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We analyze blowup solutions in infinite time of the Neumann boundary value problem for the fully parabolic chemotaxis system with local sensing: \begin{equation*} \begin{cases} u_t = \Delta(e^{-v}u)\qquad &\mathrm{in}\ \Omega \times…
The existence and the properties of self-bound quark matter in the NJL model at zero temperature are investigated in mean-field approximation, focusing on inhomogeneous structures with one-dimensional spatial modulations. It is found that…
The paper should be viewed as complement of an earlier result in [8]. In the paper just mentioned it is shown that 1d case of a quasilinear parabolic-elliptic Keller-Segel system is very special. Namely, unlike in higher dimensions, there…
We report experiments on hard sphere colloidal glasses that reveal a type of shear banding hitherto unobserved in soft glasses. We present a scenario that relates this to an instability arising from shear-concentration coupling, a mechanism…
We study some attraction repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density, and for the chemosensitivities and the production rates of the chemoattractant and the chemorepellent.…
An infinite system of nonlocal, individually confining solitons is considered as a model of high-density nuclear matter. The soliton-lattice problem is discussed in the Wigner-Seitz approximation. The cell size is varied to study the…
We show that partial mass concentration can happen for stationary solutions of aggregation-diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial…
Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with…
We analytically show that mesonic bound states of confined monopoles appear inside a non-Abelian vortex-string in massless three-flavor QCD at large quark chemical potential mu. The orientational modes CP^2 in the internal space of a vortex…
Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been…
Dense suspensions of small strongly interacting particles are complex systems, which are rarely understood on the microscopic level. We investigate properties of dense suspensions and sediments of small spherical Al_2O_3 particles in a…
The focus of this paper is on solutions to a two-dimensional Keller-Segel system containing sub-logistic sources. We show that the presence of sub-logistic terms is adequate to prevent blow-up phenomena even in strongly degenerate…
In this paper we consider quasilinear Keller-Segel type systems of two kinds in higher dimensions. In the case of a nonlinear diffusion system we prove an optimal (with respect to possible nonlinear diffusions generating explosion in finite…
We report magnetotransport studies on a gated strained HgTe device. This material is a threedimensional topological insulator and exclusively shows surface state transport. Remarkably, the Landau level dispersion and the accuracy of the…
We study a singular limit of the classical parabolic-elliptic Patlak-Keller-Segel (PKS) model for chemotaxis with non linear diffusion. The main result is the $\Gamma$ convergence of the corresponding energy functional toward the perimeter…
We consider the Keller-Segel system of consumption type coupled with an incompressible fluid equation. The system describes the dynamics of oxygen and bacteria densities evolving within a fluid. We establish local well-posedness of the…
This paper is concerned with the density-suppressed motility model: $u_{t}=\Delta (\displaystyle\frac{u^m}{v^\alpha}) +\beta uf(w), v_{t}=D\Delta v-v+u, w_{t}=\Delta w-uf(w)$ in a smoothly bounded convex domain $\Omega\subset…
Chemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of fluid advection can arrest the singularity formation given…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…
We study radial solutions in a ball of $\mathbb{R}^N$ of a semilinear, parabolic-elliptic Patlak-Keller-Segel system with a nonlinear sensitivity involving a critical power. For $N = 2$, the latter reduces to the classical linear model,…