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

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

FPTAS for Weighted Fibonacci Gates and Its Applications

Fibonacci gate problems have severed as computation primitives to solve other problems by holographic algorithm and play an important role in the dichotomy of exact counting for Holant and CSP frameworks. We generalize them to weighted cases and allow each vertex function to have different parameters, which is a much boarder family and #P-hard for exactly counting. We design a fully polynomial-time approximation scheme (FPTAS) for this generalization by correlation decay technique. This is the first deterministic FPTAS for approximate counting in the general Holant framework without a degree bound. We also formally introduce holographic reduction in the study of approximate counting and these weighted Fibonacci gate problems serve as computation primitives for approximate counting. Under holographic reduction, we obtain FPTAS for other Holant problems and spin problems. One important application is developing an FPTAS for a large range of ferromagnetic two-state spin systems. This is the first deterministic FPTAS in the ferromagnetic range for two-state spin systems without a degree bound. Besides these algorithms, we also develop several new tools and techniques to establish the correlation decay property, which are applicable in other problems

The onset of synchronization in large networks of coupled oscillators

We study the transition from incoherence to coherence in large networks of coupled phase oscillators. We present various approximations that describe the behavior of an appropriately defined order parameter past the transition, and generalize recent results for the critical coupling strength. We find that, under appropriate conditions, the coupling strength at which the transition occurs is determined by the largest eigenvalue of the adjacency matrix. We show how, with an additional assumption, a mean field approximation recently proposed is recovered from our results. We test our theory with numerical simulations, and find that it describes the transition when our assumptions are satisfied. We find that our theory describes the transition well in situations in which the mean field approximation fails. We study the finite size effects caused by nodes with small degree and find that they cause the critical coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two figures and improved the discussion of the range of validity of perturbative approache

Dynamics and Pattern Formation in Large Systems of Spatially-Coupled Oscillators with Finite Response Times

We consider systems of many spatially distributed phase oscillators that interact with their neighbors. Each oscillator is allowed to have a different natural frequency, as well as a different response time to the signals it receives from other oscillators in its neighborhood. Using the ansatz of Ott and Antonsen (Ref. \cite{OA1}) and adopting a strategy similar to that employed in the recent work of Laing (Ref. \cite{Laing2}), we reduce the microscopic dynamics of these systems to a macroscopic partial-differential-equation description. Using this macroscopic formulation, we numerically find that finite oscillator response time leads to interesting spatio-temporal dynamical behaviors including propagating fronts, spots, target patterns, chimerae, spiral waves, etc., and we study interactions and evolutionary behaviors of these spatio-temporal patterns

Effect of a gap on the decoherence of a qubit

We revisit the problem of the decoherence and relaxation of a central spin coupled to a bath of conduction electrons. We consider both metallic and semiconducting baths to study the effect of a gap in the bath density of states (DOS) on the time evolution of the density matrix of the central spin. We use two weak coupling approximation schemes to study the decoherence. At low temperatures, though the temperature dependence of the decoherence rate in the case of a metallic bath is the same irrespective of the details of the bath, the same is not true for the semiconducting bath. We also calculate the relaxation and decoherence rates as a function of external magnetic fields applied both on the central spin and the bath. We find that in the presence of the gap, there exists a certain regime of fields, for which surprisingly, the metallic bath has lower rates of relaxation and decoherence than the semiconducting bath.Comment: 9 pages, 9 figure

Variabilidad espacial y temporal en la comunidad de cladóceros de la Ciénaga de Paredes (Santander, Colombia) a lo largo de un ciclo anual

En la Ciénaga de Paredes (73 · 45'-73· 49'W y 7·26'-7·29'N), ubicada en el Departamento de Santander (Colombia), se determinó la composición, la variación espacial y temporal de la estructura de la comunidad de cladóceros, con base en arrastres verticales con malla de 68 μm, en ocho estaciones de muestreo en un ciclo anual (febrero de 1998 a enero de 1999).Para evaluar la estructura, se utilizaron los números de Hill (N0, N1 y N2) y la equidad. El soporte del muestreo fue calculado con los estimadores Chao 1 y 2. La existencia de diferencias significativas de los números de Hill, la equidad, la densidad numérica, la columna de agua, el pH, el OD, y la temperatura, entre campañas y entre estaciones, se realizó a través de un ANDEVA. Las especies y morfoespecies encontradas (31) poseen distribución tropical, subtropical y cosmopolita; pertenecen generalmente a cuerpos de agua temporales, llanuras de inundación o ciénagas. Las mayores abundancias fueron registradas para Moina minuta, Moina cf. micrura, Diaphanosoma brevireme y Ceriodaphnia cornuta, las cuales representaron el 81.9 % del total de individuos colectados. Los resultados obtenidos por los estimadores de riqueza indican que si se aumentara el esfuerzo de muestreo con las técnicas utilizadas, no incrementaría el número de morfoespecies. Con respecto a la variación espacial de la estructura, la estación V presento mayor equidad, riqueza y diversidad, pero menor densidad numérica, esta condición muestra la diferencia de esta estación en comparación con las demás; su tendencia atípica es explicada ya que dicha estación se encuentra cerca del afluente principal de la Ciénaga (Quebrada La Gómez). En la variación temporal, la estructura de la comunidad de cladóceros cambió entre campañas de muestreo ya que la equidad y la riqueza presentaron diferencias significativas, que se evidencian en el cambio de la abundancia relativa de las morfoespecies, mas no en la abundancia de cladóceros. Esto es causado por las fluctuaciones de la precipitación y el alto de la columna de agua.In the Ciénaga de Paredes (73 · 45'-73· 49'W y 7·26'-7·29'N), located in the Department of Santander (Colombia), the composition, and the spatial and temporal variation of the cladoceran community structure was determined with samples taken with a 68 μm vertical-hauled net, at eight sampling stations in an annual cycle (February 1998 to January 1999). To evaluate the structure, Hill numbers (N0, N1 and N2) and evenness were used. The sampling support was calculated with the Chao 1 and 2 estimators. The existence of significant differences for Hill numbers, evenness, numeric density, water column, pH, OD, and temperature among field trips and among stations, was analysed through an ANOVA. The species and morphospecies found (31), had a tropical, subtropical, and cosmopolitan distribution; belonging to temporary water bodies, floodplains or "ciénagas". The highest abundances were registered for Moina minuta, Moina cf. micrura, Diaphanosoma brevireme and Ceriodaphnia cornuta, which represented 81.9 % of the total collected individuals. The results obtained with the richness estimates suggest that if the sampling effort were increased using the same techniques, the morphospecies' number would have not increased. With regard to the structure's spatial variation, the station V showed higher evenness, richness, and diversity, but lower numeric density; this condition shows the difference between this station and the other ones; ical trend is explained by this station being near to the main tributary of the "Ciénaga" ("Quebrada La Gómez").Regarding the temporal variation, the cladocerans' community structure changed between field trips, since the evenness and the richness showed significant differences, reflected by the variation in the relative abundance of the morphospecies but not in the cladocerans' abundance. This was caused by the fluctuations in rainfall and water level

Enfermedad carcinoide cardiaca multivalvular

ResumenHombre de 67 años de edad, enviado a valoración ecocardiográfica por cuadro clínico de 6meses de evolución con: disnea de esfuerzo, edemas de miembros inferiores y fatiga. Se encuentra doble lesión de la válvula tricúspide con: estenosis e insuficiencia severa, insuficiencia pulmonar severa; y compromiso valvular izquierdo con: insuficiencia mitral y aórtica severas, asociadas a engrosamiento y rigidez valvular. El paciente tenía como antecedente tumor neuroendocrino de íleon, metastásico a pulmón e hígado.En este caso se discuten los hallazgos ecocardiográficos característicos del síndrome carcinoide con compromiso multivalvular como hallazgo inusual de este raro síndrome.AbstractA 67 year-old man is sent to echocardiographic assessment for 6 month history of exertional: dyspnea, edema of the lower extremities, fatigue, double lesions in tricuspid valve with: severe stenosis and severe regurgitation, severe pulmonary valve regurgitation; and left side valvular disease with: severe aortic regurgitation and severe mitral regurgitation, all of them associated with valvular thickening, rigidity, in a patient with history of neuroendocrine tumor, with lung and liver metastases.This case discuss the echocardiographic findings suggestive of carcinoid multivalvular and left side valvular disease as unusual finding in this rare syndrome