Plane Condenser Research Articles

Generalized Padé approximants for plane condenser and distribution of points

Abstract Given a regular plane condenser (E, F), let α and β be triangular point tables; α ∈ E, β ∈ F. In the present paper, a criterium relating to the extremal distribution of the tables α and β is proved. The results are provided in terms of generalized Padé approximant, associated with the point tables α and β.

Point charge potential and weighting field of a pixel or pad in a plane condenser

We derive expressions for the potential of a point charge as well as the weighting potential and weighting field of a rectangular pad for a plane condenser, which are well suited for numerical evaluation. We relate the expressions to solutions employing the method of image charges, which allows discussion of convergence properties and estimation of errors, providing also an illuminating example of a problem with an infinite number of image charges.

Capacity of shrinking condensers in the plane

We show that the capacity of a class of plane condensers is comparable to the capacity of corresponding “dyadic condensers”. As an application, we show that for plane condensers in that class the capacity blows up as the distance between the plates shrinks, but there can be no asymptotic estimate of the blow-up.

On the preservation of conformal capacity under meromorphic functions

It is proved that a meromorphic function that preserves the capacity of a plane condenser is univalent in the field of the condenser. Bibliography: 12 titles.

A very large dew and rain ridge collector in the Kutch area (Gujarat, India)

The world’s largest dew and rain collecting system, comprised of ridge-and-trough modules, was constructed in March 2006 at Panandhro in the semi-arid area of Kutch (NW India). The main goals were (i) to collect dew on a scale that could be beneficial to the local population (ii) to determine the efficiency of this new module shape, (iii) to determine whether results obtained from small measurement condensers can be projected to large condensers, (iv) to apply a computational fluid dynamic simulation to improve the condenser set-up. Preliminary studies performed with four standard plane condensers of 1 m2 surface area, inclined 30° from horizontal, identified Panandhro as a promising site. The cumulated dew water during 192 days was 12.6 mm with a maximum of 0.556 mm/night. A large dew condenser (850 m2 net total surface) was designed with 10 ridge-and-trough modules. The ridges are trapezoidal, 33 m long, 0.5 m wide at the top, 2.2 m wide at the base and sloping 30° from horizontal. The depth of the troughs between the ridges is 0.5 m. A 2.5 cm thick polystyrene foam rests on the surface as insulation with a radiative foil on top (similar to that developed by OPUR, see www.opur.fr). Numerical simulations using the computational fluid dynamic software PHOENICS were performed. The most profitable orientation was with the condenser oriented back to the wind direction, a configuration that lowers the wind velocity near the foil due to the combination of free convection and wind recirculation flows. A comparison of water yields over one year of measurements between four 1 m2 plane condensers and a 850 m2 ridge condenser showed a 42% lower yield on the large condenser. The difference is attributed mainly to folds in the plastic foil allowing water to fill the central ridge, thus decreasing radiative cooling. The output for 2007 was 6545 L, corresponding to 7.7 mm/day on average. The largest event was 251.4 L/night (0.3 mm). Such a condenser can also collect rain (and, to a lesser extent, fog). Chemical and biological analyses showed that dew water, once filtered and bottled, could be used for drinking after a light treatment to increase the pH. The price of this water could be lowered to reach 30% (dew only) or even 3% (dew plus rain) of the market prize.

Capacities of certain plane condensers and sets under simple geometric transformations

In this article, we investigate the behaviour of conformal capacities of several plane condensers and logarithmic capacities of some compact sets under the following types of geometric transformations: a gap moving in one or two plates, translation, and rotation of plates and breaking plates. Main motivating examples are provided by parallel plate condensers although the majority of our results are true for more general condensers. We prove monotonicity theorems in most cases and find extremal configurations with maximal capacity in more difficult ones. Our main tools are polarization and direct application of the extended Dirichlet principle. The last section of this article contains several open problems and conjectures.

Experimental Investigation of New Flat-Plate-Type Capillary Pumped Loop

A capillary pumped loop is a two-phase heat transfer device which has been increasingly applied in thermal control of satellite or spacecraft and electronic cooling. However, startup performance of a normal capillary pumped loop is poor and hydrodynamic oscillation in the system appears sometime during its operation. A flat-plate-type capillary pumped loop is constructed and tested in the present study, which combines the advantages of a capillary pumped loop and a loop heat pipe by improving both system and components. In the present capillary pumped loop, both evaporator and condenser are designed as a type of flat plate with porous wick, and a reservoir is used to control and adjust operation temperature of the system. In addition, a subcooler is adopted to improve the quality of working fluid flowing back to the evaporator. A plane type of evaporator with a cross channel for the liquid supply was made to reduce the probability of a dry-out point caused by strong evaporation in the case of high heat flux, and therefore to enhance the stability of the system. Also, a plane type of condenser with a porous wick is designed, which is of the three ports for vapor-pipe inlet, liquid-pipe outlet, and an adjusting pipe connected to a reservoir. The startup performance of the system benefits greatly from this three-port design, as liquid in the system can be easily pressed into a reservoir due to resistance reduction. The performance of a capillary pumped loop prototype was tested in startup, persistence operations, and different vacuum. Startup experiments under different heat loads and working conditions were conducted. Excellent startup performance, being stable and easy, has been shown for the plane-type capillary pumped loop system, which validates the new configuration. Pressure oscillation and temperature fluctuation in the system were reduced largely owing to the induction of a porous wick in the plane condenser. During experimental processes lasting more than 10 h, the new type capillary pumped loop shows outstanding thermal behavior and no dry-out phenomena were observed. The testing results indicate that 1) the new capillary pumped loop system shows excellent startup performance without pressure priming and liquid clearing of vapor line; and 2) the new capillary pumped loop system is stable under very severe operational conditions, such as low load, sudden power step, etc.

Determination of the interactions in confined macroscopic Wigner islands: theory and experiments

Macroscopic Wigner islands present an interesting complementary approach to explore the properties of two-dimensional confined particles systems. In this work, we characterize theoretically and experimentally the interaction between their basic components, viz., conducting spheres lying on the bottom electrode of a plane condenser. We show that the interaction energy can be approximately described by a decaying exponential as well as by a modified Bessel function of the second kind. In particular, this implies that the interactions in this system, whose characteristics are easily controllable, are the same as those between vortices in type-II superconductors.

Capacity of a condenser whose plates are circular arcs

We find an asymptotic formula for the conformal capacity of a plane condenser both plates of which are concentric circular arcs as the distance between them vanishes. This result generalizes the formula for the capacity of parallel linear plate condenser found by Simonenko and Chekulaeva (1972). On a capacity of a condenser consisting of infinite bands, Izv. Vyssh. Uchebn. Zaved. Elektromekh., 4, 362–370 (in Russian) and sheds light on the problem of finding an asymptotic formula for the capacity of condenser whose plates are arbitrary parallel curves. This problem was posed and partially solved by R. Kühnau (1998). Randeffekten beim elektostatischen Kondensator, Zap. Nauchn. Semin. POMI, 254, 132–154.

THE AREAS OF POLYNOMIAL IMAGES AND PRE-IMAGES

Let $p$ be a monic complex polynomial of degree $n$ , and let $K$ be a measurable subset of the complex plane. Then the area of $p(K)$ , counted with multiplicity, is at least $\pi n ( \Area (K)/\pi )^n$ , and the area of the pre-image of $K$ under $p$ is at most $\pi^{1-1/n} (\Area (K) )^{1/n}$ . Both bounds are sharp. The special case of the pre-image result in which $K$ is a disc is a classical result, due to Polya. The proof is based on Carleman's classical isoperimetric inequality for plane condensers.

Static electric fields in an infinite plane condenser with one or three homogeneous layers

Expressions for the electrostatic field of a point charge in an infinite plane condenser comprising one or three homogeneous isolating parallel dielectric layers are presented. These solutions are essential for detector physics simulations of parallel plate chambers and resistive plate chambers. In addition, expressions for the weighting field of a strip electrode are presented which allow calculation of induced signals and crosstalk in these detectors. A detailed discussion of the derivation of these solutions can be found in [Heubrandtner et al. (CERN-OPEN-2001-074, CERN, October 2001)].

Mesure en laboratoire de la permittivité diélectrique moyenne fréquence de végétaux à 430 kHz à l'aide d'un capacimètre. Relation entre permittivité apparente d'un ensemble d'épis de blé et leur contenu en eau

The laboratory measurements presented here are additional measurements to those performed on a wheat crop by an electrostatic quadrupole at 430 kHz. They give a first calibration for the correlation between water content and apparent dielectric permittivity of ears. These measurements are performed by means of a capacimeter or a plane condenser of which the apparent permittivity is determined. Wheat ears are placed within the condenser and their permittivity is correlated to their water content. A theoretical approach (method of moments) presents the response of the condenser, containing ears similated to a 3D parallelepipedic body in an electromagnetic field.

Oversimplified, compact double focusing mass spectrometer geometries

The simplest ways to construct double focusing mass spectrometer designs are those resulting from inserting plane condenser plates in the gap of two rectangular pole pieces or a cylindric condenser at the pole piece corner. The first order ion-optical parameters and aberration coefficients were calculated for double focusing Wien filter-magnetic deflector geometries over the useful range of the deflection angles. Similar calculations were performed for cylindric electric-magnetic crossed field sectors, for comparison. The illustrating numerical examples indicate the highest resolutions for the 90° deflecting Wien filter-magnet and crossed field geometries.

Partial pressure gauge proposal based on a stigmatic double focusing mass spectrometer design

A substantial sensitivity improvement is predicted for partial pressure gauges using triple focusing mass spectrometer geometries. The simultaneous stigmatic and energy focusing is obtained by locating the plates of a plane condenser in the magnetic pole gap. Two ways to reach this purpose are indicated: a homogeneous magnetic field with oblique beam entry and exit or a ‘wedge’ magnet with normal field boundaries. A complete second-order ion optical description is given for both cases. Numerical values for the aberration coefficients are given for some particular cases. The resolution increase is estimated with the usual ion source parameters in a ‘wedge’ field design, compared with a stigmatic but single focusing mass spectrometer the main path radius being the same.

Estimates of capacities of plane condensers

We derive an exact lower estimate for the capacity of a plane condenser in terms of logarithmic capacities of the boundary sets of its plates and study the case of an equality.

Some inequalities for the capacity of plane condensers

Some inequalities for the capacity of plane condensers

On the capacity of a plane condenser and conformal mapping.

On the capacity of a plane condenser and conformal mapping.

Design and characteristics of soft X-ray sealed gas electroluminescence detector

The design of a sealed type for a gas electroluminescence (proportional scintillation) detector having a plane condenser field is considered. The results of the main detector characteristics study are given. Energy resolution determined with a 55Fe source (5.9 keV) amounted to 9.7%, a peak-to-valley ratio being 200.

Ion optics of parallel plane condensers

The trajectory of a charged particle in the parallel plane condenser is calculated for the case where the deflection angle is not large (⪅ 20°). All ion optical properties are given by the product of three transfer matrices corresponding to the entrance fringing field, the idealized main field and the exit fringing field. The matrix elements of these three matrices are calculated in the third-order approximation. The finite distribution of the fringing field is taken into consideration.

A Simple Double Focusing Mass Spectrometer of New Type

A new ion optical system is proposed for a simple double focusing mass spectrometer. The apparatus consists of a parallel plane condenser, a doublet electrostatic Q lens and a simple homogeneous magnet having pole pieces of rectangular shape.(γm=30cm, φm=30°, e′=e″=15°). A weak magnetic field(∼5000 gauss)is sufficient to analyze ions of A∼1000 because γm is large. Stigmatic double focusing is obtained by the doublet Q lens and the plane condenser. The adjustment of the energy focusing as well as the directional focusing can be achieved by changing potentials on the electrodes of two Q lenses. Therefore, no mechanical adjustment is necessary at all. Several examples of suitable parameters are shown, and the method of the electrical focus adj ustment is explained. The second order focusing character is also described.