A functionally flexible interatomic energy function based on classical potentials

Background: The penetration level of a wind farm with transient stability constraint and static security constraint has been a key problem in wind power applications. Objective: The study explores maximum penetration level problem of wind considering transient stability constraint and uncertainty of wind power out, based on credibility theory and corrected energy function method. Methods: According to the corrected energy function, the transient stability constraint of the power grid is transferred to the penetration level problem of a wind farm. Wind speed forecast error is handled as a fuzzy variable to express the uncertainty of wind farm output. Then this paper builds a fuzzy chance-constrained model to calculate wind farm penetration level. To avoid inefficient fuzzy simulation, the model is simplified to a mixed integer linear programming model. Results: The results validate the proposed model and investigate the influence of grid-connection node, wind turbine characteristic, fuzzy reliability index, and transient stability index on wind farm penetration level. Conclusion: The result shows that the model proposed in this study can consider the uncertainty of wind power out and establish a quantitative transient stability constraint to determine the wind farm penetration level with a certain fuzzy confidence level.

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A canonical ensemble derivation of the McMillan-Mayer solution theory

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19832888 ◽

1983 ◽

Vol 48 (10) ◽

pp. 2888-2892 ◽

Cited By ~ 2

Author(s):

Vilém Kodýtek

Keyword(s):

Free Energy ◽

Partition Function ◽

Energy Function ◽

Special Function ◽

Helmholtz Free Energy ◽

Canonical Ensemble ◽

Free Energy Function ◽

Solution Theory ◽

Pure Solvent ◽

The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

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Mechanical power and hyperelasticity

10.1093/oso/9780198567783.003.0003 ◽

2017 ◽

Author(s):

David J. Steigmann

Keyword(s):

Energy Function ◽

Strain Energy ◽

Strain Energy Function ◽

Mechanical Power ◽

Elastic Materials ◽

Cyclic Motion

This chapter covers the notion of hyperelasticity—the concept that stress is derived from a strain—energy function–by invoking an analogy between elastic materials and springs. Alternatively, it can be derived by invoking a work inequality; the notion that work is required to effect a cyclic motion of the material.

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Integrating genome sequence and structural data for statistical learning to predict transcription factor binding sites

Nucleic Acids Research ◽

10.1093/nar/gkaa1134 ◽

2020 ◽

Vol 48 (22) ◽

pp. 12604-12617

Author(s):

Pengpeng Long ◽

Lu Zhang ◽

Bin Huang ◽

Quan Chen ◽

Haiyan Liu

Keyword(s):

Genome Sequence ◽

Energy Function ◽

Structural Information ◽

Structural Data ◽

P Values ◽

A Genome ◽

Z Scores ◽

Transcription Regulators ◽

Dna Specificity ◽

Tetracycline Repressor

Abstract We report an approach to predict DNA specificity of the tetracycline repressor (TetR) family transcription regulators (TFRs). First, a genome sequence-based method was streamlined with quantitative P-values defined to filter out reliable predictions. Then, a framework was introduced to incorporate structural data and to train a statistical energy function to score the pairing between TFR and TFR binding site (TFBS) based on sequences. The predictions benchmarked against experiments, TFBSs for 29 out of 30 TFRs were correctly predicted by either the genome sequence-based or the statistical energy-based method. Using P-values or Z-scores as indicators, we estimate that 59.6% of TFRs are covered with relatively reliable predictions by at least one of the two methods, while only 28.7% are covered by the genome sequence-based method alone. Our approach predicts a large number of new TFBs which cannot be correctly retrieved from public databases such as FootprintDB. High-throughput experimental assays suggest that the statistical energy can model the TFBSs of a significant number of TFRs reliably. Thus the energy function may be applied to explore for new TFBSs in respective genomes. It is possible to extend our approach to other transcriptional factor families with sufficient structural information.

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Run-and-Tumble Motion: The Role of Reversibility

Journal of Statistical Physics ◽

10.1007/s10955-021-02787-1 ◽

2021 ◽

Vol 183 (3) ◽

Author(s):

Bart van Ginkel ◽

Bart van Gisbergen ◽

Frank Redig

Keyword(s):

Free Energy ◽

Diffusion Coefficient ◽

Large Deviations ◽

Energy Function ◽

Internal State ◽

Rate Function ◽

Free Energy Function ◽

Large Deviations Principle ◽

Preferred Direction ◽

State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

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