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The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
The key parameter controlling the glass transition of colloidal suspensions is $\varphi$, the fraction of the sample volume occupied by the particles. Unfortunately, changing $\varphi$ by varying an external parameter, \textit{e.g.}…
The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which…
In this paper, conformal fractional order discretization [20, 24, 25] is used to analyze bifurcation analysis and stability of a predator-prey system. A continuous model has been discretized into a discrete one while preserving the…
We present an analysis of the dynamics of the equifacial pentahedron on the Kapovich-Millson phase space under a volume preserving Hamiltonian. The classical dynamics of polyhedra under such a Hamiltonian may arise from the classical limit…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
We probe the effects of particle shape on the global and local behavior of a two-dimensional granular pillar, acting as a proxy for a disordered solid, under uniaxial compression. This geometry allows for direct measurement of global…
The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses,…
Using Brownian dynamics computer simulations we show that a two-dimensional suspension of self-propelled ("active") colloidal particles crystallizes at sufficiently high densities. Compared to the equilibrium freezing of passive particles…
We have studied systematically the influence of particle-hole symmetric and asymmetric kinetic terms on the ordered phases that we may observe competing or coexisting in a tetragonal system. We show that there are precise patterns of…
In the context of the entangled $B^0 \bar B^0$ state produced at the $\Upsilon(4S)$ resonance, we consider a modification of the usual quantum-mechanical time evolution with a dissipative term, which contains only one parameter denoted by…
Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles.…
The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
We examine the changeover in the particle configurations and the dynamics in dense Lennard-Jones binary mixtures composed of small and large particles. By varying the composition at a low temperature, we realize crystal with defects,…
In this combined experimental and simulation study, we utilize bond-order topology to quantitatively match particle volume fraction in mechanically uniformly compressed colloidal suspensions with temperature in atomistic simulations. The…
Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred…
Structural defects are ubiquitous in condensed matter, and not always a nuisance. For example, they underlie phenomena such as Anderson localization and hyperuniformity, and they are now being exploited to engineer novel materials. Here, we…
Glasses remain an elusive and poorly understood state of matter. For example, it is not clear how we can design an efficient macroscopic glass former by tuning the properties of its microscopic building blocks. In this paper, we propose a…
In this paper the amorphous/solid to disorder liquid structural phase transitions of an anomalous confined fluid is analyzed using their local fractal dimension. The model is a system of particles interacting through a two length scales…