Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes

2012 ◽  
Vol 11 (4) ◽  
pp. 1144-1168 ◽  
Author(s):  
Juan Cheng ◽  
Chi-Wang Shu
Keyword(s):  
Spherical Symmetry ◽  
Gas Dynamics ◽  
Control Volume ◽  
Two Dimensional ◽  
Cylindrical Coordinates ◽  
One Dimensional ◽  
First Order ◽  
Conservation Of Momentum ◽  
Numerical Fluxes ◽  
Geometric Conservation Law

AbstractIn, Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates. These schemes use a node-based discretization of the numerical fluxes. The control volume version has several distinguished properties, including the conservation of mass, momentum and total energy and compatibility with the geometric conservation law (GCL). However it also has a limitation in that it cannot preserve spherical symmetry for one-dimensional spherical flow. An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry, at the price of sacrificing conservation of momentum. In this paper, we apply the methodology proposed in our recent work to the first order control volume scheme of Maire in to obtain the spherical symmetry property. The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid, and meanwhile it maintains its original good properties such as conservation and GCL. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry, non-oscillation and robustness properties.

scholarly journals CABARET scheme on moving grids for two-dimensional equations of gas dynamics and dynamic elasticity

2021 ◽  
pp. 306-321
Author(s):  
Н.А. Афанасьев ◽  
П.А. Майоров
Keyword(s):  
Gas Dynamics ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Arbitrary Lagrangian Eulerian ◽  
Cabaret Scheme ◽  
One Dimensional ◽  
Equations Of Gas Dynamics ◽  
Dynamic Elasticity ◽  
First Case ◽  
Lagrangian Variables

Схема КАБАРЕ, являющаяся представителем семейства балансно-характеристических методов, широко используется при решении многих задач для систем дифференциальных уравнений гиперболического типа в эйлеровых переменных. Возрастающая актуальность задач взаимодействия деформируемых тел с потоками жидкости и газа требует адаптации этого метода на лагранжевы и смешанные эйлерово-лагранжевы переменные. Ранее схема КАБАРЕ была построена для одномерных уравнений газовой динамики в массовых лагранжевых переменных, а также для трехмерных уравнений динамической упругости. В первом случае построенную схему не удалось обобщить на многомерные задачи, а во втором — использовался необратимый по времени алгоритм передвижения сетки. В данной работе представлено обобщение метода КАБАРЕ на двумерные уравнения газовой динамики и динамической упругости в смешанных эйлерово-лагранжевых и лагранжевых переменных. Построенный метод является явным, легко масштабируемым и обладает свойством временн´ой обратимости. Метод тестируется на различных одномерных и двумерных задачах для обеих систем уравнений (соударение упругих тел, поперечные колебания упругой балки, движение свободной границы идеального газа). The conservative-characteristic CABARET scheme is widely used in solving many problems for systems of differential equations of hyperbolic type in Euler variables. The increasing urgency of the problems of interaction of deformable bodies with liquid and gas flows requires the adaptation of this method to Lagrangian and arbitrary Lagrangian-Eulerian variables. Earlier, the CABARET scheme was constructed for one-dimensional equations of gas dynamics in mass Lagrangian variables, as well as for three-dimensional equations of dynamic elasticity. In the first case, the constructed scheme could not be generalized to multidimensional problems, and in the second, a time-irreversible grid movement algorithm was used. This paper presents a generalization of the CABARET method to two-dimensional equations of gas dynamics and dynamic elasticity in arbitrary Lagrangian-Eulerian and Lagrangian variables. The constructed method is explicit, easily scalable, and has the property of temporal reversibility. The method is tested on various one-dimensional and two-dimensional problems for both systems of equations (collision of elastic bodies, transverse vibrations of an elastic beam, motion of the free boundary of an ideal gas).

scholarly journals Two-dimensional ground-state mapping of a Mott-Hubbard system in a flexible field-effect device

2019 ◽  
Vol 5 (5) ◽  
pp. eaav7282 ◽  
Author(s):  
Yoshitaka Kawasugi ◽  
Kazuhiro Seki ◽  
Satoshi Tajima ◽  
Jiang Pu ◽  
Taishi Takenobu ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Field Effect ◽  
Mott Insulator ◽  
Two Dimensional ◽  
Superconducting Transition ◽  
Microscopic Mechanism ◽  
One Dimensional ◽  
First Order ◽  
Insulating Phase

A Mott insulator sometimes induces unconventional superconductivity in its neighbors when doped and/or pressurized. Because the phase diagram should be strongly related to the microscopic mechanism of the superconductivity, it is important to obtain the global phase diagram surrounding the Mott insulating state. However, the parameter available for controlling the ground state of most Mott insulating materials is one-dimensional owing to technical limitations. Here, we present a two-dimensional ground-state mapping for a Mott insulator using an organic field-effect device by simultaneously tuning the bandwidth and bandfilling. The observed phase diagram showed many unexpected features such as an abrupt first-order superconducting transition under electron doping, a recurrent insulating phase in the heavily electron-doped region, and a nearly constant superconducting transition temperature in a wide parameter range. These results are expected to contribute toward elucidating one of the standard solutions for the Mott-Hubbard model.

Parity inversion property of the double ring-shaped oscillator in cylindrical coordinates

2015 ◽  
Vol 30 (39) ◽  
pp. 1550200 ◽  
Author(s):  
Dong-Sheng Sun ◽  
Fa-Lin Lu ◽  
Yuan You ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Functional Analysis ◽  
Singular Point ◽  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Spherical Coordinates ◽  
Analysis Method ◽  
Cylindrical Coordinates ◽  
One Dimensional ◽  
Double Ring ◽  
The One

Using the functional analysis method, we present the exact solutions of the double ring-shaped oscillator (DRSO) potential with certain parity in the cylindrical coordinates. Such a quantum system is separated to two differential equations, i.e. a one-dimensional harmonic oscillator plus an inverse square term and a two-dimensional harmonic oscillator plus an inverse square term. The key point is how to find the adapted symmetrical solutions of the one-dimensional harmonic oscillator plus an inverse square term at the singular point [Formula: see text]. The obtained results are compared with those in the spherical coordinates. We also explore intimate connections [Formula: see text] and [Formula: see text] by substituting [Formula: see text] and [Formula: see text].

scholarly journals Die Zeit in zweidimensionaler Betrachtung

2016 ◽  
Vol 64 (6) ◽  
Author(s):  
Anton Friedrich Koch
Keyword(s):  
Second Order ◽  
Temporal Scale ◽  
Two Dimensional ◽  
Temporal Scales ◽  
One Dimensional ◽  
First Order ◽  
The Past ◽  
The Future

AbstractB-time, i. e. the temporal scale of the B-series of events, is one and the same for all times, while A-times (the temporal scales of A-series) are as many as there are moments of time. This means that A-theorists will have to consider one-dimensional time two-dimensionally: as changing within itself at every moment. The two-dimensional view is here put to service for a meta-compatibilist theory of freedom, a theory, that is, which reconciles freedom, determinism and their first order incompatibility at the second order. Kant’s position is interpreted as meta-compatibilist as well, but as having the drawback of separating time and freedom. In order to appreciate the connection of time and freedom, one has to acknowledge that in free acts the future is determined further according to plan, while at the same time the past is (with nomological necessity) co-determined further in countless unclear and inscrutable ways. A free act thus consumes its own range of freedom by positing retroactively the sufficient causal antecedents for its taking place: It was free before it occurred and is part of nature after.

scholarly journals The Design of One-Dimensional Motion and Two-Dimensional Motion Learning Media Using Digital Camera and Tracker-Based Air Track

2020 ◽  
Vol 6 (1) ◽  
pp. 65-74
Author(s):  
Fransisca Indra Dewi ◽  
Nur Aji Wibowo ◽  
Debora Natalia Sudjito ◽  
Ferdy Rondonuwu
Keyword(s):  
Digital Camera ◽  
Object Motion ◽  
Frame Rate ◽  
Two Dimensional ◽  
Digital Cameras ◽  
One Dimensional ◽  
Before And After ◽  
Conservation Of Momentum ◽  
Frictional Forces ◽  
Almost All

This research describes the results of the development of 2D air track tools designed for one and two-dimensional motion experiments with small frictional forces. Friction is minimized by using wind gusts through small holes made in all parts of the runway. Motion detection devices used are digital cameras and trackers. Digital cameras are used to record the motion of objects on a platform in the form of video with a specific frame-rate. Tracker is used to analyzing videos that contain information about object motion. This tool has been tested on one-dimensional motion, that is, an object that slides over an inclined plane and two-dimensional motion in the case of a collision of two objects. In the case of one-dimensional position graphs against time can be displayed, the instantaneous velocity and average and acceleration can be accurately determined. In the case of the collision of two objects, the position graph against time can also be displayed for each object before and after the collision. The velocity vector can be determined accurately so that the law of conservation of momentum and kinetic energy can be verified. One and two-dimensional motion are the concepts that underlie almost all other concepts in physics. Therefore one and two-dimensional motion experiments are important to build students’ experiences of the concept. Thus 2D air track platform based on digital cameras and Tracker software can be used as a physics learning media on motion kinematics materials that can display various kinematics graphs so that information about motion is complete.

scholarly journals Mapping Epistatic Quantitative Trait Loci With One-Dimensional Genome Searches

Genetics ◽  
2001 ◽  
Vol 157 (1) ◽  
pp. 445-454 ◽  
Author(s):  
Jean-Luc Jannink ◽  
Ritsert Jansen
Keyword(s):  
Maximum Likelihood ◽  
Doubled Haploid ◽  
Quantitative Trait ◽  
Genetic Background ◽  
Two Dimensional ◽  
Qtl Detection ◽  
One Dimensional ◽  
First Order ◽  
Large Populations ◽  
Different Levels

AbstractThe discovery of epistatically interacting QTL is hampered by the intractability and low power to detect QTL in multidimensional genome searches. We describe a new method that maps epistatic QTL by identifying loci of high QTL by genetic background interaction. This approach allows detection of QTL involved not only in pairwise but also higher-order interaction, and does so with one-dimensional genome searches. The approach requires large populations derived from multiple related inbred-line crosses as is more typically available for plants. Using maximum likelihood, the method contrasts models in which QTL allelic values are either nested within, or fixed over, populations. We apply the method to simulated doubled-haploid populations derived from a diallel among three inbred parents and illustrate the power of the method to detect QTL of different effect size and different levels of QTL by genetic background interaction. Further, we show how the method can be used in conjunction with standard two-locus QTL detection models that use two-dimensional genome searches and find that the method may double the power to detect first-order epistasis.

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