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The main objective of this and its accompanying articles is to derive a mathematical theory associated with the thermohaline circulations (THC). This article provides a general transition and stability theory for the Boussinesq system,…
Microscopic thermal machines promise to play an important role in future quantum technologies. Making such devices widely applicable will require effective strategies to channel their output into easily accessible storage systems like…
The possibility to derive an equation for the mean velocity field in turbulent flow by using classical statistical mechanics is investigated. An application of projection operator technique available in the literature is used for this…
We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and the neighbouring…
We derive the Hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an…
Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays…
A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is…
We formulate equations of time-dependent density functional theory (TDDFT) in the co-moving Lagrangian reference frame. The main advantage of the Lagrangian description of many-body dynamics is that in the co-moving frame the current…
We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…
We numerically study the effect of an active turbulent environment on a passive deformable droplet. The system is simulated using coupled hydrodynamic and nematodynamic equations for nematic liquid crystals with an active stress which is…
In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function $T$, which represents the…
An approach to non-adiabatic dynamics of atoms in molecular and condensed matter systems under general non-equilibrium conditions is proposed. In this method interaction between nuclei and electrons is considered explicitly up to the second…
Enskog-Vlasov equation is currently the most sophisticated kinetic model for describing non-equilibrium evaporative flows. While it enables more efficient simulations than the molecular dynamics (MD) methods, its accuracy in reproducing the…
Efficient molecular dynamics (MD) simulation is vital for understanding atomic-scale processes in materials science and biophysics. Traditional density functional theory (DFT) methods are computationally expensive, which limits the…
Two models involving particles moving by ``hopping'' in disordered media are investigated: I) A model glass-forming liquid is investigated by molecular dynamics under (pseudo-) equilibrium conditions. ``Standard'' results such as mean…
An atomic-orbital basis set framework is presented for carrying out velocity- gauge real-time time-dependent density functional theory (TDDFT) simulations in periodic systems employing range-separated hybrid functionals. Linear optical…
We show that all existing methods quantifying rotational motion in molecular fluids eventually fail in systems undergoing complex rotational motion characterised by slow, heterogeneous, or intermittent dynamics. This impacts in particular…
Thermal transport in classical fluids is analyzed in terms of a Higher-Order Generalized Hydrodynamics (or Mesoscopic Hydro-Thermodynamics), that is, depending on the evolution of the energy density and its fluxes of all orders. It is…