Search Results (6)

A potential flow theory-based fully nonlinear 2D NWT is developed in the time domain to investigate the hydrodynamic performance of a submerged circular cylindrical WEC device under combined wave–current conditions. The hydrodynamic force on the submerged cylinder is evaluated using the acceleration potential method coupled with the desingularized boundary integral equation method (DBIEM). The impacts of the wave height, current speed, and parameters of the power take-off mechanism on the extracted power capability of the WEC device are investigated. The results show that for the scenario of an opposing current, the dimensionless mean extracted power is reduced by as much as 14.3% with increasing wave height. Except for long waves, the extracted power under a co-flowing current exceeds that of the current-free case and an opposing current yields lower power. In contrast to the current-free scenario, the peak power extraction point shifts to slightly higher values of the spring and damper constants when the current is co-flowing, whereas the opposite trend is observed for the opposing current. Full article

A local bifurcation analysis of a high-dimensional dynamical system $\frac{dx}{dt}=f\left(x\right)$ is performed using a good deformation of the polynomial mapping $P:{\mathbb{C}}^n\to {\mathbb{C}}^n$. This theory is used to construct geometric aspects of the resolution of multiple zeros of the polynomial vector field $P\left(x\right)$. Asymptotic bifurcation rules are derived from Grothendieck’s theory of residuals. Following the Coxeter–Dynkin classification, the singularity graph is constructed. A detailed study of three types of multidimensional mappings with a large symmetry group has been carried out, namely: 1. A linear singularity (behaves similarly to a one-dimensional complex analysis theory); 2. The lattice singularity (generalized the linear and resembling regular crystal growth models); 3. The fan-shaped singularity (can be split radially like nuclear fission and fusion models). Full article

Finding four-dimensional de Sitter spacetime solutions in string theory has been a vexing quest ever since the discovery of the accelerating expansion of the universe. Building on a recent analysis of bubble-nucleation in the decay of (false-vacuum) AdS backgrounds where the interfacing bubbles themselves exhibit a de Sitter geometry we show that this resonates strongly with a stringy cosmic brane construction that naturally provides for an exponential mass-hierarchy and the localization of both gravity and matter, in addition to an exponentially suppressed positive cosmological constant. Finally, we argue that these scenarios can be realized in terms of a generalization of a small resolution of a conifold singularity in the context of a (Lorentzian) Calabi–Yau 5-fold, where the isolated (Lorentzian) two complex dimensional Fano variety is a four-dimensional de Sitter spacetime. Full article

The Kummer surface was constructed in 1864. It corresponds to the desingularization of the quotient of a 4-torus by 16 complex double points. Kummer surface is known to play a role in some models of quantum gravity. Following our recent model of the DNA genetic code based on the irreducible characters of the finite group $G_5:=(240,105)\cong {\mathbb{Z}}_5⋊2O$ (with $2O$ the binary octahedral group), we now find that groups $G_6:=(288,69)\cong {\mathbb{Z}}_6⋊2O$ and $G_7:=(336,118)\cong {\mathbb{Z}}_7⋊2O$ can be used as models of the symmetries in hexamer and heptamer proteins playing a vital role for some biological functions. Groups $G_6$ and $G_7$ are found to involve the Kummer surface in the structure of their character table. An analogy between quantum gravity and DNA/RNA packings is suggested. Full article

In this paper, an improved potential flow model is proposed for the hydrodynamic analysis of ships advancing in waves. A desingularized Rankine panel method, which has been improved with the added effect of nonlinear steady wave-making (NSWM) flow in frequency domain, is employed for 3D diffraction and radiation problems. Non-uniform rational B-splines (NURBS) are used to describe the body and free surfaces. The NSWM potential is computed by linear superposition of the first-order and second-order steady wave-making potentials which are determined by solving the corresponding boundary value problems (BVPs). The so-called m_j terms in the body boundary condition of the radiation problem are evaluated with nonlinear steady flow. The free surface boundary conditions in the diffraction and radiation problems are also derived by considering nonlinear steady flow. To verify the improved model and the numerical method adopted in the present study, the nonlinear wave-making problem of a submerged moving sphere is first studied, and the computed results are compared with the analytical results of linear steady flow. Subsequently, the diffraction and radiation problems of a submerged moving sphere and a modified Wigley hull are solved. The numerical results of the wave exciting forces, added masses, and damping coefficients are compared with those obtained by using Neumann–Kelvin (NK) flow and double-body (DB) flow. A comparison of the results indicates that the improved model using the NSWM flow can generally give results in better agreement with the test data and other published results than those by using NK and DB flows, especially for the hydrodynamic coefficients in relatively low frequency ranges. Full article

We are concerned with rigid analytic geometry in the general setting of Henselian fields K with separated analytic structure, whose theory was developed by Cluckers–Lipshitz–Robinson. It unifies earlier work and approaches of numerous mathematicians. Separated analytic structures admit reasonable relative quantifier elimination in a suitable analytic language. However, the rings of global analytic functions with two kinds of variables seem not to have good algebraic properties such as Noetherianity or excellence. Therefore, the usual global resolution of singularities from rigid analytic geometry is no longer at our disposal. Our main purpose is to give a definable version of the canonical desingularization algorithm (the hypersurface case) due to Bierstone–Milman so that both of these powerful tools are available in the realm of non-Archimedean analytic geometry at the same time. It will be carried out within a category of definable, strong analytic manifolds and maps, which is more flexible than that of affinoid varieties and maps. Strong analytic objects are those definable ones that remain analytic over all fields elementarily equivalent to K. This condition may be regarded as a kind of symmetry imposed on ordinary analytic objects. The strong analytic category makes it possible to apply a model-theoretic compactness argument in the absence of the ordinary topological compactness. On the other hand, our closedness theorem enables application of resolution of singularities to topological problems involving the topology induced by valuation. Eventually, these three results will be applied to such issues as the existence of definable retractions or extending continuous definable functions. The established results remain valid for strictly convergent analytic structures, whose classical examples are complete, rank one valued fields with the Tate algebras of strictly convergent power series. The earlier techniques and approaches to the purely topological versions of those issues cannot be carried over to the definable settings because, among others, non-Archimedean geometry over non-locally compact fields suffers from lack of definable Skolem functions. Full article