# Current Distributions

## Top PDF Current Distributions:

### Polarizability Tensor Calculation Using Induced Charge and Current Distributions

Nonreciprocal particles and their applications are comprehensively discussed in [1]. These particles may be realized using a biased magnetic element (e.g., ferrites) and some conducting wires. Two famous examples are Tellegen-omega/“moving”-chiral particles which simultaneously presents the properties of Tellegen and omega/“moving” and chiral bianisotropies, respectively. A Tellegen-omega particle as shown in Fig. 2(b) may be composed of a ferrite sphere and two orthogonal wires. When an incident electric ﬁeld excites one of the wire arms, the induced electric current will produce two crossed magnetic moments in the ferrite sphere which in turn they induce currents on the wires. From the symmetry of the structure with respect to the x and y axes, one can deduce that

### Visualization of Eddy Current Distributions for Arbitrarily Shaped Coils Parallel to a Moving Conductor Slab

Abstract—To visualize eddy current distribution (ECD) of an arbitrarily shaped coil arranged parallel to a moving conductor slab, an exact theoretical solution is derived using an analytical method based on the double Fourier transform method. The arbitrarily shaped coil is regarded as a plane coil of a single turn, and both DC and AC excitation currents can be applied. Furthermore, ECD charts are obtained when the conductor slab is moving. We calculate some examples with respect to a circular coil, rectangular coil, and triangular coil and show the eﬀect of coil excitation frequency and speed of the conductor on ECDs. Results show that the eddy current generated in the moving conductor slab is composed of current induced by the excitation frequency and conductor speed.

### On the Design of Slot Cut Circularly Polarized Circular Microstrip Antennas

Circularly polarized microstrip antenna is frequently realized by cutting the slot inside the patch and feeding it along the diagonal axis. In the reported literature, procedure to design them at any given frequency is not available. In proposed work, circularly polarized slot cut circular micro- strip antenna at 900 MHz is discussed. By studying the surface current distributions at two ortho- gonal modes, formulations in their resonant length are proposed. The frequencies calculated us- ing them closely agree with simulated results. Using proposed formulation, procedure to design circular polarized antennas at different frequencies is presented that gives circular polarized re- sponse. Thus, proposed work will be helpful to design similar circular polarized circular micro- strip antenna at any desired frequency.

### A Novel Compact Printed Antenna with Circularly Polarized Characteristic

direction of the surface current in the ground plane varied with similar fashion as the principle surface current which rotates in the clockwise (CW) direction. As a result, the antenna is able to radiate the left- hand circular polarization (LHCP) in the +Z direction. By varying the surface current distributions as a function of frequency within the circularly polarized bandwidth, the proposed design is able to generate LHCP radiation at the boresight (+Z) and RHCP radiation at the backside (−Z) direction in a similar fashion.

### Numerical simulation of the current, potential and concentration distributions along the cathode of a rotating cylinder Hull cell

The primary, secondary and tertiary current distributions along the cathode of the rotating cylinder Hull cell have been calculated under turbulent flow conditions using commercially available finite element software. Three regimes of operation were observed. At low applied currents, kinetic limited con- ditions prevail and hence a relatively uniform current density distribution was obtained. As the applied current was increased, the effect of the potential distribution due to ohmic effects became more significant and large variations in the local current density along the electrode were observed. At high currents, the electrode approached mass transport limiting conditions and a uniform current distribution was obtained. Simulations demonstrated that a wide range of concentration, local current density and overpotential was achievable in the rotating cylinder Hull cell.

### Electromagnetic Modeling of Coupled Carbon Nanotube Dipole Antennas Based on Integral Equations System

In previous works CNT antennas bundle is studied based on eﬀective axial surface conductivity for low coupling distances [8, 9]. In terahertz and infrared frequency range, the radiation characteristics of CNT dipole antenna arrays have been investigated by CST MICROWAVE STUDIO. It was shown that, N × N antenna arrays have a higher radiation eﬃciency than single CNT dipole antenna [10, 11]. For the CNT antennas array without coupling, the array factor approach is used to investigate the antenna radiation pattern. In this paper, some fundamental properties of ﬁnite length coupled CNT dipole antennas are rigorously described using a proposed system of N coupled integral equations. The input impedances, current distributions and the radiation antenna patterns are presented and discussed for diﬀerent coupling distances. For validity purpose, obtained results are compared to those obtained by the array factor method or eﬀective conductivity method according to the coupling distance. This paper is organized as following: in Section 2 we are interested in studying the performance of a single CNT dipole antenna. A comparison has been made to a conventional thin wire antenna of same size and shape. Section 3 presents an electromagnetic formulation based on a system of N integral equations to accurately describe the CNT dipole antenna coupling. The proposed formulation has been applied for two identical coupled CNT dipole antennas. In Section 4, we conclude this work.

### Electromagnetic Analysis on Propagation Characteristics of CRLH Waveguide Loaded with Double Ridge Corrugations

accordance with each other for the frequencies at 33 GHz (left-handed region) and 35 GHz (right-handed region), and they both show similar surface current distribution on the broadwall to that of traditional waveguide, as concluded by Eq. (15). Only x components are observed at the two sides of the broadwall ( x = 0 and x = a ) while at the centerline ( x = a/ 2), there is only z component. It is interesting to ﬁnd that diﬀerent surface current distributions are exhibited at the transition frequency of 33.65 GHz in Fig. 6 and Fig. 7. In Fig. 6, there is only z direction surface current, while both x and z direction surface currents are observed in Fig. 7. This is because the propagation constant β equals zero strictly in the theoretical analysis, while in the actual prototype simulation, the strict zero propagation constant (or the strict balanced condition) is usually hard to achieve [5, 10]. Furthermore, the surface current at 33.7 GHz, which is near the transition frequency, has also been analyzed theoretically and plotted in Fig. 8. It is in accordance with the current distribution in Fig. 7(b).

### Development of Fundamental Theory of Thin Impedance Vibrators

The theory of thin vibrators is now considered as classic both for perfectly conducting [1, 2] and impedance vibrators [3–10]. The theory was outlined in a large number of well-known articles and monographs (see, e.g., references in [3]). However, this problem is still of great interest, since the vibrator structures are widely used in various devices and systems to provide the required mode of excitation. Since the problem is multivariable, an experimental optimization of devices is almost impossible, and physically adequate mathematical models are needed for compound boundary value problems, non- coordinate border of spatial domains, presence of scattering irregularities, medium inhomogeneity, etc. In any case, a key stage of modeling consists in a search of current distributions on a vibrator surface. The problem solution can be greatly simpliﬁed by selection of the basic current distribution. This choice should be done taking into account the vibrator surrounding which cannot always be done relying only on analysis of available publications. Therefore, the generalization of the theoretical results concerning the inﬂuence of surrounding media upon the current distribution on the thin impedance vibrator is an actual problem.

### Computational modeling of the effects of auditory nerve dysmyelination

We used these morphological changes to determine conduc- tion properties under two conditions. Firstly, we modeled the effect of altering current distributions such that the compart- ments resulting from AOE treatment contained the same number of channels, but the density of these channels was altered to reflect an even distribution of the channels along the altered nodal, PN and JP length (AOE1 condition illustrated in Figure 3A). This condition named AOE1 resulted in morphological values contained in Table 1. Secondly, we modeled the axon as if the channels had remained in place and did not encroach on the AOE-induced changes in compartment size (AOE2 condition illustrated in Figure 3A). In this condition, the nodal compart- ment had the same altered dimensions as the nodal compartment in AOE1. However, the expression of I Na and I HT remained the

To ﬁgure out the mechanism of wideband polarization conversion with the proposed structure, the surface current distributions on the PCM unit cell and metallic ground sheet are studied at three resonant frequencies of 10.4, 13.1 and 17.5 GHz, respectively, as revealed by Figs. 4(a)–(c). In the v - polarized case, the currents on the PCM unit cell ﬂow from the cut-wire resonator to the double SRR, which can be viewed as an electric dipole. Diﬀerently, in the u -polarized case, the currents on the PCM unit cell ﬂow mainly along the double SRR, which makes the unit cell equivalent to a cut-wire resonator. Moreover, the induced currents on the ground sheet arise from the surface currents on the PCM unit cell. We can judge the resonance type through the directions between the surface currents on the PCM unit cell and the ground sheet. As shown in Figs. 4(a) and (b), the surface currents on the PCM unit cell are antiparallel to those induced on the ground sheet, which produce the magnetic resonances. On the contrary, the surface currents on the PCM unit cell are parallel to those induced on the ground sheet in Fig. 4(c), which generate the electric resonance. The multiple resonance characteristic contributes to the wide polarization conversion bandwidth.

### Examining current or future trade-offs for biodiversity conservation in north-eastern Australia

With the high rate of ecosystem change already occurring and predicted to occur in the com- ing decades, long-term conservation has to account not only for current biodiversity but also for the biodiversity patterns anticipated for the future. The trade-offs between prioritising future biodiversity at the expense of current priorities must be understood to guide current conservation planning, but have been largely unexplored. To fill this gap, we compared the performance of four conservation planning solutions involving 662 vertebrate species in the Wet Tropics Natural Resource Management Cluster Region in north-eastern Australia. Input species data for the four planning solutions were: 1) current distributions; 2) projected distributions for 2055; 3) projected distributions for 2085; and 4) current, 2055 and 2085 pro- jected distributions, and the connectivity between each of the three time periods for each species. The four planning solutions were remarkably similar (up to 85% overlap), suggest- ing that modelling for either current or future scenarios is sufficient for conversation planning for this region, with little obvious trade-off. Our analyses also revealed that overall, species with small ranges occurring across steep elevation gradients and at higher elevations were more likely to be better represented in all solutions. Given that species with these character- istics are of high conservation significance, our results provide confidence that conservation planning focused on either current, near- or distant-future biodiversity will account for these species.

### Loss of Linear Momentum in an Electrodynamics System: from an Analytical Approach to Simulations

Into the frame of classical electrodynamics, the explanation of the created force in the coil-ring system may be detailed considering the retarded regime. Thus, the current pulse generates a spectrum of electromagnetic waves that leave the coil, covers the coil-to-ring distance at light speed and reaches the conductive ring surface. Here, it induces eddy currents which become the source of repulsive electromotive force. The newly created electromagnetic spectrum covers back the ring-to-coil distance at light speed to produce an induced current in the coil and so on. The electromagnetic waves in retarded regime for time dependent current distributions are entirely described by the generalized Jefimenko equations [4] (also called Heaviside-Feynman formula [5]). These equations take into account retardation effects becoming important at extremely high frequencies, by essence. At lower frequencies the retardation can be neglected. It is shown in the paper that only high frequencies (> 3 GHz) are involved, by looking at the spatial scales. The retarded fields were mainly studied in particle physics [6–9] and for moving atomic dipoles [10, 11] More recently, Jim´enez et al. [12] gave the exact electromagnetic field in retarded and static regime produced by a finite wire. So far, the electromagnetic field produced by a single circular ring in retarded coordinates with a time dependent current has not been reported in the literature. In this study, the dimension of wire sections is very small compared to the diameter of rings.

### A ModiEd Planar Inverted-F Antenna with Triple-Band for Wi-Fi and LTE Applications

The magnitudes of surface current distributions at three resonant frequencies are plotted in Fig. 8. In Fig. 8(a), the segments labeled by 1, 1 ′ , 2, and 2 ′ all contribute to the radiation pattern at 2.4 GHz because all four segments have a current flow in the x-y plane. In addition, the segments function as dipoles, so the radiation pattern E φ in the plane is in a four-petal shape, and E θ is small. The radiation

### Magnetic field effects on the vestibular system: calculation of the pressure on the cupula due to ionic current induced Lorentz force

and sinks are the dominant factors to be taken into account. Accurate modeling of the vestibular system is crucial to calculate the effect of the current distributions on the cupula. Better knowledge of vestibular current geometries (including better measurements of their magnitude) would be vital in order to refine the model described here. Better knowledge of utricle and saccule geometry and current flow would also increase the validity of the model. However, even with current understanding it should be possible to model a full head system with both the inner-ear vestibular systems and hence all 6-ampullae. In this way the exact response of the human to magnetic field strength and orientation can be modeled and compared to human perception and response.

### Application of Protruded Strip Resonators to Design an UWB Slot Antenna with WLAN Band-Notched Characteristic

of the interior and exterior of the protruded cross-shaped strips. Therefore, the antenna impedance changes at this frequency due to the resonant properties of the embedded structure in the ground plane [16]. As shown in Fig. 5(b), at the notched frequency the current flows are more dominant around the T-shaped strips inside the square-ring radiating stub. As a result, the desired high attenuation near the notched frequency can be produced [13, 14].

### Alterations in regional vascular geometry produced by theoretical stent implantation influence distributions of wall shear stress: analysis of a curved coronary artery using 3D computational fluid dynamics modeling

region[12] suggesting that the present results may be valid within the stent. However, the results may differ from those observed clinically as several studies have also inves- tigated the compliance mismatch introduced by stent implantation [38-41]. The curvature of the idealized coro- nary arteries simulated in the current investigation was based on the average curvature measured during a repre- sentative canine cardiac cycle using ultrasonic segment length transducers placed on the epicardial surface of the LAD perfusion territory and a corresponding location on the posterior surface of the heart[12]. Therefore, the distri- butions of WSS that occur at other points during the car- diac cycle may differ from those observed assuming a constant vascular curvature[19,42,43]. The examination of flow profiles in the proximal coronary arteries consti- tutes a current area of ongoing research. Although an approximate LAD coronary artery curvature was modeled in the current investigation, the physiologic curvature may result in velocity profiles that differ from those used in the current investigation. The average velocity value corre- sponding to the waveform used in this investigation is on the order of that measured after acute stent implantation in humans[44]. However, blood flow values vary greatly from one person to the next and may result in different distributions of WSS than those reported here. The current investigation was also conducted using a simplified outlet boundary condition and therefore does not replicate the ability of the distal vasculature to dilate in response to local metabolic needs, or reproduce the physiologic pres- sure observed within the stented region. The current inves- tigation is among the first to consider acute distributions of WSS through a stented, curved coronary arterial model, but the LAD may not be symmetric in vivo. In fact, Myers

### On the Mechanism of CDOs behind the Current Financial Crisis and Mathematical Modeling with Levy Distributions

It was Paul Lévy who first grappled in-depth with probability distributions with infinite moments. Such distributions are now called Lévy distributions. Today, Lévy distributions have been expanded into diverse areas including turbulent diffusion, polymer transport and Hamiltonian chaos, just to mention a few. Although Lévy's ideas and algebra of random variables with infinite moments appeared in the 1920s and the 1930s (cf. [49,50]), it is only from the 1990s that the greatness of Lévy's theory became much more appreciated as a foundation for probabilistic aspects of chaotic dynamics with high entropy in statistical analysis in mathematical modelling (cf. [51,52], see also [53,54]). Indeed, in statistical analysis, systems with highly complexity and (nonlinear) chaotic dynamics became a vast area for the application of Lévy processes and the phenomenon of dynamical chaos became a real laboratory for developing generalizations of Lévy processes to create new tools to study nonlinear dynamics and kinetics. Following up this point, Lévy type processes and their influence on long time statistical asymptotic will be unavoidably encountered.

### 3D Field-Circuit Analysis of Measurement Properties of Current Transformers with Axially and Radially Connected Cores Made of Different Magnetic Materials

Abstract—We report results continuing the research which looks at the influence of two different magnetic materials in a core construction on the transformation errors of a current transformer [1]. In this paper we consider the behaviour of two different magnetic materials in a core. They are joined in a different way to the previous study; not axially (one-by-one), but also radially (one inside the second). We have conducted 3D analyses of the electromagnetic field distribution for different cases of current transformers and carried out computations based on the finite-element numerical method. We compare the results with tests of real-life models.

### Space charge formation and its modified electric field under applied voltage reversal and temperature gradient in XLPE cable

Here we present results for the space charge evolution and response to external voltage polarity reversal measured on full size XLPE power cables using the pulsed electro- acoustic (PEA) technique. The corresponding electric field distributions along the radial direction are derived from the space charge distribution, and the local field distribution is discussed in terms of the evolution of mirror space charge distributions in the steady state, and the basic physics behind the formation of an inverted space charge distribution on reversing the polarity of the conductor potential. The effect of a temperature gradient on space charge in cable insulation is also investigated, and it is argued that the reduction of space charge observed is caused by differences in the temperature dependence of the bulk conductivity and those applying to the cross-interface currents.

### Existing Climate Change Will Lead to Pronounced Shifts in the Diversity of Soil Prokaryotes

To assess whether the soil prokaryotic communities are in equilibrium with con- temporary climate in the Tibetan Plateau, we built a regression model of OTU richness (number of OTUs) as a function of historical and contemporary climate variables. By performing all-subset model selection in which climate variables from different time periods compete with each other based on how well they can explain variation in OTU richness across sampling locations, we assessed the extent to which the contemporary distribution of prokaryotic diversity is associated with historic and contemporary climate (Materials and Methods). We also performed analogous analyses to assess correlations of contemporary and historical climate with Shannon diversity (evenness of OTUs) and with relative abundance of each prevalent bacterial family (n ⫽ 53) and OTU (n ⫽ 317) found in 40 or more soil samples. No archaea met this prevalence threshold. Soil prokaryotic distributions that are signiﬁcantly correlated with the climate from several decades ago as opposed to the climate from the time of sampling could be explained by distributions that are out of equilibrium with contemporary climate, among other potential contributing forces (see below). Consistent with this, climate from before 1974 predicted contemporary prokaryotic richness (i.e., was frequently chosen over many iterations of model selection in models with different numbers of variables as quantiﬁed by the Lindeman, Merenda, and Gold statistic [LMG] [35]): 1960 –1969 PC1 LMG ⫽ 0.183, 1960 –1969 PC3 LMG ⫽ 0.202. Contemporary climate variables were also predictive: 2002–2011 PC2 LMG ⫽ 0.415, 2002–2011 PC3 LMG ⫽ 0.200. In contrast, intervening years’ climatologies were less often chosen during model selection. Contemporary Shannon diversity is highly correlated with richness and hence is also predicted by both historic and contemporary climate. For models to predict the relative abundance of prevalent families and OTUs, the importance of climate across the decades spanning 1959 to 2012 was substantial and consistent (Fig. S2A and S3A). However, the frequency with which climate variables from different decades were predictive was bimodal: both historic variables from circa 1969 and contemporary variables were frequently predictive of the distributions of families and OTUs, while variables from circa 1980 were less frequently predictive (i.e., less often chosen in model selection) (Fig. 1A and Fig. S2B). This bimodality held quite generally across different climate variables for both OTUs (Fig. 1B) and families (Fig. S2C). Furthermore, contem- porary distributions of families and OTUs were often simultaneously associated with both historic and contemporary climate (Fig. 1C and Fig. S2D). These results suggest that contemporary distributions of the diversity of soil prokaryotes and of individual taxa are associated with climate from today and from close to 50 years ago, or