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result(s) for
"Hyperbolic structures."
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Shock Capturing and High-Order Methods for Hyperbolic Conservation Laws
Long description:
This thesis is concerned with the numerical treatment of hyperbolic conservation laws. These play an important role in describing many natural phenomena. Challenges in their theoretical as well as numerical study stem from the fact that spontaneous shock discontinuities can arise in their solutions, even in finite time and smooth initial states.
Moreover, the numerical treatment of hyperbolic conservations laws involves many different fields from mathematics, physics, and computer science. As a consequence, this thesis also provides contributions to several different fields of research -- which are still connected by numerical conservation laws, however. These contributions include, but are not limited to, the construction of stable high order quadrature rules for experimental data, the development of new stable numerical methods for conservation laws, and the investigation and design of shock capturing procedures as a means to stabilize high order numerical methods in the presence of (shock) discontinuities.
eBook
Hyperbolic structures : Shukhov's lattice towers - forerunners of modern lightweight construction
Hyperbolic structures analyses the interactions of form with the structural behaviour of hyperbolic lattice towers, and the effects of the various influencing factors were determined with the help of parametric studies and load capacity analyses. This evaluation of Shukhov's historical calculations and the reconstruction of the design and development process of his water towers shows why the Russian engineer is considered not only a pathfinder for lightweight structures but also a pioneer of parametrised design processes.
eBook
A primer on mapping class groups (Princeton mathematical series)
The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.
eBook
Symmetries of hyperbolic spatial graphs and realization of graph symmetries
In a closed connected orientable 3-manifold associated with an orientation-preserving smooth finite group action, we construct setwise invariant hyperbolic spatial graphs with given singularity. As an application, we provide a condition under which symmetries of abstract graphs are realizable by symmetries of the 3-sphere through hyperbolic spatial embeddings.
Journal Article
Global Conjugacy of Vector Fields via Tame Hyperbolic Structure
In this work, we first show that the closed subspace
E
of smooth vector fields on
R
n
which are rapidly decreasing together with all derivatives admits a tame hyperbolic structure first for a hyperbolic linear vector field
X
0
then with respect to a perturbation
X
0
+
Y
of
X
0
where
Y
is an infinitely flat vector field at the origin 0 with small support. As a consequence of the tameness property of
E
, we show that these fields are globally conjugate to their perturbations by any vector field from a small neighborhood of 0 in
E
.
Journal Article
Analytical construction and visualization of nonlinear waves in the (2+1) dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with stability analysis
In this study, we investigate the (2+1)-dimensional Kadomtsev–Petviashvili–Sawada–Kotera–Ramani (KPSKR) equation, a physically significant model describing nonlinear wave phenomena in higher-dimensional spaces. Utilizing the improved modified extended tanh-function method, we derive a diverse spectrum of exact analytical solutions. These include bright solitons, singular solitons, singular periodic waves, and hyperbolic function solutions. The physical characteristics and dynamical behaviors of the obtained solutions are further elucidated through comprehensive two-dimensional and three-dimensional graphical visualizations, offering insight into the complex wave structures governed by the KPSKR equation. The results highlight the versatility of the proposed method and the rich nonlinear dynamics inherent in the model.
Journal Article
On the Double-Stranded DNA Model by Using an Analytical Method in Soliton Theory
In this work, with the aid of computational program, the modified exp[-Q(§)]-expansion function method (MEFM) is considered to obtain some new results to the double-stranded Deoxyribonucleic acid (DNA) model. We extract some new complex polynomial and soliton solutions to the governing system of equations. Moreover, we plot 2D and 3D graphical distributions of dependant variable of the double stranded DNA model.
Journal Article
Hyperbolic structures
Hyperbolic structures analyses the interactions of form with the structural behaviour of hyperbolic lattice towers, and the effects of the various influencing factors were determined with the help of parametric studies and load capacity analyses. This evaluation of Shukhov's historical calculations and the reconstruction of the design and development process of his water towers shows why the Russian engineer is considered not only a pathfinder for lightweight structures but also a pioneer of parametrised design processes.
eBook
Effect of Clamp Deletion on Static Behavior and Dynamic Characteristics of Loop-Free Cable Net Structures
The loop-free single-layer hyperbolic cable net structure (LSHCS) is a new tensile cable structure for buildings, and it can overcome the disadvantages of key elements and the high tension in tensile cable structures with loop cables. The imperfection of the LSHCS is that cable clamps near the inside boundary are redundant. In this paper, the static behavior and dynamic characteristics of thirty-one schemes in five levels of deleting cable clamps are carried out with ANSYS software and Midas/Gen software. The results show that SE1/1, SE2/1, SE3/1, and SE4/1 are the best cable clamp deleting schemes for their respective levels. Displacements are the most sensitive to deleting cable clamps, the natural vibration period comes in second, and tensions are not sensitive with the growth rates of 6.09%, 5.11%, 15.97%, and 19.28% in the best scheme of each level. It is concluded that schemes involving the virtual rings of cable clamps closest to the inside boundary cause the smallest effect on static behavior and dynamic characteristics. Deleting the cable clamps affects the structural stiffness significantly, but the bearing capacity is not seriously affected. It turns out that removing redundant cable clamps in the dense part of the LSHCS is feasible.
Journal Article