Search results for "Mathematica"
showing 10 items of 7971 documents
The monodromy groups of Dolgachev's CY moduli spaces are Zariski dense
2014
Let $\mathcal{M}_{n,2n+2}$ be the coarse moduli space of CY manifolds arising from a crepant resolution of double covers of $\mathbb{P}^n$ branched along $2n+2$ hyperplanes in general position. We show that the monodromy group of a good family for $\mathcal{M}_{n,2n+2}$ is Zariski dense in the corresponding symplectic or orthogonal group if $n\geq 3$. In particular, the period map does not give a uniformization of any partial compactification of the coarse moduli space as a Shimura variety whenever $n\geq 3$. This disproves a conjecture of Dolgachev. As a consequence, the fundamental group of the coarse moduli space of $m$ ordered points in $\mathbb{P}^n$ is shown to be large once it is not…
Shock formation in the dispersionless Kadomtsev-Petviashvili equation
2016
The dispersionless Kadomtsev-Petviashvili (dKP) equation $(u_t+uu_x)_x=u_{yy}$ is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation $u_t+uu_x=0$. We show numerically that the solutions to the transformed equation do not develop shocks. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the $(x,y)$ plane, where the solution of the dKP equation exists in a weak sense only, and a…
Recollimation shocks in relativistic jets
2018
Recollimation shocks (RS) appear associated with relativistic flows propagating through pressure mismatched atmospheres. Astrophysical scenarios invoking the presence of such shocks include jets from AGNs and X-ray binaries and GRBs. We shall start reviewing the theoretical background behind the structure of RS in overpressured jets. Next, basing on numerical simulations, we will focus on the properties of RS in relativistic steady jets threaded by helical magnetic fields depending on the dominant type of energy. Synthetic radio maps from the simulation of the synchrotron emission for a selection of models in the context of parsec-scale extragalactic jets will also be discussed.© 2018 World…
High-order regularization in lattice-Boltzmann equations
2017
A lattice-Boltzmann equation (LBE) is the discrete counterpart of a continuous kinetic model. It can be derived using a Hermite polynomial expansion for the velocity distribution function. Since LBEs are characterized by discrete, finite representations of the microscopic velocity space, the expansion must be truncated and the appropriate order of truncation depends on the hydrodynamic problem under investigation. Here we consider a particular truncation where the non-equilibrium distribution is expanded on a par with the equilibrium distribution, except that the diffusive parts of high-order nonequilibrium moments are filtered, i.e., only the corresponding advective parts are retained afte…
Present-day use of an empirical wave prediction method
2016
Knowledge of the offshore wave climate is key to the design of coastal engineering structures and to the study of shoreline evolution. To date, the available wave data have been limited both in time and space; even though there are several options for obtaining wave data calculated using complex numerical models at basin scale, design issues can in some cases be solved by means of simpler models. This paper shows whether, under certain conditions and in an enclosed basin, an old empirical model can provide results that are good enough to determine the design condition necessary for engineering purposes. The empirical model chosen to answer this question is called Sverdrup–Munk–Bretschneide…
Application of Mathematical Models in Analysis of Heat Losses in the Buildings
2006
Physical model of heat balance for separate living room is discussed, which allows to analyse the distributions of the flow of air and temperature depending on the physical conditions and geometry. The model enables to choose the optimal surface area of building elements and their properties in order to decrease the heat losses and improve the conditions of thermal comfort. Room with bounding constructions and real dimensions is modelled that helps to understand the peculiarities of heat transfer process in the room as well as distribution of various characteristic quantities and their dependence on the different conditions. Multiple parameters are varied in 2D calculations and their influe…
Numerical approach for signal delay in general distributed networks
2003
The authors consider a general network with telegraph equations modelling distributed elements and having, additionally, nonlinear capacitors. A global asymptotic exponential stability of the solution is given. A simple computable upper bound of the delay time is given. Numerical examples illustrate the usefulness of the results. >
Signal integrity studies at optical multiplexer board for TileCal system
2007
6 pages.-- ISI Article Identifier: 000253651800006
Compact-like pulse signals in a new nonlinear electrical transmission line
2013
International audience; A nonlinear electrical transmission line with an intersite circuit element acting as a nonlinear resistance is introduced and investigated. In the continuum limit, the dynamics of localized signals is described by a nonlinear evolution equation belonging to the family of nonlinear diffusive Burgers' equations. This equation admits compact pulse solutions and shares some symmetry properties with the Rosenau-Hyman K(2,2) equation. An exact discrete compactly- supported signal voltage is found for the network and the dissipative effects on the pulse motion analytically studied. Numerical simulations confirm the validity of analytical results and the robustness of these …
In-Fiber Fractional Signal Processing: Recent Results and Applications
2018
The implementation of mathematical operators using photonic signal processing –as for example, conventional differentiators and integrators– is particularly well suited to overcome the speed and bandwidth limitations of electronics. In the Laboratory of Fiber Optics of the University of Valencia we work on the development of in-fiber time-domain fractional operators and their applications. In the last years we have made some specific proposals to perform photonic fractional differentiation (PFD), photonic fractional integration (PFI), photonic fractional Hilbert transform (PFHT), and photonic fractional Fourier transform (PFFT), using fiber-based technologies. Recently, we have been able to…