27 research outputs found
The dressed nonrelativistic electron in a magnetic field
We consider a nonrelativistic electron interacting with a classical magnetic
field pointing along the -axis and with a quantized electromagnetic
field. When the interaction between the electron and photons is turned off, the
electronic system is assumed to have a ground state of finite multiplicity.
Because of the translation invariance along the -axis, we consider the
reduced Hamiltonian associated with the total momentum along the -axis
and, after introducing an ultraviolet cutoff and an infrared regularization, we
prove that the reduced Hamiltonian has a ground state if the coupling constant
and the total momentum along the -axis are sufficiently small. Finally
we determine the absolutely continuous spectrum of the reduced Hamiltonian.Comment: typos correction
Multi-site study of a new approach to farm work within the framework of organic vegetable production: permanent crop beds
The mineralization rate of a commercial organic fertiliser was evaluated over the course of three years in an organic rice field in the Camargue (France). The effect of different mounts of fertiliser applied at different periods was tested. The organic fertiliser rapidly mineralised under flooded conditions. On the basis of this result, we demonstrated that an adaptation of organic fertilisation practices, similar to those employed for mineral fertilisers, would result in the optimisation of organic fertilisers, leading to improved profitability
Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems
New formulas on the inverse problem for the continuous skew-self-adjoint
Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type
system the solution of a general type inverse spectral problem is also derived
in terms of the Weyl functions. The description of the Weyl functions on the
interval is given. Borg-Marchenko type uniqueness theorems are derived for both
discrete and continuous non-self-adjoint systems too
Characterization of the pressure fluctuations within a Controlled-Diffusion airfoil boundary layer at large Reynolds numbers
The present investigation targets the generation of airfoil trailing-edge broadband noise that arises from the interaction of turbulent boundary layer with the airfoil trailing edge. Large-eddy simulations, carried out using a massively parallel compressible solver CharLESX, are conducted for a Controlled-Diffusion (CD) airfoil with rounded trailing edge for seven configurations, characterized with a Reynolds number, angle of attack and Mach number. An analysis of the unsteady pressure signals in the boundary layer is proposed in regard to classical trailing edge noise modelling ingredients
Transfer of energy to high frequencies in the cubic defocusing nonlinear Schrodinger equation
We consider the cubic defocusing nonlinear Schrödinger equation on the two dimensional torus. We exhibit smooth solutions for which the support of the conserved energy moves to higher Fourier modes. This behavior is quantified by the growth of higher Sobolev norms: given any δ[much less-than]1,K [much greater-than] 1, s > 1, we construct smooth initial data u 0 with ||u0||Hs , so that the corresponding time evolution u satisfies u(T)Hs[greater than]K at some time T. This growth occurs despite the Hamiltonian’s bound on ||u(t)||H1 and despite the conservation of the quantity ||u(t)||L2.
The proof contains two arguments which may be of interest beyond the particular result described above. The first is a construction of the solution’s frequency support that simplifies the system of ODE’s describing each Fourier mode’s evolution. The second is a construction of solutions to these simpler systems of ODE’s which begin near one invariant manifold and ricochet from arbitrarily small neighborhoods of an arbitrarily large number of other invariant manifolds. The techniques used here are related to but are distinct from those traditionally used to prove Arnold Diffusion in perturbations of Hamiltonian systems
Interaction of the tight-binding I12-X86 lac repressor with non operator DNA: salt dependence of complex formation.
The interaction of the wild-type lac repressor and its tight binding double mutant I12-X86 with a non operator-210 base pair-DNA fragment has been investigated using the nitrocellulose filter binding assay. While the affinity of the double mutant for this non specific DNA is increased as compared to that of the wild-type repressor, the number of ions released from the vicinity of the DNA upon complex formation is less important for the mutant than for the wild-type. These results demonstrate that the adaptation in the recognition surface of the repressor recently proposed by Mossing et al (J. Mol. Biol., 1985, 186, 295-305) in the case of an Oc mutant may be a more general phenomenon
Le problème spectral inverse pour les systèmes AKNS périodiques sur la droite réelle
Long-Time Existence for Semi-linear Beam Equations on Irrational Tori
We consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order n- 1 with n≥ 3 and d≥ 2. If ε≪ 1 is the size of the initial datum, we prove that the lifespan Tε of solutions is O(ε-A(n-2)-) where A≡A(d,n)=1+3d-1 when n is even and A=1+3d-1+max(4-dd-1,0) when n is odd. For instance for d= 2 and n= 3 (quadratic nonlinearity) we obtain Tε=O(ε-6-), much better than O(ε- 1) , the time given by the local existence theory. The irrationality of the torus makes the set of differences between two eigenvalues of Δ2+1 accumulate to zero, facilitating the exchange between the high Fourier modes and complicating the control of the solutions over long times. Our result is obtained by combining a Birkhoff normal form step and a modified energy step