Analysis of channel bank erosion rate using exposed roots of trees: a case study of lavij stream, northern Alborz Mountains, Iran

Powerful alluvial rivers in the northern Alborz mountain ranges erode river banks due to having high slopes.Most of these rivers flow in forest areas.In this research,the rate of the river bank erosion was examined using the exposed roots of the trees.For this purpose,8 reaches of Lavij Stream were investigated.To determine the first year of root exposure,two sets of macroscopic and microscopic indicators were utilized.Accordingly,the rate of the stream bank erosion was estimated.The results were analyzed by using statistical test,which showed insignificant differences between the two groups of indicators.Due to its more abundance(frequency)on the margins and easy detection of its root through the exposure(macroscopic and microscopic)indicators,Alnus glutinosa(black alder)species could be more easily and accurately analyzed as compared with any other tree species in the region.The mean erosion rate of the riverbank using the extruded roots was estimated to be 0.08 m/yr.The hydrological analyses of flood flows showed that 95%of Lavij Stream bank erosion was caused by the river bank full discharges with a return period of 1-3 years.

Rooted Tree Optimization for Wind Turbine Optimum Control Based on Energy Storage System

The integration of wind turbines(WTs)in variable speed drive systems belongs to the main factors causing lowstability in electrical networks.Therefore,in order to avoid this issue,WTs hybridization with a storage system is a mandatory.This paper investigates WT system operating at variable speed.The system contains of a permanent magnet synchronous generator(PMSG)supported by a battery storage system(BSS).To enhance the quality of active and reactive power injected into the network,direct power control(DPC)scheme utilizing space-vector modulation(SVM)technique based on proportional-integral(PI)control is proposed.Meanwhile,to improve the rendition of this method(DPC-SVM-PI),the rooted tree optimization technique(RTO)algorithm-based controller parameter identification is used to achieve PI optimal gains.To compare the performance ofRTO-based controllers,they were implemented and tested along with some other popular controllers under different working conditions.The obtained results have shown the supremacy of the suggested PIRTO algorithm compared to competing controllers regarding total harmonic distortion(THD),overshoot percentage,settling time,rise time,average active power value,overall efficiency,and active power steadystate error.

Table Operation Method for Optimal Spanning Tree Problem

As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.

Tanoak (Notholithocarpus densiflorus) Coarse Root Morphology: Prediction Models for Volume and Biomass of Individual Roots

Descriptions of tree root morphology inform design of belowground biomass and carbon inventories and sampling for research. We studied root morphology of tanoak (Notholithocarpus densiflorus), an important component in mixed evergreen forests of California and Oregon, USA. Tanoak re-sprouts from belowground lignotubers after disturbances, and stores an unknown amount of carbon in coarse roots underground. We sought to ascribe explanatory nomenclature to roots’ morphological features and to identify models describing tanoak root morphology. Twelve tanoak root systems were excavated, dissected, and measured. Roots tapered according to their circumference and location. Larger roots closer to the lignotuber (located at the base of the tree stem) tapered more rapidly per unit of length. Tanoak roots forked frequently. Root cross-sectional area was preserved after forking events (i.e., the sum of cross-sectional areas for smaller roots on one side of the fork correlated with the adjoining large root). Occurrence and quantity of root branches (small roots branching laterally from larger roots) was dependent upon length of the source root segment. Our models of tanoak root morphology are designed to be organized together to estimate biomass of any segment or collection of lateral roots (e.g., roots lost/missed during excavation, or in lieu of destructive sampling), given root diameter at a known distance from the lignotuber. The taper model gives distal- and proximal-end diameters for calculation of volume for segments of root tapering between forks. Frequency of forking and branching can also be predicted. Summing the predicted mass of each lateral root segment, branch, and forked segment would produce an estimate of mass for a contiguous network of lateral roots.

Design and Analysis of Some Third Order Explicit Almost Runge-Kutta Methods

In this paper, we propose two new explicit Almost Runge-Kutta (ARK) methods, ARK3 (a three stage third order method, i.e., s = p = 3) and ARK34 (a four-stage third-order method, i.e., s = 4, p = 3), for the numerical solution of initial value problems (IVPs). The methods are derived through the application of order and stability conditions normally associated with Runge-Kutta methods;the derived methods are further tested for consistency and stability, a necessary requirement for convergence of any numerical scheme;they are shown to satisfy the criteria for both consistency and stability;hence their convergence is guaranteed. Numerical experiments carried out further justified the efficiency of the methods.

Rota-Baxter TD Algebra and Quinquedendriform Algebra

A dendriform algebra defined by Loday has two binary operations that give a two-part splitting of the associativity in the sense that their sum is associative. Sim- ilar dendriform type algebras with three-part and four-part splitting of the associativity were later obtained. These structures can also be derived from actions of suitable linear operators, such as a Rota-Baxter operator or TD operator, on an associative algebra. Mo- tivated by finding a five-part splitting of the associativity, we consider the Rota-Baxter TD （RBTD） operator, an operator combining the Rota-Baxter operator and TD oper- ator, and coming from a recent study of Rota＇s problem concerning linear operators on associative algebras. Free RBTD algebras on rooted forests are constructed. We then introduce the concept of a quinquedendriform algebra and show that its defining relations are characterized by the action of an RBTD operator, similar to the cases of dendriform and tridendriform algebras.

Relative locations of operated semigroups subwords in free and Motzkin words

Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.

Time to most recent common ancestor for stationary continuous state branching processes with immigration

Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.