2017 
Dolgushev, M., Hauber, A. L., Pelagejcev, P., & Wittmer, J. P. (2017). Marginally compact fractal trees with semiflexibility. Phys. Rev. E, 96(1), 15 pp.
Abstract: We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bondbond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the tree' behavior and to consider larger structures. Due to the local stiffness, the selfcontact density gets drastically reduced.


Dolgushev, M., Schnell, S., & Markelov, D. A. (2017). Local NMR Relaxation of Dendrimers in the Presence of Hydrodynamic Interactions. Appl. Magn. Reson., 48(7), 657–671.
Abstract: We study the role of hydrodynamic interactions for the relaxation of segments' orientations in dendrimers. The dynamics is considered in the Zimm framework. It is shown that inclusion of correlations between segments' orientations plays a major role for the segments' mobility, which reveals itself in the nuclear magnetic resonance relaxation functions. The enhancement of the reorientation dynamics of segments due to the hydrodynamic interactions is more significant for the inner segments. This effect is clearly pronounced in the reduced spectral density omega J(omega), maximum of which shifts to higher frequencies when the hydrodynamic interactions are taken into account.


Dolgushev, M., Wittmer, J. P., Johner, A., Benzerara, O., Meyer, H., & Baschnagel, J. (2017). Marginally compact hyperbranched polymer trees. Soft Matter, 13(13), 2499–2512.
Abstract: Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution rho(pair)(r) or the shearstress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the selfcontact density rho(c) = rho(pair)(r approximate to 0) similar to log(N/S)/root S diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time tau p of mode p must scale as tau(p) similar to (N/p)(5/3) rather than the usual square power law for linear chains.


Mulken, O., Heinzelmann, S., & Dolgushev, M. (2017). Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties. J. Stat. Phys., 167(5), 1233–1243.
Abstract: We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its nonequilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation's transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochastic) information dimension and gives a global characterization of the dynamics on the network. These general results are corroborated by examples of regular and of fractal networks.
Keywords: Networks; Fractals; Entropy; Stochastic thermodynamics


2016 
Dolgushev, M., Liu, H. X., & Zhang, Z. Z. (2016). Extended Vicsek fractals: Laplacian spectra and their applications. Phys. Rev. E, 94(5), 7 pp.
Abstract: Extended Vicsek fractals (EVF) are the structures constructed by introducing linear spacers into traditional Vicsek fractals. Here we study the Laplacian spectra of the EVF. In particularly, the recurrence relations for the Laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing Laplacian eigenvalues. This quantity characterizes the largescale properties, such as the gyration radius of the polymeric structures, or the global meanfirst passage time for the random walk processes. Introduction of the linear spacers leads to local heterogeneities, which reveal themselves, for example, in the dynamics of EVF under external forces.


Dolgushev, M., Markelov, D. A., Furstenberg, F., & Guerin, T. (2016). Local orientational mobility in regular hyperbranched polymers. Phys. Rev. E, 94(1), 9 pp.
Abstract: 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.


Grimm, J., & Dolgushev, M. (2016). Dynamics of internally functionalized dendrimers. Phys. Chem. Chem. Phys., 18(28), 19050–19061.
Abstract: The internally functionalized dendrimers are novel polymers that differ from conventional dendrimers by having additional functional units which do not branch out further. We investigate the dynamics of these structures with the inclusion of local semiflexibility and analyze their eigenmodes. The functionalized units clearly manifest themselves leading to a group of eigenvalues which are not present for homogeneous dendrimers. This part of the spectrum reveals itself in the local relaxation, leading to a corresponding process in the imaginary part of the complex dielectric susceptibility.


Liu, H. X., Lin, Y., Dolgushev, M., & Zhang, Z. Z. (2016). Dynamics of combofcomb networks. Phys. Rev. E, 93(3), 7 pp.
Abstract: The dynamics of complex networks, a current hot topic in many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we consider the deterministic networks which can be viewed as “combofcomb” iterative structures. For their Laplacian spectra we find analytical equations involving Chebyshev polynomials whose properties allow one to analyze the spectra in deep. Here, in particular, we find that in the infinite size limit the corresponding spectral dimension goes as d(s) > 2. The d(s) leaves its fingerprint on many dynamical processes, as we exemplarily show by considering the dynamical properties of polymer networks, including single monomer displacement under a constant force, mechanical relaxation, and fluorescence depolarization.


Mielke, J., & Dolgushev, M. (2016). Relaxation Dynamics of Semiflexible Fractal Macromolecules. Polymers, 8(7), 23 pp.
Abstract: We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through Tfractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locallydendritic structure that is more pronounced for higher stiffness.
Keywords: hyperbranched polymers; semiflexibility; fractals; pseudodendrimers; mechanical relaxation; eigenmodes

