ◽  
Yong Jie Ren ◽  
Chang Jie Liu ◽  
S.H. Ye
Keyword(s):  
Measurement Error ◽  
Theoretical Analysis ◽  
High Precision ◽  
Laser Scanning ◽  
Propagation Direction ◽  
Diameter Measurement ◽  
Measurement Device ◽  
The Core ◽  
Scanning Beam ◽  
Novel Method

A novel diameter measurement device by laser scanning of which a flat-crystal was used as the core scanning part was designed. The device can generate high parallel scanning beam by means of the property that a beam won’t change its propagation direction after transmitting a flat-crystal. The influences on measurement error and range by using flat-crystal were analyzed in details. Theoretical analysis showed that the method was easy to realize and achieve high precision.

scholarly journals Multi-fidelity Gaussian Process Bandit Optimisation

2019 ◽  
Vol 66 ◽  
pp. 151-196 ◽  
Author(s):  
Kirthevasan Kandasamy ◽  
Gautam Dasarathy ◽  
Junier Oliva ◽  
Jeff Schneider ◽  
Barnabás Póczos
Keyword(s):  
Computer Simulation ◽  
Theoretical Analysis ◽  
Gaussian Process ◽  
Target Function ◽  
Black Box ◽  
Confidence Bound ◽  
Bandit Problem ◽  
Single Function ◽  
Novel Method ◽  
Upper Confidence Bound

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

A combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg–de Vries (KdV) equation

2021 ◽  
Author(s):  
Murat Polat ◽  
Ömer Oruç
Keyword(s):  
Conservation Laws ◽  
Lie Group ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equation ◽  
High Order ◽  
Basis Functions ◽  
Numerical Integrator ◽  
The Kdv Equation ◽  
De Vries ◽  
Novel Method

In this work, we develop a novel method to obtain numerical solution of well-known Korteweg–de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie group methods. This paper is a first attempt to combine DBFs and high order geometric numerical integrator for solving such a nonlinear partial differential equation (PDE) which preserves conservation laws. To demonstrate the performance of the proposed method we consider five test problems. We reckon [Formula: see text], [Formula: see text] and root mean square (RMS) errors and compare them with other results available in the literature. Besides the errors, we also monitor conservation laws of the KDV equation and we show that the method in this paper produces accurate results and preserves the conservation laws quite good. Numerical outcomes show that the present novel method is efficient and reliable for PDEs.

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