Negative-Energy Perturbations in Circularly Cylindrical Equilibria within the Framework of Maxwell-Drift Kinetic Theory

The conditions for the existence of negative-energy perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated in the framework of linearized collisionless Maxwell-drift kinetic theory for the case of equilibria of magnetically confined, circularly cylindrical plasmas and vanishing initial field perturbations. For wave vectors with a non-vanishing component parallel to the magnetic field, the plane equilibrium conditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\bf 49}, 3290 (1994)]) are shown to remain valid, while the condition for perpendicular perturbations (which are found to be the most important modes) is modified. Consequently, besides the tokamak equilibrium regime in which the existence of negative-energy perturbations is related to the threshold value of 2/3 of the quantity $\eta_\nu = \frac {\partial \ln T_\nu} {\partial \ln N_\nu}$, a new regime appears, not present in plane equilibria, in which negative-energy perturbations exist for {\em any} value of $\eta_\nu$. For various analytic cold-ion tokamak equilibria a substantial fraction of thermal electrons are associated with negative-energy perturbations (active particles). In particular, for linearly stable equilibria of a paramagnetic plasma with flat electron temperature profile ($\eta_e=0$), the entire velocity space is occupied by active electrons. The part of the velocity space occupied by active particles increases from the center to the plasma edge and is larger in a paramagnetic plasma than in a diamagnetic plasma with the same pressure profile. It is also shown that, unlike in plane equilibria, negative-energy perturbations exist in force-free reversed-field pinch equilibria with a substantial fraction of active particles.Comment: 31 pages, late

Asymptotic Bethe equations for open boundaries in planar AdS/CFT

We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries scattering theory describing the excitations of a free open string propagating in $AdS_5\times S^5$, carrying large angular momentum $J=J_{56}$, and ending on a maximal giant graviton whose angular momentum is in the same plane. We thus obtain the all-loop Bethe equations describing the spectrum, for $J$ finite but large, of the energies of such strings, or equivalently, on the gauge side of the AdS/CFT correspondence, the anomalous dimensions of certain operators built using the epsilon tensor of SU(N). We also give the Bethe equations for strings ending on a probe D7-brane, corresponding to meson-like operators in an $\mathcal N=2$ gauge theory with fundamental matter.Comment: 30 pages. v2: minor changes and discussion section added, J.Phys.A version

COMPARISON BETWEEN SINGLE AND DOUBLE INTEGRAL TRANSFORMATION SOLUTIONS OF HEAT CONDUCTION IN SOLID-STATE ELECTRONICS

The design of modern electronic devices has been dealing with challenges on thermal control. In this work, it is proposed two different ways of modeling the temperature field in Solid State Electronics (SSE) using integral transforms, with several heat generations in the domain of the microchip and external convection. Two proposed approaches solve the heat conduction formulation on the SSE using the Classical Integral Transform Technique (CITT): One performing a single transformation (CITT-ST) and the other performing a double transformation (CITT-DT). Both methodologies are compared and achieved similar results. The simpler analytical solution by CITT-DT contrasts with a complex and cumbersome analytical manipulation of CITT-ST. The results show that CITT-ST is more efficient to obtain the solution, requiring a lower truncation order, for the problem of heat conduction in Solid State Electronics even though it has a more complex formulation

Negative-energy perturbations in cylindrical equilibria with a radial electric field

The impact of an equilibrium radial electric field $E$ on negative-energy perturbations (NEPs) (which are potentially dangerous because they can lead to either linear or nonlinear explosive instabilities) in cylindrical equilibria of magnetically confined plasmas is investigated within the framework of Maxwell-drift kinetic theory. It turns out that for wave vectors with a non-vanishing component parallel to the magnetic field the conditions for the existence of NEPs in equilibria with E=0 [G. N. Throumoulopoulos and D. Pfirsch, Phys. Rev. E 53, 2767 (1996)] remain valid, while the condition for the existence of perpendicular NEPs, which are found to be the most important perturbations, is modified. For $|e_i\phi|\approx T_i$ ($\phi$ is the electrostatic potential) and $T_i/T_e > \beta_c\approx P/(B^2/8\pi)$ ($P$ is the total plasma pressure), a case which is of operational interest in magnetic confinement systems, the existence of perpendicular NEPs depends on $e_\nu E$, where $e_\nu$ is the charge of the particle species $\nu$. In this case the electric field can reduce the NEPs activity in the edge region of tokamaklike and stellaratorlike equilibria with identical parabolic pressure profiles, the reduction of electron NEPs being more pronounced than that of ion NEPs.Comment: 30 pages, late

The quark anti-quark potential and the cusp anomalous dimension from a TBA equation

We derive a set of integral equations of the TBA type for the generalized cusp anomalous dimension, or the quark antiquark potential on the three sphere, as a function of the angles. We do this by considering a family of local operators on a Wilson loop with charge L. In the large L limit the problem can be solved in terms of a certain boundary reflection matrix. We determine this reflection matrix by using the symmetries and the boundary crossing equation. The cusp is introduced through a relative rotation between the two boundaries. Then the TBA trick of exchanging space and time leads to an exact equation for all values of L. The L=0 case corresponds to the cusped Wilson loop with no operators inserted. We then derive a slightly simplified integral equation which describes the small angle limit. We solve this equation up to three loops in perturbation theory and match the results that were obtained with more direct approaches.Comment: 63 pages, 12 figures. v2: references added, typos correcte

Integrable achiral D5-brane reflections and asymptotic Bethe equations

We study the reflection of magnons from a D5-brane in the framework of the AdS/CFT correspondence. We consider two possible orientations of the D5-brane with respect to the reference vacuum state, namely vacuum states aligned along "vertical" and "horizontal" directions. We show that the reflections are of the achiral type. We also show that the reflection matrices satisfy the boundary Yang-Baxter equations for both orientations. In the horizontal case the reflection matrix can be interpreted in terms of a bulk S-matrix, S(p, -p), and factorizability of boundary scattering therefore follows from that of bulk scattering. Finally, we solve the nested coordinate Bethe ansatz for the system in the vertical case to find the Bethe equations. In the horizontal case, the Bethe equations are of the same form as those for the closed string.Comment: 27 pages, 4 figures, v2: published versio

Impacts of natural forest landslides in a rural community of Morretes, PR-Brazil.

Edição dos abstracts do 24º IUFRO World Congress, 2014, Salt Lake City. Sustaining forests, sustaining people: the role of research