High order approximations of the eigenvalues of sturm-liouville problems with coupled self-adjoint boundary conditions

Sampling theory has been used to compute with great accuracy the eigenvalues of regular and singular Sturm-Liouville problems of Bessel Type. We shall consider in this paper the case of general coupled real or complex self-adjoint boundary conditions. We shall present few examples to illustrate the power of the method and compare our results with the ones obtained using the well-known Sleign2 package.     

Oscillation quenching mechanisms: Amplitude vs. oscillation death

Oscillation quenching constitutes a fundamental emergent phenomenon in systems of coupled nonlinear oscillators. Its importance for various natural and man-made systems, ranging from climate, lasers, chemistry and a wide range of biological oscillators can be projected from two main aspects: (i) suppression of oscillations as a regulator of certain pathological cases and (ii) a general control mechanism for technical systems. We distinguish two structurally distinct oscillation quenching types: oscillation   (OD$OD$) and amplitude death   (AD$AD$) phenomena. In this review we aim to set clear boundaries between these two very different oscillation quenching manifestations and demonstrate the importance for their correct identification from the aspect of theory as well as of applications. Moreover, we pay special attention to the physiological interpretation of OD$OD$ and AD$AD$ in a large class of biological systems, further underlying their different properties. Several open issues and challenges that await further resolving are also highlighted.     

Understanding root cause of stick–slip vibrations in deep drilling with drag bits

In search for the root cause of stick–slip, a mode of torsional vibrations of a drilling assembly, a linear stability analysis of coupled axial–torsional vibrations has been carried out. It has been shown that in a rotary drilling system with axial and torsional degree of freedom two distinct modes of self-excited vibrations are present: axial and torsional. These axial (torsional) modes of vibrations are due to resonance between the cutting forces acting at the bit and the axial (torsional) natural modes of drillstring vibrations. It has been demonstrated that although axial and torsional modes of vibrations do affect each other the underlying mechanisms driving these modes of vibrations are completely different. In particular, the only driving mechanism of the axial vibrations is the regenerative effect, while there are two distinct mechanisms that drive the torsional vibrations: (i) the cutting action of the bit, and (ii) the wearflat/rock interaction. Moreover, in the case of the torsional vibrations the regenerative effect plays only a secondary role. The results of the present study indicate that the axial compliance can play a stabilizing role. In particular, the stabilizing role of the axial compliance increases as the ratio of the torsional to the axial natural frequency of the drillstring vibrations decreases.     

Synchronous states of slowly rotating pendula

Coupled systems that contain rotating elements are typical in physical, biological and engineering applications and for years have been the subject of intensive studies. One problem of scientific interest, which among others occurs in such systems is the phenomenon of synchronization of different rotating parts. Despite different initial conditions, after a sufficiently long transient, the rotating parts move in the same way — complete synchronization, or a permanent constant shift is established between their displacements, i.e., the angles of rotation — phase synchronization. Synchronization occurs due to dependence of the periods of rotating elements motion and the displacement of the base on which these elements are mounted.     

A one-way coupled chaotic map lattice based self-synchronizing stream cipher

Self-synchronizing stream cipher (SSSC) has the advantage that the receiver can automatically synchronize with the sender after receiving previously transmitted ciphertext. However, it has also serious difficulty to keep security due to its self-synchronizing structure. In this paper, a new SSSC based on one-way coupled chaotic map lattice is proposed. By combining floating-point chaotic computations with algebraic operations, the cipher has high bit confusion and diffusion rates. It has both advantages of robustness of synchronization and strong security. The cipher can serve as a new type of SSSC candidate in software implementation.     

THE NONLINEAR SCHRÖDINGER EQUATION FOR THE DELTA-COMB POTENTIAL: QUASI-CLASSICAL CHAOS AND BIFURCATIONS OF PERIODIC STATIONARY SOLUTIONS

The nonlinear Schrödinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schrödinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation to new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.     

Existence and concentration of ground states of coupled nonlinear Schrödinger equations

In this paper we consider the existence and concentration of ground states of coupled nonlinear Schrödinger equations with trap potentials. When the interaction between two states is repulsive, we prove the existence of ground states. Then concentration phenomenon of these ground states is studied as the small perturbed parameter (Planck constant) approaches zero. Roughly speaking, we prove that components of the ground states concentrate at the unique global minimum points of their potentials. Moreover, we prove the existence of ground states when the interaction is attractive.     

Exact Nonstationary Solutions of a Two-Component Bose-Einstein Condensate

We investigate the exact nonstationary solutions of a two-component Bose Einstein condensate which compose of two species having different atomic masses. We also consider the interesting behavior of the atomic velocity and the flow density. It is shown that the motion of the two components can be controlled by the experimental parameters.     

The off-axis pyroelectric effect observed for lithium tetraborate

We find a pyroelectric current along the 〈110〉 direction of stoichiometric Li₂B₄O₇ so that the pyroelectric coefficient is nonzero but roughly 10⁻³ smaller than along the 〈001〉 direction of spontaneous polarization. Abrupt decreases in the pyroelectric coefficient along the 〈110〉 direction can be correlated with anomalies in the elastic stiffness contributing to concept that the pyroelectric coefficient is not simply a vector but has qualities of a tensor, as expected. The time dependent surface photovoltaic charging suggests that an inverse piezoelectric effect occurs at the (110) surface but not the (100) surface. Both effects along the 〈110〉 direction or at the (110) surface are distinct the conventional as a bulk pyroelectric effect.     

Spin squeezing in a bimodal condensate: spatial dynamics and particle losses

We propose an analytical method to study the entangled spatial and spin dynamics of interacting bimodal Bose-Einstein condensates. We show that at particular times during the evolution spatial and spin dynamics disentangle and the spin squeezing can be predicted by a simple two-mode model. We calculate the maximum spin squeezing achievable in experimentally relevant situations with Sodium or Rubidium bimodal condensates, including the effect of the dynamics and of one, two and three-body losses.