We discuss the calculation of semi-classical wormhole vertex operators from wave functions which satisfy the Wheeler-deWitt equation and momentum constraints, together with certain ‘wormhole boundary conditions’. We consider a massless minimally coupled scalar field, initially in the spherically symmetric ‘mini-superspace’ approximation, and then in the ‘midi-superspace’ approximation, where no...

We construct a Legendrian 2-torus in the 1-jet space of S × R (or of R) from a loop of Legendrian knots in the 1-jet space of R. The differential graded algebra (DGA) for the Legendrian contact homology of the torus is explicitly computed in terms of the DGA of the knot and the monodromy operator of the loop. The contact homology of the torus is shown to depend only on the chain homotopy type o...

We investigate energy amplification in parallel channel flows, where background noise is modeled as stochastic excitation of the linearized Navier–Stokes equations. We show analytically that the energy of three-dimensional streamwise-constant disturbances achieves O(R) amplification. Our basic technical tools are explicit analytical calculations of the traces of solutions of operator Lyapunov e...

In this work we estimate rates of the linear transient growth of the perturbations of cellular flames governed by the Sivashinsky equation. The possibility and significance of such a growth was indicated earlier in both computational and analytical investigations. Numerical investigation of the norm of the resolvent of the linear operator associated with the Sivashinsky equation linearized in a...

Abstract. This article provides sharp constructive upper and lower bound estimates for the Boltzmann collision operator with the full range of physical non cut-off collision kernels (γ > −n and s ∈ (0, 1)) in the trilinear L(R) energy 〈Q(g, f), f〉. These new estimates prove that, for a very general class of g(v), the global diffusive behavior (on f) in the energy space is that of the geometric ...

This paper deals with boundary value problems for nonlinear monotone potential operators. An analysis of the nonlinear (monotone potential) Sturm–Liouville operator Au := − ( k((u′)2)u′(x) )′+q(x)u(x), x ∈ (a, b) shows that the potential of this operator as well as the potential of related boundary value problems play an important role not only for solvability of these problems, but also for li...

In this paper, we compute exactly the average density of a harmonically confined Riesz gas $N$ particles for large in presence hard wall. gas, repel each other via pairwise interaction that behaves as $|x_i - x_j|^{-k}$ $k>-2$, with $x_i$ denoting position $i^{\rm th}$ particle. This can be classified into three different regimes $k$. For $k \geq 1$, where interactions are effectively short-ran...

We study the local exponential stabilization, near a given steady-state flow, of solutions of the Navier-Stokes equations in a bounded domain. The control is performed through a Dirichlet boundary condition. We apply a linear feedback controller, provided by a well-posed infinite dimensional Riccati equation. We give a characterization of the domain of the closed-loop operator which is obtained...

The infinite-dimensional mechanics of fluids and plasmas can be formulated as “noncanonical” Hamiltonian systems on a phase space of Eulerian variables. Singularities of the Poisson bracket operator produce singular Casimir elements that foliate the phase space, imposing topological constraints on the dynamics. Here we proffer a physical interpretation of Casimir elements as adiabatic invariant...

We show under general conditions that the linearized force-based quasicontinuum (QCF) operator has a positive spectrum, which is identical to the spectrum of the quasinonlocal quasicontinuum (QNL) operator in the case of second-neighbour interactions. Moreover, we establish a bound on the condition number of a matrix of eigenvectors that is uniform in the number of atoms and the size of the ato...