Related papers: The first-order flexibility of a crystal framework
Circle packings are arrangement of circles satisfying specified tangency requirements. Many problems about packing of circles and spheres occur in nature particularly in material design and protein structure. Surprisingly, little is known…
We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in…
The phase-field crystal model (PFC) describes crystal structures at diffusive timescales through a periodic order parameter representing the atomic density. One of its main features is that it naturally incorporates elastic and plastic…
Phase transitions are caused by varying temperature, or pressure, or magnetic field. The observation of 1st order magneto-structural transitions has created application possibilities based on magnetoresistance, magnetocaloric effect,…
Understanding structural glasses using the Random First Order Transition theory requires a description in both real space and in time, taking into account sample history. A variety of nonlinear objects enter this description, in field…
[Connelly and Servatius, 1994] shows the difficulty of properly defining n-th order rigidity and flexiblity of a bar-and-joint framework for higher order (n >= 3) through the introduction of a cusp mechanism. The author proposes a "proper"…
Within the framework of the $s$-$d(f)$ exchange model in the mean-field approximation for square, simple cubic, body-centered and face-centered cubic lattices, the formation of a ferromagnetic, spiral, and commensurate antiferromagnetic…
Curved particles have been shown to stabilize a range of states with unique order in dense suspensions of colloidal bent core liquid crystals. The shape of the colloidal rods encourages the formation of curved director fields. However,…
A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending…
We develop a real space renormalisation group analysis of disordered models of glasses, in particular of the spin models at the origin of the Random First Order Transition theory. We find three fixed points respectively associated to the…
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…
Polymorphism is ubiquitous in crystalline solids. Amorphous solids, such as glassy water and silicon, may undergo amorphous-to-amorphous transitions (AATs). The nature of AATs remains ambiguous, due to diverse system-dependent behaviors and…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
A $d$-dimensional (bar-and-joint) framework $(G,p)$ consists of a graph $G=(V,E)$ and a realisation $p:V\to \mathbb{R}^d$. It is rigid if every continuous motion of the vertices which preserves the lengths of the edges is induced by an…
We investigate the dynamics of a first order transition when the order parameter field undergoes resonant oscillations, driven by a periodically varying parameter of the free energy. This parameter could be a background oscillating field as…
We find an order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
We consider the space of $C^1$-diffeomorphims equipped with the $C^1$-topology on a three dimensional closed manifold. It is known that there are open sets in which $C^1$-generic diffeomorphisms display uncountably many chain recurrences…
We discuss the phenomenology of phase transitions studied with two control variables. Such measurements have become routine with magnetic field and temperature being varied for 1st order magnetic transitions with an ease not conceivable…
Dense active matter, in the fluid or amorphous-solid form, has generated intense interest as a model for the dynamics inside living cells and multicellular systems. An extension of the random first-order transition theory (RFOT) to include…