Cartesian Method Research Articles

A hybrid RANS-LES Cartesian method based on a skew-symmetric convective operator

The paper describes the dissipative and dispersive properties of a hybrid RANS-LES Cartesian method specifically designed to study complex three-dimensional viscous flows. A skew-symmetric convective operator is employed to low the influence of numerical dissipation and dispersion on the physical phenomena especially when solving highly separated flows. The main objective is to conserve not only momentum and energy but also their quadratic forms. In principle, this should enhance the correct evolution of the turbulent kinetic energy in the wake of bluff-bodies thus allowing a confident estimate of the relevant scales. Here an immersed boundary technique is coupled with a wall-model in order to make affordable the study of high Reynolds number flows. The first part of the results is dedicated to basic one- and two-dimensional studies aiming at evaluating the performance of the scheme at the interface between cells of different size. Indeed, the refined Cartesian meshes are characterized by a fixed cell-size ratio of two and accuracy issues can locally occur. Moreover, three-dimensional test-cases are carried out whose results are compared with solutions from body-conforming methods and experimental data when available.

Aerodynamic evaluation of an unmanned aerial vehicle with variable sweep and span

Morphing aircraft can achieve optimum performances at multiple flight conditions through large geometry deformations. However, to obtain the optimum configurations, optimization design studies are required. A study on aerodynamic optimization of a morphing aircraft was conducted to obtain corresponding optimal configurations at various flight speeds. Firstly, an optimization framework being suitable to a morphing aircraft with larger deformations was established by integrating existing codes, in which aerodynamic forces for the optimization are calculated by an Euler-based solver and friction/form drag estimation code. The solver is based on a Cartesian method in which configurations are modeled in terms of components of aircraft, hence large deformations of morphing aircraft can be performed during the optimization. A surrogate-based model was employed for fitting aerodynamic forces, thus reducing computational cost in a global optimization. A generic morphing aircraft with variable sweep and span was investigated at subsonic, transonic, and supersonic conditions through the optimization process. The target of optimization is to obtain maximum lift-to-drag ratios subject to lift, trim, and static stability constrains at each flight condition. The movement of center-of-gravity of the aircraft was also considered in optimization. The results indicate that the center-of-gravity has an important effect on the optimum configurations obtained, and the aerodynamic performance will be enhanced significantly if the center-of-gravity is moved backward at transonic and supersonic cases. In the case of movable center-of-gravity, the optimum sweep angles increase with the increase in flight speeds, and the optimum spans at transonic and supersonic speeds are smaller than the subsonic case.

Blaise Pascal: Miracles and Reason by Mary Ann Caws

 Reviews ture. e book’s deep excavation of J. M. Coetzee’s interests in central Europe at the point of difficult transition from the Austro-Hungarian empire and its handling of the subversive intertextual allusion of Zoë Wicomb’s fiction demonstrates, among other things, that such writing is by its very nature global. Modelling a method of interpretation that is ultimately hopeful, this book has much to say about the fates of literary reading in uncertain times, and the potential expansiveness of scholarly interest against the segmentation and marketization of academic labour. U  B A R Blaise Pascal: Miracles and Reason. By M A C. London: Reaktion. . xx+ pp. £.. ISBN ––––. ere is a paradox in writing the biography of a writer who declared the self detestable , derided the notion of person, and excoriated Montaigne for attempting to paint a portrait of himself. Why risk reducing Pascal’s thoroughly anti-subjective project, grounded on extraordinary scientific, philosophical, and theological reflections , to the personal and the psychopathological? In this masterful short biography Mary Ann Caws avoids such pitfalls by focusing not on character but on Pascal’s style of life, and in so doing manages to introduce readers to the crux of his thought. Her Pascal is a ‘tense thinker’, who rarely spends time on ideas beyond his first brilliant intuitions and experiments, always afforded by circumstances and chance encounters. For Pascal, it is sufficient that these ideas contradict the obvious: there is void in nature, an object is an infinity of views, a machine can think, the fools are precisely those who think themselves smart, especially in politics, etc. A thinker of tensions who finds the Cartesian method naive, Pascal constantly stages contradictory perspectives on a complex universe. Each chapter links Pascal’s inventions to the pressure of circumstances. e theory of conical sections follows his move to Paris and his induction into Mersenne’s Académie. Pascal invents the calculator aer his father’s move to Rouen as a tax collector. e chance discovery of Jansenism leads to the first conversion and deepens Pascal’s relationship with his sister Jacqueline, a significant writer and actress. He invents probability theory during his ‘worldly’ period of active friendship with gamblers. is leads to the Wager argument (Caws manages to show its significance without repeating the accumulated scholarship). e second conversion follows the night of the Mémorial, a text Pascal wore sewn in the lining of his coat and which Caws reads as a poetic expression of the experience of the ineffable, leading to the first project of an Apology for Christianity presented to M. de Sacy. e war staged by Les Provinciales (a politicaltheological assault against the Jesuits as well as a phenomenology of bad faith) is linked to the miracle of his niece’s cure in Port-Royal. At the end of a trajectory linking peaks of thought to major events, Caws reads the Pensées not just as an anthropological and theological reformulation of all the strands of Pascal’s thought but also as a reflection on thinking and style which, to the modern reader, is a school of writing. MLR, .,   In places Caws could have gone further. In the Entretien with Sacy, Pascal did not just juxtapose Montaigne and Descartes, but built a philosophical ‘machine infernale’ where Stoicism and scepticism would reveal each other’s vanity, both for life and for salvation. As for the Pensées, Caws’s equation of fragment with aphorism is debatable. e Entretien, L’Esprit de la géométrie, several fragments marked as preface, chapter sections, and conclusion, and public readings given by Pascal of some of the Pensées assembled into bundles indicate a coherent apologetical project . Had he not died prematurely, he would surely have merged the fragments into chapters, while maintaining the aphoristic nature of many existential paradoxes pointing only to a solution beyond existence. More could be said in that regard on miracles and prophecies as irrational but indubitable proofs in history. Nietzsche and perhaps Char and Foucault could have been more explicitly discussed in the chapter on posterity, and the satirical Rondeau against the Jesuits needs...

Applying the free-slip boundary condition with an adaptive Cartesian cut-cell method for complex geometries

The slip condition at the interface of a multiphase flow can occur in situations including micro-and nano-fluidic flow, flow over hydrophobic surfaces, rising bubbles in quiescent liquid, and polymer extrusion processes. The aim of this work is to implement the free-slip boundary condition with an adaptive Cartesian grid method. The Navier-Stokes (NS) equations are solved by a cell-centered collocated finite volume method with adaptive mesh refinement. The arbitrarily-shaped solids imbedded in the computational domain are treated by the cut-cell method where the geometric properties of cut-cells near the boundary are computed through robust geometric operations. In discretized NS equations, the second-order-accurate center difference method is used to estimate the surface fluxes of the regular Cartesian cells in the bulk region, whereas the least-squares method is used to estimate the fluxes of the cut-cells near the boundary. A local coordinate system aligned with the normal and tangential directions of the solid boundary is defined for each cut-cell in order to properly implement the free-slip condition. The tangential velocities at the curved solid boundary are obtained using the free-slip condition and the principal curvatures of the solid surface. The proposed numerical method is implemented in the open-source code Gerris. Numerical tests have been carried out to validate our method. The tests confirm the excellent performances of the proposed method. Although our work focuses on the free-slip condition, the extension of the proposed method to more general slip conditions is straightforward.

On the effect of the contact surface definition in the Cartesian grid finite element method

The definition of the surface plays an important role in the solution of contact problems, as the evaluation of the contact force is based on the measure of the gap between the solids. In this work three different methods to define the surface are proposed for the solution of contact problems within the framework of the 3D Cartesian grid finite element method. A stabilized formulation is used to solve the contact problem and details of the kinematic description for each surface definition are provided. The three methods are compared solving some numerical tests involving frictionless contact with finite and small deformations.

Escepticismo académico y práctica de la vida: los límites de la duda cartesiana

Cartesian skepticism represents a fundamental element of the Cartesian method directed to find the metaphysical certainties that securely justify knowledge. Nonetheless, the Cartesian radical doubt has clearly defined limits insofar as it does not extend to the realm of vital praxis. The present paper develops the connection between Cartesian moral certainty and the notion of «practice of life» in order to show how Descartes’ methodological skepticism is framed in the academic tradition rather than in the Pyrrhonian one.

Independent cover meshless particle method for complex geotechnical engineering

A new Independent Cover Meshless Particle (ICMP) method is proposed for the analysis of complex geotechnical engineering. In the ICMP method, the independent rectangular cover regardless of the shape of the analysis model is employed as the influence domain of each discrete node, the general polynomial is employed as the meshless interpolation function of the independent nodal cover, and the Cartesian Transformation Method (CTM) is used for the numerical integration of the nodal covers cut by material interfaces, joints, cracks and faults. The present method has a simple formulation and a low computational cost, and is easy for the numerical analysis and modeling of complex geotechnical engineering. Several typical numerical examples are presented to demonstrate the accuracy and robustness of the proposed method.

An optimal FFT-based anisotropic power spectrum estimator

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTs of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P(k,μ), obtained by computing multipoles up to a large ℓmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≃ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓmax=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with ℓmax=4.

A novel meshfree approach for free vibration and buckling analysis of thin laminated composite plates


 
 
 A novel meshfree radial point interpolation approach which employs a new numerical integration scheme is introduced. The new integration scheme, namely Cartesian Transformation Method, transforms a domain integral into a double integral including a boundary integral and a one-dimensional integral, and thus allowing integration without discretizing domain into sub-domains usually called background mesh in traditional meshfree analysis. A new type of radial basis function that is little sensitive to user-defined parameters is also employed in the proposed approach. The present approach is applied to free vibration and buckling analysis of thin laminated composite plates using the classical Kirchhoff’s plate theory. Various numerical examples with different geometric shapes are considered to demonstrate the applicability and accuracy of the proposed method. 
 
 

Superconvergent second order Cartesian method for solving free boundary problem for invadopodia formation

In this paper, we present a superconvergent second order Cartesian method to solve a free boundary problem with two harmonic phases coupled through the moving interface. The model recently proposed by the authors and colleagues describes the formation of cell protrusions. The moving interface is described by a level set function and is advected at the velocity given by the gradient of the inner phase. The finite differences method proposed in this paper consists of a new stabilized ghost fluid method and second order discretizations for the Laplace operator with the boundary conditions (Dirichlet, Neumann or Robin conditions). Interestingly, the method to solve the harmonic subproblems is superconvergent on two levels, in the sense that the first and second order derivatives of the numerical solutions are obtained with the second order of accuracy, similarly to the solution itself. We exhibit numerical criteria on the data accuracy to get such properties and numerical simulations corroborate these criteria. In addition to these properties, we propose an appropriate extension of the velocity of the level-set to avoid any loss of consistency, and to obtain the second order of accuracy of the complete free boundary problem. Interestingly, we highlight the transmission of the superconvergent properties for the static subproblems and their preservation by the dynamical scheme. Our method is also well suited for quasistatic Hele–Shaw-like or Muskat-like problems.

Evaluating the Effects of Artistic Impregnation of Scientific Objects on Qualifiers of Perceptual Assessment Through Self-Report Questionnaires: Implications for an Emerging Experimental Neuroepistemology

This report summarizes our preliminary efforts to delineate, at controlled experimentation, the impact of art, and artistic aesthetics, on the way we assess science. Our results suggest that the analytic-synthetic axis of perceptual cognitive handling of the scientific object is unaffected by its artistic non-conventional contextualization, while cognitive abstraction, positive emotions and aesthetic impressions are favoured. Implications to philosophical foundations of the Cartesian scientific method are considered.

Obsessive-Compulsive Ir/rationality in Watt

This article argues that the novel Watt (1953) enacts a veritable thought experiment, which posits endless obsessions and compulsions as an inevitable component of rigorous adherence to the Cartesian Method. This has ironic implications as Watt depicts how adherence to the supposedly rational principles of the Method necessitates the presence of obsessions and compulsions, which, from a contemporary biomedical perspective, point towards an irrational disorder of the self: obsessive-compulsive disorder (OCD). Subsequently, Beckett challenges our ability to neatly define ‘rational’ philosophical methodology when it is so closely aligned with the components of ‘irrational’ disorder.

Apontamentos Iniciais sobre a Força Gravitacional da Jurisprudência no Novo Código de Processo Civil

O objetivo (ou referente) do presente texto é tratar da força gravitacional dos precedentes jurisprudenciais como elementos de determinação na tomada de decisões judiciais e, também, estabelecer alguns critérios quanto à sua incidência no contexto brasileiro, mormente considerando o Novo Código de Processo Civil (NCPC). A motivação para tratar deste assunto decorre do notável aumento da importância das decisões dos tribunais, notadamente os superiores, como argumentos persuasivos para formação da convicção judicial no cenário brasileiro. As conclusões foram no sentido de que a Jurisprudência é uma Fonte Jurídica de hierarquia decisiva no cenário jurídico brasileiro, posicionada logo abaixo dos Textos Normativos e dos Princípios Jurídicos, cuja relevância reside não no sentido do julgado (dispositivo), mas sim na apresentação dos argumentos pertinentes para resolução de casos similares (fundamentação estruturada), de modo a otimizar o lançamento de decisões judiciais, aumentar a coerência do Ordenamento Jurídico e preservar a história institucional do Direito. Também restou esclarecido que o NCPC conferiu um tratamento especial à força gravitacional da Jurisprudência no cenário brasileiro, de modo a alterar o funcionamento do sistema neste particular e, assim, exigir atenção dos profissionais quanto à operacionalização das categorias stare decisis, analogia, distinção, superação, ratio decidendi e obter dicta. Por fim, quanto à metodologia empregada, destaca-se que na fase de investigação foi utilizado o método indutivo, na fase de tratamento de dados o cartesiano e o texto final foi composto na base lógica dedutiva. Nas diversas fases da pesquisa, foram acionadas as técnicas do referente, da categoria, do conceito operacional e da pesquisa bibliográfica.

Formas jurígenas

The main objective of this paper is to present, classify and describe the main law production methods accepted in the Brazilian legal tradition, according to the Com¬plex Law Theory. This text is part of the current discussions about the overcoming of Legal Positivism as the main paradigm of Legal Science, because of its descriptive and prescriptive flaws. To achieve this aim, it is necessary to rebuild the classic concepts of sources of law, norms and legal system. The findings were, in summary, related to the indication of the existence of reciprocal and systemic relations between the material Legal Sources (Ethical Principles, Doctrine and Traditions) and the formal ones (Legislation, Precedents and Policies). As for the methodology, it is emphasized that in the investigation stage we used the inductive method, in the data processing phase we used the Cartesian method and the final text was composed on the basis of deductive logics. In the various stages of the research we used the techniques of the referent, the category, the operational concept and literature survey.Keywords: material and formal sources of law, law production methods, complex law theory.

Sustentabilidade, Sociedade de Risco E Alimentos Transgênicos: Disputas Definitórias e o Projeto de Lei nº. 4.148/08

O artigo terá por objeto o exame do Projeto de Lei n. 4.148/08, que altera significativamente a forma de rotulagem dos alimentos transgênicos, substituindo o símbolo atualmente existente por uma frase inserida entre outros dados do rótulo. Como objetivo do artigo, demonstrar que essa proposta, para além de uma mera alteração legislativa de menor importância, está inserida em contexto muito maior e é vem de encontro com a proposta apresentada por Ulrich Beck de que os riscos socialmente reconhecidos seriam alvo e objeto de disputas definitórias que dependeriam muito menos dos conhecimentos científicos a respeito do tema do que efetivamente do jogo politico, que envolve poder, dinheiro, informação e espaço midiático. Além disso, segue-se a afirmação em resposta ao problema da pesquisa de que, à luz do paradigma da sustentabilidade, o PL 4.148/08 representa um retrocesso socioambiental e uma ameaça à construção desse novo imperativo ético. Na metodologia foi utilizado o método indutivo na fase de investigação; na fase de tratamento de dados o método cartesiano e no relatório da pesquisa foi empregada a base indutiva. Foram também acionadas as técnicas do referente, da categoria, dos conceitos operacionais, da pesquisa bibliográfica e do fichamento.

Implications of complexity theory for clinical practice and healthcare organization

### Key points Medicine, like many other scientific fields, is founded upon the classical Cartesian method of reductionism, where a problem is broken down into its smallest components, examined, and then the information gleaned used to draw conclusions about the nature of the larger reality. Fundamental to this approach is the requirement that the problem being examined is a linear system (Table 1). When this is the case, the reductionist approach is a great success and the clinician may rightly feel confident in predicting the outcome of an intervention. An example of this might be the response of blood glucose to a dose of exogenous insulin.2 Frustrations arise however when the problem we wish to examine is not a simple linear system but rather shows non-linear behaviour (Table 1). Our inability to predict the outcome in these situations is all too painfully familiar, yet it was at this problematic interface, between reductionism and real life, that the science of complexity theory was born. View this table: Table 1 Features of linear and non-linear systems Edward Lorenz was a meteorologist at the Massachusetts Institute of Technology who in 1961 was trying to develop a computer model to allow accurate long-range weather forecasting. While inputting the data to rerun a previous weather model, he abbreviated one number from 0.50612 to 0.506 …

“THE OUTSIDE IS ALWAYS AN INSIDE”: THE IDEA OF SPACE AND ITS THEORETICAL HERITAGE IN “TOWARD AN ARCHITECTURE”

The article proposes to delve deeper in the idea of space in Le Corbusier’s Toward an Architecture (1923), focalizing in its connections with the past and urban design. When in his book Le Corbusier presents his “trois rappels a messieurs les architectes” – volume, surface and plan (in its broad sense) – he outlines the keys to his idea of space. It proves imperative to use Le Corbusier’s original term “Rappel” as its word play transcends any possible translation. Space is therefore defined as a Rappel (call) to architects, but also as a Rappel (reminder, evocation) to multiple theorizations and ideas that have traversed architecture throughout history. Le Corbusier’s argument understands the directions of space as an extension, showing his affiliation with a tradition of French thinking that, in architecture, subscribes since Viollet le Duc to the Cartesian Method, in which spatiality is understood – from the Barroque – both Outside and Inside. It is proven that, in clear continuity with French architectural tradition and drawing inspiration from the ideas of Auguste Choisy, Le Corbusier defines with the mass and the void a space in which “the Outside is always an Inside”. Thus, it is demonstrated that not only the links with the past but also the material resources for the definition of such space are common in different scales, from the definition of an inside up to the urban design.

Bioinspired swimming simulations

We present a method to simulate the flow past bioinspired swimmers starting from pictures of an actual fish. The overall approach requires i) a skeleton graph generation to get a level-set function from pictures; ii) optimal transportation to obtain the velocity on the body surface; iii) flow simulations realized with a Cartesian method based on penalization. This technique can be used to automate modeling swimming motion from data collected by biologists. We illustrate this paradigm by simulating the swimming of a mackerel fish.

SENSITIVITY KERNELS FOR FLOWS IN TIME–DISTANCE HELIOSEISMOLOGY: EXTENSION TO SPHERICAL GEOMETRY

ABSTRACT We extend an existing Born approximation method for calculating the linear sensitivity of helioseismic travel times to flows from Cartesian to spherical geometry. This development is necessary for using the Born approximation for inferring large-scale flows in the deep solar interior. As first sanity check, we compare two f-mode kernels from our spherical method and from an existing Cartesian method. The horizontal and total integrals agree to within 0.3%. As a second consistency test, we consider a uniformly rotating Sun and a travel distance of 42°. The analytical travel-time difference agrees with the forward-modeled travel-time difference to within 2%. In addition, we evaluate the impact of different choices of filter functions on the kernels for a meridional travel distance of 42°. For all filters, the sensitivity is found to be distributed over a large fraction of the convection zone. We show that the kernels depend on the filter function employed in the data analysis process. If modes of higher harmonic degree (90 ≲ l ≲ 170) are permitted, a noisy pattern of a spatial scale corresponding to l ≈ 260 appears near the surface. When mainly low-degree modes are used (l ≲ 70), the sensitivity is concentrated in the deepest regions and it visually resembles a ray-path-like structure. Among the different low-degree filters used, we find the kernel for phase-speed-filtered measurements to be best localized in depth.

Transient Combined Radiative–Conductive Heat Transfer in Two-Dimensional Complex Geometries with Variable Gas Properties

Radiation is a major component of heat transfer in the modeling of furnaces. In the present work, transient coupled radiative and conductive heat transfer problems are analyzed in two-dimensional irregular geometries with a simple Cartesian practical method named the blocked-off. By this technique, Cartesian coordinate-based ray-tracing algorithm can be applied to the geometries with inclined or curved boundaries. The S–N discrete ordinates method used to solve the radiative transfer equation and finite difference method by applying the Taylor series for solving the energy equation to obtain the transient temperature distributions inside the participating medium. The walls of the enclosures are opaque, diffuse, and gray with specified temperatures. The medium was considered to be absorbing-emitting and linear anisotropic scattering with variable thermal conductivity, variable density, and variable specific heat, as a function of temperature. In the case of constant thermophysical gas properties, results have been compared with those reported in the literature, and good agreement was found.