Nonlinear edge waves in mechanical topological insulators

We show theoretically that the classical 1D nonlinear Schrödinger (NLS) and coupled nonlinear Schrödinger (CNLS) equations govern the envelope(s) of localised and unidirectional nonlinear travelling edge waves in a 2D mechanical topological insulator (MTI). The MTI consists of a collection of pendula with weak Duffing nonlinearity connected by linear springs that forms a mechanical analogue of the quantum spin Hall effect (QSHE). It is found, through asymptotic analysis and dimension reduction, that the NLS and CNLS respectively describe the unimodal and bimodal properties of the nonlinear system. The governing bimodal CNLS is found to be non-integrable by nature and as such we discover new solutions by exploring the spatial dynamics of the reduced travelling wave ODE with general parameters. Such solutions include travelling fronts and, by numerically continuing these fronts, one can find vector soliton (VS) in non integrable CNLS equations. The equilibria can also undergo both pitchfork and Turing bifurcation in the reversible spatial dynamical system and we discuss relevant conditions for the existence and consequences of such critical values. We briefly discuss the necessity of the developed front condition in forming such structures and present an analytical framework for front-grey soliton collisions by utilising conserved quantities of the non-integrable CNLS. The existence/stability of front and VS solutions can be inferred by spatial hyperbolicity and linear stability of the background fields, with the criteria presented here. VS solutions are considered in the form of bright-bright, bright-dark, and dark-dark solitons and their collision dynamics are explored qualitatively in the non-integrable regime. The Turing analysis presents the existence of periodic and localised patterned states in the CNLS, and we compare these solutions to those found in the analysis of the Swift-Hohenberg equation. Theoretical predictions from the 1D (C)NLS are confirmed by numerical simulations of the original 2D MTI for various types of travelling waves and rogue waves. As a result of topological protection the edge solitons persist over long time intervals and through irregular boundaries. Due to the robustness of topologically protected edge solitons (TPES) it is suggested that their existence may have significant implications on the design of acoustic devices. Spacetime simulations show a clear possibility of utilising MTIs in acoustical cloaking with TPES a vital player in such processes

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Dedication to Professor Michael Tribelsky

Professor Tribelsky's accomplishments are highly appreciated by the international community. The best indications of this are the high citation rates of his publications, and the numerous awards and titles he has received. He has made numerous fundamental contributions to an extremely broad area of physics and mathematics, including (but not limited to) quantum solid-state physics, various problems in light–matter interaction, liquid crystals, physical hydrodynamics, nonlinear waves, pattern formation in nonequilibrium systems and transition to chaos, bifurcation and probability theory, and even predictions of the dynamics of actual market prices. This book presents several extensions of his results, based on his inspiring publications

Hydrodynamics

The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics

Physics of Impurities in Quantum Gases

The Special Issue contains theoretical and experimental works that report on studies of impurities in quantum gases, fundamental properties and universal aspects of quasiparticles and other related many-body phenomena. Particular focus is placed on the Fermi and Bose polarons. The Special Issue contains ten research articles and two reviews. M. G. Skou et al. report on the experimental observation of time dynamics of Bose polarons. Theoretical studies by H. Tajima et al., L. A. Ardila, and G. Panochko and V. Pastukhov touch upon the physics of multiple impurities, in particular, the induced impurity–impurity interactions in different spatial dimensions and the formation of multi-polaron states. G. M. Koutentakis et al. elaborate on the phenomenon of temporal orthogonality catastrophe in low dimensions. Polaritons in an electron gas are discussed by M. A. Bastarrachea-Magnani et al. M. Brooks et al. describe the emergence of anyons originating from angulons. F. Scazza et al. provide an overview of our current understanding of repulsive Bose and Fermi polarons. C. D’Errico and M. G. Tarallo explicate the effects of disorder in bosonic systems. The Special Issue also includes studies of correlated atom pairs in bosonic mixtures by O. Alon, the behavior of the three-body decay rate coefficients into shallow dimers in mass-imbalanced three-atom systems by P. Giannakeas and C. H. Greene, population and angular momentum transfer in Raman-coupled Bose–Einstein condensates by K. Mukherjee et al