Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

We investigate several two-dimensional guillotine cutting stock problems and their variants in which orthogonal rotations are allowed. We first present two dynamic programming based algorithms for the Rectangular Knapsack (RK) problem and its variants in which the patterns must be staged. The first algorithm solves the recurrence formula proposed by Beasley; the second algorithm - for staged patterns - also uses a recurrence formula. We show that if the items are not so small compared to the dimensions of the bin, then these algorithms require polynomial time. Using these algorithms we solved all instances of the RK problem found at the OR-LIBRARY, including one for which no optimal solution was known. We also consider the Two-dimensional Cutting Stock problem. We present a column generation based algorithm for this problem that uses the first algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We also investigate a variant of this problem where the bins have different sizes. At last, we study the Two-dimensional Strip Packing problem. We also present a column generation based algorithm for this problem that uses the second algorithm above mentioned where staged patterns are imposed. In this case we solve instances for two-, three- and four-staged patterns. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances. We give a detailed description (a pseudo-code) of all the algorithms presented here, so that the reader may easily implement these algorithms. (c) 2007 Elsevier B.V. All rights reserved.

Monte Carlo Neutronics and Thermal-hydraulics coupling applied to Fast Reactors

Un escenario habitualmente considerado para el uso sostenible y prolongado de la energía nuclear contempla un parque de reactores rápidos refrigerados por metales líquidos (LMFR) dedicados al reciclado de Pu y la transmutación de actínidos minoritarios (MA). Otra opción es combinar dichos reactores con algunos sistemas subcríticos asistidos por acelerador (ADS), exclusivamente destinados a la eliminación de MA. El diseño y licenciamiento de estos reactores innovadores requiere herramientas computacionales prácticas y precisas, que incorporen el conocimiento obtenido en la investigación experimental de nuevas configuraciones de reactores, materiales y sistemas. A pesar de que se han construido y operado un cierto número de reactores rápidos a nivel mundial, la experiencia operacional es todavía reducida y no todos los transitorios se han podido entender completamente. Por tanto, los análisis de seguridad de nuevos LMFR están basados fundamentalmente en métodos deterministas, al contrario que las aproximaciones modernas para reactores de agua ligera (LWR), que se benefician también de los métodos probabilistas. La aproximación más usada en los estudios de seguridad de LMFR es utilizar una variedad de códigos, desarrollados a base de distintas teorías, en busca de soluciones integrales para los transitorios e incluyendo incertidumbres. En este marco, los nuevos códigos para cálculos de mejor estimación ("best estimate") que no incluyen aproximaciones conservadoras, son de una importancia primordial para analizar estacionarios y transitorios en reactores rápidos. Esta tesis se centra en el desarrollo de un código acoplado para realizar análisis realistas en reactores rápidos críticos aplicando el método de Monte Carlo. Hoy en día, dado el mayor potencial de recursos computacionales, los códigos de transporte neutrónico por Monte Carlo se pueden usar de manera práctica para realizar cálculos detallados de núcleos completos, incluso de elevada heterogeneidad material. Además, los códigos de Monte Carlo se toman normalmente como referencia para los códigos deterministas de difusión en multigrupos en aplicaciones con reactores rápidos, porque usan secciones eficaces punto a punto, un modelo geométrico exacto y tienen en cuenta intrínsecamente la dependencia angular de flujo. En esta tesis se presenta una metodología de acoplamiento entre el conocido código MCNP, que calcula la generación de potencia en el reactor, y el código de termohidráulica de subcanal COBRA-IV, que obtiene las distribuciones de temperatura y densidad en el sistema. COBRA-IV es un código apropiado para aplicaciones en reactores rápidos ya que ha sido validado con resultados experimentales en haces de barras con sodio, incluyendo las correlaciones más apropiadas para metales líquidos. En una primera fase de la tesis, ambos códigos se han acoplado en estado estacionario utilizando un método iterativo con intercambio de archivos externos. El principal problema en el acoplamiento neutrónico y termohidráulico en estacionario con códigos de Monte Carlo es la manipulación de las secciones eficaces para tener en cuenta el ensanchamiento Doppler cuando la temperatura del combustible aumenta. Entre todas las opciones disponibles, en esta tesis se ha escogido la aproximación de pseudo materiales, y se ha comprobado que proporciona resultados aceptables en su aplicación con reactores rápidos. Por otro lado, los cambios geométricos originados por grandes gradientes de temperatura en el núcleo de reactores rápidos resultan importantes para la neutrónica como consecuencia del elevado recorrido libre medio del neutrón en estos sistemas. Por tanto, se ha desarrollado un módulo adicional que simula la geometría del reactor en caliente y permite estimar la reactividad debido a la expansión del núcleo en un transitorio. éste módulo calcula automáticamente la longitud del combustible, el radio de la vaina, la separación de los elementos de combustible y el radio de la placa soporte en función de la temperatura. éste efecto es muy relevante en transitorios sin inserción de bancos de parada. También relacionado con los cambios geométricos, se ha implementado una herramienta que, automatiza el movimiento de las barras de control en busca d la criticidad del reactor, o bien calcula el valor de inserción axial las barras de control. Una segunda fase en la plataforma de cálculo que se ha desarrollado es la simulació dinámica. Puesto que MCNP sólo realiza cálculos estacionarios para sistemas críticos o supercríticos, la solución más directa que se propone sin modificar el código fuente de MCNP es usar la aproximación de factorización de flujo, que resuelve por separado la forma del flujo y la amplitud. En este caso se han estudiado en profundidad dos aproximaciones: adiabática y quasiestática. El método adiabático usa un esquema de acoplamiento que alterna en el tiempo los cálculos neutrónicos y termohidráulicos. MCNP calcula el modo fundamental de la distribución de neutrones y la reactividad al final de cada paso de tiempo, y COBRA-IV calcula las propiedades térmicas en el punto intermedio de los pasos de tiempo. La evolución de la amplitud de flujo se calcula resolviendo las ecuaciones de cinética puntual. Este método calcula la reactividad estática en cada paso de tiempo que, en general, difiere de la reactividad dinámica que se obtendría con la distribución de flujo exacta y dependiente de tiempo. No obstante, para entornos no excesivamente alejados de la criticidad ambas reactividades son similares y el método conduce a resultados prácticos aceptables. Siguiendo esta línea, se ha desarrollado después un método mejorado para intentar tener en cuenta el efecto de la fuente de neutrones retardados en la evolución de la forma del flujo durante el transitorio. El esquema consiste en realizar un cálculo cuasiestacionario por cada paso de tiempo con MCNP. La simulación cuasiestacionaria se basa EN la aproximación de fuente constante de neutrones retardados, y consiste en dar un determinado peso o importancia a cada ciclo computacial del cálculo de criticidad con MCNP para la estimación del flujo final. Ambos métodos se han verificado tomando como referencia los resultados del código de difusión COBAYA3 frente a un ejercicio común y suficientemente significativo. Finalmente, con objeto de demostrar la posibilidad de uso práctico del código, se ha simulado un transitorio en el concepto de reactor crítico en fase de diseño MYRRHA/FASTEF, de 100 MW de potencia térmica y refrigerado por plomo-bismuto. ABSTRACT Long term sustainable nuclear energy scenarios envisage a fleet of Liquid Metal Fast Reactors (LMFR) for the Pu recycling and minor actinides (MAs) transmutation or combined with some accelerator driven systems (ADS) just for MAs elimination. Design and licensing of these innovative reactor concepts require accurate computational tools, implementing the knowledge obtained in experimental research for new reactor configurations, materials and associated systems. Although a number of fast reactor systems have already been built, the operational experience is still reduced, especially for lead reactors, and not all the transients are fully understood. The safety analysis approach for LMFR is therefore based only on deterministic methods, different from modern approach for Light Water Reactors (LWR) which also benefit from probabilistic methods. Usually, the approach adopted in LMFR safety assessments is to employ a variety of codes, somewhat different for the each other, to analyze transients looking for a comprehensive solution and including uncertainties. In this frame, new best estimate simulation codes are of prime importance in order to analyze fast reactors steady state and transients. This thesis is focused on the development of a coupled code system for best estimate analysis in fast critical reactor. Currently due to the increase in the computational resources, Monte Carlo methods for neutrons transport can be used for detailed full core calculations. Furthermore, Monte Carlo codes are usually taken as reference for deterministic diffusion multigroups codes in fast reactors applications because they employ point-wise cross sections in an exact geometry model and intrinsically account for directional dependence of the ux. The coupling methodology presented here uses MCNP to calculate the power deposition within the reactor. The subchannel code COBRA-IV calculates the temperature and density distribution within the reactor. COBRA-IV is suitable for fast reactors applications because it has been validated against experimental results in sodium rod bundles. The proper correlations for liquid metal applications have been added to the thermal-hydraulics program. Both codes are coupled at steady state using an iterative method and external files exchange. The main issue in the Monte Carlo/thermal-hydraulics steady state coupling is the cross section handling to take into account Doppler broadening when temperature rises. Among every available options, the pseudo materials approach has been chosen in this thesis. This approach obtains reasonable results in fast reactor applications. Furthermore, geometrical changes caused by large temperature gradients in the core, are of major importance in fast reactor due to the large neutron mean free path. An additional module has therefore been included in order to simulate the reactor geometry in hot state or to estimate the reactivity due to core expansion in a transient. The module automatically calculates the fuel length, cladding radius, fuel assembly pitch and diagrid radius with the temperature. This effect will be crucial in some unprotected transients. Also related to geometrical changes, an automatic control rod movement feature has been implemented in order to achieve a just critical reactor or to calculate control rod worth. A step forward in the coupling platform is the dynamic simulation. Since MCNP performs only steady state calculations for critical systems, the more straight forward option without modifying MCNP source code, is to use the flux factorization approach solving separately the flux shape and amplitude. In this thesis two options have been studied to tackle time dependent neutronic simulations using a Monte Carlo code: adiabatic and quasistatic methods. The adiabatic methods uses a staggered time coupling scheme for the time advance of neutronics and the thermal-hydraulics calculations. MCNP computes the fundamental mode of the neutron flux distribution and the reactivity at the end of each time step and COBRA-IV the thermal properties at half of the the time steps. To calculate the flux amplitude evolution a solver of the point kinetics equations is used. This method calculates the static reactivity in each time step that in general is different from the dynamic reactivity calculated with the exact flux distribution. Nevertheless, for close to critical situations, both reactivities are similar and the method leads to acceptable practical results. In this line, an improved method as an attempt to take into account the effect of delayed neutron source in the transient flux shape evolutions is developed. The scheme performs a quasistationary calculation per time step with MCNP. This quasistationary simulations is based con the constant delayed source approach, taking into account the importance of each criticality cycle in the final flux estimation. Both adiabatic and quasistatic methods have been verified against the diffusion code COBAYA3, using a theoretical kinetic exercise. Finally, a transient in a critical 100 MWth lead-bismuth-eutectic reactor concept is analyzed using the adiabatic method as an application example in a real system.

Dynamic interactions between solids and viscous liquids with free surface = Interacciones dinámicas entre sólidos y líquidos viscosos con superficie libre

En esta tesis se investiga la interacción entre un fluido viscoso y un cuerpo sólido en presencia de una superficie libre. El problema se expresa teóricamente poniendo especial atención a los aspectos de conservación de energía y de la interacción del fluido con el cuerpo. El problema se considera 2D y monofásico, y un desarrollo matemático permite una descomposición de los términos disipativos en términos relacionados con la superficie libre y términos relacionados con la enstrofía. El modelo numérico utilizado en la tesis se basa en el método sin malla Smoothed Particle Hydrodynamics (SPH). De manera análoga a lo que se hace a nivel continuo, las propiedades de conservación se estudian en la tesis con el sistema discreto de partículas. Se tratan también las condiciones de contorno de un cuerpo que se mueve en un flujo viscoso, implementadas con el método ghost-fluid. Se ha desarrollado un algoritmo explícito de interacción fluido / cuerpo. Se han documentado algunos casos de modo detallado con el objetivo de comprobar la capacidad del modelo para reproducir correctamente la disipación de energía y el movimiento del cuerpo. En particular se ha investigado la atenuación de una onda estacionaria, comparando la simulación numérica con predicciones teóricas. Se han realizado otras pruebas para monitorizar la disipación de energía para flujos más violentos que implican la fragmentación de la superficie libre. La cantidad de energía disipada con los diferentes términos se ha evaluado en los casos estudiados con el modelo numérico. Se han realizado otras pruebas numéricas para verificar la técnica de modelización de la interacción fluido / cuerpo, concretamente las fuerzas ejercidas por las olas en cuerpos con formas simples, y el equilibrio de un cuerpo flotante con una forma compleja. Una vez que el modelo numérico ha sido validado, se han realizado simulaciones numéricas para obtener una comprensión más completa de la física implicada en casos (casi) realistas sobre los había aspectos que no se conocían suficientemente. En primer lugar se ha estudiado el el flujo alrededor de un cilindro bajo la superficie libre. El estudio se ha realizado con un número de Reynolds moderado, para un rango de inmersiones del cilindro y números de Froude. La solución numérica permite una investigación de los patrones complejos que se producen. La estela del cilindro interactúa con la superficie libre. Se han identificado algunos inestabilidades características. El segundo estudio se ha realizado sobre el problema de sloshing, tanto experimentalmente como numéricamente. El análisis se restringe a aguas poco profundas y con oscilación horizontal, pero se ha estudiado un gran número de condiciones, lo que lleva a una comprensión bastante completa de los sistemas de onda involucradas. La última parte de la tesis trata también sobre un problema de sloshing pero esta vez el tanque está oscilando con rotación y hay acoplamiento con un sistema mecánico. El sistema se llama pendulum-TLD (Tuned Liquid Damper - con líquido amortiguador). Este tipo de sistema se utiliza normalmente para la amortiguación de las estructuras civiles. El análisis se ha realizado analíticamente, numéricamente y experimentalmente utilizando líquidos con viscosidades diferentes, centrándose en características no lineales y mecanismos de disipación. ABSTRA C T The subject of the present thesis is the interaction between a viscous fluid and a solid body in the presence of a free surface. The problem is expressed first theoretically with a particular focus on the energy conservation and the fluid-body interaction. The problem is considered 2D and monophasic, and some mathematical development allows for a decomposition of the energy dissipation into terms related to the Free Surface and others related to the enstrophy. The numerical model used on the thesis is based on Smoothed Particle Hydrodynamics (SPH): a computational method that works by dividing the fluid into particles. Analogously to what is done at continuum level, the conservation properties are studied on the discrete system of particles. Additionally the boundary conditions for a moving body in a viscous flow are treated and discussed using the ghost-fluid method. An explicit algorithm for handling fluid-body coupling is also developed. Following these theoretical developments on the numerical model, some test cases are devised in order to test the ability of the model to correctly reproduce the energy dissipation and the motion of the body. The attenuation of a standing wave is used to compare what is numerically simulated to what is theoretically predicted. Further tests are done in order to monitor the energy dissipation in case of more violent flows involving the fragmentation of the free-surface. The amount of energy dissipated with the different terms is assessed with the numerical model. Other numerical tests are performed in order to test the fluid/body interaction method: forces exerted by waves on simple shapes, and equilibrium of a floating body with a complex shape. Once the numerical model has been validated, numerical tests are performed in order to get a more complete understanding of the physics involved in (almost) realistic cases. First a study is performed on the flow passing a cylinder under the free surface. The study is performed at moderate Reynolds numbers, for various cylinder submergences, and various Froude numbers. The capacity of the numerical solver allows for an investigation of the complex patterns which occur. The wake from the cylinder interacts with the free surface, and some characteristical flow mechanisms are identified. The second study is done on the sloshing problem, both experimentally and numerically. The analysis is restrained to shallow water and horizontal excitation, but a large number of conditions are studied, leading to quite a complete understanding of the wave systems involved. The last part of the thesis still involves a sloshing problem but this time the tank is rolling and there is coupling with a mechanical system. The system is named pendulum-TLD (Tuned Liquid Damper). This kind of system is normally used for damping of civil structures. The analysis is then performed analytically, numerically and experimentally for using liquids with different viscosities, focusing on non-linear features and dissipation mechanisms.

Real-Time Dynamic PGD Calculation of Non-Linear Soil Behavior

El estudio sísmico en los últimos 50 años y el análisis del comportamiento dinámico del suelo revelan que el comportamiento del suelo es altamente no lineal e histéretico incluso para pequeñas deformaciones. El comportamiento no lineal del suelo durante un evento sísmico tiene un papel predominante en el análisis de la respuesta de sitio. Los análisis unidimensionales de la respuesta sísmica del suelo son a menudo realizados utilizando procedimientos lineales equivalentes, que requieren generalmente pocos parámetros conocidos. Los análisis de respuesta de sitio no lineal tienen el potencial para simular con mayor precisión el comportamiento del suelo, pero su aplicación en la práctica se ha visto limitada debido a la selección de parámetros poco documentadas y poco claras, así como una inadecuada documentación de los beneficios del modelado no lineal en relación al modelado lineal equivalente. En el análisis del suelo, el comportamiento del suelo es aproximado como un sólido Kelvin-Voigt con un módulo de corte elástico y amortiguamiento viscoso. En el análisis lineal y no lineal del suelo se están considerando geometrías y modelos reológicos más complejos. El primero está siendo dirigido por considerar parametrizaciones más ricas del comportamiento linealizado y el segundo mediante el uso de multi-modo de los elementos de resorte-amortiguador con un eventual amortiguador fraccional. El uso del cálculo fraccional está motivado en gran parte por el hecho de que se requieren menos parámetros para lograr la aproximación exacta a los datos experimentales. Basándose en el modelo de Kelvin-Voigt, la viscoelasticidad es revisada desde su formulación más estándar a algunas descripciones más avanzada que implica la amortiguación dependiente de la frecuencia (o viscosidad), analizando los efectos de considerar derivados fraccionarios para representar esas contribuciones viscosas. Vamos a demostrar que tal elección se traduce en modelos más ricos que pueden adaptarse a diferentes limitaciones relacionadas con la potencia disipada, amplitud de la respuesta y el ángulo de fase. Por otra parte, el uso de derivados fraccionarios permite acomodar en paralelo, dentro de un análogo de Kelvin-Voigt generalizado, muchos amortiguadores que contribuyen a aumentar la flexibilidad del modelado para la descripción de los resultados experimentales. Obviamente estos modelos ricos implican muchos parámetros, los asociados con el comportamiento y los relacionados con los derivados fraccionarios. El análisis paramétrico de estos modelos requiere técnicas numéricas eficientemente capaces de simular comportamientos complejos. El método de la Descomposición Propia Generalizada (PGD) es el candidato perfecto para la construcción de este tipo de soluciones paramétricas. Podemos calcular off-line la solución paramétrica para el depósito de suelo, para todos los parámetros del modelo, tan pronto como tales soluciones paramétricas están disponibles, el problema puede ser resuelto en tiempo real, porque no se necesita ningún nuevo cálculo, el solucionador sólo necesita particularizar on-line la solución paramétrica calculada off-line, que aliviará significativamente el procedimiento de solución. En el marco de la PGD, parámetros de los materiales y los diferentes poderes de derivación podrían introducirse como extra-coordenadas en el procedimiento de solución. El cálculo fraccional y el nuevo método de reducción modelo llamado Descomposición Propia Generalizada han sido aplicado en esta tesis tanto al análisis lineal como al análisis no lineal de la respuesta del suelo utilizando un método lineal equivalente. ABSTRACT Studies of earthquakes over the last 50 years and the examination of dynamic soil behavior reveal that soil behavior is highly nonlinear and hysteretic even at small strains. Nonlinear behavior of soils during a seismic event has a predominant role in current site response analysis. One-dimensional seismic ground response analysis are often performed using equivalent-linear procedures, which require few, generally well-known parameters. Nonlinear analyses have the potential to more accurately simulate soil behavior, but their implementation in practice has been limited because of poorly documented and unclear parameter selection, as well as inadequate documentation of the benefits of nonlinear modeling relative to equivalent linear modeling. In soil analysis, soil behaviour is approximated as a Kelvin-Voigt solid with a elastic shear modulus and viscous damping. In linear and nonlinear analysis more complex geometries and more complex rheological models are being considered. The first is being addressed by considering richer parametrizations of the linearized behavior and the second by using multi-mode spring-dashpot elements with eventual fractional damping. The use of fractional calculus is motivated in large part by the fact that fewer parameters are required to achieve accurate approximation of experimental data. Based in Kelvin-Voigt model the viscoelastodynamics is revisited from its most standard formulation to some more advanced description involving frequency-dependent damping (or viscosity), analyzing the effects of considering fractional derivatives for representing such viscous contributions. We will prove that such a choice results in richer models that can accommodate different constraints related to the dissipated power, response amplitude and phase angle. Moreover, the use of fractional derivatives allows to accommodate in parallel, within a generalized Kelvin-Voigt analog, many dashpots that contribute to increase the modeling flexibility for describing experimental findings. Obviously these rich models involve many parameters, the ones associated with the behavior and the ones related to the fractional derivatives. The parametric analysis of all these models require efficient numerical techniques able to simulate complex behaviors. The Proper Generalized Decomposition (PGD) is the perfect candidate for producing such kind of parametric solutions. We can compute off-line the parametric solution for the soil deposit, for all parameter of the model, as soon as such parametric solutions are available, the problem can be solved in real time because no new calculation is needed, the solver only needs particularize on-line the parametric solution calculated off-line, which will alleviate significantly the solution procedure. Within the PGD framework material parameters and the different derivation powers could be introduced as extra-coordinates in the solution procedure. Fractional calculus and the new model reduction method called Proper Generalized Decomposition has been applied in this thesis to the linear analysis and nonlinear soil response analysis using a equivalent linear method.

Integrating runtime assertions with dynamic types: Structuring a derivation from an incomputable specification

An inherent incomputability in the specification of a functional language extension that combines assertions with dynamic type checking is isolated in an explicit derivation from mathematical specifications. The combination of types and assertions (into "dynamic assertion-types" - DATs) is a significant issue since, because the two are congruent means for program correctness, benefit arises from their better integration in contrast to the harm resulting from their unnecessary separation. However, projecting the "set membership" view of assertion-checking into dynamic types results in some incomputable combinations. Refinement of the specification of DAT checking into an implementation by rigorous application of mathematical identities becomes feasible through the addition of a "best-approximate" pseudo-equality that isolates the incomputable component of the specification. This formal treatment leads to an improved, more maintainable outcome with further development potential.

Dynamic simulation of chemical plant

A CSSL- type modular FORTRAN package, called ACES, has been developed to assist in the simulation of the dynamic behaviour of chemical plant. ACES can be harnessed, for instance, to simulate the transients in startups or after a throughput change. ACES has benefited from two existing simulators. The structure was adapted from ICL SLAM and most plant models originate in DYFLO. The latter employs sequential modularisation which is not always applicable to chemical engineering problems. A novel device of twice- round execution enables ACES to achieve general simultaneous modularisation. During the FIRST ROUND, STATE-VARIABLES are retrieved from the integrator and local calculations performed. During the SECOND ROUND, fresh derivatives are estimated and stored for simultaneous integration. ACES further includes a version of DIFSUB, a variable-step integrator capable of handling stiff differential systems. ACES is highly formalised . It does not use pseudo steady- state approximations and excludes inconsistent and arbitrary features of DYFLO. Built- in debug traps make ACES robust. ACES shows generality, flexibility, versatility and portability, and is very convenient to use. It undertakes substantial housekeeping behind the scenes and thus minimises the detailed involvement of the user. ACES provides a working set of defaults for simulation to proceed as far as possible. Built- in interfaces allow for reactions and user supplied algorithms to be incorporated . New plant models can be easily appended. Boundary- value problems and optimisation may be tackled using the RERUN feature. ACES is file oriented; a STATE can be saved in a readable form and reactivated later. Thus piecewise simulation is possible. ACES has been illustrated and verified to a large extent using some literature-based examples. Actual plant tests are desirable however to complete the verification of the library. Interaction and graphics are recommended for future work.

Dynamic simulation of chemical processes

This thesis describes the design and implementation of an interactive dynamic simulator called DASPRII. The starting point of this research has been an existing dynamic simulation package, DASP. DASPII is written in standard FORTRAN 77 and is implemented on universally available IBM-PC or compatible machines. It provides a means for the analysis and design of chemical processes. Industrial interest in dynamic simulation has increased due to the recent increase in concern over plant operability, resiliency and safety. DASPII is an equation oriented simulation package which allows solution of dynamic and steady state equations. The steady state can be used to initialise the dynamic simulation. A robust non linear algebraic equation solver has been implemented for steady state solution. This has increased the general robustness of DASPII, compared to DASP. A graphical front end is used to generate the process flowsheet topology from a user constructed diagram of the process. A conversational interface is used to interrogate the user with the aid of a database, to complete the topological information. An original modelling strategy implemented in DASPII provides a simple mechanism for parameter switching which creates a more flexible simulation environment. The problem description generated is by a further conversational procedure using a data-base. The model format used allows the same model equations to be used for dynamic and steady state solution. All the useful features of DASPI are retained in DASPII. The program has been demonstrated and verified using a number of example problems, Significant improvements using the new NLAE solver have been shown. Topics requiring further research are described. The benefits of variable switching in models has been demonstrated with a literature problem.

Dynamic simulation of chemical plant

This thesis describes the design and implementation of a new dynamic simulator called DASP. It is a computer program package written in standard Fortran 77 for the dynamic analysis and simulation of chemical plants. Its main uses include the investigation of a plant's response to disturbances, the determination of the optimal ranges and sensitivities of controller settings and the simulation of the startup and shutdown of chemical plants. The design and structure of the program and a number of features incorporated into it combine to make DASP an effective tool for dynamic simulation. It is an equation-oriented dynamic simulator but the model equations describing the user's problem are generated from in-built model equation library. A combination of the structuring of the model subroutines, the concept of a unit module, and the use of the connection matrix of the problem given by the user have been exploited to achieve this objective. The Executive program has a structure similar to that of a CSSL-type simulator. DASP solves a system of differential equations coupled to nonlinear algebraic equations using an advanced mixed equation solver. The strategy used in formulating the model equations makes it possible to obtain the steady state solution of the problem using the same model equations. DASP can handle state and time events in an efficient way and this includes the modification of the flowsheet. DASP is highly portable and this has been demonstrated by running it on a number of computers with only trivial modifications. The program runs on a microcomputer with 640 kByte of memory. It is a semi-interactive program, with the bulk of all input data given in pre-prepared data files with communication with the user is via an interactive terminal. Using the features in-built in the package, the user can view or modify the values of any input data, variables and parameters in the model, and modify the structure of the flowsheet of the problem during a simulation session. The program has been demonstrated and verified using a number of example problems.

An investigation of the dynamic characteristics of a bolted-rotor system

A Jeffcott rotor consists of a disc at the centre of an axle supported at its end by bearings. A bolted Jeffcott rotor is formed by two discs, each with a shaft on one side. The discs are held together by spring loaded bolts near the outer edge. When the rotor turns there is tendency for the discs to separate on one side. This effect is more marked if the rotor is unbalanced, especially at resonance speeds. The equations of motion of the system have been developed with four degrees of freedom to include the rotor and bearing movements in the respective axes. These equations which include non-linear terms caused by the rotor opening, are subjected to external force such from rotor imbalance. A simulation model based on these equations was created using SIMULINK. An experimental test rig was used to characterise the dynamic features. Rotor discs open at a lateral displacement of the rotor of 0.8 mm. This is the threshold value used to show the change of stiffness from high stiffness to low stiffness. The experimental results, which measure the vibration amplitude of the rotor, show the dynamic behaviour of the bolted rotor due to imbalance. Close agreement of the experimental and theoretical results from time histories, waterfall plots, pseudo-phase plots and rotor orbit plot, indicated the validity of the model and existence of the non-linear jump phenomenon.

Implementation of pseudo J-integral based Paris’ law for fatigue cracking in asphalt mixtures and pavements

Pavement analysis and design for fatigue cracking involves a number of practical problems like material assessment/screening and performance prediction. A mechanics-aided method can answer these questions with satisfactory accuracy in a convenient way when it is appropriately implemented. This paper presents two techniques to implement the pseudo J-integral based Paris’ law to evaluate and predict fatigue cracking in asphalt mixtures and pavements. The first technique, quasi-elastic simulation, provides a rational and appropriate reference modulus for the pseudo analysis (i.e., viscoelastic to elastic conversion) by making use of the widely used material property: dynamic modulus. The physical significance of the quasi-elastic simulation is clarified. Introduction of this technique facilitates the implementation of the fracture mechanics models as well as continuum damage mechanics models to characterize fatigue cracking in asphalt pavements. The second technique about modeling fracture coefficients of the pseudo J-integral based Paris’ law simplifies the prediction of fatigue cracking without performing fatigue tests. The developed prediction models for the fracture coefficients rely on readily available mixture design properties that directly affect the fatigue performance, including the relaxation modulus, air void content, asphalt binder content, and aggregate gradation. Sufficient data are collected to develop such prediction models and the R2 values are around 0.9. The presented case studies serve as examples to illustrate how the pseudo J-integral based Paris’ law predicts fatigue resistance of asphalt mixtures and assesses fatigue performance of asphalt pavements. Future applications include the estimation of fatigue life of asphalt mixtures/pavements through a distinct criterion that defines fatigue failure by its physical significance.

Development of a dynamic headspace concentration technique for the non-contact sampling of human odor samples and the creation of canine training aids

Human scent and human remains detection canines are used to locate living or deceased humans under many circumstances. Human scent canines locate individual humans on the basis of their unique scent profile, while human remains detection canines locate the general scent of decomposing human remains. Scent evidence is often collected by law enforcement agencies using a Scent Transfer Unit, a dynamic headspace concentration device. The goals of this research were to evaluate the STU-100 for the collection of human scent samples, and to apply this method to the collection of living and deceased human samples, and to the creation of canine training aids. The airflow rate and collection material used with the STU-100 were evaluated using a novel scent delivery method. Controlled Odor Mimic Permeation Systems were created containing representative standard compounds delivered at known rates, improving the reproducibility of optimization experiments. Flow rates and collection materials were compared. Higher air flow rates usually yielded significantly less total volatile compounds due to compound breakthrough through the collection material. Collection from polymer and cellulose-based materials demonstrated that the molecular backbone of the material is a factor in the trapping and releasing of compounds. The weave of the material also affects compound collection, as those materials with a tighter weave demonstrated enhanced collection efficiencies. Using the optimized method, volatiles were efficiently collected from living and deceased humans. Replicates of the living human samples showed good reproducibility; however, the odor profiles from individuals were not always distinguishable from one another. Analysis of the human remains samples revealed similarity in the type and ratio of compounds. Two types of prototype training aids were developed utilizing combinations of pure compounds as well as volatiles from actual human samples concentrated onto sorbents, which were subsequently used in field tests. The pseudo scent aids had moderate success in field tests, and the Odor pad aids had significant success. This research demonstrates that the STU-100 is a valuable tool for dog handlers and as a field instrument; however, modifications are warranted in order to improve its performance as a method for instrumental detection.

Dynamic Behavior and Fatigue Life of Highway Bridges Due to Doubling Heavy Vehicles

An increase in the demand for the freight shipping in the United States has been predicted for the near future and Longer Combination Vehicles (LCVs), which can carry more loads in each trip, seem like a good solution for the problem. Currently, utilizing LCVs is not permitted in most states of the US and little research has been conducted on the effects of these heavy vehicles on the roads and bridges. In this research, efforts are made to study these effects by comparing the dynamic and fatigue effects of LCVs with more common trucks. Ten Steel and prestressed concrete bridges with span lengths ranging from 30’ to 140’ are designed and modeled using the grid system in MATLAB. Additionally, three more real bridges including two single span simply supported steel bridges and a three span continuous steel bridge are modeled using the same MATLAB code. The equations of motion of three LCVs as well as eight other trucks are derived and these vehicles are subjected to different road surface conditions and bumps on the roads and the designed and real bridges. By forming the bridge equations of motion using the mass, stiffness and damping matrices and considering the interaction between the truck and the bridge, the differential equations are solved using the ODE solver in MATLAB and the results of the forces in tires as well as the deflections and moments in the bridge members are obtained. The results of this study show that for most of the bridges, LCVs result in the smallest values of Dynamic Amplification Factor (DAF) whereas the Single Unit Trucks cause the highest values of DAF when traveling on the bridges. Also in most cases, the values of DAF are observed to be smaller than the 33% threshold suggested by the design code. Additionally, fatigue analysis of the bridges in this study confirms that by replacing the current truck traffic with higher capacity LCVs, in most cases, the remaining fatigue life of the bridge is only slightly decreased which means that taking advantage of these larger vehicles can be a viable option for decision makers.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Reference Values For High-density Lipoprotein Particle Size And Volume By Dynamic Light Scattering In A Brazilian Population Sample And Their Relationships With Metabolic Parameters.

Current data indicate that the size of high-density lipoprotein (HDL) may be considered an important marker for cardiovascular disease risk. We established reference values of mean HDL size and volume in an asymptomatic representative Brazilian population sample (n=590) and their associations with metabolic parameters by gender. Size and volume were determined in HDL isolated from plasma by polyethyleneglycol precipitation of apoB-containing lipoproteins and measured using the dynamic light scattering (DLS) technique. Although the gender and age distributions agreed with other studies, the mean HDL size reference value was slightly lower than in some other populations. Both HDL size and volume were influenced by gender and varied according to age. HDL size was associated with age and HDL-C (total population); non- white ethnicity and CETP inversely (females); HDL-C and PLTP mass (males). On the other hand, HDL volume was determined only by HDL-C (total population and in both genders) and by PLTP mass (males). The reference values for mean HDL size and volume using the DLS technique were established in an asymptomatic and representative Brazilian population sample, as well as their related metabolic factors. HDL-C was a major determinant of HDL size and volume, which were differently modulated in females and in males.

Interaction Between Fiscal And Monetary Policy In A Dynamic Nonlinear Model.

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case.