Abstracts

# Abstracts

**Stepan Apunevych and Bohdan Novosyadlyj (Ivan Franko National University of Lviv, Astronomical Observatory, Ukraine), Robin de Regt and Christian von Ferber (Applied Mathematics Research Centre, Coventry University, United Kingdom), Yurij Holovatch (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukrain, Ukraine). Complex networks for modeling large-scale structure of Universe.**

The on-going observational programmes in cosmology constantly update us with new rich datasets on the spatial galaxy distribution as well as spectral and evolutional characteristics of galaxies. The complex topology of such structure and the dependence of the evolution of a galaxy upon its location in this structure are open questions so far. To explore the connection of galaxy evolution properties (e.g. color, stellar mass, star formation rate) with topological environment we use complex networks for modeling the structure. Based on data of COSMOS survey [1] (data releases of 2013 and 2015) we draw various observables in terms of complex networks and build appropriate classification of the galaxies into sub-populations. Thus, we can estimate how the location of galaxy defines its distinct evolutionary behaviour.

[1] http://cosmos.astro.caltech.edu/

**Henrik Christiansen, Suman ****Majumder and Wolfhard Janke (Institut für Theoretische Physik, Universität Leipzig). The influence of bond fluctuations on the coarsening and aging of lattice polymers****.**

Results are presented for the nonequilibrium dynamics of flexible homopolymer collapse on simple cubic lattices with fixed and fluctuating bonds between the monomers. Our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are more or less independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a nonuniversal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a more or less temperature independent growth. We also examine the related aging phenomenon, probed by a suitable two-time density-density autocorrelation function showing a simple power-law scaling with respect to the growing cluster size. Unlike the growth exponent, the dynamical exponent governing the aging during the collapse, however, turns out to be independent of the bond type.

**Khrystyna Gnatenko (Ivan Franko National University of Lviv, Department for Theoretical Physics, Ukraine). Many-particle system in noncommutative phase-space.**

We consider quantized space which is realized with the help of noncommutativity of coordinates and noncommutativity of momenta. The problem of describing the motion of composite system in this space is studied. We conclude that the motion of the center-of-mass of composite system is described by effective parameters of noncommutativity, the motion of the center-of-mass and the relative motion are not independent in noncommutative phase-space. We propose condition on the parameters of noncommutativity on which a list of important results can be obtained [1,2]. Namely, we show that in the case when parameters of noncommutativity corresponding to a particle are determined by its mass the motion of the center-of-mass of composite system and relative motion are independent, weak equivalence principle is recovered in noncommutative phase-space, kinetic energy of composite system has additivity property and does not depend on the systems composition, coordinates of a particle can be considered as kinematic variables in noncommutative phase-space [3]. As an example of many-particle system we consider two particles with harmonic oscillator interaction. We exactly find energy levels of the system in noncommutative phase-space.

[1] Kh. P. Gnatenko , Phys. Lett. A 377, No. 43, 3061-3066 (2013).

[2] Kh. P. Gnatenko, V. M. Tkachuk , Mod. Phys. Lett. A 31, No. 5, 1650026 [9 p.] (2016).

[3] Kh. P. Gnatenko, V. M. Tkachuk , arXiv:1701.00809, 2016.

**Khrystyna Haydukivska, Viktoriya Blavatska (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, Ukraine). Probabilities of loop formation on polymer chains in disordered environment.**

We analyze the probabilities of loop formations on polymer chains in the environment with structural impurities. Both linear and star-like polymers are considered. The calculations for the case of long-range correlated disorder (~ r^{-a}) are made within the continuous chain model and corresponding scaling exponents are calculated up to the first order of double ϵ=4-d, δ=4-a expansion, by applying the direct polymer renormalization scheme. Some numerical results for anisotropy are also discussed.

** Wolfhard Janke and Niklas Fricke (Institut für Theoretische Physik, Universität Leipzig). Exact enumeration of self-avoiding walks on critical percolation clusters in two to seven dimensions.**

We study self-avoiding walks on critical percolation clusters by means of a recently developed exact enumeration method, which can handle walks of several thousand steps. We had previously presented results for the two- and three-dimensional cases; here we take a wider perspective and vary the system's dimensions up to D=7, beyond the supposed upper critical dimension of D_{uc}=6. These results may serve to check analytical predictions and help understand how the medium's fractal structure impacts on the walks' scaling behavior. For the physically relevant, smaller dimensions, the scaling exponent ν for the end-to-end distance turns out to be smaller than previously thought and appears to be the same on the backbones as on full clusters. We find strong evidence against the widely assumed scaling law for the number of conformations and propose an alternative, which perfectly fits our data.

N. Fricke and W. Janke, Phys. Rev. Lett. 113, 255701 (2014);

N. Fricke and W. Janke, J. Phys. A: Math. Theor. (2017), in print.

**Bohdan Novosyadlyj, Maxym Tsizh, Yurij Kulinich (Ivan Franko National University of Lviv, Astronomical Observatory, Ukraine). Whether can be the cosmic voids a "Rosetta Stone" for nature of dark energy?**

The cosmological constant has been introduced into general relativity one hundred years ago by Albert Einstein. Since it has no consistent physical interpretation, other essences have been proposed to explain the accelerated expansion of the Universe discovered 17 years ago. They have been commonly referred to as the "dark energy". Theorists have proposed a number of models which can be tested by observations. We show that the data on dynamical structure of the cosmic voids are sensitive to the parameters of dark energy models.

**Vasyl Palchykov (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, Ukraine). Ground truth? Clustering scientific publications.**

Community detection techniques are widely used to infer hidden structures within interconnected systems. Despite demonstrating high accuracy on benchmarks, they reproduce the external classification for many real-world systems with a significant level of discrepancy. A widely accepted reason behind such outcome is the unavoidable loss of non-topological information (such as node attributes) encountered when the original complex system is converted to a network. We systematically show that the observed discrepancies may also be caused by a different reason: the external classification itself. For this end we use scientific publication data, which (i) exhibit a well-defined modular structure and (ii) hold an expert-made classification of research articles. Our analysis shows that the discrepancies may carry essential information about the system, mainly related to the use of similar techniques and methods across different (sub)disciplines, that is otherwise omitted when only the external classification is considered.

** Massimiliano D. Rosini (Maria Curie-Skłodowska University, Lublin, Poland) Many-particle approximation of conservation laws in 1D. **

In this talk we present recent our results on the deterministic many-particle approximation of nonlinear Conservation Laws (CLs). The unique entropy solution to a scalar CL was rigorously approximated in [MD15, MSD] by a discrete density constructed from the follow-the-leader particle system. Said result can be based on a discrete version of the classical Oleinik one-sided jump condition or on a BV contraction estimate for BV initial data. The initial-boundary value problem for a scalar CL has been considered in [4]. The results in [1] have been extended in [3] to the 2×2 system of conservation laws describing the multi-population vehicular traffic model by Aw, Rascle and Zhang. Finally, we present the extension of these techniques obtained in [5] for the one dimensional version of the Hughes model for pedestrian folws in a bounded interval with Dirichlet boundary conditions.

**Volodymyr Tkachuk (Ivan Franko National University of Lviv, Department for Theoretical Physics, Ukraine). Galilean and Lorentz transformations in quantized space.**

Existence of minimal length or quantum of space was predicted by string theory and quantum gravity. A space with the minimal length (quantized space) can be described with the help of deformation of the Heisenberg algebra. On the classical level such a space is characterized by the deformed Poisson brackets. One of the fundamental problems in this space is the problem of description of composite system which is called soccer-ball problem. This problem is related to the problem of finding Galilean and Lorentz transformations in quantized space [1]. On this issue the talk will be focused on.

[1] V. M. Tkachuk, Found. Phys. 46, No. 12, 1666-1679 (2016).

**Taras Yavorskii (Applied Mathematics Research Centre, Coventry University, UK). Three-dimensional periodic nearest neighbor Ising models with exact relations among their partition functions.**

The nearest neighbor Ising model on the three dimensional (d = 3) cubic lattice has so far evaded exact solution. I introduce triplets of nearest neighbor Ising models on d = 3 periodic lattices, whose partition functions are related exactly. The relationship among the partition functions is obtained by a star- triangle transformation due to Onsager. The lattices are of cubic symmetry and have more than one site per cubic unit cell. With respect to their roles in the star-triangle transformation, they can be thought of as d = 3 analogues of the d = 2 kagome, hexagonal and triangular lattices. The models can undergo phase transitions at nite temperature or remain disordered, depending on the coupling and lattice. Some models admit quasi-exact calculation of their spin- spin pair correlation functions [1].

[1] T. Yavorskii, The large-m limit, and spin liquid correlations in kagome-like spin models, Condensed Matter Physics, 20 13701 (2017).

**Martin Weigel (Applied Mathematics Research Centre, Coventry University, UK). Population annealing: Massively parallel simulations in statistical physics.**

Population annealing is a promising recent approach for Monte Carlo simulations in statistical physics, in particular for the simulation of systems with complex free-energy landscapes. It is a hybrid method, combining importance sampling through Markov chains with elements of sequential Monte Carlo in the form of population control. In its established formulation, it appears to have algorithmic capabilities for the simulation of such systems that are roughly comparable to those of more established approaches such as parallel tempering, but it is intrinsically much more suitable for massively parallel computing.

Besides presenting a highly efficient implementation of the algorithm for GPU devices, we present an upgrade of the method to a fully adaptive algorithm for the simulation of complex systems by an automatized choice of (1) the temperature step, (2) the time step, and (3) the population size. It is shown that in combination with the availability of a free-energy estimator, weighted averages and a multi-histograming technique the algorithm has the potential to successfuly tackle previously intractable problems and to become the approach of choice for a wide range of applications.