A non-linear analysis of lying a floating pipeline on the seabed

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Numerical modelling of braided fibres for reinforced concrete

Fire has been always a major concern for designers of steel and concrete structures. Designing fire-resistant structural elements is not an easy task due to several limitations such as the lack of fire-resistant construction materials. Concrete reinforcement cover and external insulation are the most commonly adopted systems to protect concrete and steel from overheating, while spalling of concrete is minimised by using HPFRC instead of standard concrete. Although these methodologies work very well for low rise concrete structures, this is not the case for high-rise and inaccessible buildings where fire loading is much longer. Fire can permanently damage structures that cost a lot of money. This is unsafe and can lead to loss of life. In this research, the author proposes a new type of main reinforcement for concrete structures which can provide better fire-resistance than steel or FRP re-bars. This consists of continuous braided fibre rope, generally made from fire-resistant materials such as carbon or glass fibre. These fibres have excellent tensile strengths, sometimes in excess of ten times greater than steel. In addition to fire-resistance, these ropes can produce lighter and corrosive resistant structures. Avoiding the use of expensive resin binders, fibres are easily bound together using braiding techniques, ensuring that tensile stress is evenly distributed throughout the reinforcement. In order to consider braided ropes as a form of reinforcement it is first necessary to establish the mechanical performance at room temperature and investigate the pull-out resistance for both unribbed and ribbed ropes. Ribbing of ropes was achieved by braiding the rope over a series of glass beads. Adhesion between the rope and concrete was drastically improved due to ribbing, and further improved by pre-stressing ropes and reducing the slacked fibres. Two types of material have been considered for the ropes: carbon and aramid. An implicit finite element approach is proposed to model braided fibres using Total Lagrangian formulation, based on the theory of small strains and large rotations. Modelling tows and strands as elastic transversely isotropic materials was a good assumption when stiff and brittle fibres such as carbon and glass fibres are considered. The rope-to-concrete and strand-to-strand bond interaction/adhesion was numerically simulated using newly proposed hierarchical higher order interface elements. Elastic and linear damage cohesive models were used effectively to simulate non-penetrative 'free' sliding interaction between strands, and the adhesion between ropes and concrete respectively. Numerical simulation showed similar de-bonding features when compared with experimental pull-out results of braided ribbed rope reinforced concrete.

GPU implementation of the simplex identification via split augmented Lagrangian

Hyperspectral imaging can be used for object detection and for discriminating between different objects based on their spectral characteristics. One of the main problems of hyperspectral data analysis is the presence of mixed pixels, due to the low spatial resolution of such images. This means that several spectrally pure signatures (endmembers) are combined into the same mixed pixel. Linear spectral unmixing follows an unsupervised approach which aims at inferring pure spectral signatures and their material fractions at each pixel of the scene. The huge data volumes acquired by such sensors put stringent requirements on processing and unmixing methods. This paper proposes an efficient implementation of a unsupervised linear unmixing method on GPUs using CUDA. The method finds the smallest simplex by solving a sequence of nonsmooth convex subproblems using variable splitting to obtain a constraint formulation, and then applying an augmented Lagrangian technique. The parallel implementation of SISAL presented in this work exploits the GPU architecture at low level, using shared memory and coalesced accesses to memory. The results herein presented indicate that the GPU implementation can significantly accelerate the method's execution over big datasets while maintaining the methods accuracy.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Lagrangian-Hamiltonian unified formalism for field theory

The RuskSkinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations. 2004 American Institute of Physics.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Lagrangian-informed mixed integer programming reformulations

La programmation linéaire en nombres entiers est une approche robuste qui permet de résoudre rapidement de grandes instances de problèmes d'optimisation discrète. Toutefois, les problèmes gagnent constamment en complexité et imposent parfois de fortes limites sur le temps de calcul. Il devient alors nécessaire de développer des méthodes spécialisées afin de résoudre approximativement ces problèmes, tout en calculant des bornes sur leurs valeurs optimales afin de prouver la qualité des solutions obtenues. Nous proposons d'explorer une approche de reformulation en nombres entiers guidée par la relaxation lagrangienne. Après l'identification d'une forte relaxation lagrangienne, un processus systématique permet d'obtenir une seconde formulation en nombres entiers. Cette reformulation, plus compacte que celle de Dantzig et Wolfe, comporte exactement les mêmes solutions entières que la formulation initiale, mais en améliore la borne linéaire: elle devient égale à la borne lagrangienne. L'approche de reformulation permet d'unifier et de généraliser des formulations et des méthodes de borne connues. De plus, elle offre une manière simple d'obtenir des reformulations de moins grandes tailles en contrepartie de bornes plus faibles. Ces reformulations demeurent de grandes tailles. C'est pourquoi nous décrivons aussi des méthodes spécialisées pour en résoudre les relaxations linéaires. Finalement, nous appliquons l'approche de reformulation à deux problèmes de localisation. Cela nous mène à de nouvelles formulations pour ces problèmes; certaines sont de très grandes tailles, mais nos méthodes de résolution spécialisées les rendent pratiques.

Gauge formulation for higher order gravity

This work is an application of the second order gauge theory for the Lorentz group, where a description of the gravitational interaction is obtained that includes derivatives of the curvature. We analyze the form of the second field strength, G=partial derivative F+fAF, in terms of geometrical variables. All possible independent Lagrangians constructed with quadratic contractions of F and quadratic contractions of G are analyzed. The equations of motion for a particular Lagrangian, which is analogous to Podolsky's term of his generalized electrodynamics, are calculated. The static isotropic solution in the linear approximation was found, exhibiting the regular Newtonian behavior at short distances as well as a meso-large distance modification.

Geometrical Lagrangian for a supersymmetric Yang-Mills theory on the group manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N = 2, d = 5 Yang-Mills - SYM, N = 2, d = 5 - is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein-Cartan formulation of gravity and in the 'group manifold approach to gravity and supergravity theories'. The group SYM, N = 2, d = 5, turns out to be the direct product of supergravity and a general gauge group g: G = g circle times <(SU(2, 2/1))over bar>.

First-order equivalent to Einstein-Hilbert Lagrangian

A first-order Lagrangian L ∇ variationally equivalent to the second-order Einstein- Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by L ∇ is proved to be regular and its Hamiltonian formulation is studied, including its covariant Hamiltonian attached to ∇ .

Eulerian-Lagrangian two phase debris flow model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier-Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Eulerian-Lagrangian Two Phase Debris Flow Model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier–Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.

Lawsonia Inermis-mediated Synthesis Of Silver Nanoparticles: Activity Against Human Pathogenic Fungi And Bacteria With Special Reference To Formulation Of An Antimicrobial Nanogel.

Lawsonia inermis mediated synthesis of silver nanoparticles (Ag-NPs) and its efficacy against Candida albicans, Microsporum canis, Propioniabacterium acne and Trichophyton mentagrophytes is reported. A two-step mechanism has been proposed for bioreduction and formation of an intermediate complex leading to the synthesis of capped nanoparticles was developed. In addition, antimicrobial gel for M. canis and T. mentagrophytes was also formulated. Ag-NPs were synthesized by challenging the leaft extract of L. inermis with 1 mM AgNO₃. The Ag-NPs were characterized by Ultraviolet-Visible (UV-Vis) spectrophotometer and Fourier transform infrared spectroscopy (FTIR). Transmission electron microscopy (TEM), nanoparticle tracking and analysis sytem (NTA) and zeta potential was measured to detect the size of Ag-NPs. The antimicrobial activity of Ag-NPs was evaluated by disc diffusion method against the test organisms. Thus these Ag-NPs may prove as a better candidate drug due to their biogenic nature. Moreover, Ag-NPs may be an answer to the drug-resistant microorganisms.