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L Friedland

Publications and source records attributed to L Friedland.

At least 19 recordsLinked to original sources

Emergence and control of multiphase nonlinear waves by synchronization.

Large amplitude multiphase solutions of the periodic Korteweg-de Vries equation are excited and controlled by a small forcing. The approach uses passage through an ensemble of resonances and subsequent multiphase self-locking of the system with eikonal-type perturbations. The synchronization of each phase in the Korteweg-de Vries wave is robust, provided the corresponding driving amplitude exceeds a threshold.

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Spatial control of a classical electron state in a Rydberg atom by adiabatic synchronization.

An adiabatic synchronization approach is used to control orbital eccentricity and inclination of a highly excited electron in a hydrogen atom. The approach is based on persisting nonlinear phase locking (autoresonance) between spatially uniform, chirped frequency oscillating electric field, and the classical Keplerian motion of the electron in the atom. Efficient control in three dimensions is achieved by slow passage through and capture into different resonances. Scenarios guaranteeing the capture and continuing synchronization in the system are outlined, all requiring the driving field amplitude to exceed a threshold. The threshold scales as A(3/4), where A is the sweep rate of the driving frequency at resonance. The adiabatic synchronization allows one to accelerate the electron gradually by using dipolar fields, until approaching the stochastic ionization limit.

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Resonant formation and control of 2D symmetric vortex waves.

It is shown that m-fold symmetric vortex waves in two dimensions ( V states) preserve their functional form in a weak straining flow having appropriate symmetry, but arbitrary time dependence. This phenomenon is used in driving the V states into a highly nonlinear excitation by subjecting a circular vortex patch to rotation and strain with oscillating strain rate and varying the rotation angular velocity. The effect is due to autoresonance in the system as the excited vortex state boundary self-adjusts its aspect ratio to synchronize with the external flow.

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Subharmonic autoresonance

Adiabatic passage through higher order resonances in a perturbatively driven dynamical system with a slow control parameter, yields persisting phase locking and a strong long time response. The phenomenon has a sharp threshold on the driving amplitude, which scales with the control parameter chirp rate A and resonance order n, as A(3/(4n)).

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Second harmonic autoresonant control of the l=1 diocotron mode in pure-electron plasmas

An oscillator whose frequency is amplitude dependent can be controlled by a drive whose frequency sweeps through a resonance with the oscillator's fundamental frequency. This phenomenon is called autoresonance, and has been previously investigated for drives with frequencies near the oscillator's fundamental or subharmonic frequencies. This paper examines autoresonance for drives at twice the fundamental frequency, i.e, second harmonic autoresonance. The l=1 diocotron mode in pure-electron plasmas, a very high Q nonlinear oscillator, is the focus of the paper. The theory for this oscillator is derived, and compared to experimental results. The results can be generalized to any Duffing-like driven nonlinear oscillator in which the coupling between the drive and the oscillator depends at least weakly on the oscillator amplitude.

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Characterization of single-nucleotide polymorphisms in coding regions of human genes.

A major goal in human genetics is to understand the role of common genetic variants in susceptibility to common diseases. This will require characterizing the nature of gene variation in human populations, assembling an extensive catalogue of single-nucleotide polymorphisms (SNPs) in candidate genes and performing association studies for particular diseases. At present, our knowledge of human gene variation remains rudimentary. Here we describe a systematic survey of SNPs in the coding regions of human genes. We identified SNPs in 106 genes relevant to cardiovascular disease, endocrinology and neuropsychiatry by screening an average of 114 independent alleles using 2 independent screening methods. To ensure high accuracy, all reported SNPs were confirmed by DNA sequencing. We identified 560 SNPs, including 392 coding-region SNPs (cSNPs) divided roughly equally between those causing synonymous and non-synonymous changes. We observed different rates of polymorphism among classes of sites within genes (non-coding, degenerate and non-degenerate) as well as between genes. The cSNPs most likely to influence disease, those that alter the amino acid sequence of the encoded protein, are found at a lower rate and with lower allele frequencies than silent substitutions. This likely reflects selection acting against deleterious alleles during human evolution. The lower allele frequency of missense cSNPs has implications for the compilation of a comprehensive catalogue, as well as for the subsequent application to disease association.

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Double autoresonance in two-dimensional dynamical systems.

The phenomenon of double autoresonance in dynamical systems with two degrees of freedom is examined. We analyze the motion of a particle in a two-dimensional centrally symmetric potential, subject to a homogeneous quasiperiodic external field of elliptical polarization. It is shown that if the particle has a sufficiently small initial energy, a double resonance is established when the slowly varying driving frequency approaches the linear resonance frequency. As the driving frequency is changed further, the double resonance is maintained, causing a continuous excitation of the oscillator. When nonlinearity becomes significant, the motion transforms into nearly circular oscillations. The necessary conditions for the persistence of the autoresonance are studied in detail.

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Passage through resonance and autoresonance in x(2n)-type potentials.

Resonant dynamics of a particle in an x(2n)-type potential driven by an oscillation with adiabatically varying frequency is investigated. It is shown that, under certain conditions, when the driving frequency increases in time and passes the resonance with the unperturbed system, the oscillator phase locks to the drive and, later, this phase locking is sustained, i.e., the system remains in autoresonance. The initial phase locking by passage through resonance is the main ingredient of the transition to autoresonance and comprises the generalization of previous results for nearly parabolic potentials.

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