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Part I of this paper introduced the infinite dimensional Lagrange-Dirac theory for physical systems on the space of differential forms over a smooth manifold with boundary. This approach is particularly well-suited for systems involving…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this…
Intrinsically nonlinear coupled systems present different oscillating components that exchange energy among themselves. We present a new approach to deal with such energy exchanges and to investigate how it depends on the system control…
All ground states and low-lying excitations of a +/- I Ising spin glass model on a cubic 4 x 4 x 4 lattice with periodical boundary conditions were calculated using a method of combinatorical optimization. The structure of states in the…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
We found that the differential topology of the lattice-system of Ising model determines whether there can be the continuous phase transition, the geometric topology of the space the lattice-system is embedded in determines whether the…
Theories of self-organized active fluid surfaces have emerged as an important class of minimal models for the shape dynamics of biological membranes, cells and tissues. However, due to their inherent geometric nonlinearities and the absence…
The Landau-Brazovskii model provides a theoretical framework for describing various phases arising from competing short- and long-range interactions in many physical systems. In this work, we investigate phase transitions among various…
We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field…
This paper is Part I of a two-part series. We investigate bifurcation phenomena in Lagrangian systems with various boundary conditions and constraints, focusing on the interplay between Morse theory and the existence of multiple solutions…
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…
In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. Given that the saddle point matrix is indefinite, solving…
We study a particular return map for a class of low dimensional chaotic models called Kolmogorov Lorenz systems, which received an elegant general Hamiltonian description and includes also the famous Lorenz63 case, from the viewpoint of…
The ground state properties of spin-1/2 ladders are studied, emphasizing the role of frustration and ring exchange coupling. We present a unified field theory for ladders with general coupling constants and geometry. Rich phase diagrams can…
We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian…
Body-fitted arbitrary Lagrangian-Eulerian (ALE) methods provide a sharp representation of the fluid-structure interface but rely on mesh-update strategies that incrementally deform a reference configuration. To address this issue, we…
In this paper an information geometric approach has been proposed to describe the two-dimensional (2d) phase transition of the first order in a monomolecular layer (monolayer) of amphiphilic molecules deposited on air/water interface. The…
Reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction…