A simple globular-shaped liquid ~octamethylcyclotetrasiloxane, OMCTS! was placed between two rigid mica plates at variable spacings comparable to the size of this molecule and the linear shear viscoelasticity of the confined interfacial film was measured. Strong monotonic increase of the shear relaxation time, elastic modulus, and effective viscosity were observed as the spacing was decreased b...

In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields: L = ∑m i=1X 2 i + ∆ in Rn, where ∆ is the Laplace operator, m < n, and the limit operator L = ∑m i=1X 2 i is hypoelliptic. Here we establish Schauder’s estimates, uniform with respect to the parameter , of solution of the approximated equation L u = f , using a modification of the lift...

In this paper, we present a weighted ENO (essentially non-oscillatory) scheme to approximate the viscosity solution of the Hamilton-Jacobi equation: = 0: This weighted ENO scheme is constructed upon and has the same stencil nodes as the 3 rd order ENO scheme but can be as high as 5 th order accurate in the smooth part of the solution. In addition to the accuracy improvement, numerical compariso...

Viscosity and enthalpy relaxation from the amorphous state into the supercooled liquid state was investigated in the bulk metallic glass forming Zr46.75Ti8.25Cu7.5Ni10Be27.5 alloy below the calorimetric glass transition. At different temperatures, the viscosities relax into states that obey the same Vogel–Fulcher–Tammann relation as the data obtained at higher temperatures in the supercooled li...

Consider the hyperbolic system of conservation laws u t + F(u) x = 0. Let u be the unique viscosity solution with initial condition u(0; x) = u(x), and let u " be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes x, t = O((x). With a suitable choice of the sampling sequence, we prove the estimate u " (t;) ? u(t;) L 1 = o(1) p x ln((x) :

We revisit the idea that density-wave wakes of planets drive accretion in protostel-lar disks. The effects of many small planets can be represented as a viscosity if the wakes damp locally, but the viscosity is proportional to the damping length. Damping occurs mainly by shocks even for earth-mass planets. The excitation of the wake follows from standard linear theory including the torque cutof...

We consider a situation where dislocations are parallel lines moving in a single plane. For this simple geometry, dislocations dynamics is modeled by a one-dimensional non-local transport equation. We prove a result of existence and uniqueness for all time of the continuous viscosity solution for this equation. A finite difference scheme is proposed to approximate the continuous viscosity solut...

Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

Following the framework of Çetin, Jarrow and Protter [4] we study the problem of super-replication in presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized Black-Scholes economy. We find that the minimal super-replication price is different from the one suggested by the Black-Scholes formula and is the unique viscosity solution of the ...

The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the viscosity approximation method with a sequence of contractions is convergent whenever so is every iterative sequence generated by the Halpern type iterative method. Then, using our results, we show some convergence theorems for variational inequality problems, zero point problems, and fi...