Equivalent Circuit of the Field Equations of Maxwell-I

Kron, Gabriel

doi:10.1109/jrproc.1944.231021

Cited by 135 publications

(34 citation statements)

References 1 publication

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“…1a). The electric circuit models can be used for simulation of a variety of problems in physics (electromagnetic field equations, Schro¨dinger equations), chemistry (fluid dynamics), and biology (irreversible thermodynamics) (Kron 1944(Kron , 1945aOster et al 1973;Hjelmfelt and Ross 1992;Mikulecky 2001).…”

Section: Electrical Circuit Model Of Releasementioning

confidence: 99%

Simulation and parameter estimation of dynamics of synaptic depression

Aristizabal¹,

Glavinović

2004

Biological Cybernetics

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Synaptic release was simulated using a Simulink sequential storage model with three vesicular pools. Modeling was modular and easily extendable to the systems with greater number of vesicular pools, parallel input, or time-varying parameters. Given an input (short or long tetanic trains, patterned or random stimulation) and the storage model, the vesicular release, the replenishment of various vesicular pools, and the vesicular content of all pools could be simulated for the time-invariant and time-varying storage systems. From the input stimuli and either a noiseless or a noisy output, the parameters of such storage systems could also be estimated using the optimization technique that minimizes in the least square sense the error between the observed release and the predicted release. All parameters of the storage model could be evaluated with sufficiently long input-output data pairs. Not surprisingly, the parameters characterizing the processes near the release locus, such as the fractional release and the size of the immediately available pool and its coupling to the small store, as well as the state variables associated with the immediately available pool, such as its vesicular content and replenishment, could be determined with fewer stimuli. The possibility of estimating parameters with random inputs extends the applicability of the method to in vivo synapses with the physiological inputs. The parameter estimation was also possible under the time-variant, but slowly changing, conditions as well as for open systems that are part of larger vesicular storage systems but whose parameters can either not be reliably determined or are of no interest. The quality of parameter estimation was monitored continuously by comparing the observed and predicted output and/or estimated parameters with the true values. Finally, the method was tested experimentally using the rat phrenic-diaphragm neuromuscular junction.

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Section: Electrical Circuit Model Of Releasementioning

confidence: 99%

Simulation and parameter estimation of dynamics of synaptic depression

Aristizabal¹,

Glavinović

2004

Biological Cybernetics

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“…Kron was an early advocate of a circuit-oriented differential equation model solution of Maxwell's equations [24]. Those early concepts have received renewed attention lately, as lumped circuits for drivers and receivers are being introduced in FDTD-and TLM-based models for EIP structures for the purpose of more rigorous transient analysis of high-speed/high-frequency electronic systems [25]- [27].…”

Section: B Differential Equation-based Methodsmentioning

confidence: 99%

Progress in the methodologies for the electrical modeling of interconnects and electronic packages

2001

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The rapid growth of the electrical modeling and analysis of the interconnect structure, both at the electronic chip and package level, can be attributed to the increasing importance of the electromagnetic properties of the interconnect circuit on the overall electrical performance of state-of-the-art very large scale integration (VLSI) systems. With switching speeds well below 1 ns in today's gigahertz processors, and VLSI circuit complexity exceeding the 100 million transistors per chip mark, power and signal distribution is characterized by multigigahertz bandwidth pulses propagating through a tightly coupled three-dimensional wiring structure that exhibits resonant behavior at the upper part of the spectrum. Consequently, in addition to the inductive and capacitive coupling, present between adjacent wires across the entire frequency bandwidth, distributed electromagnetic effects, manifested as interconnect-induced delay, reflection, radiation, and long-range nonlocal coupling, become prominent at high frequencies, with a decisive impact of overall system performance. The electromagnetic nature of such high-frequency effects, combined with the geometric complexity of the interconnect structure, make the electrical design of today's performance-driven systems extremely challenging. Its success is heavily dependent on the availability of sophisticated electromagnetic modeling methodologies and computer-aided design tools. This paper presents an overview of the different approaches employed today for the development of an electromagnetic modeling and simulation framework that can effectively tackle the complexity of the interconnect circuit and facilitate its design. In addition to identifying the current state of the art, an assessment is given of the challenges that lie ahead in the signal integrity-driven electrical design of tomorrow's performance-and/or portability-driven, multifunctional ULSI systems.

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“…Originally, TLM was based on the analogy between the electromagnetic field and a mesh of transmission lines (Kron 1944). The derivation of the 3D TLM method directly from Maxwell's equations allows to deduce the TLM method in the frequency domain (FDTLM).…”

Section: Introductionmentioning

confidence: 99%

A new computationally efficient hybrid fdtLM–WCIP method

Glaoui

Trabelsi

Zairi

et al. 2009

International Journal of Electronics

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This article presents a new hybrid technique which combines two different numerical methods in the frequency domain, namely the Frequency Domain Transmission Line Matrix (FDTLM) and the Wave Concept Iterative Process, to analyse three-dimensional (3D) microwave structures. As a result, a considerable reduction of the computation time and required computer memory is achieved compared with the classic FDTLM. The good agreement between simulation results and experimental published data validates the present analysis approach.

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Equivalent Circuit of the Field Equations of Maxwell-I

Cited by 135 publications

References 1 publication

Simulation and parameter estimation of dynamics of synaptic depression

Simulation and parameter estimation of dynamics of synaptic depression

Progress in the methodologies for the electrical modeling of interconnects and electronic packages

A new computationally efficient hybrid fdtLM–WCIP method

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