Heavy inertial particles in spatially and temporally flows can form clusters if their relaxation time is in the order of the dissipation time scale of the flow. This regime, identified by St = O(1), is investigated in this study using analytical tools. We show that the nonlinear variation of segregation versus St can be explained by considering a one-dimensional canonical setting where particles are subjected to an oscillatory velocity gradient that is constant in space. Our analysis shows that the Lyapunov exponent, as a measure of particle segregation, reaches a minimum at St = O(1) and becomes positive at St >> 1 and approaches zero as St goes to 0 or infinity. These predictions, which are corroborated by the numerical results, are directly linked and compared against measurements of the dispersion and segregation in three-dimensional turbulence. Our analysis reveals a strongly nonlinear behavior of the Lyapunov exponents in the straining regimes of strong oscillations. This work was supported by the United States Department of Energy under the Predictive Science Academic Alliance Program 2 (PSAAP2) at Stanford University.