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We consider the linear stability of Hill's vortex with respect to axisymmetric perturbations. Given that Hill's vortex is a solution of a free-boundary problem, this stability analysis is performed by applying methods of shape…
Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…
We address the question of existence of nonconstant stable stationary solution to the heat equation on a class of convex domains subject to nonlinear boundary flux involving a positive parameter. Such solutions which were known to exist in…
We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a…
We study a problem involving thermosolutal convection in a fluid when the solute concentration is subject to a chemical reaction in which the solubility of the dissolved component is a function of temperature. When the spatial domain is a…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of…
Thermodynamic stable interaction pair potentials which are not of the form ``positive function + real continuous function of positive type'' are presented in dimension one. Construction of such a potential in dimension two is sketched.…
We consider the interior Stefan problem under radial symmetry in two dimension. A water ball surrounded by ice undergoes melting or freezing. We construct a discrete family of global-in-time solutions, both melting and freezing scenarios.…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for…
We study the dynamics of small perturbations to the rest state of a viscoelastic rate type fluid with temperature dependent material parameters. We show that if the material parameters are chosen appropriately, then the quiescent state of…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations in the absence of exact rotational invariance in the…
We determine the smallest instantaneous increase in the strength of an opposing wind that is necessary to permanently reverse the forward displacement flow that is driven by a two-layer thermal stratification. With an interpretation in…
The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the…
The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed…