An Overview of Emergent Order in Far-from-equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh-B\'enard Convection

Soft-matter systems when driven out-of-equilibrium often give rise to structures that usually lie in-between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh-B\'enard convection system which when driven out-of-equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out-of-equilibrium.Comment: Submitted to Entrop

Dielectric Hysteresis, Relaxation Dynamics, and Non-volatile Memory Effect in Carbon Nanotube Dispersed Liquid Crystal

The self-organizing properties of nematic liquid crystals (LC) can be used to template carbon nanotubes (CNTs) on a macroscopic dimension. The nematic director field, coupled to the dispersed CNT long-axis, enables controlled director reorientation using well-established methods of LC alignment techniques, such as patterned-electrode-surface, electric fields, and magnetic fields. Electric field induced director rotation of a nematic LC+CNT system is of potential interests due to its possible applications as a nano electromechanical system. The relaxation mechanism for a LC+CNT composite, on the removal of the applied field, reveals the intrinsic dynamics of this anisotropic system. Dielectric hysteresis and temperature dependence of the dielectric constant coherently shows the ferroelectric-type behavior of the LC+CNT system in the nematic phase. The strong surface anchoring of LC molecules on CNT walls results in forming local isolated pseudo-nematic domains in the isotropic phase. These domains, being anisotropic, respond to external fields, but, do not relax back to the original state on switching of the field off, showing non-volatile memory effect.Comment: 7 pages, 8 figure

Exponential Self-Organization and Moore\u27s Law: Measures and Mechanisms

The question of how complex systems become more organized and efficient with time is open. Examples are the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, and the formation of molecules from atoms, of organisms, and of the society. In this sequence, order appears inside complex systems and randomness (entropy) is expelled to their surroundings. Key features of self-organizing systems are that they are open and they are far away from equilibrium, with increasing energy flows through them. This work searches for global measures of such self-organizing systems, which are predictable and do not depend on the substrate of the system studied. Our results will help to understand the existence of complex systems and mechanisms of self-organization. In part we also provide insights, in this work, about the underlying physical essence of Moore’s law and the multiple logistic growth observed in technological progress

Calorimetric study of the nematic to smectic-A phase transition in octylcyanobiphenyl-hexane binary mixtures

The continuous nematic to smectic-A (N-SmA) phase transition has been studied by high-resolution ac-calorimetry in binary mixtures of the liquid crystal octylcyanobiphenyl(8CB) and a non-mesogenic, low-molecular weight, solvent n-hexane(hex) as a function of temperature and solvent concentration. Heating and cooling scans about the N-SmA transition temperature were repeatedly performed on pure and six 8CB+hex samples having hexane molar concentration ranging from x_{hex}= 0.02 to 0.12. All 8CB+hex samples in this range of x_{hex} remain macroscopically miscible and exhibit an N-SmA heat capacity peak that shifts non-monotonically to lower temperature and evolves in shape, with a reproducible hysteresis, as x_{hex} increases. The imaginary part of heat capacity remains zero up to x^{TCP}_{hex}\simeq 0.07$ above which the distinct peak is observed, corresponding to a jump in both the real and imaginary enthalpy. A simple power-law analysis reveals an effective exponent that increases smoothly from 0.30 to 0.50 with an amplitude ratio A^{-}/A^{+}\rightarrow 1 as x_{hex}\rightarrow x^{TCP}_{hex}. This observed crossover towards the N-SmA tricritical point driven by solvent concentration is consistent with previous results and can be understood as weakening of the liquid crystal intermolecular potential promoting increased nematic fluctuations

Studies of Nanocomposites of Carbon Nanotubes and a Negative Dielectric Anisotropy Liquid Crystal

The complex specific heat is reported over a wide temperature range for a negative dielectric anisotropy alkoxyphenylbenzoate liquid crystal (9OO4) and carbon nanotube (CNT) composites as a function of carbon nanotube concentration. It has been observed that the combination of nanotubes (CNT) and liquid crystal (LC) provides a very useful way to align CNTs and also dramatically increases the order in the liquid crystal performance, which is useful in liquid display technology (LCD). The calorimetric scans were performed between 25 and 95°C temperatures, first allowed cooling and then heating for CNT concentration ranging from ϕw = 0 to 0.2 wt%. All 9OO4/CNT composite mesophases have transition temperatures about 1 K higher and a crystallization temperature 4 K higher as compared to the pure 9OO4 liquid crystal. A strongly first-order specific heat feature is observed, which is 0.5 K higher than in the pure 9OO4. The transition enthalpy for the composite mesophases is observed 10% lower than the pure liquid crystal. We interpret that these results arising from the LC-CNT surface interaction lead to pinning orientational order uniformly along the CNT, without pinning the position of the 9OO4 molecule. These effects of incorporating CNTs with LC are likely due to elastic coupling between CNT and LC. These effects of incorporating CNTs into LCs are likely due to an "anisotropic orientational" coupling between CNT and LC, the change in the elastic properties of composites and thermal anisotropic properties of the CNTs