Selfadjoint and mm sectorial extensions of Sturm-Liouville operators

The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.Comment: accepted by IEOT, in IEOT 201

Adaptive high-order finite element solution of transient elastohydrodynamic lubrication problems

This article presents a new numerical method to solve transient line contact elastohydrodynamic lubrication (EHL) problems. A high-order discontinuous Galerkin (DG) finite element method is used for the spatial discretization, and the standard Crank-Nicolson method is employed to approximate the time derivative. An h-adaptivity method is used for grid adaptation with the time-stepping, and the penalty method is employed to handle the cavitation condition. The roughness model employed here is a simple indentation, which is located on the upper surface. Numerical results are presented comparing the DG method to standard finite difference (FD) techniques. It is shown that micro-EHL features are captured with far fewer degrees of freedom than when using low-order FD methods

The effect of injector-element scale on the mixing and combustion of nitrogen tetroxide-hydrazine propellants

Injector-element physical size effect on mixing and combustion of nitrogen tetroxide-hydrazine propellant

Wick's Theorem for non-symmetric normal ordered products and contractions

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special symmetry properties assumed in existing proofs of Wick's theorem. Despite this, we prove that Wick's theorem still holds in its usual form as long as the contraction is a c-number. Wick's theorem is thus shown to be much more general than existing derivations suggest, and we discuss possible simplifying applications of this result.Comment: 17 page

Steady shear flow thermodynamics based on a canonical distribution approach

A non-equilibrium steady state thermodynamics to describe shear flows is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian formalism of the classical mechanics. From this distribution we derive the Evans-Hanley shear flow thermodynamics, which is characterized by the first law of thermodynamics $dE = T dS - Q d\gamma$ relating infinitesimal changes in energy $E$, entropy $S$ and shear rate $\gamma$ with kinetic temperature $T$. Our central result is that the coefficient $Q$ is given by Helfand's moment for viscosity. This approach leads to thermodynamic stability conditions for shear flow, one of which is equivalent to the positivity of the correlation function of $Q$. We emphasize the role of the external work required to sustain the steady shear flow in this approach, and show theoretically that the ensemble average of its power $\dot{W}$ must be non-negative. A non-equilibrium entropy, increasing in time, is introduced, so that the amount of heat based on this entropy is equal to the average of $\dot{W}$. Numerical results from non-equilibrium molecular dynamics simulation of two-dimensional many-particle systems with soft-core interactions are presented which support our interpretation.Comment: 23 pages, 7 figure

Spontaneous Symmetry Breaking in a Non-Conserving Two-Species Driven Model

A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within mean-field approximation, and compared with Monte-Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to zero, an exact solution is obtained. We present and analyze a physical picture which serves to explain the different phases of the model

Symmetry breaking through a sequence of transitions in a driven diffusive system

In this work we study a two species driven diffusive system with open boundaries that exhibits spontaneous symmetry breaking in one dimension. In a symmetry broken state the currents of the two species are not equal, although the dynamics is symmetric. A mean field theory predicts a sequence of two transitions from a strongly symmetry broken state through an intermediate symmetry broken state to a symmetric state. However, a recent numerical study has questioned the existence of the intermediate state and instead suggested a single discontinuous transition. In this work we present an extensive numerical study that supports the existence of the intermediate phase but shows that this phase and the transition to the symmetric phase are qualitatively different from the mean-field predictions.Comment: 19 pages, 12 figure