Linear and nonlinear response functions for an exact state and for an MCSCF state

1985 ◽  
Vol 82 (7) ◽  
pp. 3235-3264 ◽  
Author(s):  
Jeppe Olsen ◽  
Poul Jo/rgensen
Keyword(s):  
Nonlinear Response ◽  
Response Functions ◽  
Linear And Nonlinear

Nonlinear Response of Resin Matrix Laminates Using Endochronic Theory

1991 ◽  
Vol 113 (4) ◽  
pp. 449-455 ◽  
Author(s):  
S. R. Mathison ◽  
M. J. Pindera ◽  
C. T. Herakovich
Keyword(s):  
Elastic Constants ◽  
Nonlinear Response ◽  
Resin Matrix ◽  
Excellent Correlation ◽  
Shear Tests ◽  
Endochronic Theory ◽  
Constitutive Response ◽  
Linear And Nonlinear ◽  
Theory And Experiment ◽  
Angle Ply Laminates

The nonlinear response of laminated, resin matrix fibrous composites is modeled using orthotropic endochronic theory. The theory is formulated in terms of elastic constants and endochronic parameters characterizing the linear and nonlinear response, respectively, of unidirectional composites. All constants and parameters can be determined from normal (tension and/or compression) and shear tests on unidirectional and off-axis specimens. The nonlinear constitutive response relations for the unidirectional lamina are presented and the procedure for determining constants and parameters from test is described. The results are then used to predict the nonlinear response of unidirectional laminae and angle-ply laminates. Comparison between theory and experiment for compression loading of AS4/3502 graphite-epoxy, angle-ply laminates shows excellent correlation.

scholarly journals Systems-based analysis of dendritic nonlinearities reveals temporal feature extraction in mouse L5 cortical neurons

2017 ◽  
Vol 117 (6) ◽  
pp. 2188-2208 ◽  
Author(s):  
Brian E. Kalmbach ◽  
Richard Gray ◽  
Daniel Johnston ◽  
Erik P. Cook
Keyword(s):  
High Frequency ◽  
Cortical Neurons ◽  
Action Potentials ◽  
Nonlinear Response ◽  
Functional Model ◽  
Low Frequency ◽  
Fast Variable ◽  
Nonlinear Component ◽  
Dendritic Spikes ◽  
Linear And Nonlinear

What do dendritic nonlinearities tell a neuron about signals injected into the dendrite? Linear and nonlinear dendritic components affect how time-varying inputs are transformed into action potentials (APs), but the relative contribution of each component is unclear. We developed a novel systems-identification approach to isolate the nonlinear response of layer 5 pyramidal neuron dendrites in mouse prefrontal cortex in response to dendritic current injections. We then quantified the nonlinear component and its effect on the soma, using functional models composed of linear filters and static nonlinearities. Both noise and waveform current injections revealed linear and nonlinear components in the dendritic response. The nonlinear component consisted of fast Na+ spikes that varied in amplitude 10-fold in a single neuron. A functional model reproduced the timing and amplitude of the dendritic spikes and revealed that they were selective to a preferred input dynamic (~4.5 ms rise time). The selectivity of the dendritic spikes became wider in the presence of additive noise, which was also predicted by the functional model. A second functional model revealed that the dendritic spikes were weakly boosted before being linearly integrated at the soma. For both our noise and waveform dendritic input, somatic APs were dependent on the somatic integration of the stimulus, followed a subset of large dendritic spikes, and were selective to the same input dynamics preferred by the dendrites. Our results suggest that the amplitude of fast dendritic spikes conveys information about high-frequency features in the dendritic input, which is then combined with low-frequency somatic integration. NEW & NOTEWORTHY The nonlinear response of layer 5 mouse pyramidal dendrites was isolated with a novel systems-based approach. In response to dendritic current injections, the nonlinear component contained mostly fast, variable-amplitude, Na+ spikes. A functional model accounted for the timing and amplitude of the dendritic spikes and revealed that dendritic spikes are selective to a preferred input dynamic, which was verified experimentally. Thus, fast dendritic nonlinearities behave as high-frequency feature detectors that influence somatic action potentials.

Linear and nonlinear response of 2-D single carrier dots: Role of impurity perturbations

2007 ◽  
Vol 333 (1) ◽  
pp. 18-25 ◽  
Author(s):  
Ram Kuntal Hazra ◽  
Manas Ghosh ◽  
S.P. Bhattacharyya
Keyword(s):  
Nonlinear Response ◽  
Single Carrier ◽  
Linear And Nonlinear

scholarly journals Linear and nonlinear optical properties of hybrid metallic–dielectric plasmonic nanoantennas

2016 ◽  
Vol 7 ◽  
pp. 111-120 ◽  
Author(s):  
Mario Hentschel ◽  
Bernd Metzger ◽  
Bastian Knabe ◽  
Karsten Buse ◽  
Harald Giessen
Keyword(s):  
Refractive Index ◽  
Optical Properties ◽  
Nonlinear Optical ◽  
Nonlinear Response ◽  
High Efficiency ◽  
Dielectric Materials ◽  
Nonlinear Optical Properties ◽  
Linear Optical Properties ◽  
Linear And Nonlinear ◽  
Linear Optical

We study the linear and nonlinear optical properties of hybrid metallic–dielectric plasmonic gap nanoantennas. Using a two-step-aligned electron beam lithography process, we demonstrate the ability to selectively and reproducibly fill the gap region of nanoantennas with dielectric nanoparticles made of lithium niobate (LiNbO3) with high efficiency. The linear optical properties of the antennas are modified due to the large refractive index of the material. This leads to a change in the coupling strength as well as an increase of the effective refractive index of the surrounding. The combination of these two effects causes a red- or blue-shift of the plasmonic modes, respectively. We find that the nonlinear optical properties of the combined system are only modified in the range of one order of magnitude. The observed changes in our experiments in the nonlinear emission can be traced to the changed dielectric environment and thus the modified linear optical properties. The intrinsic nonlinearity of the dielectric used is in fact small when compared to the nonlinearity of the metallic part of the hybrid antennas. Thus, the nonlinear signals generated by the antenna itself are dominant in our experiments. We demonstrate that the well-known nonlinear response of bulk dielectric materials cannot always straightforwardly be used to boost the nonlinear response of nanoscale antenna systems. Our results significantly deepen the understanding of these interesting hybrid systems and offer important guidelines for the design of nanoscale, nonlinear light sources.

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