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Numerical simulations of turbulent fluids are paramount to real-life applications, from predicting and modeling flows to diagnostic purposes in engineering. However, they are also computationally challenging due to their intrinsically…
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
Amplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analyzing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations.…
We consider a perturbative approach to the Vlasov-Poisson system for cosmic structure formation that does not rely on any truncation of the momentum-cumulant hierarchy. The generally non-trivial linear solution is computed by solving a…
We develop an analytical theory to explain the experimentally-observed morphological transitions of giant vesicles induced by AC electric fields (1). The model treats the inner and suspending media as lossy dielectrics, while the membrane…
We develop a covariant formalism to study nonlinear perturbations of dissipative and interacting relativistic fluids. We derive nonlinear evolution equations for various covectors defined as linear combinations of the spatial gradients of…
In applied mathematics generally and fluid dynamics in particular, the role of complex variable methods is normally confined to two-dimensional motion and the association of points with complex numbers via the assignment w = x+i y. In this…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The nonlinearity of the equation is assumed to have exponential growth or have critical growth in view of Trudinger-Moser type inequality. Under some…
Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behaviour. When subjected to external flows, dilute polymer solutions develop elastic turbulence - a unique chaotic flow…
This paper proposes a modeling structure for the relativistic constitutive equations of inelastic deformation in materials moving at high speeds. While the theory of relativity has successfully approximated material motion in space-time,…
We introduce the Compression-Directional Entropic Stress (CoDeS) method inspired by information geometric regularization. CoDeS replaces scalar multidimensional entropic pressure with a tensor stress aligned with the principal directions of…
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
We present a macro-scale description of quasi-periodically developed flow in channels, which relies on double volume-averaging. We show that quasi-developed macro-scale flow is characterized by velocity modes which decay exponentially in…
We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear…
An extended body orbiting a compact object undergoes tidal deformations by the background gravitational field. Tidal invariants built up with the Riemann tensor and their derivatives evaluated along the world line of the body are essential…
The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…
We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of nonnormal dynamical systems when they experience transient growth or respond to harmonic forcing. This approach reconciles the…