Quasilinear dirichlet problems in RN with critical growth

In this study, a given quasilinear problem is solved using variational methods. In particular, the existence of nontrivial solutions for GP is examined using minimax methods. The main theorem on the existence of a nontrivial solution for GP is detailed.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Energy and the AdS/CFT correspondence

We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for 'regular' and 'irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformai dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart.

Interaction of pulses in the nonlinear Schrödinger model

A study was conducted on the interaction of two pulses in the nonlinear Schrodinger (NLS) model. The presence of different scenarios of the behavior depending on the initial parameters of the pulses, such as the pulse areas, the relative phase shift, the spatial and frequency separations were shown. It was observed that a pure real initial condition of the NLS equation can result in additional moving solitons.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

Modal Analysis of a Beam with a Tip Rotor by Using a Fundamental Response

The shape modes of a damped-free beam model with a tip rotor are determined by using a dynamical basis that is generated by a fundamental spatial free response. This is a non-classical distributed model for the displacements in the transverse directions of the beam which turns out to be coupled through boundary conditions due to rotation. Numerical calculations are performed by using the Ritz-Rayleigh method with several approximating basis.

Pressure field in the cathode-anode region of a high-power klystron amplifier

The pressure field of a high-power klystron amplifier in the cathode and anode region was investigated. The investigation was performed using a 1.3 GHz, 100 A and 240 kV high-power klystron with five reentrant coaxial cavities, assembled in cylindrical drift tube 1.2 m long. The diffusion equation in mathematical model was also solved by using a 3-D finite element method code, in order to obtain pressure profile in region of interest. The results show that density profile of molecules between cathode-anode region was determined, where cathode pressure is approximately 10% higher than anode pressure.

Thermally developing forced convection of non-Newtonian fluids inside elliptical ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.

Quantum topology change and large-N gauge theories

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g) = (A X, script H sign X, D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter β and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at β = ∞ for any value of N. Moreover, the system undergoes a third-order phase transition at β = 1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. © SISSA/ISAS 2004.

CH and C2 radicals characterization in natural gas turbulent diffusion flames

This paper reports the construction of an axisymmetric nonpremixed piloted jet burner, with well-defined initial and boundary conditions, known as the Delft burner, to assess turbulence-chemistry interaction in non-premixed turbulent flames. Detailed experimental information is described, involving hot-wire anemometry, thin-wire thermocouples and chemiluminescence visualization measurements. Radial profile of the axial mean velocity indicates excellent agreement between flow patterns developed within Delft installation and the one described herein. Chemiluminescence emissions from CH and C2 free-radicals were acquired with a CCD camera. Tomography reconstruction analysis was utilised to compare radical emissions and temperature spatial distributions. There was a strong dependence between temperature and CH/C 2 emissions. This is an indication that these radicals can be used in flame front studies.

Pressure field distribution in a conical tube with transient and outgassing gas sources

This work presents and describes in detail the pressure profile in a conical tube with the unavoidable steady-state outgassing, plus a transient gas source, like, for instance, in an accelerator, when particles from the beam hit the walls. Mathematical and physical formulations are given and detailed; specific conductance, specific throughput and a detailed discussion about the boundary conditions are presented. These concepts and approach are applied to usual realistic cases, such as conical tubes, with typical laboratory dimensions. © 2005 IEEE.

Including the sub-grid scale plume rise of vegetation fires in low resolution atmospheric transport models

We describe and begin to evaluate a parameterization to include the vertical transport of hot gases and particles emitted from biomass burning in low resolution atmospheric-chemistry transport models. This sub-grid transport mechanism is simulated by embedding a 1-D cloud-resolving model with appropriate lower boundary conditions in each column of the 3-D host model. Through assimilation of remote sensing fire products, we recognize which columns have fires. Using a land use dataset appropriate fire properties are selected. The host model provides the environmental conditions, allowing the plume rise to be simulated explicitly. The derived height of the plume is then used in the source emission field of the host model to determine the effective injection height, releasing the material emitted during the flaming phase at this height. Model results are compared with CO aircraft profiles from an Amazon basin field campaign and with satellite data, showing the huge impact that this mechanism has on model performance. We also show the relative role of each main vertical transport mechanisms, shallow and deep moist convection and the pyro-convection (dry or moist) induced by vegetation fires, on the distribution of biomass burning CO emissions in the troposphere.

Podolsky's electromagnetic theory on the null-plane gauge

Following the Dirac's technique for constrained systems we performed a detailed analysis of the constraint structure of Podolsky's electromagnetic theory on the null-plane coordinates. The null plane gauge condition was extended to second order theories and appropriate boundary conditions were imposed to guarantee the uniqueness of the inverse of the constraints matrix of the system. Finally, we determined the generalized Dirac brackets of the independent dynamical variables. © 2010 American Institute of Physics.