Artificial potential function

Rimon, E., Koditschek, D. (1992). Exact robot navigation using artificial potential functions. 

Rimon, E., Koditschek, D. (1992). Exact robot navigation using artificial potential functions. IEEE Transactions on Robotics and Automation, 8(5), 501-518. doi 10.1109/70.163777... 

Umbrella sampling is aimed at overcoming the sampling problem by modifying the potential function so that different favorable states separated by energetic barriers are sufficiently sampled. An artificial umbrella potential is introduced ... 

KNN)13 14 and potential function methods (PFMs).15,16 Modeling methods establish volumes in the pattern space with different bounds for each class. The bounds can be based on correlation coefficients, distances (e.g. the Euclidian distance in the Pattern Recognition by Independent Multicategory Analysis methods [PRIMA]17 or the Mahalanobis distance in the Unequal [UNEQ] method18), the residual variance19,20 or supervised artificial neural networks (e.g. in the Multi-layer Perception21). 

The comparison of the Xj, thermodynamic data with the corresponding MXn x data also appears to suggest a viable method for making predictions from the dimensional model. In every case tested except the Xy species, the MX -i line lies close to the points for the Xj, polymers. We believe that the disparity In the Xy case Is probably due to the lack of enough MX5(g) data points (Fig. 1). Note In Table I that for every species tested except the MXg molecules the Oq values at 1000 K lie close to 20. Interestingly, If we artificially Increase the value for the MX5 from 17.9 to 20, the discrepancy between the two Xy points and the MX5 line Is reduced considerably (Fig. 5). Ultimately we plan to numerically evaluate the configuration Integral with various potential functions for homonuclear clusters. 

The most popular classification methods are Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Regularized Discriminant Analysis (RDA), K th Nearest Neighbours (KNN), classification tree methods (such as CART), Soft-Independent Modeling of Class Analogy (SIMCA), potential function classifiers (PFC), Nearest Mean Classifier (NMC) and Weighted Nearest Mean Classifier (WNMC). Moreover, several classification methods can be found among the artificial neural networks. 

A method which attempts to take into account the effects of the form (14b) via brute-force diagonalization is the "complex absorption potential" (CAP) method [193]. In essence, in this method, the complex quantity K re ) of Eq. (14b) is replaced by an artificial complex function, such as /jSr , acting mainly in the outer region of space (fi is an adjustable parameter). The papers [193] also discuss the connection between the CAP and the ECS methods, the essence of which is in harmony with that ofEq. (14). 

It can be shown that the algebraic linkage of state functions provides a definition of other state functions. Thus, the three state functions energy E, pressure p, and volume V yield a new state function H, known as enthalpy H=E+p-V. Many other state functions can be defined in this mannen A few of such artificial state functions besides enthalpy have proven their significance in thermodynamics. These functions, also known as thermodynamic potenticd Junctions or thermodynamic potentials, are discussed in Section 3.1.2. It is noteworthy that these new definitions... 

The application of classical Molecular Dynamics to zeolites, as in other systems, has been originally limited to problems which do not involve chemical reactions,i.e., structure analysis or diffusion of host molecules in pores ". A method combining Quantum Mechanics and Molecular Mechanics, similar to the (QM/MD) method (called Interatomic Potential Function Approach) has been developed with new procedures that eliminate the artificial... 

The utility of the approach was much enhanced through the development of umbrella sampling by Valleau and co-wor-kers. An artificial biasing function ( ) can be added to the potential energy to extend the range of sampling of e.g., by flattening the problematic barriers. The true distribution can subsequently be recovered from the biased one, g K), via... 

Cao, Huang, and Zhou (2006) propose a methodology based on artificial potential fields forpath planning in dynamic environments where the target and obstacles are moving. Here, a force fimction and the relative threat coefficient function are defined. 

In Section 2.1. we examined solution to the Schrodinger equation in free space and in a periodic potential and foimd families of wave functions having a simple, quadratic relationship between wave energy and momentum over wide ranges of energy values. Because there are a very large number of such states in a solid, it is normally impossible to distinguish one individual state from another. In this Section, we will examine, briefly, the impact of artificial potential structures on the wave solutions. For a complete discussion of such effects, the reader is referred to books on quantum mechanics. 

Strictly speaking, the concept of itself makes no sense for a potential like the Eckart one, unless one artificially introduces Zo as the partition function of a bound initial state, which is not described by this potential. That is to say, it is reasonable to consider the combination kZo, not k alone. 

---