Self-filtering unstable resonator: An approximate analytical model with comparison to computed and XeCl laser experimental results

Approximate analytical solutions for the lowest-order transverse mode of empty self-filtering unstable resonator have been deduced for magnification M 》 1, and compared with some experimental measurements on an X-ray preionized XeCl discharge laser.     

Stratonovich model driven by dichotomous noise: analytical results

Stationary and dynamic properties of the Stratonovich model driven by a dichotomous Markovian process (DMP) are investigated analytically. The stationary probability densityp _st and its moments are calculated exactly and the shape ofp _st is discussed in the whole parameter region. The location of the maxima ofp _st shows a behaviour similar to order parameters in continuous phase transitions. The time dependence of moments and the probability density is studied investigating (i) a series expansion of the formal solution for a given realization of the driving process, and (ii) the analytic behaviour of the Laplace transform of the probability density. As a function of physical parameters, qualitative changes of the long time behaviour may occur. Method (i) is generalized to determine the dynamics of moments for a superposition of independent DMP's (pregaussian noise).     

Search for low-mass exotic mesonic structures. I. Experimental results

Recently, several papers have discussed the existence of a new low-mass structure at a mass close to M = 214.3 MeV. It was suggested that the Σ⁺ disintegration Σ⁺ → pP ⁰, P ⁰ → μ⁻μ⁺ proceeds through an intermediate particle P ⁰ having such a mass. The present work intends to look at the other new or available data, in order to observe the eventual existence of small narrow peaks or shoulders in very low mesonic masses. Indeed, narrow structures were already extracted from various data in dibaryons, baryons, and mesons (at larger masses than those studied here). The text was submitted by the authors in English.     

The Hubbard model on a complete graph: exact analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.     

A model of modulated diffusion. I. Analytical results

We introduce an integrable isochronous system and perturb its frequency by an external-deterministic or purely random-noise. Under the perturbation the action variable evolves in time: the corresponding diffusion coefficient is exactly computed and its dependence on the magnitude of the perturbation is carefully investigated. Different behaviors are found and justified: the quasilinear approximation, the superlinear regime, and the ballistic motion.     

The Hubbard model on a complete graph: exact analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.     

Effective-mass approaches for one-dimensional quantum well structures. Comparison with multi-band results

Exactk-space equations are employed to calculate the energy levels and envelope functions of several one-dimensional quantum well structures having both step and graded-potential profile. We consider finite as well as infinite structures and compare the results obtained with those given by standard effective-mass methods.     

The propagation of the crowdion. One-dimensional model

With a method based on the harmonic analysis of the configuration of the defect, and using the empirical phonon dispersion relation, we prove that a typical one-dimensional crowdion is unstable and that it suffers a severe distortion while it diffuses.     

Dispersion of interface waves in sediments with power-law shear speed profiles. I. Exact and approximate analytical results.

In the upper tens of meters of ocean bottom, unconsolidated marine sediments consisting of clay, silt, or fine sand with high porosity are "almost incompressible" in the sense that the shear wave velocity is much smaller than the compressional wave velocity. The shear velocity has very large gradients close to the ocean floor leading to strong coupling of compressional and shear waves in such "soft" sediments. The weak compressibility opens an avenue for developing a theory of elastic wave propagation in continuously stratified soft sediments that fully accounts for the coupling. Elastic waves in soft sediments consist of "fast" waves propagating with velocities close to the compressional velocity and "slow" waves propagating with velocities on the order of the shear velocity. For the slow waves, the theory predicts the existence of surface waves at the ocean-sediment boundary. In the important special case of the power-law depth-dependence of shear rigidity, phase and group velocities of the interface waves are shown to scale as a certain power of frequency. An explicit, exact solution was obtained for the surface waves in sediments characterized by constant density and a linear increase of shear rigidity with depth, that is, for the case of shear speed proportional to the square root of the depth below the sediment-water interface. Asymptotic and perturbation techniques were used to extend the result to more general environments. Theoretical dispersion relations agreed well with numerical simulations and available experimental data and, as demonstrated in a companion paper [D. M. F. Chapman and O. A. Godin, J. Acoust. Soc. Am 110, 1908 (2001)] led to a simple and robust inversion of interface wave travel times for shear velocity profiles in the sediment.     

The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states

We present a rigorous study of the classical ground-states under boundary conditions of a class of one-dimensional models generalizing the discrete Frenkel-Kontorova model. The extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic, quasi-periodic and chaotic orbits. For all boundary conditions, we select among all the extremum solutions of the energy of the model, those which correspond to the ground-states of the infinite system. We prove that these ground-states are either periodic (commensurate) or quasi-periodic (incommensurate) but are never chaotic. We also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions. The topological structure of the whole set of ground-states is described in details. In addition to physical applications, consequences for twist map homeomorphisms are mentioned. Part II (S. Aubry, P.Y. LeDaeron and G. Andre) will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map.     

Metastability of commensurate and incommensurate structures in epitaxial films

Limits of stability for the range of metastable phases in two-dimensional epitaxial monolayers are calculated. The mean misfit between the monolayer and the substrate changes by addition or removal of solitons (or misfit dislocations) and metastability arises from the energy barrier for these processes. The behaviour is similar to that of a one-dimensional modulated chain of atoms with free ends.     

Comparison of analytical and numerical analysis of the reference region model for DCE-MRI

This study compared three methods for analyzing DCE-MRI data with a reference region (RR) model: a linear least-square fitting with numerical analysis (LLSQ-N), a nonlinear least-square fitting with numerical analysis (NLSQ-N), and an analytical analysis (NLSQ-A). The accuracy and precision of estimating the pharmacokinetic parameter ratios K_R and V_R, where K_R is defined as a ratio between the two volume transfer constants, K^trans,TOI and K^trans,RR, and V_R is the ratio between the two extracellular extravascular volumes, v_e,TOI and v_e,RR, were assessed using simulations under various signal-to-noise ratios (SNRs) and temporal resolutions (4, 6, 30, and 60 s). When no noise was added, the simulations showed that the mean percent error (MPE) for the estimated K_R and V_R using the LLSQ-N and NLSQ-N methods ranged from 1.2% to 31.6% with various temporal resolutions while the NLSQ-A method maintained a very high accuracy (< 1.0×10^− 4 %) regardless of the temporal resolution. The simulation also indicated that the LLSQ-N and NLSQ-N methods appear to underestimate the parameter ratios more than the NLSQ-A method. In addition, seven in vivo DCE-MRI datasets from spontaneously occurring canine brain tumors were analyzed with each method. Results for the in vivo study showed that K_R (ranging from 0.63 to 3.11) and V_R (ranging from 2.82 to 19.16) for the NLSQ-A method were both higher than results for the other two methods (K_R ranging from 0.01 to 1.29 and V_R ranging from 1.48 to 19.59). A temporal downsampling experiment showed that the averaged percent error for the NLSQ-A method (8.45%) was lower than the other two methods (22.97% for LLSQ-N and 65.02% for NLSQ-N) for K_R, and the averaged percent error for the NLSQ-A method (6.33%) was lower than the other two methods (6.57% for LLSQ-N and 13.66% for NLSQ-N) for V_R. Using simulations, we showed that the NLSQ-A method can estimate the ratios of pharmacokinetic parameters more accurately and precisely than the NLSQ-N and LLSQ-N methods over various SNRs and temporal resolutions. All simulations were validated with in vivo DCE MRI data.