Related papers: Dynamic Landau Theory for Supramolecular Self-Asse…
We present a new simulation scheme which allows an efficient sampling of reconfigurable supramolecular structures made of polymeric constructs functionalized by reactive binding sites. The algorithm is based on the configurational bias…
We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…
Superposition of sigmoid function over a finite time interval is shown to be equivalent to the linear combination of the solutions of a linearly parameterized system of logistic differential equations. Due to the linearity with respect to…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and…
We consider the self-assembly of composite structures from a group of nanocomponents, each consisting of particles within an $N$-atom system. Self-assembly pathways and rates for nanocomposites are derived via a multiscale analysis of the…
A Landau theory is constructed for the vulcanization transition in cross-linked polymer systems with spontaneous nematic ordering. The neo-classical theory of the elasticity of nematic elastomers is derived via the minimization of this…
We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based…
The kinetics of ordering and concurrent ordering and clustering is analyzed with an equation of motion initially developed to account for dissipative processes in quantum systems. A simplified energy eigenstructure, or…
We present an improved analysis of the phase transitions in rare earth superconductor using Ginzburg-Landau theory. Our work is based on the systematic study of critical field and superconducting order parameter in the presence of localized…
In this work, the Ginzburg-Landau theory is represented on a symplectic manifold with a phase space content. The order parameter is defined by a quasi-probability amplitude, which gives rise to a quasi-probability distribution function,…
Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
A ring-kinetic theory for Vicsek-style models of self-propelled agents is derived from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular…
The thermodynamic model of ultrathin lubricant film melting, confined between two atomically-flat solid surfaces, is built using the Landau phase transition approach. Non-equilibrium entropy is introduced describing the part of thermal…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
We construct an effective field theory, a two-dimensional two-component metallic system described by a model with two Fermi surfaces ("pockets"). This model describes a translationally invariant metallic system with two types of fermions,…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
We propose a new approach for constructing synthetic pseudo-panel data from cross-sectional data. The pseudo panel and the preferences it intends to describe is constructed at the individual level and is not affected by aggregation bias…