scholarly journals Stored Coulomb Self-Energy of a Uniformly Charged Rectangular Plate

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Orion Ciftja
Keyword(s):  
Rectangular Plate ◽  
Finite Size ◽  
Exact Result ◽  
Exact Expression ◽  
Consumer Electronics ◽  
Electrostatic Energy ◽  
Current Status ◽  
Flat Plates ◽  
Arbitrary Length ◽  
Self Energy

A large number of electronic devices contain charged, flat plates (electrodes) as their components. The approximation of considering such components as infinitely large plates is not satisfactory for the current status of consumer electronics where size is now extremely small. In particular, the nanotechnology revolution has made the fabrication of truly finite systems with arbitrary shape and characteristic lengths that measure in nanometers possible. As a result the only accurate approach for such situations is to consider the system realistically as one with a finite size extent. In this work we calculate the amount of electrostatic energy that is stored in a charged finite size electrode that is modelled as a uniformly charged rectangular plate with arbitrary length and width. Nontrivial mathematical transformations allow us to derive a closed form exact expression for the Coulomb self-energy of such a system as a function of its length and width (therefore, shape, too). The exact result derived can be useful to understand the storage process of electrostatic energy as a function of size/shape in uniformly charged plate systems. The result also applies to calculations that deal with the properties of a finite two-dimensional electron gas within the jellium model where the finite jellium domain can have an arbitrary rectangular shape.

scholarly journals Energy Stored and Capacitance of a Circular Parallel Plate Nanocapacitor

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1255
Author(s):  
Orion Ciftja
Keyword(s):  
Energy Storage ◽  
Parallel Plate ◽  
Finite Size ◽  
Analytic Form ◽  
High Energy ◽  
Exact Expression ◽  
Electrostatic Energy ◽  
Circular Plates ◽  
Dielectric Thin Film ◽  
High Energy Storage

Nanocapacitors have received a great deal of attention in recent years due to the promises of high energy storage density as device scaling continues unabated in the nanoscale era. High energy storage capacity is a key ingredient for many nanoelectronic applications in which the significant consumption of energy is required. The electric properties of a nanocapacitor can be strongly modified from the expected bulk properties due to finite-size effects which means that there is an increased need for the accurate characterization of its properties. In this work, we considered a theoretical model for a circular parallel plate nanocapacitor and calculated exactly, in closed analytic form, the electrostatic energy stored in the nanocapacitor as a function of the size of the circular plates and inter-plate separation. The exact expression for the energy is used to derive an analytic formula for the geometric capacitance of this nanocapacitor. The results obtained can be readily amended to incorporate the effects of a dielectric thin film filling the space between the circular plates of the nanocapacitor.

Finite-size pion effect on its self-energy

1985 ◽  
Vol 437 (3-4) ◽  
pp. 619-629 ◽  
Author(s):  
Sadataka Furui ◽  
S.B. Khadkikar ◽  
Amand Faessler
Keyword(s):  
Finite Size ◽  
Self Energy

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

2020 ◽  
Vol 41 (7-8) ◽  
pp. 607-614
Author(s):  
Arghyadeep Paul ◽  
Siddhartha Mukherjee ◽  
Jayabrata Dhar ◽  
Sandip Ghosal ◽  
Suman Chakraborty
Keyword(s):  
Finite Size ◽  
Coulomb Interactions ◽  
Flat Plates ◽  
Debye Layer

scholarly journals Active Structural Acoustic Control of Clamped Flat Plates Using a Weighted Sum of Spatial Gradients

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
William R. Johnson ◽  
Daniel R. Hendricks ◽  
Scott D. Sommerfeldt ◽  
Jonathan D. Blotter
Keyword(s):  
Rectangular Plate ◽  
Acoustic Radiation ◽  
Wave Number ◽  
Effective Control ◽  
Weighted Sum ◽  
Rectangular Plates ◽  
Flat Plates ◽  
Spatial Gradients ◽  
Acoustic Control ◽  
Structural Acoustic Control

The weighted sum of spatial gradients (WSSG) control minimization parameter is developed for use in active structural acoustic control (ASAC) on a clamped flat rectangular plate. The WSSG minimization parameter is measured using four accelerometers grouped closely together on the test structure. In previous work, WSSG was developed on a simply supported flat rectangular plate and showed promise as a control metric. The displacement on the clamped plate has been modeled using an approximate analytical solution assuming shape functions corresponding to clamped-clamped beams. From the analytical formulation, weights, which were found to be the reciprocal of the wave number squared, have been derived to produce a uniform WSSG field across the plate. In active control simulations, this quantity has been shown to provide better global control of acoustic radiation than volume velocity. Analysis is presented which shows that comparable control, regardless of the sensor location, can be achieved using WSSG. Experimental results are presented which demonstrate that WSSG works effectively in practice, with results similar to the simulations. The results show that minimization of WSSG can be used as an effective control objective on clamped rectangular plates to achieve attenuation of acoustic radiation.

Oscillating Flow About Two and Three-Dimensional Bilge Keels

1996 ◽  
Vol 118 (1) ◽  
pp. 1-6 ◽  
Author(s):  
T. Sarpkaya ◽  
J. L. O’Keefe
Keyword(s):  
Rectangular Plate ◽  
Three Dimensional ◽  
Free Edge ◽  
Proximity Effects ◽  
Oscillating Flow ◽  
Solid Boundary ◽  
Flat Plates ◽  
Ambient Flow ◽  
Sharp Edges ◽  
Wall Proximity

The paper describes an experimental investigation of the damping provided by bilge keels in an oscillating flow (in a large U-shaped water tunnel). Rectangular and square flat plates were placed adjacent to a solid boundary (with no gap) in order to simulate flow about bilge keels. The single free edge of the rectangular plate and the three free edges of the square plates were beveled to 60-deg angles so as to form sharp edges with included angles of about 60 deg. For comparison, another sharpedged rectangular plate was tested without the wall proximity effects. All plates were held normal to the direction of the ambient flow. The Fourier-averaged drag and inertia coefficients were then calculated as a function of a suitable Keulegan-Carpenter number through the use of the instantaneous force acting on each plate.

scholarly journals Electrons in one dimension

2010 ◽  
Vol 368 (1914) ◽  
pp. 1141-1162 ◽  
Author(s):  
K.-F. Berggren ◽  
M. Pepper
Keyword(s):  
Wave Functions ◽  
Electrostatic Energy ◽  
One Dimension ◽  
Current Status ◽  
Electron Configuration ◽  
Two Dimensional ◽  
Size Quantization ◽  
Many Body ◽  
Spin Degeneracy ◽  
Wigner Lattice

In this article, we present a summary of the current status of the study of the transport of electrons confined to one dimension in very low disorder GaAs–AlGaAs heterostructures. By means of suitably located gates and application of a voltage to ‘electrostatically squeeze’ the electronic wave functions, it is possible to produce a controllable size quantization and a transition from two-dimensional transport. If the length of the electron channel is sufficiently short, then transport is ballistic and the quantized subbands each have a conductance equal to the fundamental quantum value 2 e 2 / h , where the factor of 2 arises from the spin degeneracy. This mode of conduction is discussed, and it is shown that a number of many-body effects can be observed. These effects are discussed as in the spin-incoherent regime, which is entered when the separation of the electrons is increased and the exchange energy is less than kT . Finally, results are presented in the regime where the confinement potential is decreased and the electron configuration relaxes to minimize the electron–electron repulsion to move towards a two-dimensional array. It is shown that the ground state is no longer a line determined by the size quantization alone, but becomes two distinct rows arising from minimization of the electrostatic energy and is the precursor of a two-dimensional Wigner lattice.

scholarly journals The current status of the consumer electronics repair industry in the U.S.: A survey-based study

2017 ◽  
Vol 116 ◽  
pp. 137-151 ◽  
Author(s):  
Mostafa Sabbaghi ◽  
Willie Cade ◽  
Sara Behdad ◽  
Ann M. Bisantz
Keyword(s):  
Consumer Electronics ◽  
Current Status ◽  
The U.S

scholarly journals On the perturbative expansion of exact bi-local correlators in JT gravity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Luca Griguolo ◽  
Jacopo Papalini ◽  
Domenico Seminara
Keyword(s):  
Exact Result ◽  
Bernoulli Polynomials ◽  
Exact Expression ◽  
Zero Temperature ◽  
Leading Order ◽  
Positive Weight ◽  
Perturbative Series ◽  
Compact Expression ◽  
Semiclassical Expansion ◽  
Perturbative Result

Abstract We study the perturbative series associated to bi-local correlators in Jackiw-Teitelboim (JT) gravity, for positive weight λ of the matter CFT operators. Starting from the known exact expression, derived by CFT and gauge theoretical methods, we reproduce the Schwarzian semiclassical expansion beyond leading order. The computation is done for arbitrary temperature and finite boundary distances, in the case of disk and trumpet topologies. A formula presenting the perturbative result (for λ ∈ ℕ/2) at any given order in terms of generalized Apostol-Bernoulli polynomials is also obtained. The limit of zero temperature is then considered, obtaining a compact expression that allows to discuss the asymptotic behaviour of the perturbative series. Finally we highlight the possibility to express the exact result as particular combinations of Mordell integrals.

Quantum electrodynamics. II

1939 ◽  
Vol 35 (3) ◽  
pp. 438-462
Author(s):  
F. Hoyle
Keyword(s):  
Quantum Electrodynamics ◽  
Finite Size ◽  
Direct Calculation ◽  
High Energy ◽  
Low Energy ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Self Energy ◽  
Energy Processes ◽  
Real Test

It is shown in this paper and the preceding one that two separate forms of theory can be developed in which a “finite size” is attributed to a charged particle by means of its interaction with the radiation field. The region attributed in this way to the particle is four dimensional and is determined in such a manner that the usual difficulties with relativistic invariance do not arise.The advantage of such a theory becomes clear when the theory is applied to those problems in which the usual calculations give infinite results. The problem of the method of successive approximations is considered and satisfactory results are obtained provided that the space dimensions of the finite region are of the order of the classical radius of the electron, when the electron is at rest.It may be noted explicitly that the difficulty that has been associated with the emission of low energy quanta by “Bremsstrahlung” will not arise in the present formulation of the electromagnetic interaction between field and particles. This case is interesting since an infinity arises here which is not analogous to the self energy infinities, but occurs in the direct calculation of a physical process and not in a virtual transition.The theory seems satisfactory so far as low energy processes (< 137 mc2) are concerned and the real test of its applicability may be expected to arise in discussing processes of high energy. It is hoped to treat these in a later paper.

Dislocation Emission at Surfaces

1994 ◽  
Vol 356 ◽  
Author(s):  
G. E. Beltz ◽  
L. B. Freund
Keyword(s):  
Thin Film ◽  
Dislocation Loop ◽  
Critical Radius ◽  
Continuum Theory ◽  
Exact Expression ◽  
The Self ◽  
Dislocation Theory ◽  
Dislocation Emission ◽  
Self Energy ◽  
Atomic Spacing

AbstractAn exact expression for the elastic energy associated with a semicircular shear dislocation loop emanating from a free surface, such as that of a stressed thin film, is derived (within continuum dislocation theory) and compared with earlier approximations. The energy required to activate a semicircular dislocation loop into its unstable “saddle-point” configuration is then re-calculated, based on the modified expression for the self-energy. It is found that the shear stress necessary to emit a loop, as a function of temperature, is almost 50% less than earlier estimates. The effects of ledges on the surface, as well as loop geometry, are discussed. The principal drawback to this type of calculation is pointed out, namely, that the critical radius of an incipient dislocation loop can be on the order of one atomic spacing, which is too small for a continuum theory to be valid.

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