The dynamics of soft colloids in solutions is characterized by internal collective motion as well as center-of-mass diffusion. Using neutron scattering we demonstrate that the competition between the relaxation processes associated with these two degrees of freedom results in strong dependence of dynamics and structure on colloid concentration, c, even well below the overlap concentration c*. We show that concurrent with increasing inter-particle collisions, substantial structural dehydration and slowing-down of internal dynamics occur before geometrically defined colloidal overlap develops. While previous experiments have shown that the average size of soft colloids changes very little below c*, we find a marked change in both the internal structure and internal dynamics with concentration. The competition between these two relaxation processes gives rise to a new dynamically-defined dilute threshold concentration well below c*.
The conventional cancer stem cell (CSC) theory indicates a hierarchy of CSCs and non-stem cancer cells (NSCCs), that is, CSCs can differentiate into NSCCs but not vice versa. However, an alternative paradigm of CSC theory with reversible cell plasticity among cancer cells has received much attention very recently. Here we present a generalized multi-phenotypic cancer model by integrating cell plasticity with the conventional hierarchical structure of cancer cells. We prove that under very weak assumption, the nonlinear dynamics of multi-phenotypic proportions in our model has only one stable steady state and no stable limit cycle. This result theoretically explains the phenotypic equilibrium phenomena reported in various cancer cell lines. Furthermore, according to the transient analysis of our model, it is found that cancer cell plasticity plays an essential role in maintaining the phenotypic diversity in cancer especially during the transient dynamics. Two biological examples with experimental data show that the phenotypic
Efficiently controlling the trapping process, especially the trapping efficiency, is central in the study of trap problem in complex systems, since it is a fundamental mechanism for diverse other dynamic processes. Thus, it is of theoretical and practical significance to study the control technique for trapping problem. In this paper, we study the trapping problem in a family of proposed directed fractals with a deep trap at a central node. The directed fractals are a generalization of previous undirected fractals by introducing the directed edge weights dominated by a parameter. We characterize all the eigenvalues and their degeneracies for an associated matrix governing the trapping process. The eigenvalues are provided through an exact recursive relation deduced from the self-similar structure of the fractals. We also obtain the expressions for the smallest eigenvalue and the mean first-passage time (MFPT) as a measure of trapping efficiency, which is the expected time for the walker to first visit the trap. The MFPT is evaluated according to the proved fact that it is approximately equal to reciprocal of the smallest eigenvalue. We show that the MFPT is controlled by the weight parameter, by modifying which, the MFPT can scale superlinealy, linearly, or sublinearly with the system size. Thus, this work paves a way to delicately controlling the trapping process in the fractals.
We consider the creation of the cosmological baryon asymmetry in the Two Higgs Doublet Model. We imagine a situation where the masses of the five Higgs particles and the two Higgs vevs are constrained by collider experiments, and demonstrate how the requirement of successful baryogenesis can be used to further constrain the remaining 4-dimensional parameter space of the model. We numerically compute the asymmetry within the scenario of Cold Electroweak Baryogenesis, which is particularly straightforward to simulate reliably.
