Corner transport upwind lattice Boltzmann model for bubble cavitation

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann (LB) model that describes a two-dimensional ($2D$) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner transport upwind (CTU) numerical scheme on large square lattices (up to $6144 \times 6144$ nodes). The numerical viscosity and the regularization of the model are discussed for first and second order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows to recover the solution of the $2D$ Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient $D$ and the capillary number $Ca$ is found at small $Ca$ but with a different factor than in equilibrium liquids. A non-linear regime is observed for $Ca \gtrsim 0.2$.Comment: Accepted for publication in Phys. Rev.

Reputation and Accountability Relationships: Managing Accountability Expectations through Reputation

ArticleAccountability is said to be about the management of expectations. Empirical studies reveal considerable variation in organizational interest, intensity and investment in accountability relationships. Less is known, however, as to what explains these observed variations. Drawing on accountability and reputation-concerned literatures, this paper argues that a reputation-based perspective to accountability offers an underlying logic that explains how account-giving actors and account-holding forums actually manage these expectations, how organisations make sense of and prioritise among accountability responsibilities. Reputational considerations act as a filtering mechanism of external demands and help account for variations in degrees of interest in, and intensity of, accountability. The resulting accountability outcomes are co-produced by the reputational investment of both account-giver and account-holder, resulting in distinct accountability constellations and outcome

Velocity distribution function of spontaneously evaporating atoms

Numerical solutions of the Enskog-Vlasov (EV) equation are used to determine the velocity distribution function of atoms spontaneously evaporating into near-vacuum conditions. It is found that an accurate approximation is provided by a half-Maxwellian including a drift velocity combined with different characteristic temperatures for the velocity components normal and parallel to the liquid-vapor interface. The drift velocity and the temperature anisotropy reduce as the liquid bulk temperature decreases but persist for relatively low temperatures corresponding to a vapor behaviour which is only slightly non-ideal. Deviations from the undrifted isotropic half-Maxwellian are shown to be consequences of collisions in the liquid-vapor interface which preferentially backscatter atoms with lower normal-velocity component

Reputation and accountability relationships: managing accountability expectations through reputation

Accountability is said to be about the management of expectations. Empirical studies reveal considerable variation in organizational interest, intensity and investment in accountability relationships. Less is known, however, as to what explains these observed variations. Drawing on accountability and reputation-concerned literatures, this paper argues that a reputation-based perspective to accountability offers an underlying logic that explains how account-giving actors and account-holding forums actually manage these expectations, how organisations make sense of and prioritise among accountability responsibilities. Reputational considerations act as a filtering mechanism of external demands and help account for variations in degrees of interest in, and intensity of, accountability. The resulting accountability outcomes are co-produced by the reputational investment of both account-giver and account-holder, resulting in distinct accountability constellations and outcome

The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coeffcients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution

Modular symbols in Iwasawa theory

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous conjecture and result for $d = 2$ over $\mathbb{F}_q(t)$. In the third, we pose questions for general $d$ over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page

Global generalized solutions for Maxwell-alpha and Euler-alpha equations

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit