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The high volatility of renewable energies calls for more energy efficiency. Thus, different physical systems need to be coupled efficiently although they run on various time scales. Here, the port-Hamiltonian (pH) modeling framework comes…
This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile which is divided by…
We investigate the dynamics of polar systems coupled to classical external beams in the ultrastrong coupling regime. The permanent dipole moments (PDMs) sustained by polar systems can couple to the electromagnetic field, giving rise to a…
We study a tripartite system of coupled spins, where a first set of one or two spins is our central system which is coupled to another set considered, the near environment, in turn coupled to the third set, the far environment. The dynamics…
Ocean dynamics are often sidelined in exoplanet climate studies due to the high computational cost of fully coupled atmosphere-ocean general circulation models (GCMs). However, ocean heat transport (OHT) can play a critical role in shaping…
Phase effect on the modal interaction of flow instabilities is investigated for laminar-to-turbulent transition in a flat-plate boundary layer flow. Primary and secondary instabilities are numerically studied with 2D Tollmien-Schlichting…
In this paper, we leverage Koopman mode decomposition to analyze the nonlinear and high-dimensional climate systems acting on the observed data space. The dynamics of atmospheric systems are assumed to be equation-free, with the linear…
Clouds are important components of the atmosphere. Since it is usually not possible to treat them as ensembles of huge numbers of particles, parameterizations on the basis of averaged quantities (mass and/or number concentration) must be…
High-multiplicity Kepler systems (referred to as Kepler multis) are often tightly packed and may be on the verge of instability. Many systems of this type could have experienced past instabilities, where the compact orbits and often low…
In this study, we consider a linearized compressible flow structure interaction PDE model for which the interaction interface is under the effect of material derivative term. While the linearization takes place around a constant pressure…
Sea ice plays a crucial role in the climate system, particularly in the Marginal Ice Zone (MIZ), a transitional area consisting of fragmented ice between the open ocean and consolidated pack ice. As the MIZ expands, understanding its…
By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a…
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the…
Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear waves-settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to…
Understanding sustainability through modeling involves one of the complex and interdisciplinary activities where mathematics plays a key role. We provide arguments favoring the need for developing global models for measuring the status of…
The Ghil-Sellers energy balance model of Earth's climate, features -- for a considerable range of the solar intensity -- two stable climate states (a warm and a cold snowball Earth), where the bistability results from the celebrated…
We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…
Using molecular dynamics simulations we study the slow dynamics of a hard sphere fluid confined in a disordered porous matrix. The presence of both discontinuous and continuous glass transitions as well as the complex interplay between…
We show that imposition of non-periodic, in place of periodic, boundary conditions (BC) can alter stability of modes in the Method of characteristics (MoC) employing certain ordinary-differential equation (ODE) numerical solvers. Thus,…
How do landscape fragmentation affects ecosystems diversity and stability is an important and complex question in ecology with no simple answer, as spatially separated habitats where species live are highly dynamic rather than just static.…