On tetrahedratic order and chiral symmetry breaking

講演者: Prof. Helmut R. Brand (Theoretische Physik III, Universitat Bayreuth, Germany)
日時 : 2016年3月7日（火）11：00～12：30
場所 : 中央大学理工学部3号館3階3300教室
概要 :
We investigate how tetrahedratic order can influence chirality in nonchiral systems. For nematic phases composed of achiral bent-core molecules the occurence of chiral domains of opposite hand is well-established experimentally [1,2] and has been modeled as being due to a linear gradient term between quadrupolar and octupolar order [3].
Recently there have been experimental results not only on liquid crystals, but also on optically isotropic phases.
It turns out that in such materials mesoscopic to macroscopic domains of either hand can occur spontaneously [4]-[7].
We argue [8] that transient elasticity coupled to tetrahedratic order can lead to chiral domains of opposite hand in an optically isotropic system even for achiral molecules. This issue is related to the question of chiral symmetry breaking in condensed matter physics, but also potentially relevant for biological systems.

[1] G. Pelzl et al., J. Mater. Chem. 12, 2591 (2002).
[2] T. Niori, J. Yamamoto, and H. Yokoyama, Mol. Cryst. Liq. Cryst. 409, 475 (2004).
[3] H.R. Brand, H. Pleiner, and P.E. Cladis, Physica A 351. 189 (2005).
　　H.R. Brand and H. Pleiner, Eur. Phys. J. E 31, 37 (2010).
　　H. Pleiner and H.R. Brand, Eur. Phys. J. E 37, 11 (2014).
[4] M. Jasinski, D.Pociecha, H. Monobe, J. Szczytko, and P. Kaszynski, J. Am. Chem. Soc. 136, 14658 (2014).
[5] C. Dressel, T. Reppe, M. Prehm, M. Brautzsch, and C. Tschierske, Nat. Chem. 6, 971 (2014).
[6] C. Dressel, W. Weissflog, and C. Tschierske, Chem. Comm. 51, 15850 (2015).
[7] M. Alaasar, M. Prehm, Y. Cao, F. Liu, and C. Tschierske, Angew. Chem. Int. Ed. 55, 312 (2016).
[8] H.R. Brand and H. Pleiner, submitted for publication

Influence of noise on dissipative solitons and their interaction

講演者: Prof. Helmut R. Brand (Theoretische Physik III, Universitat Bayreuth, Germany)
日時 : 2015年3月16日（水）16：00～17：30
場所 : 中央大学理工学部3号館3階3300教室
概要 :
We give an overview of the influence of noise on spatially localized patterns and their interaction. Localized patterns include stationary dissipative solitons, oscillatory dissipative solitons with one and two frequencies as well as exploding dissipative solitons. The influence of noise on spatially localized structures of arbitrary length, which are localized due to the trapping mechanism, has been investigated in [1] and it was shown that the logarithm of the lifetime scales inversely with the noise intensity. Thus the picture of a noise-activated barrier crossing has been demonstrated. A long standing puzzle in the field of pattern formation has been the experimental observation of the partial annihilation of pulses in binary fluid convection [2] and during CO oxidation in surface reactions [3,4] it has been shown that already a small amount of additive noise can account for the experimental observation. The mechanism will be elucidated in the presentation. Recently it has been shown that a small amount of noise can induce explosions for dissipative solitons in the vicinity of the transition sequence from stationary dissipative solitons to exploding dissipative solitons via three different routes [6,7]. We also investigate the influence of large noise on the formation of localized patterns in the framework of the cubic-quintic complex Ginzburg-Landau equation. The interaction of localization and noise can lead to filling-in or noisy localized structures for fixed noise strength. To focus on the interaction between noise and localization we cover a region in parameter space, in particular subcriticality, for which stationary stable deterministic pulses do not exist [8]. Possible experimental tests of the work presented for autocatalytic chemical reactions and bio-inspired systems are outlined. Finally we present some of our recent results on the influence of spatially homogeneous multiplicative noise on spatially localized solutions in nonequilibrium systems.

[1] H. Sakaguchi, H. R. Brand : Physica D - Nonlinear Phenomena 97, 274 (1996).
[2] P. Kolodner : Phys. Rev. A 44, 6466 (1991).
[3] H. H. Rotermund, S. Jakubith, A. von Oertzen, G. Ertl : Phys. Rev. Lett. 66, 3083 (1991).
[4] A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, G. Ertl : J. Chem. Phys. B 102, 4966 (1998).
[5] O. Descalzi, J. Cisternas, D. Escaff, H. R. Brand : Phys. Rev. Lett. 102, 188302 (2009).
[6] C. Cartes, O. Descalzi, H. R. Brand : Phys. Rev. E 85, 015205 (2012).
[7] C. Cartes, O. Descalzi, H. R. Brand : Eur. Phys. J. Special Topics 223, 2145 (2014).
[8] O. Descalzi, C. Cartes, H. R. Brand : Phys. Rev. E 91, 020901 (2015).

Macroscopic behavior of systems with a dynamic preferred direction

講演者: Prof. Helmut R. Brand (Theoretische Physik III, Universitat Bayreuth, Germany)
日時 : 2015年3月10日（火）15：30～17：00
場所 : 中央大学理工学部3号館5階3507教室
概要 :
We present the derivation of the macroscopic equations for systems with a dynamic preferred direction, which can be axial or polar in nature.
In addition to the usual hydrodynamic variables we introduce the time derivative of the local preferred direction [1] or the macroscopic velocity associated with the motion of the active units [2] as a new variable and discuss their macroscopic consequences [1,2]. Such an approach is expected to be useful for a number of biological systems including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such as Proteus mirabilis, shoals of fish, flocks of birds and migrating insects.
As a concrete application we set up a macroscopic model of bacterial growth and transport based on a polar dynamic preferred direction -- the collective velocity of the bacteria [3]. This collective velocity is subject to the isotropic-nematic transition modeling the density-controlled transformation between immotile and motile bacterial states.
The approach can be applied also to other systems spontaneously switching between individual (disordered) and collective (ordered) behavior, and/or collectively responding to density variations, e.g., bird flocks, fish schools etc. We observe a characteristic and robust nonlinear stop-and-go behavior of the type also observed for the growth of bacteria experimentally [4]. We also discuss our recent work on the stress tensor critically comparing the results of our model with those of other groups [5].

[1] H.R. Brand, H. Pleiner and D. Svensek, Eur. Phys. J. E34, 128 (2011).
[2] H. Pleiner, D. Svensek and H.R. Brand, Eur. Phys. J. E36, 135 (2013).
[3] D. Svensek, H. Pleiner and H.R. Brand, Phys. Rev. Lett. 111, 228101 (2013).
[4] Y. Yamazaki et al., Physica D - Nonlinear Phenomena, 205 D, 236 (2005).
[5] H.R. Brand, H. Pleiner and D. Svensek, Eur. Phys. J. E37, 83 (2014).