Finite element methods for deterministic simulation of polymeric fluids

In this work we consider a finite element method for solving the coupled Navier-Stokes (NS) and Fokker-Planck (FP) multiscale model that describes the dynamics of dilute polymeric fluids. Deterministic approaches such as ours have not received much attention in the literature because they present a formidable computational challenge, due to the fact that the analytical solution to the Fokker-Planck equation may be a function of a large number of independent variables. For instance, to simulate a non-homogeneous flow one must solve the coupled NS-FP system in which (for a 3-dimensional flow, using the dumbbell model for polymers) the Fokker-Planck equation is posed in a 6-dimensional domain. In this work we seek to demonstrate the feasibility of our deterministic approach. We begin by discussing the physical and mathematical foundations of the NS-FP model. We then present a literature review of relevant developments in computational rheology and develop our deterministic finite element based method in detail. Numerical results demonstrating the efficiency of our approach are then given, including some novel results for the simulation of a fully 3-dimensional flow. We utilise parallel computation to perform the large-scale numerical simulations

Formal Proofs for Nonlinear Optimization

We present a formally verified global optimization framework. Given a semialgebraic or transcendental function $f$ and a compact semialgebraic domain $K$, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of $f$ over $K$. This method allows to bound in a modular way some of the constituents of $f$ by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.Comment: 24 pages, 2 figures, 3 table

Communication in membrana Systems with symbol Objects.

Esta tesis está dedicada a los sistemas de membranas con objetos-símbolo como marco teórico de los sistemas paralelos y distribuidos de procesamiento de multiconjuntos.Una computación de parada puede aceptar, generar o procesar un número, un vector o una palabra; por tanto el sistema define globalmente (a través de los resultados de todas sus computaciones) un conjunto de números, de vectores, de palabras (es decir, un lenguaje), o bien una función. En esta tesis estudiamos la capacidad de estos sistemas para resolver problemas particulares, así como su potencia computacional. Por ejemplo, las familias de lenguajes definidas por diversas clases de estos sistemas se comparan con las familias clásicas, esto es, lenguajes regulares, independientes del contexto, generados por sistemas 0L tabulados extendidos, generados por gramáticas matriciales sin chequeo de apariciones, recursivamente enumerables, etc. Se prestará especial atención a la comunicación de objetos entre regiones y a las distintas formas de cooperación entre ellos.Se pretende (Sección 3.4) realizar una formalización los sistemas de membranas y construir una herramienta tipo software para la variante que usa cooperación no distribuida, el navegador de configuraciones, es decir, un simulador, en el cual el usuario selecciona la siguiente configuración entre todas las posibles, estando permitido volver hacia atrás. Se considerarán diversos modelos distribuidos. En el modelo de evolución y comunicación (Capítulo 4) separamos las reglas tipo-reescritura y las reglas de transporte (llamadas symport y antiport). Los sistemas de bombeo de protones (proton pumping, Secciones 4.8, 4.9) constituyen una variante de los sistemas de evolución y comunicación con un modo restrictivo de cooperación. Un modelo especial de computación con membranas es el modelo puramente comunicativo, en el cual los objetos traspasan juntos una membrana. Estudiamos la potencia computacional de las sistemas de membranas con symport/antiport de 2 o 3 objetos (Capítulo 5) y la potencia computacional de las sistemas de membranas con alfabeto limitado (Capítulo 6).El determinismo (Secciones 4.7, 5.5, etc.) es una característica especial (restrictiva) de los sistemas computacionales. Se pondrá especial énfasis en analizar si esta restricción reduce o no la potencia computacional de los mismos. Los resultados obtenidos para sistemas de bombeo del protones están transferidos (Sección 7.3) a sistemas con catalizadores bistabiles. Unos ejemplos de aplicación concreta de los sistemas de membranas (Secciones 7.1, 7.2) son la resolución de problemas NP-completos en tiempo polinomial y la resolución de problemas de ordenación.This thesis deals with membrane systems with symbol objects as a theoretical framework of distributed parallel multiset processing systems.A halting computation can accept, generate or process a number, a vector or a word, so the system globally defines (by the results of all its computations) a set of numbers or a set of vectors or a set of words, (i.e., a language), or a function. The ability of these systems to solve particular problems is investigated, as well as their computational power, e.g., the language families defined by different classes of these systems are compared to the classical ones, i.e., regular, context-free, languages generated by extended tabled 0L systems, languages generated by matrix grammars without appearance checking, recursively enumerable languages, etc. Special attention is paid to communication of objects between the regions and to the ways of cooperation between the objects.An attempt to formalize the membrane systems is made (Section 3.4), and a software tool is constructed for the non-distributed cooperative variant, the configuration browser, i.e., a simulator, where the user chooses the next configuration among the possible ones and can go back. Different distributed models are considered. In the evolution-communication model (Chapter 4) rewriting-like rules are separated from transport rules. Proton pumping systems (Sections 4.8, 4.9) are a variant of the evolution-communication systems with a restricted way of cooperation. A special membrane computing model is a purely communicative one: the objects are moved together through a membrane. We study the computational power of membrane systems with symport/antiport of 2 or 3 objects (Chapter 5) and the computational power of membrane systems with a limited alphabet (Chapter 6).Determinism (Sections 4.7, 5.5, etc.) is a special property of computational systems; the question of whether this restriction reduces the computational power is addressed. The results on proton pumping systems can be carried over (Section 7.3) to the systems with bi-stable catalysts. Some particular examples of membrane systems applications are solving NP-complete problems in polynomial time, and solving the sorting problem

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry

A compiler level intermediate representation based binary analysis system and its applications

Analyzing and optimizing programs from their executables has received a lot of attention recently in the research community. There has been a tremendous amount of activity in executable-level research targeting varied applications such as security vulnerability analysis, untrusted code analysis, malware analysis, program testing, and binary optimizations. The vision of this dissertation is to advance the field of static analysis of executables and bridge the gap between source-level analysis and executable analysis. The main thesis of this work is scalable static binary rewriting and analysis using compiler-level intermediate representation without relying on the presence of metadata information such as debug or symbolic information. In spite of a significant overlap in the overall goals of several source-code methods and executables-level techniques, several sophisticated transformations that are well-understood and implemented in source-level infrastructures have yet to become available in executable frameworks. It is a well known fact that a standalone executable without any meta data is less amenable to analysis than the source code. Nonetheless, we believe that one of the prime reasons behind the limitations of existing executable frameworks is that current executable frameworks define their own intermediate representations (IR) which are significantly more constrained than an IR used in a compiler. Intermediate representations used in existing binary frameworks lack high level features like abstract stack, variables, and symbols and are even machine dependent in some cases. This severely limits the application of well-understood compiler transformations to executables and necessitates new research to make them applicable. In the first part of this dissertation, we present techniques to convert the binaries to the same high-level intermediate representation that compilers use. We propose methods to segment the flat address space in an executable containing undifferentiated blocks of memory. We demonstrate the inadequacy of existing variable identification methods for their promotion to symbols and present our methods for symbol promotion. We also present methods to convert the physically addressed stack in an executable to an abstract stack. The proposed methods are practical since they do not employ symbolic, relocation, or debug information which are usually absent in deployed executables. We have integrated our techniques with a prototype x86 binary framework called \emph{SecondWrite} that uses LLVM as the IR. The robustness of the framework is demonstrated by handling executables totaling more than a million lines of source-code, including several real world programs. In the next part of this work, we demonstrate that several well-known source-level analysis frameworks such as symbolic analysis have limited effectiveness in the executable domain since executables typically lack higher-level semantics such as program variables. The IR should have a precise memory abstraction for an analysis to effectively reason about memory operations. Our first work of recovering a compiler-level representation addresses this limitation by recovering several higher-level semantics information from executables. In the next part of this work, we propose methods to handle the scenarios when such semantics cannot be recovered. First, we propose a hybrid static-dynamic mechanism for recovering a precise and correct memory model in executables in presence of executable-specific artifacts such as indirect control transfers. Next, the enhanced memory model is employed to define a novel symbolic analysis framework for executables that can perform the same types of program analysis as source-level tools. Frameworks hitherto fail to simultaneously maintain the properties of correct representation and precise memory model and ignore memory-allocated variables while defining symbolic analysis mechanisms. We exemplify that our framework is robust, efficient and it significantly improves the performance of various traditional analyses like global value numbering, alias analysis and dependence analysis for executables. Finally, the underlying representation and analysis framework is employed for two separate applications. First, the framework is extended to define a novel static analysis framework, \emph{DemandFlow}, for identifying information flow security violations in program executables. Unlike existing static vulnerability detection methods for executables, DemandFlow analyzes memory locations in addition to symbols, thus improving the precision of the analysis. DemandFlow proposes a novel demand-driven mechanism to identify and precisely analyze only those program locations and memory accesses which are relevant to a vulnerability, thus enhancing scalability. DemandFlow uncovers six previously undiscovered format string and directory traversal vulnerabilities in popular ftp and internet relay chat clients. Next, the framework is extended to implement a platform-specific optimization for embedded processors. Several embedded systems provide the facility of locking one or more lines in the cache. We devise the first method in literature that employs instruction cache locking as a mechanism for improving the average-case run-time of general embedded applications. We demonstrate that the optimal solution for instruction cache locking can be obtained in polynomial time. Since our scheme is implemented inside a binary framework, it successfully addresses the portability concern by enabling the implementation of cache locking at the time of deployment when all the details of the memory hierarchy are available