On the vacuum stability in the σ model

It is shown that with certain relations between coupling constants, the state with spontaneous symmetry breaking in the σ model is unstable, and an extremely strong dynamical symmetry breaking takes place.     

Small Deviations of Stable Processes via Metric Entropy

Let X=(X(t)) _tT be a symmetric -stable, 0<<2, process with paths in the dual E ^* of a certain Banach space E. Then there exists a (bounded, linear) operator u from E into some L (S,) generating X in a canonical way. The aim of this paper is to compare the degree of compactness of u with the small deviation (ball) behavior of as 0. In particular, we prove that a lower bound for the metric entropy of u implies a lower bound for () under an additional assumption on E. As applications we obtain upper small deviation estimates for weighted -stable Levy motions, linear fractional -stable motions and d-dimensional -stable sheets. Our results rest upon an integral representation of L -valued operators as well as on small deviation results for Gaussian processes due to Kuelbs and Li and to the authors.     

Velocity and velocity-difference distributions in Burgers turbulence

We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions and confirm the results with high-resolution numerical simulations.     

Spectral broadening of 40-fs Ti:sapphire laser pulses in photonic-molecule modes of a cobweb-microstructure fiber

Photonic-molecule modes of a cobweb-microstructure fiber allow efficient nonlinear optical spectral broadening of nanojoule femtosecond light pulses. Spectral widths of approximately 200 nm are achieved at the output of a 6-cm sample of such a fiber for 40-fs Ti:sapphire laser pulses with an energy of a few nanojoules coupled into photonic-molecule modes. Higher values of the group index and a lower group-velocity dispersion, attainable with higher-order photonic-molecule modes, allow the efficiency of spectral broadening of femtosecond laser pulses to be increased relative to the efficiency of spectral broadening in the fundamental photonic-molecule mode. Received: 9 June 2002 / Revised version: 29 June 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +7-095/939-3959, E-mail: zheltikov@top.phys.msu.su     

Spectral broadening of femtosecond laser pulses in fibers with a photonic-crystal cladding

Changes in the spectra of femtosecond laser pulses propagating through fibers with a cladding having the structure of a two-dimensional photonic crystal are experimentally investigated. It is demonstrated that the waveguide properties of defect modes of photonic-crystal fibers provide an opportunity to considerably increase the efficiency of spectral broadening of short laser pulses as compared with conventional fibers.     

Einige neue qualitative Beobachtungen beim oszillatorischen Regime der Marangoni-Instabilität

Zusammenfassung Es wird experimentell nachgewiesen, daß das oszillatorische Regime der Marangoni-Instabilität a) mit den Gefäßbegrenzungen bzw. mit Hindernissen in eine reflexionsartige bzw. beugungsartige Wechselwirkung tritt und b) an der Phasengrenze flüssig-flüssig bei Stoffübergängen auftreten kann, die mit einer chemischen Reaktion an der Grenze verbunden sind.

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Some new qualitative observations in the oscillatory regime of the Marangoni instability

In an experimental investigation it is shown that the oscillatory regime of the Marangoni-instability a) is subject to a reflexiontype or diffractiontype interaction with container boundaries or obstacles, and b) can occur on the liquid-liquid interphase for mass transfer with chemical reaction in the interphase.

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Bezeichnungen Grenzflächenspannung - c Konzentration der diffundierenden Substanz - e ² Verhältnis der kinematischen Viskositäten der beiden Phasen - r ² Verhältnis der Diffusionskoeffizienten der diffundierenden Substanz in den beiden Phasen - V Volumen     

饱和土地基的非轴对称固结

固结问题是土力学的基础课题之一，现有的研究主要针对饱和土的平面固结和轴对称固结问题。本文应用Fourier展开、Laplace变换和Hankel变换求解了各向同性饱和土的Blot固结方程；讨论了半空间各向同性饱和土的非轴对称固结。借助数值计算，本文的方法可以用于分析各向同性饱和土的非轴对称固结问题。