Ratchet effect on a relativistic particle driven by external forces

We study the ratchet effect of a damped relativistic particle driven by both asymmetric temporal bi-harmonic and time-periodic piecewise constant forces. This system can be formally solved for any external force, providing the ratchet velocity as a non-linear functional of the driving force. This allows us to explicitly illustrate the functional Taylor expansion formalism recently proposed for this kind of systems. The Taylor expansion reveals particularly useful to obtain the shape of the current when the force is periodic, piecewise constant. We also illustrate the somewhat counterintuitive effect that introducing damping may induce a ratchet effect. When the force is symmetric under time-reversal and the system is undamped, under symmetry principles no ratchet effect is possible. In this situation increasing damping generates a ratchet current which, upon increasing the damping coefficient eventually reaches a maximum and decreases toward zero. We argue that this effect is not specific of this example and should appear in any ratchet system with tunable damping driven by a time-reversible external force.Comment: 1 figur

Symmetries shape the current in ratchets induced by a bi-harmonic force

Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force $f(t)=\epsilon_1\cos(q \omega t+\phi_1)+\epsilon_2\cos(p\omega t+\phi_2)$ does it for almost any choice of $\phi_{1}$ and $\phi_{2}$, provided $p$ and $q$ are two co-prime integers such that $p+q$ is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape $v\propto\epsilon_1^p\epsilon_2^q\cos(p \phi_{1} - q \phi_{2} + \theta_0)$ for small amplitudes, where $\theta_0$ depends on the damping ($\theta_0=\pi/2$ if there is no damping, and $\theta_0=0$ for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.Comment: 4 page

State space formulas for a solution of the suboptimal Nehari problem on the unit disc

We give state space formulas for a ("central") solution of the suboptimal Nehari problem for functions defined on the unit disc and taking values in the space of bounded operators in separable Hilbert spaces. Instead of assuming exponential stability, we assume a weaker stability concept (the combination of input-, output- and input-output stability), which allows us to solve the problem for general H-infinity functions

Berberine and Coptidis Rhizoma as novel antineoplastic agents: A review of traditional use and biomedical investigations

Ethnopharmacological relevance: Coptidis Rhizoma (Huanglian) and its major component, berberine, have drawn extensive attention toward their antineoplastic effects in the recent years. The antineoplastic effects are related to the Chinese Medicine (CM) properties of Huangliang in treating diseases by removing damp-heat and purging fire and counteracting toxicity. Aim of the review: To trace the long history of the traditional use of Huanglian from folk medicines, especially from Chinese medicine, to recent pharmacological studies of Huanglian and berberine, with an emphasis on their antineoplastic effects and the promise as novel antineoplastic agents. Methods: A total of seven databases were extensively searched for literature research. The terms and keywords for searching included Huanglian, berberine, Coptis, Coptidis Rhizoma, anticancer, anti-invasion, antimatastasis and mechanism. The papers including ours with studies on anticancer and mechanism, pharmacology and toxicology of Huanglian and/or berberine were focused. Results: In view of traditional use, the anticancer effects of Huanglian can be ascribed to its CM trait by removing damp-heat, fire and toxicity. From modern biomedical studies, anticancer effects have been demonstrated in both Huanglian and berberine. The underlying molecular mechanisms involve cell-cycle arrest, apoptosis induction and anti-inflammation. Berberine is an essential anticancer compound in Huanglian. In some studies, the use of Huanglian was shown to be more effective and beneficial than the use of berberine alone. The presence of other protoberberine-type alkaloids in Huanglian might give synergistic effects for the anticancer effects. Berberine also demonstrates effects of antiangiogenesis, anti-invasion and anti-metastasis in some cancer cell lines, however, more investigations are required to unravel the underlying mechanisms involved. Conclusions: The modern evidences of treating cancer with Huanglian and berberine have a strong linkage with traditional concept and rules of using Huanglian in CM practice. As anticancer candidates with low toxicity, berberine and its altered structure, as well as Huanglian and its formulae, will attract scientists to pursue the potential anticancer effects and the mechanisms by using technologies of genomics, proteomics and other advanced approaches. On the other hand, relatively few in vivo studies have been conducted on anticancer effects of Huanglian and berberine. The clinical application of berberine or Huanglian as novel cancer therapeutic agents requires in vivo validations and further investigations of their anticancer mechanisms. © 2009 Elsevier Ireland Ltd. All rights reserved.published_or_final_versio

Coprime factorization and robust stabilization for discrete-time infinite-dimensional systems

We solve the problem of robust stabilization with respect to right-coprime factor perturbations for irrational discrete-time transfer functions. The key condition is that the associated dynamical system and its dual should satisfy a finite-cost condition so that two optimal cost operators exist. We obtain explicit state space formulas for a robustly stabilizing controller in terms of these optimal cost operators and the generating operators of the realization. Along the way we also obtain state space formulas for Bezout factors

Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE's. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed)

BIBO stability of some classes of delay systems and fractional systems

A new test is presented for the BIBO stability of delay systems of neutral type with a single delay, specified in terms of their transfer functions, enabling us to decide on some cases that were previously open. Next, a class of fractional systems is considered, and a method is given for determining the stability intervals for such systems

Language support for immigrant children: a study of state schools in the UK and US

In recent decades, immigrants, refugees and asylum seekers have sought a new way of life in large numbers, often leaving their countries of origin behind in search of places that offer a better way of life. The purpose of this study was to investigate how elementary and middle school students in state schools in Reading, England (primarily speakers of Asian languages), and Richmond, Virginia (primarily speakers of Spanish), were supported academically, when most children’s first language was not English. The authors were interested in exploring whether or not there were cultural or structural differences in the way each country helped or hindered these students as they progressed through the school systems. Three UK schools in a district of approximately 100,000 and three US schools in a district of approximately 250,000 were the focus of this exploration from 2000 to 2003. Findings indicated that there were cultural and legislative differences and similarities. Teachers and administrators in both countries attempted to provide services with limited and sometimes diminishing resources. Community support varied based on resources, attitudes toward various ethnic groups, and the coping strategies adopted by these groups in their new environments. Marked differences appeared with regard to the manner in which assessments took place and how the results were made available to the public