Traveling Waves in Elastic Rods with Arbitrary Curvature and Torsion

The dynamic Kirchhoff equations, describing a thin elastic rod of infinite length, are considered in connection with the study of the conformations of polymeric chains. A?novel special traveling wave solution that can be interpreted as a conformational soliton propagating at constant speed is obtained, featuring arbitrary non-constant curvature and torsion of the rod, in the simple case of constant cross-section, homogeneous density and elastic isotropy. This traveling wave corresponds to a specific constraint on the twist-to-bend ratio of the constant stiffness parameters, which in turn appears to be compatible with the experimental evidence for the mechanical properties of real polymeric chains. Due to such a constraint, the square of the velocity of the solitary wave is directly proportional to the bending stiffness and inversely proportional to the density and to the principal momentum of inertia of the rod. Several applications to the study of conformational changes in polymeric chains are given.     

Identifiability of the MAP 2/G/1 queueing system

In this paper, we study how the lack of a unique representation for the two-state Markovian arrival process (MAP ₂) can influence statistical estimation for the MAP ₂/G/1 queueing system. In particular, given two equivalent representations of the same MAP ₂, we find that the steady-state distributions of the queuing system can be identified.     

The Ginzburg-Landau parameter in the case of non-pure superconductors

The concept of the Ginzburg-Landau parameter, κ, and of its extension to the case of non-pure materials is discussed in the framework of the BCS formulation and of the boson formulation. The data derived from several experiments performed on different samples containing various concentrations of scalar impurities are analyzed. We find that the value of κ for pure Ta, Nb and V is 0.350, 0.778 and 0.802, respectively. The theoretical dependence of κ by the electron mean free path is compared with the experimental behavior.     

A G/M/1-queue with exponential retrial

Summary We consider a G/M/1 retrial model in which the delays between retrials are i.i.d. exponentially distributed random variables. We investigate the steady-state distribution of the embedded Markov chain at completion service epochs, the stationary distribution at anytime and the virtual waiting time.     

Zr(IV) and Hf(IV) β-diketonate complexes as precursors for the photochemical deposition of ZrO2 and HfO2 thin films

In this paper amorphous ZrO₂ and HfO₂ thin films were obtained by direct UV irradiation of Zr(IV) and Hf(IV) β-diketonate precursor complexes on Si(1 0 0) and fused silica substrates. The precursors, Zr(CH₃COCHCOCH₃)₄ and Hf(C₆H₅COCHCOCH₃)₄ were deposited as amorphous thin films by spin coating. The photochemistry of these films was monitored by FT-IR spectroscopy. The photolysis with 254 nm light led to the loss of the ligands from the coordination complexes, and the production of metallic oxides. The thin films products were characterized by X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). These analyses revealed that as-deposited films are amorphous and that the presence of carbon is thought to arise from the ligands. However, post-annealing of the photodeposited films favors the stoichiometric and optical properties of ZrO₂ and HfO₂ thin films.     

An Iterative Sparse-Group Lasso

In high-dimensional supervised learning problems, sparsity constraints in the solution often lead to better performance and interpretability of the results. For problems in which covariates are grouped and sparse structure are desired, both on group and within group levels, the sparse-group lasso (SGL) regularization method has proved to be very efficient. Under its simplest formulation, the solution provided by this method depends on two weight parameters that control the penalization on the coefficients. Selecting these weight parameters represents a major challenge. In most of the applications of the SGL, this problem is left aside, and the parameters are either fixed based on a prior information about the data, or chosen to minimize some error function in a grid of possible values. However, an appropriate choice of the parameters deserves more attention, considering that it plays a key role in the structure and interpretation of the solution. In this sense, we present a gradient-free coordinate descent algorithm that automatically selects the regularization parameters of the SGL. We focus on a more general formulation of this problem, which also includes individual penalizations for each group. The advantages of our approach are illustrated using both real and synthetic datasets. Supplementary materials for this article are available online.     

On the well-posedness of the Eckhaus equation

The Eckhaus equation, which is a nonlinear Schrödinger type equation that can be linearized to the free linear Schrödinger equation, is considered. A linearized analysis of the nonlinear problem indicates that the periodic boundary value problem is ill-posed. The exact solution also demonstrates the ill-posedness, even though the L² norm of the solution is a constant of the motion. The ill-posedness disappears on the infinite line with square integrable data, but the solitonic solutions, which are not square integrable, are seriously unstable.     

Weak equilibrium in a spatial model

Spatial models of two-player competition in spaces with more than one dimension almost never have pure-strategy Nash equilibria, and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to avoid the uniqueness of the equilibrium position. As a result, a “region of equilibrium” appears, which can be located by geometric methods. In this area, the players can move around in an “almost-equilibrium” situation and do not necessarily have to adopt the same position.     

A simple photochemical method to synthesize Ga2O3-Dy-M thin films and their evaluation as optical materials (where M=Cr or Co)

We report the photochemical method to synthesize Ga₂O₃-Dy³⁺-Co³⁺ and Ga₂O₃-Dy³⁺-Cr³⁺ thin films. X-ray photoelectron spectroscopy, X-ray diffraction and photoluminescence were used to characterize the products. These analyses revealed that as-deposited and annealed films are amorphous. The optical characterization of the films showed that these are highly transparent in the visible spectrum but decrease significantly with doped and co-doped films. Under the excitation of UV light (254 nm) the doped films (Ga₂O₃-Dy³⁺) show the characteristic emissions of Dy³⁺ at 500, 575, 594, 605 and 652 nm corresponding to ⁴F_9/2→⁶H_J ( J=15/2, 13/2 and 11/2) transitions but the emissions decrease with the co-doped films (Ga₂O₃-Dy³⁺-M³⁺, where M=Cr or Co); a possible emission mechanism and energy transfer have been proposed.