This chapter will discuss self-organization of ultrahigh molecular weight atactic polystyrene (a-PS) in dioctyl phthalate (DOP) as a solvent under externally applied flow fields. The system is a dynamically asymmetric systemDynamically asymmetric system, where a-PS and DOP are the slow and fast component, respectively. All the solutions studied form thermodynamically stable single-phase solutions in the absence of the applied flow and in the presence of the applied flow at the shear rate \(\dot{\gamma }\) satisfying \(0\le \dot{\gamma }<{\Gamma }_{\text{MD}}\) , the relaxation rateRelaxation rate of molecular deformation-orientation, at all temperatures covered in this study (Regime I). Upon increasing the flow rate at \(\dot{\gamma }>{\Gamma }_{\text{MD}}\) , the solutions are brought under the strong flow with respect to the molecular deformation-orientationStrong flow with respect to the molecular deformation-orientation, where the single-phase solutions become thermodynamically unstable under the flow, giving rise to a cascade evolution of a series of flow-rate dependent dissipative structures: from the dissipative structures in Regime II (where the flow-induced spinodal decomposition (SD) occurs to evolve the plane wave concentration fluctuationsFluctuation with the wave vectors oriented along the flow direction (FD)) to those in Regime IV at \(\dot{\gamma }\ge {\dot{\gamma }}_{\text{a}}\gg {\Gamma }_{\text{MD}}\) (strings composed of phase-separated domains aligned along the string axis and FD) through thoseIn Regime III in Regime III (phase-separated domains). The strings have a weak and strong birefringence in the early and late stage of Regime IV, defined as Regime IV-1 and IV-2, respectively. In Regime IV-2, the domains in the strings are predicted to be interconnected by bundles of stretched chains oriented along the string axis and FD. The same series of dissipative structures are elucidated to be self-organized in cascade with time after the step-up shear to a constant \(\dot{\gamma }\ge {\dot{\gamma }}_{\text{a}},\) the critical shear rate for the string formation, which is brought about through the dissipation of mechanical work imposed to the system upon increased \(\dot{\gamma }\) or increased time spent after the step-up shear.