scholarly journals Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

2018 ◽  
Vol 8 (12) ◽  
pp. 2559 ◽  
Author(s):  
Gang Xu ◽  
Adrien Fusaro ◽  
Josselin Garnier ◽  
Antonio Picozzi
Keyword(s):  
Phase Space ◽  
Theoretical Analysis ◽  
Collective Behavior ◽  
Optical Pulse ◽  
Random Wave ◽  
Kerr Medium ◽  
Linear Regime ◽  
Nonlinear Media ◽  
Strong Amplitude ◽  
Space Dynamics

We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.

Phase‐space dynamics and Hermite polynomials of two variables and two indices

1994 ◽  
Vol 35 (9) ◽  
pp. 4451-4462 ◽  
Author(s):  
G. Dattoli ◽  
S. Lorenzutta ◽  
G. Maino ◽  
A. Torre
Keyword(s):  
Phase Space ◽  
Hermite Polynomials ◽  
Two Indices ◽  
Space Dynamics

scholarly journals Fringe structure in the phase-space dynamics of atomic stabilization in an intense field

2000 ◽  
Vol 9 (1) ◽  
pp. 24-30 ◽  
Author(s):  
Liu Jie ◽  
Chen Shi-gang ◽  
Li Baowen ◽  
Hu Bambi
Keyword(s):  
Phase Space ◽  
Intense Field ◽  
Space Dynamics

scholarly journals Market of Stocks During Crisis Looks Like a Flock of Birds

2020 ◽  
Author(s):  
Bahar Afsharizand ◽  
Pooya H. Chaghoei ◽  
A A. Kordbacheh ◽  
A Trufanov ◽  
G.Reza Jafari
Keyword(s):  
Phase Space ◽  
Collective Behavior ◽  
Unique Point ◽  
Property A ◽  
Vicsek Model ◽  
Cooperative Effects ◽  
Cooperative Movement ◽  
Vector Velocity ◽  
Work Cooperative ◽  
The One

According to its inner property, a crisis in the financial market can be considered as a collective behavior phenomenon. Through the prism of collective behavior, the crisis does not happen if the companies are independent of each other. In this work, cooperative movement processes in a stock market are investigated in a manner similar to that Vicsek first described collective behavior for self-propelled entities. To this end, a phase space is defined as the one in which the return of volume of transactions versus return of price is represented with each share in each day corresponding to a unique point in the space. The findings of the observation show that during times of crisis, the phase space is limited with the vector velocity of shares in the same direction. In contrast, on a regular day, the phase space is entirely accessible, with vector velocity aligned randomly. Moreover, in line with the Vicsek model, an order parameter is introduced, which evaluates the cooperative effects for the shares so that the higher the value of this parameter, the stronger the collective behavior of the shares.

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