This mostly expository paper shows how weak convergence methods provide simple, elegant proofs of (i) the stabilization of an inverted pendulum under fast vertical oscillations, (ii) the existence of particle traps induced by rapidly varying electric fields and (iii) the adiabatic invariance of ∫ Γ p dx for slowing varying planar Hamiltonian dynamics. Under an appropriate, but very restrictive,...

D X : A(X) = Sym (H0(X)⊕H2(X)) → C, where w ∈ H(X ;Z). As for the grading of A(X), the elements in H2(X) have degree 2 and the point x ∈ H0(X) has degree 4. Let d0 = −w 2 − 32 (1 + b ), so that for homogeneous z ∈ A(X), D X(z) is non-zero only if 1 2 deg z ≡ d0 (mod 4). Set ℘ = x−4 ∈ A(X) as in [12]. By definition, X is of simple type if the condition D X(℘z) = 0 is satisfied for any z ∈ A(X). ...

Granada oscillation code (GraCo) is a software constructed to compute adiabatic and non-adiabatic oscillation eigenfunctions and eigenvalues. The adiabatic version gives the standard numerical resolution, and also the Richardson extrapolation, different sets of eigenfunctions, different outer mechanical boundary conditions or different integration variables. The non-adiabatic version can includ...

This paper presents low-power characteristics of adiabatic complementary pass-transistor logic (ACPL) using four-phase AC power supply. Adiabatic CPL circuits consist of pure NMOS transistors, use CPL blocks for evaluation and bootstrapped NMOS switches to eliminate non-adiabatic loss of output loads. In this paper, combinational circuit (4-bit ripple carry adder) and sequential circuit (4-bit ...

We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adi...

The basic adiabatic theorems of classical and quantum mechanics are overviewed and an adiabatic theorem in quantum mechanics without a gap condition is described. 1 Classical Adiabatic Invariants Consider a (mathematical) pendulum whose period is slowly modulated, for example by shortening the length of the pendulum, fig 1, [1, 18]. Figure 1: An adiabatic pendulum The Hamiltonian describing the...

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We investigate the interaction of ocean vortex patches with boundaries via the elliptic moment model of Melander, Zabusky & Stysek [13], under which vortex patches are approximated as elliptic regions of uniform vorticity. The interaction with a straight boundary is shown to reduce to the problem of an ellipse in constant strain, as previously investigated by Kida [9]. Interactions with more co...

We construct Ionel-Parker’s proposed refinement of the standard relative Gromov-Witten invariants in terms of abelian covers of the symplectic divisor and discuss in what sense it gives rise to invariants. We use it to obtain some vanishing results for the standard relative GromovWitten invariants. In a separate paper, we describe to what extent this refinement sharpens the usual symplectic sum...

in this paper, free convection in an inclined stepped chamber has been studied. one wall of this enclosure is kept cold and the opposite wall equipped with constant heat source. the remaining walls are maintained adiabatic. there is one adiabatic step on the bottom wall. the aim of the present study is to forecast the effect of raleigh number, slope of enclosure, step dimension, and heat source...