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We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the…
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds.…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
In this paper, we use the properties of the self-polar triangle to not only show a novel method for a basic point-line enumerative problem of conics, but also present a series of closed-form solutions to the conics from all minimal…
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are…
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…
A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try…
We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and…
We study a class of non-autonomous boundary control and observation linear systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by different fundamental partial differential equations, such as…
We consider linear arrays of cells of volume $V_\mathrm{c}$ populated by monodisperse rods of size $\sigma V_\mathrm{c}$, $\sigma=1,2,\ldots$, subject to hardcore exclusion interaction. Each rod experiences a position-dependent external…
A representation of partially spatially coherent and partially polarized stationary electromagnetic fields is given in terms of mutually uncorrelated, transversely shifted, fully coherent and polarized elementary electric-field modes. This…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via…
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary…
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
Many classical examples of models of self-organized dynamics, including the Cucker-Smale, Motsch-Tadmor, multi-species, and several others, include an alignment force that is based upon density-weighted averaging protocol. Those protocols…
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
Collective behavior occurs ubiquitously in nature and it plays a key role in bacterial colonies, mammalian cells or flocks of birds. Here, we examine the average density and velocity of self-propelled particles, which are described by a…