All orders structure and efficient computation of linearly reducible elliptic Feynman integrals

We define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand, which we call the inner polylogarithmic part (IPP). The solution is obtained by direct integration of the Feynman parametric representation. When the IPP depends on one elliptic curve (and no other algebraic functions), this class of Feynman integrals can be algorithmically solved in terms of elliptic multiple polylogarithms (eMPLs) by using integration by parts identities. We then elaborate on the differential equations method. Specifically, we show that the IPP can be mapped to a generalized integral topology satisfying a set of differential equations in $\epsilon$-form. In the examples we consider the canonical differential equations can be directly solved in terms of eMPLs up to arbitrary order of the dimensional regulator. The remaining 1-dimensional integral may be performed to express such integrals completely in terms of eMPLs. We apply these methods to solve two- and three-points integrals in terms of eMPLs. We analytically continue these integrals to the physical region by using their 1-dimensional integral representation.Comment: The differential equations method is applied to linearly reducible elliptic Feynman integrals, the solutions are in terms of elliptic polylogarithms, JHEP version, 50 page

Baikov-Lee Representations Of Cut Feynman Integrals

We develop a general framework for the evaluation of $d$-dimensional cut Feynman integrals based on the Baikov-Lee representation of purely-virtual Feynman integrals. We implement the generalized Cutkosky cutting rule using Cauchy's residue theorem and identify a set of constraints which determine the integration domain. The method applies equally well to Feynman integrals with a unitarity cut in a single kinematic channel and to maximally-cut Feynman integrals. Our cut Baikov-Lee representation reproduces the expected relation between cuts and discontinuities in a given kinematic channel and furthermore makes the dependence on the kinematic variables manifest from the beginning. By combining the Baikov-Lee representation of maximally-cut Feynman integrals and the properties of periods of algebraic curves, we are able to obtain complete solution sets for the homogeneous differential equations satisfied by Feynman integrals which go beyond multiple polylogarithms. We apply our formalism to the direct evaluation of a number of interesting cut Feynman integrals.Comment: 37 pages; v2 is the published version of this work with references added relative to v

Abiotic and Biotic Factors Contributing to Invasive Aquatic Plant Cover in Southern Connecticut Ponds

Much is known about how invasive aquatic plants affect communities they inhabit; however, few surveys have been conducted to determine the chemical, physical, and biological factors correlated with invasive aquatic plant abundances. This study took a first step toward understanding the correlations among water quality, native plant and invertebrate communities, and invasive aquatic plant abundance in small ponds. Preliminary surveys were conducted in four ponds in southern Connecticut: Colony Pond in Ansonia, Osbournedale Pond in Derby, West Campus Pond at Sacred Heart University in Fairfield, and Mondo Pond in Milford. Water quality parameters (depth, Secchi depth, nitrate, phosphate, coliform bacteria) and aquatic plant and invertebrate abundances were measured at five locations in each pond. Osbournedale pond had high invasive plant cover (53%). Colony and Mondo Pond had low invasive plant cover (2-3%). West Campus at Sacred Heart University contained no invasive plants. Principal component analysis revealed correlations between invasive plant abundance, phosphate, and coliform bacteria. Analysis of similarities (ANOSIM) showed distinct biological communities at each site, which may correspond to invasion risk. The preliminary data collected from this survey can guide future studies to predict invasive plant cover

Kennel Disinfectants for Microsporum canis

The antifungal efficacy of commonly used kennel disinfectants for large surfaces was tested using naturally infective material from untreated animals (M. canis and Trichophyton sp.) soaked and macerated but unfiltered leaving visible fluorescing hairs and/or scales in the test inoculum to create a robust challenge. Disinfectants included sodium hypochlorite (1 : 32 and 1 : 100), enilconazole (1 : 100), accelerated hydrogen peroxide (1 : 16), potassium peroxymonosulfate (1% and 2%), and calcium hypochlorite “dry bleach.” Disinfectants were tested at a 1 : 10, 1 : 5, and 1 : 1 dilution of test inoculum to disinfectant with a 10 min contact time. Good efficacy was defined as a disinfectant resulting in no growth. Control plates grew >300 colonies of each pathogen per plate. Enilconazole, sodium hypochlorite (all dilutions), accelerated hydrogen peroxide, and 2% potassium peroxymonosulfate (but not 1%) inhibited all growth of both pathogens at 1 : 10, 1 : 5, and 1 : 1 dilutions. Calcium hypochlorite showed no antifungal efficacy (>300 colonies per plate). Enilconazole (1 : 100), sodium hypochlorite (1 : 32 or 1 : 100), accelerated hydrogen peroxide (1 : 16), and 2% potassium peroxymonosulfate are recommended for decontamination of kennels exposed to dermatophyte pathogens

Failure of impulsively loaded thin-walled pipes and plates

The capability to predict the modes of deformation of thin-walled structures is a paramount safety concern in military, civil and industrial environments. Finite element analysis offers a valid, cost-effective alternative to experimental programs when performing preliminary safety studies. This thesis investigates numerical procedures to study two typical safety-related problems of impulsively loaded thin-walled structures. When a pressurised pipe experiences a guillotine break, the sudden fluid release causes a rapid whip-like motion, with possible damage to nearby structures. An element code is here developed to predict the pipe flexural and torsional behaviour, which adopts a corotational kinematic formulation for delivering reliable results at a fraction of the computational cost of conventional FEA techniques. The validated code, implemented with commercial FEA software, is employed in parametric studies leading to the discovery of new dimensionless groups that completely characterise the flexural behaviour of pipes. With the newfound understanding, simple empirical laws are established that predict the pipe response and the hazard conditions. A shell element numerical model is built to study the rupture mechanisms of steel plates subjected to impulsive blast loadings. Tensile and shear experiments on steel specimens were performed to characterise the parameters of a triaxiality-dependent failure criterion, obtaining a mesh-size independent fracture model. The numerical predictions allowed to establish a novel phenomenological criterion, providing an answer to the previously unsolved question on the transition between different types of failure modes. Dimensionless failure maps are developed that elucidate the influence of plate topology and boundary conditions on the rupture mechanisms. The study highlights the similarities in the response between simply-supported plates, and fully-clamped plates exposed to localised blast loadings. A new failure mode is discovered for simply-supported rectangular plates, where, under certain loading conditions, rupture propagates in the central area of the plate, rather than along the support

Planar master integrals for the two-loop light-fermion electroweak corrections to Higgs plus jet production

We present the analytic calculation of the planar master integrals which contribute to compute the two-loop light-fermion electroweak corrections to the production of a Higgs boson in association with a jet in gluon-gluon fusion. The complete dependence on the electroweak-boson mass is retained. The master integrals are evaluated by means of the differential equations method and the analytic results are expressed in terms of multiple polylogarithms up to weight four.Comment: 21 pages, ancillary file

A repetitive control scheme for industrial robots based on b-spline trajectories

In this paper, a novel repetitive control scheme is presented and discussed. The general framework is the control of repetitive tasks of robotic systems or, more in general, of automatic machines. The key idea of the proposed scheme consists in modifying the reference trajectory provided to the plant in order to compensate for external loads or unmodelled dynamics that cyclically affect it. By exploiting the dynamic filters for the B-spline trajectory planning, it has been possible to integrate the trajectory generation within a repetitive control scheme able to modify in real-time the reference signal with the aims of nullify interpolation errors. Experimental results obtained controlling two joints of a standard industrial manipulator are reported, showing the effectiveness of the proposed method

Feedforward control of Variable Stiffness Joints robots for vibrations suppression

This paper presents a new feedforward controller based on a continuous-time finite impulse response filter, designed to minimize the vibrations that usually affect robot manipulators with elastic joints. In particular, Variable Stiffness Joints (VSJ) robots are considered, since they are usually characterized by a very low level of damping which makes the problem of the oscillations quite important. The proposed approach allows to simplify the overall control structure of VSJ robots, which is based on a decentralized control of each servomotor, imposing the desired position and the desired stiffness at each joint, and on a novel feedforward control, filtering the reference signals. After analyzing some of the filter properties and the method for the parameters choice, experimental results on a VSJ robot demonstrate the importance of the proposed filtering action for minimizing vibrations and oscillations

A Repetitive Control Scheme Based on B-Spline Trajectories Modification

In many applications of interest in industrial robotics, tasks are cyclic and must be repeated over and over. In this context, it seems natural to exploit the intrinsic properties of repetitive control schemes, where the cyclic nature of "disturbances" and/or unmodeled dynamic effects can be exploited to reduce the tracking errors. In this paper, we propose a new repetitive control scheme, where the main idea consists in the modification of the reference trajectory in order to compensate for the periodic undesired effects. By exploiting the dynamic filters for the B-spline generation, it is possible to integrate the trajectory planning within a repetitive control scheme able to modify in real-time the reference signal with the aims of nullify interpolation errors. By means of an extensive experimental activity on a servo mechanism pros and cons of the proposed approach are analyzed

Multidimensional Trajectories Generation with Vibration Suppression Capabilities: the Role of Exponential B-splines

In this paper, exponential B-spline trajectories are presented and discussed. They are generated by means of a chain of filters characterized by a truncated exponential impulse response. If properly tuned, the filters applied to a vibrating plant are able to cancel the oscillations and in this sense the resulting splines are optimized with respect to the problem of vibrations suppression. Different types of exponential B-spline are illustrated, with one or more exponential filters in the chain, and the procedure for the interpolation of a given set of desired via-points, with a proper choice of the control points, is shown. As a matter of fact, exponential B-splines, generated by means of dynamic filters, combine the vibration suppression capability of input shapers and smoothing filters with the possibility of exactly interpolating some via-points. The advantages of these curves are experimental proved by considering the motion of a spherical pendulum connected to the flange of an industrial robot