We study the influence of boundary conditions on the finite-size corrections of a one-dimensional (1D) quantum spin model by exact and perturbative theoretic calculations. We obtain two new infinite sets of universal amplitude ratios for the finite-size correction terms of the 1D quantum spin model of N sites with free and antiperiodic boundary conditions. The results for the lowest two orders ...

We consider a particle dragged through a medium at constant temperature as described by a Langevin equation with a time-dependent potential. The time dependence is specified by an external protocol. We give conditions on potential and protocol under which the fluctuations of the dissipative work satisfy an exact symmetry for all times. We also present counterexamples to that fluctuation theorem...

In this paper we study and derive explicit formulas for the linearized Navier–Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and bou...

Shattuck and Leahy [4] conjectured—and Abrams, Fishkind, and Priebe [1],[2] proved—that the boundary of a digital image is topologically equivalent to a sphere if and only if certain related foreground and background graphs are both trees. In this manuscript we extend this result by proving upper and lower bounds on digital image boundary genus in terms of the foreground and background graphs, ...

This paper treats the development and validation of a numerical method for the solution of the unsteady incompressible Navier-Stokes equations in two dimensions. The method of choice is a Godunov-type pressure-free correction method similar to the method developed by Lee and LeVeque. Validation is done by considering a two-dimensional boundary-layer flow along a flatplate. The resulting method ...

Correction for ‘Imaging the reactivity and width of graphene's boundary region’ by Huda S. AlSalem et al., Chem. Commun., 2020, 56, 9612–9615, DOI: 10.1039/D0CC02675A.

This paper mentions a method for the detection and correction of films damaged by tear. The method includes estimation of motion vectors between two frames in an image sequence, delineating the tear boundary and restoring the damaged frame using suitable missing data treatment. Thus loss of data along the tear boundary is also corrected. The paper also includes the comparison of performance of ...

Two-step nonparametric estimators have become standard in empirical auctions. A drawback concerns boundary effects which cause inconsistencies near the endpoints of the support and bias in finite samples. To cope, sample trimming is typically used which leads to non-random data loss. Monte Carlo experiments show this leads to poor performance near the support boundaries and on the interior due ...

We present in this paper a numerical scheme for incompressible Navier-Stokes equations with open and traction boundary conditions, in the framework of pressure-correction methods. A new way to enforce this type of boundary condition is proposed and provides higher pressure and velocity convergence rates in space and time than found in the present state of the art. We illustrate this result by c...