Related papers: Topologically enhanced time crystals and molecular…

We systematically study the relationship between equilibrium and non-equilibrium phase diagrams of a system of short-ranged attractive colloids. Using Monte Carlo and Brownian dynamics simulations we find a window of enhanced…

A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal…

Using molecular dynamics simulations, with a realistic many-body embedded-atom potential, and a novel method to characterize local order, we study the structure of pure nickel during the rapid quench of the liquid and in the resulting…

Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…

Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…

The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that…

This study investigates the probability of threading in star catenanes under good solvent conditions using molecular dynamics simulations, emphasizing the influence of ring rigidity. Threading in these systems arises from the interplay…

Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators…

After more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are…

Topological constraint theory has become an increasingly popular tool to predict the compositional dependence of glass properties or pinpoint promising compositions with tailored functionalities. This approach reduces complex disordered…

We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different…

Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation, which dictate their interactions. Here,…

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…

We propose that cosmological time is {\it effectively} the conjugate of the constants of nature. Different definitions of time arise, with the most relevant related to the constant controlling the dynamics in each epoch. The Hamiltonian…

In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…

Active materials are capable of converting free energy into directional motion, giving rise to striking dynamical phenomena. Developing a general understanding of their structure in relation to the underlying non-equilibrium physics would…

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases…

We investigate the Rouse dynamics of a flexible ring polymer with a prime knot. Within a Monte Carlo approach, we locate the knot, follow its diffusion, and observe the fluctuations of its length. We characterise a topological time scale,…

We solve the Cauchy problem for the relativistic closed string in Minkowski space $M^{3+1}$, including the cases where the initial data has a knot like topology. We give the general conditions for the world sheet of a closed knotted string…