A kinetic scheme for unsteady pressurised flows in closed water pipes

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel system of equations, and the we recall how to obtain the corresponding kinetic formulation. Then we build the kinetic scheme ensuring an upwinding of the source term due to the topography performed in a close manner described by Perthame et al. using an energetic balance at microscopic level for the Shallow Water equations. The validation is lastly performed in the case of a water hammer in a uniform pipe: we compare the numerical results provided by an industrial code used at EDF-CIH (France), which solves the Allievi equation (the commonly used equation for pressurised flows in pipes) by the method of characteristics, with those of the kinetic scheme. It appears that they are in a very good agreement

A pseudo active kinematic constraint for a biological living soft tissue: an effect of the collagen network

Recent studies in mammalian hearts show that left ventricular wall thickening is an important mechanism for systolic ejection and that during contraction the cardiac muscle develops significant stresses in the muscular cross-fiber direction. We suggested that the collagen network surrounding the muscular fibers could account for these mechanical behaviors. To test this hypothesis we develop a model for large deformation response of active, incompressible, nonlinear elastic and transversely isotropic living soft tissue (such as cardiac or arteries tissues) in which we include a coupling effect between the connective tissue and the muscular fibers. Then, a three-dimensional finite element formulation including this internal pseudo-active kinematic constraint is derived. Analytical and finite element solutions are in a very good agreement. The numerical results show this wall thickening effect with an order of magnitude compatible with the experimental observations

Air entrainment in transient flows in closed water pipes: a two-layer approach

In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme in which a special treatment for the "missing" boundary condition is performed. Several numerical tests on closed water pipes are performed and the impact of the loss of hyperbolicity is discussed and illustrated. Finally, we make a numerical study of the order of the kinetic method in the case where the system is mainly non hyperbolic. This provides a useful stability result when the spatial mesh size goes to zero

A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme

We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the local perturbation caused by the changes of section and slope. Then an asymptotic analysis is performed to obtain a model for free surface flows and another one for pressurized flows. By coupling these models through the transition points by the use of a common set of variables and a suitable pressure law, we obtain a simple formulation called PFS-model close to the shallow water equations with source terms. It takes into account the changes of section and the slope variation in a continuous way through transition points. Transition point between the two types of flows is treated as a free boundary associated to a discontinuity of the gradient of pressure. The numerical simulation is performed by making use of a Roe-like finite volume scheme that we adapted to take into account geometrical source terms in the convection matrix. Finally some numerical tests are presented

A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms

We present a numerical kinetic scheme for an unsteady mixed pressurised and free surface model. This model has a source term depending on both the space variable and the unknown, U, of the system. The source term is composed by a topography, a section variation, a curvature (also called corrective) and a friction term. Using the Finite Volume and Kinetic (FVK) framework, we propose an approximation of the source terms following the principle of interfacial upwind with a kinetic interpretation: the source term is not treated as a volumic term, but included in the numerical fluxes. Then, several numerical tests are presented

Asymptotic error distribution for the Ninomiya-Victoir scheme in the commutative case

In a previous work, we proved strong convergence with order $1$ of the Ninomiya-Victoir scheme $X^{NV}$ with time step $T/N$ to the solution $X$ of the limiting SDE when the Brownian vector fields commute. In this paper, we prove that the normalized error process $N \left(X - X^{NV}\right)$ converges to an affine SDE with source terms involving the Lie brackets between the Brownian vector fields and the drift vector field. This result ensures that the strong convergence rate is actually $1$ when the Brownian vector fields commute, but at least one of them does not commute with the drift vector field. When all the vector fields commute the limit vanishes. Our result is consistent with the fact that the Ninomiya-Victoir scheme solves the SDE in this case.Comment: arXiv admin note: text overlap with arXiv:1601.0526

Ninomiya-Victoir scheme: strong convergence, antithetic version and application to multilevel estimators

In this paper, we are interested in the strong convergence properties of the Ninomiya-Victoir scheme which is known to exhibit weak convergence with order 2. We prove strong convergence with order $1/2$. This study is aimed at analysing the use of this scheme either at each level or only at the finest level of a multilevel Monte Carlo estimator: indeed, the variance of a multilevel Monte Carlo estimator is related to the strong error between the two schemes used on the coarse and fine grids at each level. Recently, Giles and Szpruch proposed a scheme permitting to construct a multilevel Monte Carlo estimator achieving the optimal complexity $O\left(\epsilon^{-2}\right)$ for the precision $\epsilon$. In the same spirit, we propose a modified Ninomiya-Victoir scheme, which may be strongly coupled with order $1$ to the Giles-Szpruch scheme at the finest level of a multilevel Monte Carlo estimator. Numerical experiments show that this choice improves the efficiency, since the order $2$ of weak convergence of the Ninomiya-Victoir scheme permits to reduce the number of discretization levels

Korelasi Pemerolehan Bahasa Terhadap Keterampilan Berbicara Bahasa Arab Perspektif Neurolinguistik (Studi Kasus Mahasiswa Pendidikan Bahasa Arab Unja)

Penelitian ini bertujuan untuk mengetahui sejauh mana korelasi Pemerolehan bahasa terhadap keterampilan berbicara bahasa arab sebagai bagian dari hasil belajar Muhadatsah yang telah mereka ampu mulai muhadatsah satu hingga muhadatsah tiga. Adapun jenis penelitian ini merupakan jenis penelitian dengan pendekatan Kuantitatif dan menerapkan strategi penellitian studi kasus. Sumber data dalam penelitian ini adalah mahasiswa program studi PBA tahun akademik 2019. Penelitian ini merupakan penelitian kuantitatif dengan menggunakan metode korelasional. Populasi dari penelitian ini adalah mahasiswa yang seluruhnya terhitung mulai dari angkatan (2016) hingga (2019) berjumlah 135 orang. Dan pengambilan sampel menggunakan rumus Simple Random Sampling dengan jumlah mahasiswa 23 orang, Metode pengumpulan data yang digunakan ialah model Pemeriksaan Komunikasi Hemisfer Kanan (PKHK) yang meliputi daftar pertanyaan yang di kelompokkan dalam beberapa tes  dikembangkan atas dasar tinjuan aspek kebahasaan komunikasi hemisfer kanan yang terlingkup akan aspek leksiko-semantik, makrostruktur, dan pragmatik. pengkajian instrumen menggunakan uji validitas dan uji reabilitas. Analisis korelasi antara Pemerolehan Bahasa terhadap keterampilan berbicara bahasa Arab menggunakan uji Korelasi Product Moment. Hasil penelitian ini menunjukkan bahwa Pemerolehan bahasa yang dimiliki mahasiswa berkorelasi dengan keterampilan berbicara bahasa arabnya dengan melihat Kompetensi Kebahasaan leksikosemantik, dan makrostruktur terhadap keterampilan berbicara pragmatik yang mereka miliki. Berdasarkan tes yang telah di ujikan dengan menggunakan rumus, maka diperoleh angka 0,8154 yang secara nilai lebih besar dari r tabel Product moment dengan angka 0,432 pada taraf kepercayaan 5% dan 1%. Sehingga dapat ditunjukkan  bahwa terdapat korelasi pada pemerolehan bahasa terhadap keterampilan berbicara bahasa arab perspektif neurolinguistik studi kasus mahasiswa pendidikan bahasa arab Unja

Quantifying Syntectonic Weakening in Deep Orogenic Crust

The primary intellectual impact of this project will be in improving our understanding of the mechanics that shape the Earth\u27s crust. In recent years, earth scientists have used the increasing body of geodetic data towards that end, but the mechanical properties of the middle and lower crust remain only loosely constrained. This project focuses on the magnitude of strain weakening in shear zone networks. In detail, the research will explore the grain-scale and outcrop-scale deformation mechanisms in minerals that lead to this weakening, followed by modeling of the results to understand the weakening process on the larger scale. These conceptual and numerical models will allow better prediction of where and how fast the continental crust will deform and in turn this will benefit society. In the future, locations that have recently been deglaciated, and those in tectonically active areas where earthquakes are likely, may be interesting targets for further application of this research. This project also serves as a vehicle to continue and enhance ongoing educational and outreach initiatives at the K-16 and graduate levels. Support for students enrolled in the University of Maine\u27s Master of Science in Teaching program will allow pre-service K-12 teachers to become involved in an active research project and to participate in creating an environment where science is more accessible. The PI and colleagues will develop new content based around supercomputer, visualization, and field video library projects, the combined results of which will enhance professional development, graduate and undergraduate courses, and outreach to K-12 students in Maine\u27s rural areas.Throughout the lithosphere, strain localization plays a fundamental role in tectonic processes affecting, for example, seismicity, exhumation, fluid migration and mineralization, magma transport, and topographic and plate boundary evolution. Previous research involving field observations and numerical modeling has produced many constraints on the causes and consequences of strain localization, but researchers lack a thorough understanding of the magnitude of strength variation in the deep crust in particular. Due to exceptional exposure and deep exhumation this research group will use the Parry Sound domain of the Grenville Province, southern Ontario, as a natural laboratory. Along one margin of the domain, granulite facies mineral assemblages have been transformed under upper amphibolite facies conditions along meter-scale shear zones. After field-based mapping, the PI will quantify the change in strength associated with the development of the interconnected meter-scale shear zones through model calculations using the natural geometric framework. In addition, to develop better tools to predict weakening of this magnitude elsewhere, he will determine the mechanisms by which the shear zones developed and the weakening occurred. The PI has hypothesized that one such mechanism involved pegmatite-derived fluids that infiltrated adjacent zones, allowing mineralogical changes along which shear zones could nucleate. Establishing the crustal-scale significance of strength changes requires determining if meter-scale processes produced, for example, the regional-scale, domain-bounding Twelve Mile Bay shear zone. Preliminary observations indicate that fractures with no lateral offset assisted full transposition of the fabric as they evolved into interconnected meter-scale shear zones during progressive deformation. This research group will evaluate whether these preliminary interpretations are valid through the mapping of thermobarometric and geochronologic patterns along the inferred length of the Twelve Mile Bay shear zone