Absolute bounds on pion-pion amplitudes in the physical region and threshold behaviour.—II

1983 ◽  
Vol 76 (1) ◽  
pp. 52-72
Author(s):  
A. D. Gangal ◽  
S. M. Roy
Keyword(s):  
Physical Region ◽  
Threshold Behaviour

scholarly journals Optofluidic Platform Based on Liquid Crystals in X-Cut Lithium Niobate: Thresholdless All-Optical Response

Crystals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 908
Author(s):  
Fabrizio Ciciulla ◽  
Annamaria Zaltron ◽  
Riccardo Zamboni ◽  
Cinzia Sada ◽  
Francesco Simoni ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Light Intensity ◽  
Lithium Niobate ◽  
Photovoltaic Effect ◽  
Optical Control ◽  
Crystal Layer ◽  
Liquid Crystal Layer ◽  
Threshold Behaviour ◽  
All Optical

In this study, we present a new configuration of the recently reported optofluidic platform exploiting liquid crystals reorientation in lithium niobate channels. In order to avoid the threshold behaviour observed in the optical control of the device, we propose microchannels realized in a x-cut crystal closed by a z-cut crystal on the top. In this way, the light-induced photovoltaic field is not uniform inside the liquid crystal layer and therefore the conditions for a thresholdless reorientation are realized. We performed simulations of the photovoltaic effect based on the well assessed model for Lithium Niobate, showing that not uniform orientation and value of the field should be expected inside the microchannel. In agreement with the re-orientational properties of nematic liquid crystals, experimental data confirm the expected thresholdless behaviour. The observed liquid crystal response exhibits two different regimes and the response time shows an unusual dependence on light intensity, both features indicating the presence of additional photo-induced fields appearing above a light intensity of 107 W/m2.

Threshold Behaviour of the X-Ray Spectrum of Sodium

1970 ◽  
Vol 38 (1) ◽  
pp. K9-K12
Author(s):  
R. V. Vedrinskii ◽  
J. Richter
Keyword(s):  
Threshold Behaviour ◽  
X Ray

scholarly journals Predecessors and Successors in Random Mappings with Exchangeable In-Degrees

2013 ◽  
Vol 50 (3) ◽  
pp. 721-740 ◽  
Author(s):  
Jennie C. Hansen ◽  
Jerzy Jaworski
Keyword(s):  
Asymptotic Behaviour ◽  
Preferential Attachment ◽  
Degree Sequence ◽  
Discrete Distributions ◽  
Threshold Behaviour ◽  
Mapping Model ◽  
Random Mapping ◽  
Exact Distributions ◽  
Random Mappings ◽  
Expected Values

In this paper we characterise the distributions of the number of predecessors and of the number of successors of a given set of vertices, A, in the random mapping model, TnD̂ (see Hansen and Jaworski (2008)), with exchangeable in-degree sequence (D̂1,D̂2,…,D̂n). We show that the exact formulae for these distributions and their expected values can be given in terms of the distributions of simple functions of the in-degree variables D̂1,D̂2,…,D̂n. As an application of these results, we consider two special examples of TnD̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine the exact distributions for the number of predecessors and the number of successors in these cases. We also characterise, for these two special examples, the asymptotic behaviour of the expected numbers of predecessors and successors and interpret these results in terms of the threshold behaviour of epidemic processes on random mapping graphs. The families of discrete distributions obtained in this paper are also of independent interest.

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