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This paper extends the transmission-line simulation method of [1] to nonuniform lines. The method is applicable to multiconductor lossy frequency-dependent transmission lines characterized by sampled frequency-domain responses. The resulting model can be directly incorporated into a circuit simulator. The implementation includes ac, dc, and transient analyses. The method is reliable, accurate, and as efficient as the simple replacement of interconnects by lumped resistors. The method is based on approximation, and its accuracy and efficiency result from the simplicity of characteristic responses. To apply the method to nonuniform lines, two novel nonuniform line models are introduced. An open-loop model completely separates forward and backward waves and results in the simplest aperiodic responses, but does not guarantee their stability. An open-loop distributed-reflection model explicitly includes the internal distributed reflections, and provides the simplest stable characterization. It is shown that for nonuniform lines, the generalized method of characteristics no longer separates forward and backward waves. Numerical example of a parabolically tapered frequency-dependent four-conductor line is given. Index Terms - Circuit simulation, interconnect simulation, nonuniform transmission lines, signal-integrity analysis, transient analysis, transmission lines.

This paper presents an attempt to formulate a high-level description of the optimal transmission line simulation method. To formulate the optimal approach, most significant aspects of the problem are identified, and alternative approaches in each of the aspects are analyzed and compared to find the combination that results in the maximum efficiency, accuracy and applicability for the transient analysis of digital circuits. The practical implementation of the optimal method for uniform multiconductor lossy frequency-dependent lines characterized by samples of their responses is outlined. It is shown on an extensive set of runtime data that, based on the optimal approach, the accurate line modeling in a circuit simulator is as efficient as the simple replacement of interconnects with lumped resistors.

An efficient method to compute the 2-D and 3-D capacitance matrices of multiconductor interconnects in a multilayered dielectric medium is presented. The method is based on an integral equation approach and assumes the quasi-static condition. It is applicable to conductors of arbitrary polygonal shape embedded in a multilayered dielectric medium with possible ground planes on the top or bottom of the dielectric layers. The computation time required to evaluate the space-domain Green's function for the multilayered medium, which involves an infinite summation, has been greatly reduced by obtaining a closed-form expression, which is derived by approximating the Green's function using a finite number of images in the spectral domain. Then the corresponding space-domain Green's functions are obtained using the proper closed-form integrations. In both 2-D and 3-D cases, the unknown surface charge density is represented by pulse basis functions, and the delta testing function (point matching) is used to solve the integral equation. The elements of the resulting matrix are computed using the closed-form formulation, avoiding any numerical integration. The presented method is compared with other published results and showed good agreement. Finally, the equivalent microstrip crossover capacitance is computed to illustrate the use of a combination of 2-D and 3-D Green's functions.

A model for the motion of an elastic string is studied numerically and analytically. An elastic string in two dimensions and restricted by two pinning centers is considered. We consider two stable configurations (positively or negatively curved) with pinned ends due to the action of a bistable potential. It is further assumed that the string is driven externally by periodic and white noisy forces. The noise enables the string to flip between the two configurations. The small temporally periodic force synchronizes these flippings and the phenomenon of stochastic resonance is observed. The signal-to-noise ratio (SNR) of the output is investigated and shows a maximum for a nonvanishing intensity of the applied noise. Its dependence on the stiffness of the string is studied. The peak of SNR versus the noise intensity D is found to be more pronounced and to be shifted to small values of D with an increase in the effective stiffness of a string. The calculation is extended to stochastic resonance of vortex motion in a type II superconductor. For vortices restricted by two pinning centers, the characteristic time scale τ[sub R] relevant to the vortex dynamics is shown to depend crucially on the effective vortex stiffness, with the time τ[sub R] being extremely small for flexible vortices. Therefore, the effects of noise color on the vortex dynamics should be taken into account in many practical situations. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Using scaling theory, we determine the equilibrium behavior of a melt of functionalized and nonfunctionalized polymers confined between two infinite, planar surfaces, which model clay sheets. The functionalized chains contain two end groups (one at each chain end) that are highly attracted to the surfaces. Through these calculations, we delineate the conditions for the formation of thermodynamically stable polymer/clay mixtures in terms of the end-group adsorption energy, volume fraction of the end-functionalized chains, and polymer chain lengths. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the conformational properties of linear polymer brushes. Usage of the Monte Carlo method and molecular dynamics simulations in conformational property description; Focus on the isotropic-nematic phase transitions from collapsed to strongly stretched regimes of the brushes; Impact of orientational interactions on the isotropic temperature.

The chain stiffness is an important characteristic that affects the properties of many biological and synthetic polymers. We develop a perturbation theory in the framework of a Green's-function approach to treat the chain stiffness effects systematically. This scheme incorporates the standard flexible-chain Edwards equation in the zeroth order. When applied to the chains on the surface, the theory predicts novel features in adsorption-desorption transitions coupled with types of isotropic to nematic ordering transitions, giving a rigorous quantitative basis for our previous scaling theory results. We analyze the phase diagrams, and various quantities that detail the chain distribution including orientation-order-parameter distribution of the adsorbed semiflexible polymers. [ABSTRACT FROM AUTHOR]

Onsager-type (Khokhlov–Semenov) theory of the nematic ordering in an athermic system of long polymers, which accounts for two-body interactions only, is extended to take into account three-body interactions. The orientation distribution function, the free energy, the isotropic-nematic coexistence and the spinodal conditions are computed numerically for both persistent wormlike chains and chains with freely joint rigid segments. Even though second virial approximation is known to be asymptotically correct at large values of the polymer segment asymmetry l/d, three-body interactions are shown to cause the nontrivial dependence of the nematic ordering critical concentrations on l/d for the realistic values of l/d. Conditions of applicability of the second virial approximation are analyzed quantitatively. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]