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We consider the kinetics of first contact between two monomers of the same macromolecule. Relying on a fractal description of the macromolecule, we develop an analytical method to compute the mean first contact time for various molecular sizes. In our theoretical description, the non-Markovian feature of monomer motion, arising from the interactions with the other monomers, is captured by accounting for the nonequilibrium conformations of the macromolecule at the very instant of first contact. This analysis reveals a simple scaling relation for the mean first contact time between two monomers, which involves only their equilibrium distance and the spectral dimension of the macromolecule, independently of its microscopic details. Our theoretical predictions are in excellent agreement with numerical stochastic simulations. [ABSTRACT FROM AUTHOR]

We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity, which is assumed to be periodic. When the system is asymptotically diffusive, the mean-squared displacement, characterizing the dispersion in the system, is, at late times, a linear function of time. A Kubo-type formula is given for the mean-squared displacement, which allows the recovery of some known results for the effective diffusion constant De in a direct way, but also allows an understanding of the asymptotic approach to the diffusive limit. In particular, as well as as computing the slope of a linear fit to the late-time mean-squared displacement, we find a formula for the constant where the fit intersects the y axis. [ABSTRACT FROM AUTHOR]

The forces acting on optically trapped particles are commonly assumed to be conservative. Nonconservative scattering forces induce toroidal currents in overdamped liquid environments, with negligible effects on position fluctuations. However, their impact in the underdamped regime remains unexplored. Here, we study the effect of nonconservative scattering forces on the underdamped nonlinear dynamics of trapped nanoparticles at various air pressures. These forces induce significant low-frequency position fluctuations along the optical axis and the emergence of toroidal currents in both position and velocity variables. Our experimental and theoretical results provide fundamental insights into the functioning of optical tweezers and a means for investigating nonequilibrium steady states induced by nonconservative forces. [ABSTRACT FROM AUTHOR]

We consider a model of a particle trapped in a harmonic optical trap but with the addition of a nonconservative radiation induced force. This model is known to correctly describe experimentally observed trapped particle statistics for a wide range of physical parameters, such as temperature and pressure. We theoretically analyze the effect of nonconservative force on the underlying steady state distribution as well as the power spectrum for the particle position. We compute perturbatively the probability distribution of the resulting nonequilibrium steady states for all dynamical regimes underdamped through to overdamped and give expressions for the associated currents in phase space (position and velocity). We also give the spectral density of the trapped particle's position in all dynamical regimes and for any value of the nonconservative force. Signatures of the presence of nonconservative forces are shown to be particularly strong for the underdamped regime at low frequencies. [ABSTRACT FROM AUTHOR]

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes. [ABSTRACT FROM AUTHOR]

Domain decay is at the heart of the so-called evaporation-condensation Ostwald-ripening regime of phase ordering kinetics, where the growth of large domains occurs at the expense of smaller ones, which are expected to "evaporate." We experimentally investigate such decay dynamics at the level of a single spherical domain picked from one phase in coexistence and brought into the other phase by an optomechanical approach, in a near-critical phase-separated binary liquid mixture. We observe that the decay dynamics is generally not compatible with the theoretically expected surface-tension decay laws for conserved order parameters. Using a mean-field description, we quantitatively explain this apparent disagreement by the gradient of solute concentrations induced by gravity close to a critical point. Finally, we determine the conditions for which buoyancy becomes negligible compared to capillarity and perform dedicated experiments that retrieve the predicted surface-tension induced decay exponent. The surface-tension driven decay dynamics of conserved order parameter systems in the presence and the absence of gravity, is thus established at the level of a single domain.

We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations that take place along a circle or a straight line. Our results are confirmed by numerical simulations.

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

We propose a continuum theory for the conformational transitions of viral shells. Conformational transitions of viral shells, as encountered during viral maturation, are associated with a soft mode instability of the capsid proteins [F. Tama and C. L. Brooks, J. Mol. Biol. 345(2), 299 (2005)]. The continuum theory presented here is an adaptation of the Ginzburg-Landau theory of soft-mode structural phase transitions of solids to viral shells. The theory predicts that the conformational transitions are characterized by a pronounced softening of the shell elasticity in the critical region. We demonstrate that the thermodynamics of the conformational transition can be probed quantitatively by a micromechanical atomic force microscope study. The external force can drive a capsid into a state of phase coexistence characterized by a highly nonlinear force deformation curve.