Gauss Law Research Articles

Design and Simulation of 5–20-kV GaN Enhancement-Mode Vertical Superjunction HEMT

The systematic design process using numerical simulations of the novel gallium nitride (GaN) enhancement-mode vertical superjunction high electron mobility transistor (HEMT) with breakdown voltage (BV) in the range of 5-20 kV is presented. The GaN superjunction pillar structure in the drift region of the vertical HEMT is first optimized using a simpler GaN superjunction diode structure, and the optimum half-pillar charge dosage is obtained to be 8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , which is consistent with the value estimated from the Gauss's Law. The GaN vertical superjunction HEMT is then simulated and optimized, and the Ron,sp-BV tradeoff curves in the range of 5-20 kV are obtained by varying the epi thickness. The Ron,sp-BV tradeoff is found to improve with smaller pillar width as in silicon superjunction MOSFETs, and the best Ron,sp of 4.2 mΩ-cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with BV of 12.4 kV is projected with half-pillar width of 3 μm. The robustness of the superjunction HEMT is also examined using structure with half-pillar width of 8 μm, and compared with the GaN vertical HEMT with conventional drift layer and same dimensions. The simulated on-state BV of the GaN vertical superjunction HEMT shows a 4.5% drop from the off-state BV and is only slightly higher than the 1.7% drop of the conventional GaN vertical HEMT.

Modified Colloidal Primitive Model as a Homogeneous Surface Charge Distribution: ζ-Potential

An integral equations theory is derived and applied to a modified colloidal primitive model (MCPM), for finite concentration colloidal dispersions. In MCPM, the charge on the colloidal particle is assumed to be smeared on its surface. We find important quantitative and qualitative differences of the ζ-potential, induced charge, and the colloid-colloid electric effective force, calculated in the MCPM, with those obtained from the colloidal primitive model (CPM), where the colloidal charge is assumed to be in the center of the particle, in spite of the fact that, due to Gauss's law, both models have the same particle distribution function. In particular, for the same parameters, while the ζ-potential is positive in MCPM, is negative in the CPM, implying opposite electrophoretic mobilities, μ. An inverse μ has been theoretically predicted in the past, for infinite dilution colloidal dispersions. The MCPM could be a better model for some colloidal particles. In both models, the CPM and the MCPM, it is found a very long-range colloid-colloid correlation, in accordance with previous Monte Carlo simulations. The electrostatic, as well as entropic, like-charged colloid-colloid forces are oscillatory, implying a long-range attraction.

Quantum simulations of gauge theories with ultracold atoms: Local gauge invariance from angular-momentum conservation

Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge and Lorentz invariance. In this paper we discuss these special requirements, and present a new method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: compact QED (U(1)), SU(N) and Z_N, which can be used to build quantum simulators in 1+1 dimensions. We also present a new loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for d+1 dimensional lattice gauge theories (d>1), without having to use Gauss's law as a constraint, as in previous proposals. We discuss in detail the quantum simulation of 2+1 dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge invariant elementary interactions of this model suggests it may be useful for future experimental realizations.

A semi-analytical study of positive corona discharge in wire–plane electrode configuration

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

Counting Elementary Charges on Nanoparticles by Electron Holography

The distribution and movement of charge is fundamental to many physical phenomena, particularly for applications involving nanoparticles, nanostructures, and electronic devices. However, there are very few ways of quantifying charge at the necessary length scale. Here, we show that aberration-corrected electron holography is capable of counting the charge on individual nanoparticles to a precision of one elementary unit of charge. We present a method that measures charges within predefined contours by directly applying Gauss's law at the nanoscale. We perform a statistical analysis to reveal the relationship between the size of the contours and the precision of the charge measurement and present strategies to optimize the spatial and signal resolution for the presented method.

Telegraph signals as a solution of the time dependent Schrödinger equation let standard Copenhagen quantum mechanics emerge

A particle switching between two sites of a symmetric system in weak interaction with an environmental continuum of high density of states exhibits a telegraph-signal-like time development without the need of the Born-Bohr principle of reduction on eigenstates of the measuring equipment. The origin of the telegraph signal is a very weak local coupling of the particle to the continuum of gravitons which is connected with an enormous slow down of the particle motion. The proposed mechanism envisages entanglement to gravitons in high dimensional spacetime, which, in accord with Gauss law, gives rise to a local and much stronger gravitational law compared to classical gravitation. The physics behind the quantum jumps and the telegraph-signal-like time development is elucidated. The model might be useful for studying environmental decoherence effects on adsorbate localization and quantum diffusion on solid surface.

Cutoff Frequency and Switching Delay of Underlap Carbon Nanotube FETs

We have studied the effects of underlap's length and doping on the cutoff frequency, switching delay and on/off ratio of carbon nanotube field effect transistors (CNTFETs). We have proposed underlaps with different lengths, doping levels and doping profiles. Intrinsic and fringing field capacitances, transconductance, cutoff frequency, switching time and on/off ratio have been calculated for different CNTFET designs. Proposed CNTFETs have been simulated using nonequilibrium Green's function (NEGF) method. The gate capacitance has been calculated based on the charge on the gate contact according to Gauss law. Linear, uniform-light and two types of Gaussian dopant distributions have been studied. All the proposed devices improved the figures of merit. The charge density and the electric field under the gate are responsible for limiting the cutoff frequency. Our proposed underlaps with linear and uniform light doping have improved both switching delay and cutoff frequency. We have found that CNTFETs with longer underlaps and lighter doping have superior performance.

GMRES Solution of FEM-BEM Global Systems for Electrostatic Problems Without Voltaged Conductors

This paper extends an iterative method to efficiently solve the global algebraic system of equations obtained by applying the hybrid FEM-BEM method to cases in which the field is due to charge distributions only, that is, when conductors with assigned potential (Dirichlet conditions) are not present. In the proposed approach, a conjugate gradient solver is used to solve the singular FEM equations, whereas the BEM equations are modified by means of the Gauss law.

Anomalous spin of the Chern-Simons-Georgi-Glashow model

With the Coulomb gauge, the Chern-Simons-Georgi-Glashow (CSGG) model is quantized in the Dirac formalism for the constrained system. Combining the Gauss law and Coulomb gauge consistency condition, the difference between the Schwinger angular momentum and canonical angular momentum of the system is found to be an anomalous spin. The reason for this result lies in the fact that the Schwinger energy momentum tensor and the canonical one have different symmetry properties in the presence of the Chern-Simons term.

Solvable model for quantum gravity?

We study a type of geometric theory with a non-dynamical 1-form field. Its dynamical variables are an su(2) gauge field and a triad of su(2) valued 1-forms. Hamiltonian decomposition reveals that the theory has a true Hamiltonian, together with spatial diffeomorphism and Gauss law constraints, which generate the only local symmetries. Although perturbatively non-renormalizable, the model provides a test bed for the non-perturbative quantization techniques of loop quantum gravity.

QCD on an Infinite Lattice

We construct a mathematically well–defined framework for the kinematics of Hamiltonian QCD on an infinite lattice in \({\mathbb{R}^3}\) , and it is done in a C*-algebraic context. This is based on the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph e.a.. To extend this model to an infinite lattice, we need to take an infinite tensor product of nonunital C*-algebras, which is a nonstandard situation. We use a recent construction for such situations, developed by Grundling and Neeb. Once the field C*-algebra is constructed for the fermions and gauge bosons, we define local and global gauge transformations, and identify the Gauss law constraint. The full field algebra is the crossed product of the previous one with the local gauge transformations. The rest of the paper is concerned with enforcing the Gauss law constraint to obtain the C*-algebra of quantum observables. For this, we use the method of enforcing quantum constraints developed by Grundling and Hurst. In particular, the natural inductive limit structure of the field algebra is a central component of the analysis, and the constraint system defined by the Gauss law constraint is a system of local constraints in the sense of Grundling and Lledo. Using the techniques developed in that area, we solve the full constraint system by first solving the finite (local) systems and then combining the results appropriately. We do not consider dynamics.

Piezoelectric energy harvesting from morphing wing motions for micro air vehicles

Wing flapping and morphing can be very beneficial to managing the weight of micro air vehicles through coupling the aerodynamic forces with stability and control. In this letter, harvesting energy from the wing morphing is studied to power cameras, sensors, or communication devices of micro air vehicles and to aid in the management of their power. The aerodynamic loads on flapping wings are simulated using a three-dimensional unsteady vortex lattice method. Active wing shape morphing is considered to enhance the performance of the flapping motion. A gradient-based optimization algorithm is used to pinpoint the optimal kinematics maximizing the propellent efficiency. To benefit from the wing deformation, we place piezoelectric layers near the wing roots. Gauss law is used to estimate the electrical harvested power. We demonstrate that enough power can be generated to operate a camera. Numerical analysis shows the feasibility of exploiting wing morphing to harvest energy and improving the design and performance of micro air vehicles.

A Novel Dual-Electrode Plug to Achieve Intensive Electric Field for High Performance Ignition

A thorough analysis of electric field is carried out so as to verify that a novel dual-electrode plug can build intensive electric field and can improve the main drawbacks of feeble electric field and low ignition efficiency of the traditional plug. With intensive electric field, the proposed novel plug can achieve high performance ignition, resulting in fuel saving and exhaust reduction. Gauss law is applied for electric field analysis to show that intensive electric field can be built by the novel plug. Then, according to Faraday law a lower-voltage ignition feature accomplished by the plug is discussed. Compared with traditional plug, the novel dual-electrode plug has the following advantages. (1) Much higher energy density is built between the plug electrodes, lowering ignition voltage requirement. (2) Electromagnetic interference (EMI) problem caused by high ignition voltage is readily resolved. (3) Ignition time delay can be improved. (4) The feature to save fuel consuming is achieved. (5) The exhaust of CO and HC is reduced significantly. Practical measurements are fulfilled to validate the electric field analysis and to demonstrate the features of the proposed dual-electrode plug.

Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwell’s equations on Cartesian grids

In this paper, a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations is developed and analyzed. The spatial discretization is based on staggered Cartesian grids so that many good properties are obtained. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Moreover, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Our method is high order accurate and the optimal order of convergence is rigorously proved. It is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee’s scheme as well as the quadrilateral edge finite elements. Furthermore, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. Numerical results are shown to confirm our theoretical statements, and applications to problems in unbounded domains with the use of PML are presented. A comparison of our staggered method and non-staggered method is carried out and shows that our method has better accuracy and efficiency.

Construction of bulk fields with gauge redundancy

We extend the construction of field operators in AdS as smeared single trace operators in the boundary CFT to gauge fields and gravity. Bulk field operators in a fixed gauge can be thought of as non-local gauge invariant observables. Non-local commutators result from the Gauss law constraint, which for gravity implies a perturbative notion of holography. We work out these commutators in a generalized Coulomb gauge and obtain leading order smearing functions in radial gauge.

Non-planar anomalous dimensions in the [formula omitted] sector

In this Letter we compute the non-planar one loop anomalous dimension of restricted Schur polynomials that belong to the sl(2) sector of N=4 super Yang–Mills theory and have a bare dimension of order N. Although the details are rather different, ultimately the problem of diagonalizing the dilatation operator in the sl(2) sector can be reduced to the su(2) sector problem. In this way we establish the expected dynamical emergence of the Gauss Law for giant gravitons and further show that the dilatation operator reduces to a set of decoupled harmonic oscillators.

A hybrid CSS and PSO algorithm for optimal design of structures

A new hybrid meta-heuristic optimization algorithm is presented for design of structures. The algorithm is based on the concepts of the charged system search (CSS) and the particle swarm optimization (PSO) algorithms. The CSS is inspired by the Coulomb and Gauss's laws of electrostatics in physics, the governing laws of motion from the Newtonian mechanics, and the PSO is based on the swarm intelligence and utilizes the information of the best fitness historically achieved by the particles (local best) and by the best among all the particles (global best). In the new hybrid algorithm, each agent is affected by local and global best positions stored in the charged memory considering the governing laws of electrical physics. Three different types of structures are optimized as the numerical examples with the new algorithm. Comparison of the results of the hybrid algorithm with those of other meta-heuristic algorithms proves the robustness of the new algorithm.

A double coset ansatz for integrability in AdS/CFT

We give a proof that the expected counting of strings attached to giant graviton branes in AdS_5 x S^5, as constrained by the Gauss Law, matches the dimension spanned by the expected dual operators in the gauge theory. The counting of string-brane configurations is formulated as a graph counting problem, which can be expressed as the number of points on a double coset involving permutation groups. Fourier transformation on the double coset suggests an ansatz for the diagonalization of the one-loop dilatation operator in this sector of strings attached to giant graviton branes. The ansatz agrees with and extends recent results which have found the dynamics of open string excitations of giants to be given by harmonic oscillators. We prove that it provides the conjectured diagonalization leading to harmonic oscillators.

Electron Density Distribution in Endohedral Complexes of Fullerene C60, Calculated Based on the Gauss Law

This study demonstrates that different partial charge methodologies, consisting of an attribution of the total electron density to particular atoms of a molecule, generate very divergent results in the case of atoms doped into a fullerene cage. A new method of calculating the density distribution inside and outside fullerene complexes has been proposed and applied in the case of C₆₀, [F@C₆₀]⁻, [Na@C₆₀]⁺, and He@C₆₀. It allowed for the calculation of the electron density between surfaces, isomorphic with the C₆₀ cage, lying inside and outside the latter, as well as the charge in the space surrounding the central atom (or the central point in the case of empty C₆₀).

GUIDING CENTER DRIFT INDUCED BY HOMOGENIZATION

The guiding center drift induced by the homogenization of the Lorentz forces is studied. It generates memory effects. The memory (or nonlocal) kernel is described by the Volterra integral equation. The memory kernel can be characterized explicitly in terms of a Radon measure. It describes the extra velocity drift. By way of velocity drift, we view the Gauss's law with polarization charges.