Academic literature on the topic 'Geometrical Partition'

The partition functions of Pasquier models on the cylinder, and the associated intertwiners, are considered. It is shown that earlier results due to Saleur and Bauer can be rephrased in a geometrical way, reminiscent of formulae found in certain purely elastic scattering theories. This establishes the positivity of these intertwiners in a general way and elucidates connections between these objects and the finite subgroups of SU(2). It also offers the hope that analogous geometrical structures might lie behind the so-far mysterious results found by DiFrancesco and Zuber in their search for generalisations of these models.

AbstractThe permeability of rocks fractured by random, planar cracks, is expressed as a classical bond percolation problem on a random lattice, by Voronoi partition of space. The percolation threshold is determined as a function of the statistical characteristics of the cracks, or of their traces on an arbitrary face of the rock, by using an empirical quasi-invariant of percolation theory.

The 3D scanning device can capture millions of points with the excellent geometrical precision except for large amount of redundant ones, which could bring some difficulties for the subsequent digital geometrical processing (DGP), so the simplification of the point cloud has become a considerable study in point cloud applications. Given this problem, we propose a novel approach, which could decrease the geometrical error by partitioning the surface into many patches with some similar geometrical features before using the adaptive hierarchical space partition (AHSP) approach, in order to improve the AHSP simplification. We also experiment on three models and do comparative analysis. Fortunately, the results prove that our algorithm can make the anisotropy feature in the surface of the models described explicitly, the geometrical error decreased by 15.8 percent, and the simplification rate kept up with other approaches. In addition, it can provide the high quality models for the 3D digital model editing, such as the geometrical modeling, the point cloud blending.

Partitions [Formula: see text] of A+ into m pairwise disjoint languages L1, L2, …, Lm such that [Formula: see text] for k = 1, 2, …, m are considered. It is proved that such a closed partition of A+ can separate the words u1, u2, …, um ∈ A+ (i.e., each Lk contains exactly one word of the sequence u1, u2, …, um) if and only if for each pair i, j of distinct elements in {1, 2, …, m}, the words ui and uj do not commute. Furthermore, it is proved that the separating languages can be chosen to be regular. In case that the Parikh images of the words are linearly independent, the choice of the separating languages may be based on geometrical intuition.

The parallel implementation of image processing algorithms implies an important choice of data distribution strategy. In order to handle the specific constraints associated with images, data distribution must take into account not only the locality of the data and its geometrical regularity but also the possible irregular computation costs associated with different image elements. A widely studied field to tackle this problem is the family of methods related to rectilinear partitioning. We introduce two fully parallel heuristics that compute suboptimal partitions, with a better complexity than the best known algorithms that compute optimal partitions. In this paper, we compare our heuristics to an optimal partitioning, both in terms of execution time and accuracy of the partition. We give some theoretical bounds on the quality of these heuristics that are corroborated by results of random numerical experiments and real applications.

We provide a non-perturbative geometrical characterization of the partition function of ndimensional quantum gravity based on a rough classification of Riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.

By increasing the application of lightweight constructions, sound transmission between the adjacent enclosures becomes a more important consideration in designing new buildings. In this article, the parameters that may significantly affect the sound transmission level through a partition between two adjacent enclosures are investigated, i.e. geometrical dimensions, arrangement of enclosures, boundary conditions, multi-layered partitions, and framed (or reinforced) conditions of the partitions. For this purpose, sound transmission is modelled using the finite-element method. The obtained results from sound transmission using Perspex party walls with different width and boundary conditions are compared with those obtained from a double-layered wall with an air layer. The effects of an enclosure's arrangements and dimensions on sound transmission of the party walls are also studied. Using the cross-framed party wall causes more noise reduction than the double-layered party wall. The results also show that sound transmission between rooms with an asymmetric arrangement is less than that obtained from a symmetric configuration.

We study the asymptotic behavior of the free partition function in thet→0+limit for a diffusion process which consists ofd-independent, one-dimensional, symmetric,2s-stable processes in a hyperrectangular cavityK⊂Rdwith an absorbing boundary. Each term of the partition function for this polyhedron ind-dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis.

This paper presents a simple and efficient coupled finite element-element free Galekrin (FE-EFG) approach to simulate three-dimensional composite patch repair problem. In coupled FE-EFG approach, extended element free Galerkin (XEFG) is used near the crack surface as it can accurately model the discontinuities while the rest of domain is approximated by standard finite element (FE) method. The transition between FE and XEFG was modelled by a ramp function. The geometric discontinuities like crack and material interface are modeled by adding enrichment functions in EFG displacement approximation through partition of unity (PU). The location of geometrical discontinuity is traced by vector level set method. A domain based J-integral approach is used for the evaluation of stress intensity factors.

La presente tesi tratta due argomenti distinti. Il Capitolo 1 e il Capitolo 2 riguardano problemi di evoluzione di interfacce nel piano. Nel Capitolo 1 viene considerata l’evoluzione di un materiale policristallino con tre (o più) fasi, in presenza di un’anisotropia cristallina (pari) ϕo la cui linea di livello 1, Fϕ :={ϕo ≤1} (Frank diagram), è un poligono regolare di n lati. La funzione duale ϕ : R2 →R definita da ϕ(ξ) := sup{ξ·η : ϕo(η)≤1}´e anch’essa un’anisotropia cristallina e Wϕ := {ϕ ≤ 1} è detta Wulff shape. In particolare, viene studiato il moto per curvatura cristallina di triodi elementari, ossia speciali reti piane di curve che sono frontiere regolari di insiemi rappresentanti tre fasi distinte di un materiale. Un triodo elementare è formato dall’unione di tre curve Lipschitziane, le interfacce, che si intersecano in un unico punto detto giunzione tripla. Ogni interfaccia è l’unione di un segmento di lunghezza finita e di una semiretta che riproduce due lati consecutivi della Wulff shape Wϕ. Viene analizzata l’esitenza locale e globale e la stabilità del flusso. Si dimostra l’esistenza locale di un unico flusso regolare stabile a partire da un dato iniziale regolare stabile: se n, il numero dei lati della Wulff shapeWϕ, è un multiplo di 6 allora il flusso è globale e converge a un flusso omotetico per t →+∞. L’analisi del comportamento del flusso per tempi grandi richiede lo studio della stabilità. La stabilità è l’ingrediente che assicura che nessun segmento si sviluppa dalla giunzione tripla durante il flusso. In generale, il flusso può diventare instabile in un tempo finito: se ciò accade e tutte le lunghezze dei segmenti finiti sono strettamente positive per tale tempo,è possibile costruire un flusso regolare per tempi successivi aggiungendo in corrispondenza della giunzione tripla in una delle tre interfacce un segmento infinitesimo opportuno (o addirittura un arco di curva a curvatura cristallina nulla). ´E anche possibile che durante il flusso uno dei tre segmenti scompaia in un tempo finito. In tal caso, in tale tempo il campo vettoriale di Cahn-Hoffman ha un salto di discontinuità e ai tempi successivi la giunzione tripla si muove traslando lungo la semiretta adiacente. Ognuno di questi flussi ha la proprietà che tutte le curvature cristalline rimangono limitate (persino se un segmento appare o scompare). ´E importante sottolineare che Taylor aveva già predetto la nascita di nuovi segmenti dalla giunzione tripla (senza però dimostrarlo). Viene inoltre considerato il flusso per curvatura cristalina di una partizione regolare stabile formata da due triodi elementari adiacenti. Vengono discussi alcuni esempi di situazioni di colasso che portano a cambi di topologia, come ad esempio la collisione di due giunzioni triple. Questi esempi (come anche il risultato di esistenza per tempi piccoli) mostrano uno dei vantaggi del flusso per curvatura cristallino rispetto, ad esempio, all’usuale moto per curvatura: calcoli espliciti possono essere fatti, e nel caso di non unicità, è possibile confrontare le energie delle diverse evoluzioni (difficile nel caso euclideo). Nel Capitolo 2 viene introdotta, usando la teoria delle funzioni a variazione limitata a valori in S1, la sfera diR2, una nuova classe di funzionali energia definiti su partizioni. Attraverso la variazione prima del funzionale energia, viene fornito un nuovo modello per l’evoluzione di interfacce che parzialmente estende quello introdotto nel Capitolo 1 e che consiste in un problema di frontiera libera definito sulle funzioni a variazione limitata a valori in S1. Questo modello è legato all’evoluzione di materiali policristallini dove è consentito alla Wulff shape di ruotare. Assumendo l’esitenza locale del flusso, si dimostra che durante il flusso curve chiuse convesse rimangono convesse e curve chiuse embedded rimangono embedded. Il secondo argomento della tesi è trattato nel Capitolo 3: l’obiettivo è quello di estendere il metodo delle linee di livello a sistemi di equazioni differenziali alle derivate parziali. Il metodo che viene proposto è consistente con la precedente ricerca portata avanti da Evans per l’equazione del calore e da Giga e Sato per equazioni di Hamilton-Jacobi. Il nostro approccio segue una costruzione geometrica che è legate alla nozione di barriera introdotta da De Giorgi. L’idea principale è quella di forzare un principio di confronto tra varietà di diversa codimensione e richiedere che ogni sottolivello di una soluzione dell’equazione per le linee di livello, detta level set equation, sia una barriera per i grafici di soluzioni del corrispondente sistema. Tale metodo ben si applica a una classe di sistemi di equazioni quasi-lineari del primo ordine. Viene fornita la level set equation associata ad opportuni sitemi di leggi di conservazione del primo ordine, al flusso per curvatura media di una varietà di codimensione arbitraria e a sitemi di equazioni di reazione-diffusione. Infine, viene calcolata la level set equation associata al sistema soddisfatto dalle parametrizzazioni di curve piane che si muovono per curvatura.<br>The present thesis deals with two different subjects. Chapter 1 and Chapter 2 concern interfaces evolution problems in the plane. In Chapter 1 I consider the evolution of a polycrystalline material with three (or more) phases, in presence of for an even crystalline anisotropy ϕo whose one-sublevel set Fϕ := {ϕo ≤ 1} (the Frank diagram) is a regular polygon of n sides. The dual function ϕ : R2 → R defined by ϕ(ξ) := sup{ξ ·η : ϕo(η) ≤ 1} is crystalline too and Wϕ := {ϕ ≤ 1} is called the Wulff shape. I am particularly interested in the motion by crystalline curvature of special planar networks called elementary triods, namely a regular three-phase boundary given by the union of three Lipschitz curves, the interfaces, intersecting at a point called triple junction. Each interface is the union of a segment of finite length and a half-line, reproducing two consecutive sides of Wϕ. I analyze local and global existence and stability of the flow. I prove that there exists, locally in time, a unique stable regular flow starting from a stable regular initial datum. I show that if n, the number of sides of Wϕ, is a multiple of 6 then the flow is global and converge to a homothetic flow as t → +∞. The analysis of the long time behavior requires the study of the stability. Stability is the ingredient that ensures that no additional segments develop at the triple junction during the flow. In general, the flow may become unstable at a finite time: if this occurs and none of the segments desappears, it is possible to construct a regular flow at subsequent times by adding an infinitesimal segment (or even an arc with zero crystalline curvature) at the triple junction. I also show that a segment may desappear. In such a case, the Cahn-Hoffman vector field Nmin has a jump discontinuity and the triple junction translates along the remaining adjacent half-line at subsequent times. Each of these flows has the property that all crystalline curvatures remain bounded (even if a segment appears or disappears). I want to stress that Taylor already predicted the appearance of new edges from a triple junction. I also consider the crystalline curvature flow starting from a stable ϕ-regular partition formed by two adjacent elementary triods. I discuss some examples of collapsing situations that lead to changes of topology, such as for instance the collision of two triple junctions. These examples (as well as the local in time existence result) show one of the advantages of crystalline flows with respect, for instance, to the usual mean curvature flow: explicit computations can be performed to some extent, and in case of nonuniqueness, a comparison between the energies of different evolutions (difficult in the euclidean case) can be made. In Chapter 2 we introduce, using the theory of S1-valued functions of bounded variations, a class of energy functionals defined on partitions and we produce, through the first variation, a new model for the evolution of interfaces which partially extends the one in Chapter 1 and which consists of a free boundary problem defined on S1-valued functions of bounded variation. This model is related to the evolution of polycrystals where the Wulff shape is allowed to rotate. Assuming the local existence of the flow, we show convexity preserving and embeddedness preserving properties. The second subject of the thesis is considered in Chapter 3 where we aim to extend the level set method to systems of PDEs. The method we propose is consistent with the previous research pursued by Evans for the heat equation and by Giga and Sato for Hamilton-Jacobi equations. Our approach follows a geometric construction related to the notion of barriers introduced by De Giorgi. The main idea is to force a comparison principle between manifolds of different codimension and require each sub-level of a solution of the level set equation to be a barrier for the graph of a solution of the corresponding system. We apply the method for a class of systems of first order quasi-linear equations. We compute the level set equation associated with suitable first order systems of conservation laws, with the mean curvature flow of a manifold of arbitrary codimension and with systems of reaction-diffusion equations. Finally, we provide a level set equation associated with the parametric curvature flow of planar curves.

This thesis investigates the representations of the symmetric group on the homology of the dual matroid of a complete graph. These representations arise as follows: with each graph we can associate a matroid, by taking the set of edges of the graph as ground set and the edge sets of simple cycles as the circuits of the matroid. We focus on the dual of the matroid of the complete graph. We calculate the homology of the simplicial complex L associated with this matroid. Permuting the vertices of the complete graph induces a permutation on the edge set which is a vertex map of the simplicial complex. This vertex map sends independents to independents, thus inducing a simplicial map from the polytope of L to itself, hence on the homology spaces of L. This defines a representation of the symmetric group on the homology Hi(L,C). We show that the above representation is induced from a primitive representation of the cyclic subgroup of order n.

A interação entre fluidos e estruturas caracteriza um problema multi-físico não linear e está presente numa grande variedade de áreas da engenharia. Este trabalho apresenta o desenvolvi mento de ferramentas computacionais com base no Método dos Elementos Finitos (MEF) para a análise de interação fluido-estrutura (IFE) considerando escoamentos com baixas velocidades. Dada a interdisciplinaridade do tema, se faz necessário o estudo em três diferentes assuntos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional, e o problema de acoplamento. No caso da dinâmica das estruturas empregar-se um elemento finito que seja adequado para a simulação de problemas de IFE, que claramente demandam uma análise não linear geométrica, optando-se pelo emprego de uma formulação descrita em posições, a qual evita problemas relativos à aproximação de rotações finitas. Quanto à dinâmica dos fluidos computacional, é empregado um método estável e ao mesmo tempo sensível à movimentação da estrutura, utilizando a descrição Lagrangeana-Euleriana Arbitrária (ALE). Os casos considerados neste trabalho, assim como muitos dos problemas de engenharia, ocorrem com escoamentos em baixas velocidades, implicando na incompressibilidade do fluido, o que demanda, para um método estável, a utilização de elementos que atendam à condição de Ladyzhenskaya-Babuska-Brezzi (LBB). Além disso, é necessário também o emprego de métodos que consigam neutralizar as variações espúrias decorrentes da não-linearidade de possíveis escoamentos com convecção dominante e que surgem com a aplicação do processo clássico de Galerkin. Para superar esse problema, é aplicado o método Streamline-Upwind/Petrov-Galerkin (SUPG), que adiciona difusividade artificial na direção do escoamento, controlando a amplitude dos termos convectivos. No que se refere ao acoplamento fluido-casca, buscam-se modularidade e versatilidade adotando-se o modelo particionado. O modelo de acoplamento implementado garante ainda a utilização de malhas do fluido e da estrutura sem a necessidade de coincidência de nós.<br>Interaction between fluids and structures characterizes a nonlinear multi-physics problem presente in a wide range of engineering fields. This works presets the development of computational tools based on finite element method (FEM) for fluid-structure interaction (FSI) analysis considering low speed flows (incompressible), as a great part of the engineering problems. Given the topic multidisciplinary nature, it is necessary to study three different subjects: the computational structural dynamics, the computational fluid mechanics and the coupling problem. Regarding structural mechanics, we seek to employ a finite element adequate to FSI simulation, what clearly demands a geometric nonlinear analysis. We chose to employ shell elements with formulation in terms of positions, which avoids problems related to finite rotations approximations. Concerning computational fluid dynamics, we employ a stable method, at same time sensible o structural movements, which is written in the arbitrary Lagrangian-Eulerian (ALE) description. The flow incompressibility demands, for a stable method, the use of elements according to the Ladyzhenskaya-Bbuska-Brezzi (LBB) condition. It is also necessary to employ methods able to neutralize the spurious variations that appears from convection dominated flows when applying the standard Galerking method. In order to overcome this problem, we apply the Streamline-Upwind/Petrov-Galerkin (SUPG) method, which adds artificial diffusivity to the streamline direction, controlling spurious variations. Considering the fluid-shell coupling, we seek modularity and versatility, adopting the partitioned model. The developed coupling model ensure the use of fluid and structure meshes with no need for matching nodes.

O presente trabalho consiste no uso do Método dos Elementos Finitos (MEF) para a análise de interação fluido-estruturas de barras com foco em problemas transientes envolvendo explosões ou outras ações com propagação de ondas de choque. Para isso é necessário o estudo de três diferentes aspectos: a dinâmica das estruturas computacional, a dinâmica dos fluidos computacional e o problema do acoplamento. No caso da dinâmica das estruturas computacional deve-se identificar em função da cinemática de deformações, quais são os requisitos para que um elemento seja adequado para analisar tais problemas, tendo em vista que a formulação deve admitir grandes deslocamentos. Para evitar problemas relacionados com aproximações de rotações finitas, opta-se por empregar uma formulação descrita em termos de posições e que leva em consideração os efeitos de empenamento da seção transversal. No caso da dinâmica dos fluidos computacional, busca-se uma formulação para escoamentos compressíveis que seja estável e ao mesmo tempo sensível ao movimento da estrutura, sendo empregado um algoritmo de integração temporal explícito baseado em características com as equações governantes descritas na forma Lagrangeana-Euleriana Arbitrária (ALE). No que se refere ao acoplamento, busca-se modularidade e versatilidade, empregando-se um modelo particionado fraco (explícito) de acoplamento e técnicas de transferência das condições de contorno (Dirichlet-Neummann), sendo estudados os efeitos de utilizar transferência bidirecional ou unidirecional dessas condições de contorno.<br>This work consists in the use of the Finite Element Method (FEM) for numerical analysis of fluid-bar structures, focusing on transient problems involving explosions or other actions with shock waves propagation. For this purpose, one needs to study three different aspects: the computational structural dynamics, the computational fluid dynamics and the coupling problem. Regarding computational structural dynamics, one need firstly to identify the requirements for an element to be adequate to analyze such problems, taking into account the fact that such element should admit large displacements. In order to avoid problems related to finite rotation approximations and to give a realist representation of a 3D bar structure, we chose a formulation defined in terms of positions and that considers the cross-section warping effects. Regarding computational fluid dynamics, we seek for a stable formulation for compressible flows, and at same time, sensitive to the movement of the structure, leading to an explicit time integration algorithm based on characteristics with governing equations described in the Arbitrary Lagrangian-Eulerian (ALE) form. Regarding to coupling, we chose to use a weak (explicit) partitioning coupling model in order to ensure modularity and versatility. The developed coupling scheme is bases on boundary conditions transfer techniques (Dirichlet-Neummann), and we study the effects of using bidirectional or unidirectional boundary conditions transfers.

Dissertação de Mestrado em Engenharia Informática apresentada à Faculdade de Ciências e Tecnologia<br>Os operadores de recombinação desempenham um papel importante no desempenho de Algoritmos Evolucionários. Eles geram uma nova solução através da combinação de informação de outras duas soluções. O Problema da Recombinação Ótima (PRO) consiste na geração da melhor solução descendente segundo um dado operador. No entanto, em muitos casos este problema é NP-Difícil. Em particular, isto é verdade para o Problema do Caixeiro Viajante (PCV) quando se considera a recombinação com respeito e trasmissão de arestas.Os Cruzamentos de Partição são operadores de recombinação determinística que resolvem ou aproximam o PRO, explorando as decomposições naturais dos pais tendo em vista a geração de soluções de elevada qualidade, dadas essas decomposições.Geralmente, os Cruzamentos de Partição são combinados com operadores de procura local. As regras sobre as quais estes operadores funcionam definem a estrutura de vizinhança do espaço de procura. No entanto, não se sabe como é que os Cruzamentos de Partição se relacionam com esta estrutura de vizinhança. Mostramos que de facto todos os Cruzamentos de Partição podem ser geométricos sob alguma distância e que, para o caso particular dos Cruzamentos de Partição para o PCV existentes, eles são geométricos de acordo com a distância de bond.Adicionalmente, os Cruzamentos de Partição têm sido aplicados com sucesso em vários problemas de otimização. Apesar das diferenças entre problemas, a sua implementação segue um padrão comum que pode ser generalizado até certo ponto. Portanto, propomos uma Interface de Programação de Aplicações (IPA) para o desenvolvimento de cruzamentos de partição, que identifica claramente as suas operações fundamentais e separa a parte dependente do problema destes operadores, do resto do operador que é independente do problema.Tal IPA realça as relações entre componentes que surgem das decomposições das soluções involvidas e fornece oportunidades para melhorar os cruzamentos de partição existentes. Apresentamos uma análise experimental do Cruzamento de Partição GPX2 à luz do PRO e mostramos como é que a IPA proposta pode ser usada para o melhorar.<br>Recombination operators play an important role in the performance of Evolutionary Algorithms. They generate a new solution by combining information from other two parent solutions.The Optimal Recombination Problem (ORP) concerns the generation of the best possible offspring solution by a given operator. However, in many cases, this problem is NP-Hard. In particular, this is true for the Traveling Salesman Problem (TSP) when respectful, edge-transmitting recombination is considered.Partition crossovers are deterministic recombination operators that solve or approximate the ORP. They do so by exploiting natural decompositions of the parents in order to generate high-quality solutions given those decompositions. Partition Crossovers are usually combined with local search operators. The rules on which these operators operate define the neighbourhood structure of the search space. However, it is not known how Partition Crossovers relate to this neighbourhood structure. We show that indeed, all Partition Crossovers may be geometric under some distance and, for the particular case of current Partition Crossovers for the TSP, they are geometric for the bond distance.Moreover, partition crossovers have been successfully applied in several optimisation problems. Despite the differences between problems, their implementation follows a common pattern that is generalisable to some extent. Thus, we propose an API for the development of partition crossovers that clearly identifies their basic operations, and separates a problem-dependent part of these operators from the rest of the operator, which is problem-independent.Such an API brings focus to the relations between the components arising throught the decompositions of the solutions involved, and provide opportunities for improving existing partition crossovers. We present an experimental analysis of the GPX2 partition crossover in the light of the ORP, and show how the proposed API could be used to improve it.<br>FCT<br>Outro - MobiWise: From Mobile Sensing to Mobility Advising (P2020 SAICTPAC/0011/2015), co-financed by COMPETE 2020, Portugal 2020 -- Operational Program for Competitiveness and Internationalization (POCI), European Union’s European Regional Development Fund (ERDF), and the Foundation for Science and Technology (FCT).

AbstractIn ISO Geometrical Product Specifications and Verification Standards (GPS) [1], partition is one of the fundamental operations used to obtain ideal or non-ideal features of a product. The operation of partition produces independent geometrical features by decomposing the object. A curvature-based CAD mesh partitioning framework is proposed in this paper. The framework combines several key steps including curvature-based attribute calculation, local shape type refinement, region growing, slippage analysis and statistical modeling. The partitioned features are classified into seven invariance classes of surface in the context of ISO GPS. A case study shows that not only appropriate partitioning but also accurate invariance class recognition for GPS are achieved by the proposed framework.

In the present work, a numerical study of the effect of non uniform boundary conditions on the heat transfer by natural convection in cavities with partial partitions is investigated for the laminar regime. This problem is solved by using the partial differential equations which are the equation of mass, momentum and energy. The tests were performed for different boundary conditions and different Rayleigh numbers while the Prandtl number was kept constant. Four geometrical configurations were considered namely three and five undulations with increasing and decreasing partition length. The results obtained show that the non uniform temperature in the vertical walls affects the flow and the heat transfer. The mean Nusselt number decreases comparing with the heat transfer in the undulated square cavity without partitions for all non uniform boundary conditions tested.

Control valves are one of the key steam turbine components both in terms of operational safety and flexibility. It is hence fundamental to correctly predict the valve characteristics at the various working conditions to accurately estimate machine performance and control logics. The aim of this work is to develop a simple method to predict pressure losses within the partition system to be used at preliminary design stage. Two types of partition valves typically employed in real industrial steam turbines of different power (from 1MW to 100MW) are analysed. The first type exploits a diffuser-like shape to maximize the dynamic pressure recovery before the discharge into the impulse stage. The second type, based on simple tube geometry, increases the allowable flow rate, for the same valve seat, at the cost of higher pressure losses. Geometrical dimensions have been varied to cover a wide range of configurations employed in industrial applications. An exception is made for the diffuser angle and the relative fillet radius which were fixed to guarantee product standardization among the various machine sizes. The flow is supposed axisymmetric and upstream reference condition for the entire study is 140 bar and 540 °C which are typical working conditions for such steam turbines. The influence of the shutter is also considered to properly characterize regulation of the steam flow on the basis of valve lift. Pressure losses are first modelled dividing the partition valve into singular homogeneous parts such as the intake, the straight pipe, the diffuser and the discharge, for which simple correlations are available in literature. The overall characteristic curve is validated using CFD computations conducted with the steady state RANS solver available in the commercial code CFX exploiting the SST turbulence model. The development of the correlation permitted to rapidly cover the selected range of geometries and conditions highlighting that dynamic pressure losses are the major sources of losses. Minimal passage area to discharge section ratio is hence a dimensionless value able to describe characteristic curves insensitively to any other geometrical parameter.

This paper proposes a reconfiguration mechanism modelling for puzzles with its interlocking geometric constraints analysis. Wooden puzzles consisting of interlocking assemebly of notched sticks are often referred to as bar-puzzles, sometime known as the Chinese Puzzles or Chinese Cross. The puzzle with multiple reconfigurable pieces as kinematic links leads to topology arrangements. Although its partition or assembly process can be operated as mechanism motions, there does not appear to be any evidence that the idea of its mechanism property and any configuration analysis originated. To this purpose, this paper set up a static and discrete reconfiguration theory of geometric puzzles for modeling the topology changement as Put Together, Take Apart, Sequential Movement and various others. The partition and assembly process analysis aims to extract the kinematic chains as links and joints. The puzzle unlocking leads to configuration constraints rearrangement problems which accompanying pieces of bars self-grouped as defined reconfiguration links and joints. The mathematical recreation of the mechanism structure stems from its interlocking geometric constraints property. This paper reveals its interlocking property as configuration constraints including many passive constraints and further discloses the mechanism constraints modeling in two different partition methods. The puzzle solutions are first described as reconfigurable topology mechanism and the constrained mobility is analyzed based on an ingenious and distinctive reconfiguration property.

Abstract Despite the growing application of additive manufacturing (AM) in fabricating complex designs, most machines suffer from small working envelopes and slow processing speeds. One workaround to the problem of small throughput in AM is to partition the volume of a desired object and fabricate sub-volumes in parallel. Prior related work has focused on two problems. One is the geometric division problem, disregarding AM benefits and challenges in determining partitions. Others attempt to install multiple AM processing heads on the same machine, ensuring seamless bonding between deposited material from different heads while avoiding interference among them. A missed opportunity lies in deploying many independent machines simultaneously while considering benefits and limitations of AM. To that end, objects too large to be fabricated on one machine, are divided primarily into cubes that exploit benefits of AM. Specifically, the cubes are hollowed out in the direction of printing to reduce weight while avoiding the need for support structure, and depending on load conditions, packed in different orientations to mitigate material anisotropy.