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This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
In this paper, we present an efficient energy stable scheme to solve a phase field model incorporating contact line condition. Instead of the usually used Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field model…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results…
Structural transformations at interfaces are of profound fundamental interest as complex examples of phase transitions in low-dimensional systems. Despite decades of extensive research, no compelling evidence exists for structural…
Given a $generic$ two-dimensional conformal field theory (CFT), we propose an analytically solvable setup to study the Floquet dynamics of the CFT, i.e., the dynamics of a CFT subject to a periodic driving. A complete phase diagram in the…
A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the model. We show…
Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use…
In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved when using an energetic variational framework to derive the…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
Within this work, we develop a phase-field description for simulating fractures in incompressible materials. Standard formulations are subject to volume-locking when the solid is (nearly) incompressible. We propose an approach that builds…
We propose tabular two-dimensional correlation analysis for extracting features from multifaceted characterization data, essential for understanding material properties. This method visualizes similarities and phase lags in structural…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
We present a novel phase-field approach for investigating solute segregation in a moving grain boundary. In our model, the correct choice of various parameters can control the solute-grain boundary interaction potential, resulting in…
We study the sharp interface limit and well-posedness of a phase field model for self-climb of prismatic dislocation loops in periodic settings. The model is set up in a Cahn-Hilliard/Allen-Cahn framework featured with degenerate…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
The phase structure of QCD remains an open fundamental problem of standard model physics. In particular at finite density, our knowledge is limited. Yet, numerous model studies point towards a rich and complex phase diagram at large…
Phase-field models have been widely used to investigate the phase transformation phenomena. However, it is difficult to solve the problems numerically due to their strong nonlinearities and higher-order terms. This work is devoted to…
This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model…