Free-surface disturbances due to the submersion of a cylindrical obstacle

We explore the initial perturbations that form on a liquid free surface as a result of the submersion of a circular cylinder beneath the surface, a scenario that arises in a number of diverse applications. The behaviour of the free surface is determined by transforming the equations of motion of the system via the Wehausen scheme, to variables for the free surface. A small-time series expansion is utilized to construct a recursive scheme that can be implemented numerically, and the time frame over which this approximation is valid is analysed. The resulting numerical model allows one to extend the results in the literature to study arbitrary cylinder sizes, including those where the cylinder is close to the free surface, and arbitrary cylinder motions. Of particular interest in this study was identifying the conditions under which strong jets would appear, and those were the free surface exhibited gravity waves. The formation of a central jet is found to be related to the growth of secondary, nonlinear waves, which rapidly merge as the obstacle is submerged. Classification maps are presented as a function of obstacle size and submersion speed, to identify the conditions which lead to jetting. Furthermore, the acceleration profile of the cylinder is shown to significantly affect the conditions under which jets form, which we argue is due to the rate at which energy is injected into the system.

Time-Series of Distributions Forecasting in Agricultural Applications: An Intervals’ Numbers Approach

This work represents any distribution of data by an Intervals’ Number (IN), hence it represents all-order data statistics, using a “small” number of L intervals. The INs considered are induced from images of grapes that ripen. The objective is the accurate prediction of grape maturity. Based on an established algebra of INs, an optimizable IN-regressor is proposed, implementable on a neural architecture, toward predicting future INs from past INs. A recursive scheme tests the capacity of the IN-regressor to learn the physical “law” that generates the non-stationary time-series of INs. Computational experiments demonstrate comparatively the effectiveness of the proposed techniques.

Time-Series of Distributions Forecasting in Agricultural Applications: An Intervals’ Numbers Approach

This work represents any distribution of data by an Intervals’ Number (IN), hence it represents all-order data statistics, using a “small” number of L intervals. The INs considered are induced from images of grapes that ripen. The objective is the accurate prediction of grape maturity. Based on an established algebra of INs, an optimizable IN-regressor is proposed, implementable on a neural architecture, toward predicting future INs from past INs. A recursive scheme tests the capacity of the IN-regressor to learn the physical “law” that generates the non-stationary time-series of INs. Computational experiments demonstrate comparatively the effectiveness of the proposed techniques.

DNA barcode by flossing through a cylindrical nanopore

We report a method for DNA barcoding from the dwell time measurement of protein tags (barcodes) along the DNA backbone using Brownian dynamics simulation of a model DNA and use a recursive scheme to improve the measurements to almost 100% accuracy.

Periodic codings of Bratteli-Vershik systems

We develop conditions for the coding of a Bratteli-Vershik system according to initial path segments to be periodic, equivalently for a constructive symbolic recursive scheme corresponding to a cutting and stacking process to produce a periodic sequence. This is a step toward understanding when a Bratteli-Vershik system can be essentially faithfully represented by means of a natural coding as a subshift on a finite alphabet.

Homotopy Perturbation Method for a Class of Nonlinear Singular System of Initial Value Problems

In this paper, a method based on homotopy perturbation method is used to establish the recursive scheme for the solution of nonlinear singular system of initial value problems. The convergence analysis of the proposed method is also shown. The accuracy and efficiency of the proposed method are demonstrated through various examples.

NNLO classical solution for Lipatov’s effective action for reggeized gluons

We consider the formalism of small-[Formula: see text] effective action for reggeized gluons[Formula: see text] and, following the approach developed in Refs. 11–17, calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated that for each perturbative order, the self-consistency of the equations of motion is equivalent to the transversality conditions applied to the solution of the equations, these conditions allow to construct the general recursive scheme for the solution’s calculation. The one fermion loop contribution to the classical solutions and application of the obtained results are also discussed.