Billiards with polynomial mixing rates

While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. However, mathematical methods for the analysis of systems with slow mixing rates were developed just recently and are still difficult to apply to realistic models. Here we reduce those methods to a practical scheme that allows us to obtain a nearly optimal bound on mixing rates. We demonstrate how the method works by applying it to several classes of chaotic billiards with slow mixing as well as discuss a few examples where the method, in its present form, fails.Comment: 39pages, 11 figue

Circularly polarized modes in magnetized spin plasmas

The influence of the intrinsic spin of electrons on the propagation of circularly polarized waves in a magnetized plasma is considered. New eigenmodes are identified, one of which propagates below the electron cyclotron frequency, one above the spin-precession frequency, and another close to the spin-precession frequency.\ The latter corresponds to the spin modes in ferromagnets under certain conditions. In the nonrelativistic motion of electrons, the spin effects become noticeable even when the external magnetic field $B_{0}$ is below the quantum critical\ magnetic field strength, i.e., $B_{0}<$ $B_{Q} =4.4138\times10^{9}\, \mathrm{T}$ and the electron density satisfies $n_{0} \gg n_{c}\simeq10^{32}$m$^{-3}$. The importance of electron spin (paramagnetic) resonance (ESR) for plasma diagnostics is discussed.Comment: 10 page

Acute- and late-phase matrix metalloproteinase (MMP)-9 activity is comparable in female and male rats after peripheral nerve injury.

BACKGROUND:In the peripheral nerve, pro-inflammatory matrix metalloproteinase (MMP)-9 performs essential functions in the acute response to injury. Whether MMP-9 activity contributes to late-phase injury or whether MMP-9 expression or activity after nerve injury is sexually dimorphic remains unknown. METHODS:Patterns of MMP-9 expression, activity and excretion were assessed in a model of painful peripheral neuropathy, sciatic nerve chronic constriction injury (CCI), in female and male rats. Real-time Taqman RT-PCR for MMP-9 and its endogenous inhibitor, tissue inhibitor of metalloproteinase-1 (TIMP-1) of nerve samples over a 2-month time course of CCI was followed by gelatin zymography of crude nerve extracts and purified MMP-9 from the extracts using gelatin Sepharose-beads. MMP excretion was determined using protease activity assay of urine in female and male rats with CCI. RESULTS:The initial upsurge in nerve MMP-9 expression at day 1 post-CCI was superseded more than 100-fold at day 28 post-CCI. The high level of MMP-9 expression in late-phase nerve injury was accompanied by the reduction in TIMP-1 level. The absence of MMP-9 in the normal nerve and the presence of multiple MMP-9 species (the proenzyme, mature enzyme, homodimers, and heterodimers) was observed at day 1 and day 28 post-CCI. The MMP-9 proenzyme and mature enzyme species dominated in the early- and late-phase nerve injury, consistent with the high and low level of TIMP-1 expression, respectively. The elevated nerve MMP-9 levels corresponded to the elevated urinary MMP excretion post-CCI. All of these findings were comparable in female and male rodents. CONCLUSION:The present study offers the first evidence for the excessive, uninhibited proteolytic MMP-9 activity during late-phase painful peripheral neuropathy and suggests that the pattern of MMP-9 expression, activity, and excretion after peripheral nerve injury is universal in both sexes

Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering

In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear properties of this new dynamical system by numerically calculating its Lyapunov exponents. Based on a revised method for computing Lyapunov exponents, which employs periodic orthonormalization with a constraint, we present results for the Lyapunov exponents and related quantities in equilibrium and nonequilibrium. Finally, we check whether we obtain the same relations between quantities characterizing the microscopic chaotic dynamics and quantities characterizing macroscopic transport as obtained for conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript

Dynamics of a faceted nematic-smectic B front in thin-sample directional solidification

We present an experimental study of the directional-solidification patterns of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in short, CCH4) in 12 \mu m-thick samples, and in the planar configuration (director parallel to the plane of the sample). The nematic - smectic B interface presents a facet in one direction -- the direction parallel to the smectic layers -- and is otherwise rough, and devoid of forbidden directions. We measure the Mullins-Sekerka instability threshold and establish the morphology diagram of the system as a function of the solidification rate V and the angle theta_{0} between the facet and the isotherms. We focus on the phenomena occurring immediately above the instability threshold when theta_{0} is neither very small nor close to 90^{o}. Under these conditions we observe drifting shallow cells and a new type of solitary wave, called "faceton", which consists essentially of an isolated macroscopic facet traveling laterally at such a velocity that its growth rate with respect to the liquid is small. Facetons may propagate either in a stationary, or an oscillatory way. The detailed study of their dynamics casts light on the microscopic growth mechanisms of the facets in this system.Comment: 12 pages, 19 figures, submitted to Phys. Rev.

A variational approach to Givental's nonlinear Maslov index

In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental's nonlinear Maslov index. As an application we prove a Bott-Samelson type obstruction theorem for positive loops of contactomorphisms.Comment: 14 page

Mg(2)Si(x)Sn(1-x)heterostructures on Si(111) substrate for optoelectronics and thermoelectronics

Thin (50-90 m) non-doped and doped (by Al atoms) Mg2Sn0.6Si0.4 and Mg(2)Sn(0.4)Si(0.6)films with roughness of 1.9-3.7 nm have been grown by multiple deposition and single annealing at 150 degrees C of multilayers formed by repetition deposition of three-layers (Si-Sn-Mg) on Si(111) p-type wafers with 45 cm resistivity. Transmission electron microscopy has shown that the first forming layer is an epitaxial layer of hex-Mg2Sn(300) on Si(111) substrate with thickness not more than 5-7 nm. Epitaxial relationships: hex-Mg2Sn(300)parallel to Si(111), hex-Mg2Sn[001]parallel to Si[-112] and hex-Mg2Sn[030]parallel to Si[110] have been found for the epitaxial layer. But inclusions of cub-Mg2Si were also observed inside hex-Mg2Sn layer. It was found that the remaining part of the film thickness is in amorphous state and has a layered distribution of major elements: Mg, Sn and Mg without exact chemical composition. It was established by optical spectroscopy data that both type films are semiconductor with undispersed region lower 0.18 eV with n(o) = 3.59 +/- 0.01, but only two direct interband transitions with energies 0.75-0.76 eV and 1.2 eV have been determined. The last interband transition has been confirmed by photoreflectance data at room temperature. Fourier transmittance spectroscopy and Raman spectroscopy data have established the formation of stannide, silicide and ternary compositions