The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

The benefits of one-dimensional detectors for high-pressure powder X-ray diffraction

High-pressure powder X-ray diffraction is a fundamental technique for investigating structural responses to externally applied force. Synchrotron sources and two-dimensional detectors are required. In contrast to this conventional setup, high-resolution beamlines equipped with one-dimensional detectors could offer much better resolved peaks but cannot deliver accurate structure factors because they only sample a small portion of the Debye rings, which are usually inhomogeneous and spotty because of the small amount of sample. In this study, a simple method to overcome this problem is presented and successfully applied to solving the structure of an L-serine polymorph from powder data. A comparison of the obtained high-resolution high-pressure data with conventional data shows that this technique, providing up to ten times better angular resolution, can be of advantage for indexing, for lattice parameter refinement, and even for structure refinement and solution in special cases.

The Making of Optimal and Consistent Policy: An Analytical Framework for Monetary Models

This paper shows that optimal policy and consistent policy outcomes require the use of control-theory and game-theory solution techniques. While optimal policy and consistent policy often produce different outcomes even in a one-period model, we analyze consistent policy and its outcome in a simple model, finding that the cause of the inconsistency with optimal policy traces to inconsistent targets in the social loss function. As a result, the central bank should adopt a loss function that differs from the social loss function. Carefully designing the central bank s loss function with consistent targets can harmonize optimal and consistent policy. This desirable result emerges from two observations. First, the social loss function reflects a normative process that does not necessarily prove consistent with the structure of the microeconomy. Thus, the social loss function cannot serve as a direct loss function for the central bank. Second, an optimal loss function for the central bank must depend on the structure of that microeconomy. In addition, this paper shows that control theory provides a benchmark for institution design in a game-theoretical framework.

Design and Optimization of Four-dimensional Cone-beam Computed Tomography in Image-guided Radiation Therapy

The influence of respiratory motion on patient anatomy poses a challenge to accurate radiation therapy, especially in lung cancer treatment. Modern radiation therapy planning uses models of tumor respiratory motion to account for target motion in targeting. The tumor motion model can be verified on a per-treatment session basis with four-dimensional cone-beam computed tomography (4D-CBCT), which acquires an image set of the dynamic target throughout the respiratory cycle during the therapy session. 4D-CBCT is undersampled if the scan time is too short. However, short scan time is desirable in clinical practice to reduce patient setup time. This dissertation presents the design and optimization of 4D-CBCT to reduce the impact of undersampling artifacts with short scan times. This work measures the impact of undersampling artifacts on the accuracy of target motion measurement under different sampling conditions and for various object sizes and motions. The results provide a minimum scan time such that the target tracking error is less than a specified tolerance. This work also presents new image reconstruction algorithms for reducing undersampling artifacts in undersampled datasets by taking advantage of the assumption that the relevant motion of interest is contained within a volume-of-interest (VOI). It is shown that the VOI-based reconstruction provides more accurate image intensity than standard reconstruction. The VOI-based reconstruction produced 43% fewer least-squares error inside the VOI and 84% fewer error throughout the image in a study designed to simulate target motion. The VOI-based reconstruction approach can reduce acquisition time and improve image quality in 4D-CBCT.

A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents.

A three-dimensional dynamical model of Amundsenisen icefield, Svalbard.

Amundsenisen is an ice field, 80 km2 in area, located in Southern Spitsbergen, Svalbard. Radio-echo sounding measurements at 20 MHz show high intensity returns from a nearly flat basal reflector at four zones, all of them with ice thickness larger than 500m. These reflections suggest possible subglacial lakes. To determine whether basal liquid water is compatible with current pressure and temperature conditions, we aim at applying a thermo mechanical model with a free boundary at the bed defined as solution of a Stefan problem for the interface ice-subglaciallake. The complexity of the problem suggests the use of a bi-dimensional model, but this requires that well-defined flowlines across the zones with suspected subglacial lakes are available. We define these flow lines from the solution of a three-dimensional dynamical model, and this is the main goal of the present contribution. We apply a three-dimensional full-Stokes model of glacier dynamics to Amundsenisen icefield. We are mostly interested in the plateau zone of the icefield, so we introduce artificial vertical boundaries at the heads of the main outlet glaciers draining Amundsenisen. At these boundaries we set velocity boundary conditions. Velocities near the centres of the heads of the outlets are known from experimental measurements. The velocities at depth are calculated according to a SIA velocity-depth profile, and those at the rest of the transverse section are computed following Nye’s (1952) model. We select as southeastern boundary of the model domain an ice divide, where we set boundary conditions of zero horizontal velocities and zero vertical shear stresses. The upper boundary is a traction-free boundary. For the basal boundary conditions, on the zones of suspected subglacial lakes we set free-slip boundary conditions, while for the rest of the basal boundary we use a friction law linking the sliding velocity to the basal shear stress,in such a way that, contrary to the shallow ice approximation, the basal shear stress is not equal to the basal driving stress but rather part of the solution.

Effect of Aspect Ratio on the Three-Dimensional Global Instability Analysis of Incompressible Open Cavity Flows

The stability analysis of open cavity flows is a problem of great interest in the aeronautical industry. This type of flow can appear, for example, in landing gears or auxiliary power unit configurations. Open cavity flows is very sensitive to any change in the configuration, either physical (incoming boundary layer, Reynolds or Mach numbers) or geometrical (length to depth and length to width ratio). In this work, we have focused on the effect of geometry and of the Reynolds number on the stability properties of a threedimensional spanwise periodic cavity flow in the incompressible limit. To that end, BiGlobal analysis is used to investigate the instabilities in this configuration. The basic flow is obtained by the numerical integration of the Navier-Stokes equations with laminar boundary layers imposed upstream. The 3D perturbation, assumed to be periodic in the spanwise direction, is obtained as the solution of the global eigenvalue problem. A parametric study has been performed, analyzing the stability of the flow under variation of the Reynolds number, the L/D ratio of the cavity, and the spanwise wavenumber β. For consistency, multidomain high order numerical schemes have been used in all the computations, either basic flow or eigenvalue problems. The results allow to define the neutral curves in the range of L/D = 1 to L/D = 3. A scaling relating the frequency of the eigenmodes and the length to depth ratio is provided, based on the analysis results.

Numerical analysis of axisymmetric shells by one-dimensional continuum elements suitable for high frequency excitations

Axisymmetric shells are analyzed by means of one-dimensional continuum elements by using the analogy between the bending of shells and the bending of beams on elastic foundation. The mathematical model is formulated in the frequency domain. Because the solution of the governing equations of vibration of beams are exact, the spatial discretization only depends on geometrical or material considerations. For some kind of situations, for example, for high frequency excitations, this approach may be more convenient than other conventional ones such as the finite element method.

A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

VISIONS Vehicular communication Improvement : solution based on IMS Operational Nodes and Services

Digital services and communications in vehicular scenarios provide the essential assets to improve road transport in several ways like reducing accidents, improving traffic efficiency and optimizing the transport of goods and people. Vehicular communications typically rely on VANET (Vehicular Ad hoc Networks). In these networks vehicles communicate with each other without the need of infrastructure. VANET are mainly oriented to disseminate information to the vehicles in certain geographic area for time critical services like safety warnings but present very challenging requirements that have not been successfully fulfilled nowadays. Some of these challenges are; channel saturation due to simultaneous radio access of many vehicles, routing protocols in topologies that vary rapidly, minimum quality of service assurance and security mechanisms to efficiently detect and neutralize malicious attacks. Vehicular services can be classified in four important groups: Safety, Efficiency, Sustainability and Infotainment. The benefits of these services for the transport sector are clear but many technological and business challenges need to be faced before a real mass market deployment. Service delivery platforms are not prepared for fulfilling the needs of this complex environment with restrictive requirements due to the criticism of some services To overcome this situation, we propose a solution called VISIONS “Vehicular communication Improvement: Solution based on IMS Operational Nodes and Services”. VISIONS leverages on IMS subsystem and NGN enablers, and follows the CALM reference Architecture standardized by ISO. It also avoids the use of Road Side Units (RSUs), reducing complexity and high costs in terms of deployment and maintenance. We demonstrate the benefits in the following areas: 1. VANET networks efficiency. VISIONS provide a mechanism for the vehicles to access valuable information from IMS and its capabilities through a cellular channel. This efficiency improvement will occur in two relevant areas: a. Routing mechanisms. These protocols are responsible of carrying information from a vehicle to another (or a group of vehicles) using multihop mechanisms. We do not propose a new algorithm but the use of VANET topology information provided through our solution to enrich the performance of these protocols. b. Security. Many aspects of security (privacy, key, authentication, access control, revocation mechanisms, etc) are not resolved in vehicular communications. Our solution efficiently disseminates revocation information to neutralize malicious nodes in the VANET. 2. Service delivery platform. It is based on extended enablers, reference architectures, standard protocols and open APIs. By following this approach, we reduce costs and resources for service development, deployment and maintenance. To quantify these benefits in VANET networks, we provide an analytical model of the system and simulate our solution in realistic scenarios. The simulations results demonstrate how VISIONS improves the performance of relevant routing protocols and is more efficient neutralizing security attacks than the widely proposed solutions based on RSUs. Finally, we design an innovative Social Network service based in our platform, explaining how VISIONS facilitate the deployment and usage of complex capabilities. RESUMEN Los servicios digitales y comunicaciones en entornos vehiculares proporcionan herramientas esenciales para mejorar el transporte por carretera; reduciendo el número de accidentes, mejorando la eficiencia del tráfico y optimizando el transporte de mercancías y personas. Las comunicaciones vehiculares generalmente están basadas en redes VANET (Vehicular Ad hoc Networks). En dichas redes, los vehículos se comunican entre sí sin necesidad de infraestructura. Las redes VANET están principalmente orientadas a difundir información (por ejemplo advertencias de seguridad) a los vehículos en determinadas zonas geográficas, pero presentan unos requisitos muy exigentes que no se han resuelto con éxito hasta la fecha. Algunos de estos retos son; saturación del canal de acceso de radio debido al acceso simultáneo de múltiples vehículos, la eficiencia de protocolos de encaminamiento en topologías que varían rápidamente, la calidad de servicio (QoS) y los mecanismos de seguridad para detectar y neutralizar los ataques maliciosos de manera eficiente. Los servicios vehiculares pueden clasificarse en cuatro grupos: Seguridad, Eficiencia del tráfico, Sostenibilidad, e Infotainment (información y entretenimiento). Los beneficios de estos servicios para el sector son claros, pero es necesario resolver muchos desafíos tecnológicos y de negocio antes de una implementación real. Las actuales plataformas de despliegue de servicios no están preparadas para satisfacer las necesidades de este complejo entorno con requisitos muy restrictivos debido a la criticidad de algunas aplicaciones. Con el objetivo de mejorar esta situación, proponemos una solución llamada VISIONS “Vehicular communication Improvement: Solution based on IMS Operational Nodes and Services”. VISIONS se basa en el subsistema IMS, las capacidades NGN y es compatible con la arquitectura de referencia CALM estandarizado por ISO para sistemas de transporte. También evita el uso de elementos en las carreteras, conocidos como Road Side Units (RSU), reduciendo la complejidad y los altos costes de despliegue y mantenimiento. A lo largo de la tesis, demostramos los beneficios en las siguientes áreas: 1. Eficiencia en redes VANET. VISIONS proporciona un mecanismo para que los vehículos accedan a información valiosa proporcionada por IMS y sus capacidades a través de un canal de celular. Dicho mecanismo contribuye a la mejora de dos áreas importantes: a. Mecanismos de encaminamiento. Estos protocolos son responsables de llevar información de un vehículo a otro (o a un grupo de vehículos) utilizando múltiples saltos. No proponemos un nuevo algoritmo de encaminamiento, sino el uso de información topológica de la red VANET a través de nuestra solución para enriquecer el funcionamiento de los protocolos más relevantes. b. Seguridad. Muchos aspectos de la seguridad (privacidad, gestión de claves, autenticación, control de acceso, mecanismos de revocación, etc) no están resueltos en las comunicaciones vehiculares. Nuestra solución difunde de manera eficiente la información de revocación para neutralizar los nodos maliciosos en la red. 2. Plataforma de despliegue de servicios. Está basada en capacidades NGN, arquitecturas de referencia, protocolos estándar y APIs abiertos. Siguiendo este enfoque, reducimos costes y optimizamos procesos para el desarrollo, despliegue y mantenimiento de servicios vehiculares. Para cuantificar estos beneficios en las redes VANET, ofrecemos un modelo de analítico del sistema y simulamos nuestra solución en escenarios realistas. Los resultados de las simulaciones muestran cómo VISIONS mejora el rendimiento de los protocolos de encaminamiento relevantes y neutraliza los ataques a la seguridad de forma más eficientes que las soluciones basadas en RSU. Por último, diseñamos un innovador servicio de red social basado en nuestra plataforma, explicando cómo VISIONS facilita el despliegue y el uso de las capacidades NGN.

Matrix-free time-stepping methods for the solution of TriGlobal instability problems

La inmensa mayoría de los flujos de relevancia ingenieril permanecen sin estudiar en el marco de la teoría de estabilidad global. Esto es debido a dos razones fundamentalmente, las dificultades asociadas con el análisis de los flujos turbulentos y los inmensos recursos computacionales requeridos para obtener la solución del problema de autovalores asociado al análisis de inestabilidad de flujos tridimensionales, también conocido como problema TriGlobal. En esta tesis se aborda el problema asociado con la tridimensionalidad. Se ha desarrollado una metodología general para obtener soluciones de problemas de análisis modal de las inestabilidades lineales globales mediante el acoplamiento de métodos de evolución temporal, desarrollados en este trabajo, con códigos de mecánica de fluidos computacional de segundo orden, utilizados de forma general en la industria. Esta metodología consiste en la resolución del problema de autovalores asociado al análisis de inestabilidad mediante métodos de proyección en subespacios de Krylov, con la particularidad de que dichos subespacios son generados por medio de la integración temporal de un vector inicial usando cualquier código de mecánica de fluidos computacional. Se han elegido tres problemas desafiantes en función de la exigencia de recursos computacionales necesarios y de la complejidad física para la demostración de la presente metodología: (i) el flujo en el interior de una cavidad tridimensional impulsada por una de sus tapas, (ii) el flujo alrededor de un cilindro equipado con aletas helicoidales a lo largo su envergadura y (iii) el flujo a través de una cavidad abierta tridimensinal en ausencia de homogeneidades espaciales. Para la validación de la tecnología se ha obtenido la solución del problema TriGlobal asociado al flujo en la cavidad tridimensional, utilizando el método de evolución temporal desarrollado acoplado con los operadores numéricos de flujo incompresible del código CFD OpenFOAM (código libre). Los resultados obtenidos coinciden plentamente con la literatura. La aplicación de esta metodología al estudio de inestabilidades globales de flujos abiertos tridimensionales ha proporcionado por primera vez, información sobre la transición tridimensional de estos flujos. Además, la metodología ha sido adaptada para resolver problemas adjuntos TriGlobales, permitiendo el control de flujo basado en modificaciones de las inestabilidades globales. Finalmente, se ha demostrado que la cantidad moderada de los recursos computacionales requeridos para la solución del problema de valor propio TriGlobal usando este método numérico, junto a su versatilidad al poder acoplarse a cualquier código aerodinámico, permite la realización de análisis de inestabilidad global y control de flujos complejos de relevancia industrial. Abstract Most flows of engineering relevance still remain unexplored in a global instability theory context for two reasons. First, because of the difficulties associated with the analysis of turbulent flows and, second, for the formidable computational resources required for the solution of the eigenvalue problem associated with the instability analysis of three-dimensional base flows, also known as TriGlobal problem. In this thesis, the problem associated with the three-dimensionality is addressed by means of the development of a general approach to the solution of large-scale global linear instability analysis by coupling a time-stepping approach with second order aerodynamic codes employed in industry. Three challenging flows in the terms of required computational resources and physical complexity have been chosen for demonstration of the present methodology; (i) the flow inside a wall-bounded three-dimensional lid-driven cavity, (ii) the flow past a cylinder fitted with helical strakes and (iii) the flow over a inhomogeneous three-dimensional open cavity. Results in excellent agreement with the literature have been obtained for the three-dimensional lid-driven cavity by using this methodology coupled with the incompressible solver of the open-source toolbox OpenFOAM®, which has served as validation. Moreover, significant physical insight of the instability of three-dimensional open flows has been gained through the application of the present time-stepping methodology to the other two cases. In addition, modifications to the present approach have been proposed in order to perform adjoint instability analysis of three-dimensional base flows and flow control; validation and TriGlobal examples are presented. Finally, it has been demonstrated that the moderate amount of computational resources required for the solution of the TriGlobal eigenvalue problem using this method enables the performance of instability analysis and control of flows of industrial relevance.

3-dimensional binaural sound rendering using acoustic measurements stored in the SOFA format

Several groups all over the world are researching in several ways to render 3D sounds. One way to achieve this is to use Head Related Transfer Functions (HRTFs). These measurements contain the Frequency Response of the human head and torso for each angle. Some years ago, was only possible to measure these Frequency Responses only in the horizontal plane. Nowadays, several improvements have made possible to measure and use 3D data for this purpose. The problem was that the groups didn't have a standard format file to store the data. That was a problem when a third part wanted to use some different HRTFs for 3D audio rendering. Every of them have different ways to store the data. The Spatially Oriented Format for Acoustics or SOFA was created to provide a solution to this problem. It is a format definition to unify all the previous different ways of storing any kind of acoustics data. At the moment of this project they have defined some basis for the format and some recommendations to store HRTFs. It is actually under development, so several changes could come. The SOFA[1] file format uses a numeric container called netCDF[2], specifically the Enhaced data model described in netCDF 4 that is based on HDF5[3]. The SoundScape Renderer (SSR) is a tool for real-time spatial audio reproduction providing a variety of rendering algorithms. The SSR was developed at the Quality and Usability Lab at TU Berlin and is now further developed at the Institut für Nachrichtentechnik at Universität Rostock [4]. This project is intended to be an introduction to the use of SOFA files, providing a C++ API to manipulate them and adapt the binaural renderer of the SSR for working with the SOFA format. RESUMEN. El SSR (SoundScape Renderer) es un programa que está siendo desarrollado actualmente por la Universität Rostock, y previamente por la Technische Universität Berlin. El SSR es una herramienta diseñada para la reproducción y renderización de audio 2D en tiempo real. Para ello utiliza diversos algoritmos, algunos orientados a sistemas formados por arrays de altavoces en diferentes configuraciones y otros algoritmos diseñados para cascos. El principal objetivo de este proyecto es dotar al SSR de la capacidad de renderizar sonidos binaurales en 3D. Este proyecto está centrado en el binaural renderer del SSR. Este algoritmo se basa en el uso de HRTFs (Head Related Transfer Function). Las HRTFs representan la función de transferencia del sistema formado por la cabeza y el torso del oyente. Esta función es medida desde diferentes ángulos. Con estos datos el binaural renderer puede generar audio en tiempo real simulando la posición de diferentes fuentes. Para poder incluir una base de datos con HRTFs en 3D se ha hecho uso del nuevo formato SOFA (Spatially Oriented Format for Acoustics). Este nuevo formato se encuentra en una fase bastante temprana de su desarrollo. Está pensado para servir como formato estándar para almacenar HRTFs y cualquier otro tipo de medidas acústicas, ya que actualmente cada laboratorio cuenta con su propio formato de almacenamiento y esto hace bastante difícil usar varias bases de datos diferentes en un mismo proyecto. El formato SOFA hace uso del contenedor numérico netCDF, que a su vez esta basado en un contenedor más básico llamado HRTF-5. Para poder incluir el formato SOFA en el binaural renderer del SSR se ha desarrollado una API en C++ para poder crear y leer archivos SOFA con el fin de utilizar los datos contenidos en ellos dentro del SSR.

A Three-Dimensional B.I.E.M. Program

The program PECET (Boundary Element Program in Three-Dimensional Elasticity) is presented in this paper. This program, written in FORTRAN V and implemen ted on a UNIVAC 1100,has more than 10,000 sentences and 96 routines and has a lot of capabilities which will be explained in more detail. The object of the program is the analysis of 3-D piecewise heterogeneous elastic domains, using a subregionalization process and 3-D parabolic isopara, metric boundary elements. The program uses special data base management which will be described below, and the modularity followed to write it gives a great flexibility to the package. The Method of Analysis includes an adaptive integration process, an original treatment of boundary conditions, a complete treatment of body forces, the utilization of a Modified Conjugate Gradient Method of solution and an original process of storage which makes it possible to save a lot of memory.