Biot-Savart-like law in electrostatics

The Biot-Savart law is a well-known and powerful theoretical tool used to calculate magnetic fields due to currents in magnetostatics. We extend the range of applicability and the formal structure of the Biot-Savart law to electrostatics by deriving a Biot-Savart-like law suitable for calculating electric fields. We show that, under certain circumstances, the traditional Dirichlet problem can be mapped onto a much simpler Biot-Savart-like problem. We find an integral expression for the electric field due to an arbitrarily shaped, planar region kept at a fixed electric potential, in an otherwise grounded plane. As a by-product we present a very simple formula to compute the field produced in the plane defined by such a region. We illustrate the usefulness of our approach by calculating the electric field produced by planar regions of a few nontrivial shapes.Comment: 14 pages, 6 figures, RevTex, accepted for publication in the European Journal of Physic

An experimental route to spatiotemporal chaos in an extended 1D oscillators array

We report experimental evidence of the route to spatiotemporal chaos in a large 1D-array of hotspots in a thermoconvective system. Increasing the driving force, a stationary cellular pattern becomes unstable towards a mixed pattern of irregular clusters which consist of time-dependent localized patterns of variable spatiotemporal coherence. These irregular clusters coexist with the basic cellular pattern. The Fourier spectra corresponding to this synchronization transition reveals the weak coupling of a resonant triad. This pattern saturates with the formation of a unique domain of great spatiotemporal coherence. As we further increase the driving force, a supercritical bifurcation to a spatiotemporal beating regime takes place. The new pattern is characterized by the presence of two stationary clusters with a characteristic zig-zag geometry. The Fourier analysis reveals a stronger coupling and enables to find out that this beating phenomena is produced by the splitting of the fundamental spatiotemporal frequencies in a narrow band. Both secondary instabilities are phase-like synchronization transitions with global and absolute character. Far beyond this threshold, a new instability takes place when the system is not able to sustain the spatial frequency splitting, although the temporal beating remains inside these domains. These experimental results may support the understanding of other systems in nature undergoing similar clustering processes.Comment: 12 pages, 13 figure

The prediction of liquid film journal bearing performance with a consideration of lubricant film reformation: part 2: experimental resuIts

Analyses and design data for plainjournal bearings rarely take into account the phenomenon of film reformation. The consideration of the re-establishment of the lubricantfilm after the cavitation region is difficult in a number of ways. The importance of allowingfor reformation is, however, being increasingly recognized. Tht.J is particularly true as regards the satisfactory predlction of lubricant ftowrate...and the thermal operating characteristics of a bearing. The authors have previously implemented a cavitation algorithm to enable the cavitation region in a plain journal bearing to be Iocated automatically and efficiently in a computer analysis. In Part I of the present paper theoretical results have been presentedfor the case of a plain bearing with a square-ended, axial groove located at the position of maximumfilm thickness. The second part of the paper gives detai/s of an experimental investigation designed to establish the validity of the analysis

Quasinormal modes of plane-symmetric anti-de Sitter black holes: a complete analysis of the gravitational perturbations

We study in detail the quasinormal modes of linear gravitational perturbations of plane-symmetric anti-de Sitter black holes. The wave equations are obtained by means of the Newman-Penrose formalism and the Chandrasekhar transformation theory. We show that oscillatory modes decay exponentially with time such that these black holes are stable against gravitational perturbations. Our numerical results show that in the large (small) black hole regime the frequencies of the ordinary quasinormal modes are proportional to the horizon radius $r_{+}$ (wave number $k$). The frequency of the purely damped mode is very close to the algebraically special frequency in the small horizon limit, and goes as $ik^{2}/3r_{+}$ in the opposite limit. This result is confirmed by an analytical method based on the power series expansion of the frequency in terms of the horizon radius. The same procedure applied to the Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency goes as $i(l-1)(l+2)/3r_{+}$, where $l$ is the quantum number characterizing the angular distribution. Finally, we study the limit of high overtones and find that the frequencies become evenly spaced in this regime. The spacing of the frequency per unit horizon radius seems to be a universal quantity, in the sense that it is independent of the wave number, perturbation parity and black hole size.Comment: Added new material on the asymptotic behavior of QNM

Determination of surface resistance and magnetic penetration depth of superconducting YBa2Cu3O(7-delta) thin films by microwave power transmission measurements

A novel waveguide power transmission measurement technique was developed to extract the complex conductivity of superconducting thin films at microwave frequencies. The microwave conductivity was taken of two laser ablated YBa2Cu3O(7-delta) thin films on LaAlO3 with transition temperatures of approx. 86.3 and 82 K, respectively, in the temperature range 25 to 300 K. From the conductivity values, the penetration depth was found to be approx. 0.54 and 0.43 micron, and the surface resistance (R sub s) to be approx. 24 and 36 micro-Ohms at 36 GHz and 76 K for the two films under consideration. The R sub s values were compared with those obtained from the change in the Q-factor of a 36 GHz Te sub 011-mode (OFHC) copper cavity by replacing one of its end walls with the superconducting sample. This technique allows noninvasive characterization of high transition temperature superconducting thin films at microwave frequencies

Interfacial elastic fingering in Hele-Shaw cells: a weakly nonlinear study

We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity

An antibody raised against a pathogenic serpin variant induces mutant-like behaviour in the wild-type protein

A monoclonal antibody (mAb) that binds to a transient intermediate may act as a catalyst for the corresponding reaction; here we show this principle can extend on a macro molecular scale to the induction of mutant-like oligomerization in a wild-type protein. Using the common pathogenic E342K (Z) variant of α1-antitrypsin as antigen-whose native state is susceptible to the formation of a proto-oligomeric intermediate-we have produced a mAb (5E3) that increases the rate of oligomerization of the wild-type (M) variant. Employing ELISA, gel shift, thermal stability and FRET time-course experiments, we show that mAb5E3 does not bind to the native state of α1-antitrypsin, but recognizes a cryptic epitope in the vicinity of the post-helix A loop and strand 4C that is revealed upon transition to the polymerization intermediate, and which persists in the ensuing oligomer. This epitope is not shared by loop-inserted monomeric conformations. We show the increased amenity to polymerization by either the pathogenic E342K mutation or the binding of mAb5E3 occurs without affecting the energetic barrier to polymerization. As mAb5E3 also does not alter the relative stability of the monomer to intermediate, it acts in a manner similar to the E342K mutant, by facilitating the conformational interchange between these two states

Millimeter wave transmission studies of YBa2Cu3O7-delta thin films in the 26.5 to 40.0 GHz frequency range

Millimeter wave transmission measurements through YBa2Cu3O(7-delta) thin films on MgO, ZrO2 and LaAlO3 substrates, are reported. The films (approx. 1 micron) were deposited by sequential evaporation and laser ablation techniques. Transition temperatures T sub c, ranging from 89.7 K for the Laser Ablated film on LaAlO3 to approximately 72 K for the sequentially evaporated film on MgO, were obtained. The values of the real and imaginary parts of the complex conductivity, sigma 1 and sigma 2, are obtained from the transmission data, assuming a two fluid model. The BCS approach is used to calculate values for an effective energy gap from the obtained values of sigma sub 1. A range of gap values from 2 DELTA o/K sub B T sub c = 4.19 to 4.35 was obtained. The magnetic penetration depth is evaluated from the deduced values of sigma 2. These results are discussed together with the frequency dependence of the normalized transmission amplitude, P/P sub c, below and above T sub c