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Register a new userA Formalism for Scattering of Complex Composite Structures. 1 Applications to Branched Structures of Asymmetric Sub-Units
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We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural scattering in terms of three equations expressing the sub-unit scattering. The structural scattering expressions allows a composite structures to be used as sub-units within the formalism itself. This allows the scattering expressions for complex hierarchical structures to be derived with great ease. The formalism is furthermore generic in the sense that the scattering due to structural connectivity is completely decoupled from internal structure of the sub-units. This allows sub-units to be replaced by more complex structures. We illustrate the physical interpretation of the formalism diagrammatically. By applying a self-consistency requirement we derive the pair distributions of an ideal flexible polymer sub-unit. We illustrate the formalism by deriving generic scattering expressions for branched structures such as stars, pom-poms, bottle-brushes, and dendrimers build out of asymmetric two-functional sub-units.
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Recently we developed a formalism for the scattering from linear and acyclic branched structures build of mutually non-interacting sub-units.{[}C. Svaneborg and J. S. Pedersen, J. Chem. Phys. 136, 104105 (2012){]} We assumed each sub-unit has reference points associated with it. These are well defined positions where sub-units can be linked together. In the present paper, we generalize the formalism to the case where each reference point can represent a distribution of potential link positions. We also present a generalized diagrammatic representation of the formalism. Scattering expressions required to model rods, polymers, loops, flat circular disks, rigid spheres and cylinders are derived. and we use them to illustrate the formalism by deriving the generic scattering expression for micelles and bottle brush structures and show how the scattering is affected by different choices of potential link positions.
The extremization of an appropriate entropic functional may yield to the probability distribution functions maximizing the respective entropic structure. This procedure is known in Statistical Mechanics and Information Theory as Jaynes Formalism and has been up to now a standard methodology for deriving the aforementioned distributions. However, the results of this formalism do not always coincide with the ones obtained following different approaches. In this study we analyse these inconsistencies in detail and demonstrate that Jaynes formalism leads to correct results only for specific entropy definitions.
We present a comprehensive study about the relationship between the way Detailed Balance is broken in non-equilibrium systems and the resulting violations of the Fluctuation-Dissipation Theorem. Starting from stochastic dynamics with both odd and even variables under Time-Reversal, we exploit the relation between entropy production and the breakdown of Detailed Balance to establish general constraints on the non-equilibrium steady-states (NESS), which relate the non-equilibrium character of the dynamics with symmetry properties of the NESS distribution. This provides a direct route to derive extended Fluctuation-Dissipation Relations, expressing the linear response function in terms of NESS correlations. Such framework provides a unified way to understand the departure from equilibrium of active systems and its linear response. We then consider two paradigmatic models of interacting self-propelled particles, namely Active Brownian Particles (ABP) and Active Ornstein-Uhlenbeck Particles (AOUP). We analyze the non-equilibrium character of these systems (also within a Markov and a Chapman-Enskog approximation) and derive extended Fluctuation-Dissipation Relations for them, clarifying which features of these active model systems are genuinely non-equilibrium.
We present a coarse-grained model for stochastic transport of noninteracting chemical signals inside neuronal dendrites and show how first-passage properties depend on the key structural factors affected by neurodegenerative disorders or aging: the extent of the tree, the topological bias induced by segmental decrease of dendrite diameter, and the trapping probabilities in biochemical cages and growth cones. We derive an exact expression for the distribution of first-passage times, which follows a universal exponential decay in the long-time limit. The asymptotic mean first-passage time exhibits a crossover from power-law to exponential scaling upon reducing the topological bias. We calibrate the coarse-grained model parameters and obtain the variation range of the mean first-passage time when the geometrical characteristics of the dendritic structure evolve during the course of aging or neurodegenerative disease progression (A few disorders are chosen and studied for which clear trends for the pathological changes of dendritic structure have been reported in the literature). We prove the validity of our analytical approach under realistic fluctuations of structural parameters, by comparing to the results of Monte Carlo simulations. Moreover, by constructing local structural irregularities, we analyze the resulting influence on transport of chemical signals and formation of heterogeneous density patterns. Since neural functions rely on chemical signal transmission to a large extent, our results open the possibility to establish a direct link between the disease progression and neural functions.
We study asymptotic properties of diffusion and other transport processes (including self-avoiding walks and electrical conduction) on large randomly branched polymers using renormalized dynamical field theory. We focus on the swollen phase and the collapse transition, where loops in the polymers are irrelevant. Here the asymptotic statistics of the polymers is that of lattice trees, and diffusion on them is reminiscent of the climbing of a monkey on a tree. We calculate a set of universal scaling exponents including the diffusion exponent and the fractal dimension of the minimal path to 2-loop order and, where available, compare them to numerical results.
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