Vortex lattice and matching fields for a long superconducting wire

We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner states, with boundary conditions appropriate for this geometry. Using the Monte Carlo simulated annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed states provides expressions for the matching fields. We find that, as in the case of samples of different geometry, the finite-size effect provokes a delay on the vortex penetration and a vortex accumulation in the center of the sample. The vortex patterns obtained are in good agreement with experimental results.

Two-body Dirac equation approach to the deuteron

The two-body Dirac(Breit) equation with potentials associated to one-boson-exchanges with cutoff masses is solved for the deuteron and its observables calculated. The 16-component wave-function for the Jπ = 1+ state contains four independent radial functions which satisfy a system of four coupled differential equations of first order. This system is numerically integrated, from infinity towards the origin, by fixing the value of the deuteron binding energy and imposing appropriate boundary conditions at infinity. For the exchange potential of the pion, a mixture of direct plus derivative couplings to the nucleon is considered. We varied the pion-nucleon coupling constant, and the best results of our calculations agree with the lower values recently determined for this constant.

Size effects in the magnetization of a superconducting wire

The size effects in the magnetization of a long cylindrical wire of circular cross section in the presence of an external magnetic field are investigated. For this study the London theory is used with boundary conditions appropriate for this geometry. Using the Monte Carlo simulated annealing method, the free energy of the mixed state is minimized with respect to the vortex positions. The ground state of the vortex lattice for n = 1 up to 18 vortices for a given radius of the cylinder is obtained. It is found that the finite size of the sample provokes a matching effect in the magnetization, as found in experiments with superconducting samples of finite size but different geometry. © 1999 American Institute of Physics.

Smooth landscape solvent dynamics in electron transfer reactions

Solvent effects play a major role in controlling electron-transfer reactions. The solvent dynamics happens on a very high-dimensional surface, and this complex landscape is populated by a large number of minima. A critical problem is to understand the conditions under which the solvent dynamics can be represented by a single collective reaction coordinate. When this unidimensional representation is valid, one recovers the successful Marcus theory. In this study the approach used in a previous work [V. B. P. Leite and J. N. Onuchic; J. Phys. Chem. 100, 7680 (1996)] is extended to treat a more realistic solvent model, which includes energy correlation. The dynamics takes place in a smooth and well behaved landscape. The single shell of solvent molecules around a cavity is described by a two-dimensional system with periodic boundary conditions with nearest neighbor interaction. It is shown how the polarization-dependent effects can be inferred. The existence of phase transitions depends on a factor y proportional to the contribution from the two parameters of the model. For the present model, γ suggests the existence of weak kinetic phase transitions, which are used in the analysis of solvent effects in charge-transfer reactions. © 1999 American Institute of Physics.

Dynamical calculation of direct muon-transfer rates from thermalized muonic hydrogen to C6+ and O8+

Moun-transfer reactions from muonic hydrogen to carbon and oxygen nuclei employing a full quantum-mechanical few-body description of rearrangement scattering were studied by solving the Faddeev-Hahn-type equations using close-coupling approximation. The application of a close-coupling-type ansatz led to satisfactory results for direct muon-transfer reactions from muonic hydrogen to C6+ and O8+.

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.

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.