Related papers: Energetic bounds on gyrokinetic instabilities. Par…
In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…
In this paper, we investigate the Rayleigh-Taylor instability problem for two compressible, immiscible, inviscid flows rotating with an constant angular velocity, and evolving with a free interface in the presence of a uniform gravitational…
This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the…
We consider the large polaron described by the Fr\"ohlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an…
In this paper, a parabolic type Kirchhoff equation and its stationary counterpart are considered. For the evolution problem, the precise decay rates of the weak solution and of the corresponding energy functional are derived. For the…
Solutions for a class of wave equations with effective potentials are obtained by a method of a Laplace-transform. Quasinormal modes appear naturally in the solutions only in a spatially truncated form; their coefficients are uniquely…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…
We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of…
We investigate the dynamics of an idealized model of microtubule growth that evolves by: (i) attachment of guanosine triphosphate (GTP) at rate lambda, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of…
We prove that for solutions of the Euler equation on the sphere, the vorticity gradient can grow at most double-exponentially in time, and we show that this upper bound is sharp by constructing explicit solutions with odd symmetry that…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the…
We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
The exact energy and angular-momentum conservation laws are derived by Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov-Maxwell equations. These gyrokinetic equations,…
Gyrokinetic simulations have greatly improved our theoretical understanding of turbulent transport in fusion devices. Most gyrokinetic models in use are delta-f simulations in which the slowly varying radial profiles of density and…
Energy theory for incompressible Newtonian fluids is, in many cases, capable of producing strong absolute stability criteria for steady flows. In those fluids the kinetic energy naturally defines a norm in which perturbations decay…
Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3-D instabilities, we propose a simple,…
Homo-energetic solutions to the spatially homogeneous Boltzmann equation have been extensively studied, but their global stability in the inhomogeneous setting remains challenging due to unbounded energy growth under self-similar scaling…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…